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X-Ray Spectrometry:Recent Technological Advances

X-Ray Spectrometry:Recent Technological AdvancesEdited byKouichi TsujiDepartment of Applied Chemistry, Osaka City University, JapanJasna InjukMicro and Trace Analysis Center, University of Antwerp, BelgiumRené Van GriekenMicro and Trace Analysis Center, University of Antwerp, Belgium

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ContentsContributors ..................Preface ......................vii1 Introduction .................. 11.1 Considering the Role of X-raySpectrometry in Chemical Analysisand Outlining the Volume ..... 12 X-Ray Sources ................ 132.1 Micro X-ray Sources ......... 132.2 New Synchrotron Radiation Sources 292.3 Laser-driven X-ray Sources ..... 493 X-Ray Optics ................. 633.1 Multilayers for Soft and HardX-rays .................. 633.2 Single Capillaries X-ray Optics .. 793.3 Polycapillary X-ray Optics ..... 893.4 Parabolic Compound RefractiveX-ray Lenses .............. 1114 X-Ray Detectors ............... 1334.1 Semiconductor Detectors for(Imaging) X-ray Spectroscopy ... 1334.2 Gas Proportional ScintillationCounters for X-raySpectrometry .............. 1954.3 Superconducting Tunnel Junctions 2174.4 Cryogenic Microcalorimeters .... 2294.5 Position Sensitive SemiconductorStrip Detectors ............. 2475 Special Configurations ........... 2775.1 Grazing-incidence X-raySpectrometry .............. 277xi5.2 Grazing-exit X-ray Spectrometry . 2935.3 Portable Equipment for X-rayFluorescence Analysis ........ 3075.4 Synchrotron Radiation forMicroscopic X-ray FluorescenceAnalysis ................. 3435.5 High-energy X-ray Fluorescence .. 3555.6 Low-energy Electron ProbeMicroanalysis and ScanningElectron Microscopy ......... 3735.7 Energy Dispersive X-rayMicroanalysis in Scanning andConventional Transmission ElectronMicroscopy ............... 3875.8 X-Ray Absorption Techniques ... 4056 New Computerisation Methods ..... 4356.1 Monte Carlo Simulation for X-rayFluorescence Spectroscopy ..... 4356.2 Spectrum Evaluation ......... 4637 New Applications .............. 4877.1 X-Ray Fluorescence Analysis inMedical Sciences ........... 4877.2 Total Reflection X-ray Fluorescencefor Semiconductors and Thin Films 5177.3 X-Ray Spectrometry inArchaeometry ............. 5337.4 X-Ray Spectrometry in ForensicResearch ................. 5537.5 Speciation and Surface Analysis ofSingle Particles UsingElectron-excited X-ray EmissionSpectrometry .............. 569Index ........................ 593

ContributorsF. AdamsDepartment of Chemistry, University of Antwerp,Universiteitsplein 1, B-2610 Antwerp, BelgiumJ. BörjessonDepartment of Diagnostic Radiology, CountryHospital, SE-301 85 Halmstad, SwedenA. BrunettiDepartment of Mathematics and Physics,University of Sassari, Via Vienna 2,1–07100 Sassari, ItalyR. BythewayBEDE Scientific Instruments Ltd, BelmontBusiness Park, Durham DH1 1TW, UKA. CastellanoDepartment of Materials Science, University ofLecce, I-73100 Lecce, ItalyR. CesareoDepartment of Mathematics and Physics,University of Sassari, Via Vienna 2, I-07100Sassari, ItalyC. A. CondePhysics Department, University of Coimbra,P-3004-0516 Coimbra, PortugalW. D¸abrowskiFaculty of Physics and Nuclear Techniques,AGH University of Science and Technology, Al.Mickiewicza 30, 30–059 Krakow, PolandE. Figueroa-FelicianoNASA/Goddard Space Flight Centre, Code 662,Greenbelt, MD 20771, USAM. GaleazziUniversity of Miami, Department of Physics, POBox 248046, Coral Gables, FL 33124, USAN. GaoX-ray Optical Systems, Inc., 30 Corporate Circle,Albany, NY 12203, USAP. GrybośFaculty of Physics and Nuclear Techniques, AGHUniversity of Science and Technology, Al.Mickiewicza 30, 30-059 Krakow, PolandP. HollSemiconductor Lab., MPI Halbleiterlabor,SIEMENS – Gelaende, Otto-Hahn-Ring 6,D-81739 München, GermanyJ. de HoogDepartment of Chemistry, University of Antwerp,Universiteitsplein 1, B-2610 Antwerp, BelgiumY. HosokawaX-ray Precision, Inc., Bld. #2, Kyoto ResearchPark 134, 17 Chudoji, Minami-machi,Shimogyo-ku, Kyoto 600–8813, JapanG. IsoyamaThe Institute of Scientific andIndustrial Research, Osaka University, 8-1Mihagaoka, Ibaraki, Osaka Pref. 567-0047, JapanK. JanssensDepartment of Chemistry, Universiteitsplein I,University of Antwerp, B-2610 Antwerp, Belgium

viiiCONTRIBUTORSJ. KawaiDepartment of Materials Science andEngineering, Kyoto University, Sakyo-ku, Kyoto606–8501, JapanM. KurakadoElectronics and Applied Physics, OsakaElectro-Communication University, 18-8,Hatsucho, Neyagawa, JapanS. KuypersCentre for Materials Advice and Analysis,Materials Technology Group, VITO (FlemishInstitute for Technological Research),B-2400 Mol, BelgiumP. LechnerSemiconductor Lab., MPI Halbleiterlabor,SIEMENS–Gelaerde, Otto-Hahn-Ring 6,D-81739 München, GermanyP. LembergeDepartment of Chemistry, University of Antwerp,Universiteitsplein 1, B-2610 Antwerp, BelgiumB. LengelerRWTH, Aachen University, D-52056 Aachen,GermanyG. LutzSemiconductor Lab., MPI Halbleiterlabor,SIEMENS – Gelaende, Otto-Hahn-Ring 6,D-81739 München, GermanyS. MattssonDepartment of Radiation Physics, LundUniversity, Malmö University Hospital, SE-20502 Malmö, SwedenY. MoriWacker-NSCE Corporation,3434 Shimata, Hikari, Yamaguchi 743-0063,JapanI. NakaiDepartment of Applied Chemistry, ScienceUniversity of Tokyo, 1-3 Kagurazaka, Shinjuku,Tokyo 162–0825, JapanT. NinomiyaForensic Science Laboratory, Hyogo PrefecturalPolice Headquarters, 5-4-1 Shimoyamate,Chuo-Ku, Kobe 650–8510, JapanJ. OsanKFKI Atomic Energy Research Institute,Department of Radiation andEnvironmental Physics, PO Box 49, H-1525Budapest, HungaryC. RoDepartment of Chemistry, Hallym University,Chun Cheon, Kang WonDo 200–702, KoreaM. A. Rosales MedinaUniversity of ‘Las Americas’, Puebla, CP 72820,MexicoK. SakuraiNational Institute for Materials Science, 1-2-1Sengen, Tsukuba, Ibaraki 305-0047, JapanC. SchroerRWTH, Aachen University, D-52056 Aachen,GermanyA. SimionoviciID22, ESRF, BP 220, F-38043 Grenoble, FranceH. SoltauSemiconductor Lab., MPI Halbleiterlabor,SIEMENS – Gelaende, Otto-Hahn-Ring 6,D-81739 München, GermanyC. SpielmannPhysikalisches Institut EP1,Universität Würzburg, Am Hubland, D-97074Würzburg, GermanyL. StruederSemiconductor Lab., MPI Halbleiterlabor,SIEMENS – Gelaende, Otto-Hahn-Ring 6,D-81739 München, GermanyI. SzalokiInstitute of Experimental Physics, University ofDebrecen, Bem tér 18/a, H-4026 Debrecen,Hungary

CONTRIBUTORSixB. K. TannerBEDE Scientific Instruments Ltd, BelmontBusiness Park, Durham DH1 1TW, UKM. TaylorBEDE Scientific Instruments Ltd, BelmontBusiness Park, Durham DH1 1TW, UKK. TsujiOsaka City University, 3-3-138 Sugimoto,Sumiyoshi-ku, Osaka 558-8585, JapanE. Van CappellenFEI Company, 7451 N.W. Evergreen Parkway,Hillsboro, OR 97124-5830, USAR. Van GriekenDepartment of Chemistry, University of Antwerp,Universiteitsplein I, B-2610 Antwerp, BelgiumB. VekemansDepartment of Chemistry, University of Antwerp,Universiteitsplein 1, B-2610 Antwerp,BelgiumL. VinczeDepartment of Chemistry, University of Antwerp,Universiteitsplein 1, B-2610 Antwerp, BelgiumM. WatanabeInstitute of Multidisciplinary Research forAdvanced Materials, Tohoku University,2-1-1 Katahira, Aoba-ku, Sendai 980-8577,JapanK. YamashitaDepartment of Physics, Nagoya University,Chikusa-ku, Nagoya 464-8602, JapanM. YanagiharaInstitute of Multidisciplinary Research forAdvanced Materials, Tohoku University,2-1-1 Katahira, Aoba-ku, Sendai 980-8577,JapanA. ZucchiattiInstituto Nazionale di Fisica Nucleare, Sezione diGenova, Via Dodecanesco 33, I-16146 Genova,Italy

PrefaceDuring the last decade, remarkable and often spectacularprogress has been made in the methodologicalbut even more in the instrumental aspectsof X-ray spectrometry. This progress includes, forexample, considerable improvements in the designand production technology of detectors and considerableadvances in X-ray optics, special configurationsand computing approaches. All this hasresulted in improved analytical performance andnew applications, but even more in the perspectiveof further dramatic enhancements of the potentialof X-ray based analysis techniques in the verynear future. Although there exist many books onX-ray spectrometry and its analytical applications,the idea emerged to produce a special book thatwould cover only the most advanced and high-techaspects of the chemical analysis techniques basedon X-rays that would be as up-to-date as possible.In principle, all references were supposed tobe less than five years old. Due to rapid changesand immense progress in the field, the timescalefor the book was set to be very short. A big effortwas made to cover as many sub-areas as possible,and certainly those in which progress has been thefastest. By its nature, this book cannot cover thefundamental, well-known and more routine aspectsof the technique; for this, reference is made to severalexisting handbooks and textbooks.This book is a multi-authored effort. We believethat having scientists who are actively engagedin a particular technique to cover those areas forwhich they are particularly qualified, outweighsany advantages of uniformity and homogeneitythat characterize a single-author book. In the specificcase of this book, it would have been trulyimpossible for any single person to cover a significantfraction of all the fundamental and appliedsub-fields of X-ray spectrometry in which thereare so many advances nowadays. The Editors werefortunate enough to have the cooperation of trulyeminent specialists in each of the sub-fields. Manychapters are written by Japanese scientists, and thisis a bonus because much of their intensive andinnovating research on X-ray methods is too littleknown outside Japan. The Editors wish to thankall the distinguished contributors for their considerableand timely efforts. It was, of course, necessaryto have this book, on so many advanced andhot topics in X-ray spectrometry, produced withinan unusually short time, before it would becomeobsolete; still the resulting heavy time-pressureput on the authors may have been unpleasant attimes.We hope that even experienced workers inthe field of X-ray analysis will find this bookuseful and instructive, and particularly up-to-datewhen it appears, and will benefit from the largeamount of readily accessible information availablein this compact form, some of it presented forthe first time. We believe there is hardly anyoverlap with existing published books, becauseof the highly advanced nature and actuality ofmost chapters. Being sure that the expert authorshave covered their subjects with sufficient depth,we hope that we have chosen the topics ofthe different chapters to be wide-ranging enough

xiiPREFACEto cover all the important and emerging fieldssufficiently well.We do hope this book will help analyticalchemists and other users of X-ray spectrometryto fully exploit the capabilities of this set ofpowerful analytical tools and to further expandits applications in such fields as material andenvironmental sciences, medicine, toxicology,forensics, archaeometry and many others.K. TsujiJ. InjukR. Van GriekenOsaka, Antwerp

Chapter 1Introduction1.1 Considering the Role of X-ray Spectrometry inChemical Analysis and Outlining the VolumeR. VAN GRIEKENUniversity of Antwerp, Antwerp, Belgium1.1.1 RATIONALEBasic X-ray spectrometry (XRS) is, of course,not a new technique. The milestone developmentsthat shaped the field all took place severaldecades ago. Soon after the discovery of X-raysin 1895 by Wilhelm Conrad Röntgen, the possibilityof wavelength-dispersive XRS (WDXRS) wasdemonstrated and Coolidge introduced the highvacuumX-ray tube in 1913. There was quite atime gap then until Friedmann and Birks builtthe first modern commercial X-ray spectrometerin 1948. The fundamental Sherman equation,correlating the fluorescent X-ray intensity quantitativelywith the chemical composition of asample, dates back to 1953. The fundamentalparameter (FP) approach, in its earliest version,was independently developed by Criss and Birksand Shiraiwa and Fujino, in the 1960s. Alsovarious practical and popular influence coefficientalgorithms, like those by Lachanche–Traill,de Jongh, Claisse–Quintin, Rasberry–Heinrich,Rousseau and Lucas–Tooth–Pine all date back to1960–1970. The first electron microprobe analyser(EMPA) was successfully developed in 1951by Castaing, who also outlined the fundamentalaspects of qualitative electron microprobe analysis.The first semiconductor Si(Li) detectors,which heralded the birth of energy-dispersiveXRS (EDXRS), were developed, mainly at theLawrence Berkeley Lab, around 1965. Just before1970, accelerator-based charged-particle inducedXRS or proton-induced X-ray emission (PIXE)analysis was elaborated; much of the credit wentto the University of Lund in Sweden. A descriptionof the setup for total-reflection X-ray fluorescence(TXRF) was first published by Yonedaand Horiuchi and the method was further pursuedby Wobrauschek and Aiginger, both in the early1970s. The advantages of polarised X-ray beamsfor trace analysis were pointed out in 1963 byChampion and Whittam and Ryon put this furtherinto practice in 1977. There have been demonstrationsof the potential for micro-X-ray fluorescence(XRF) since 1928 (by Glockner and Schreiber) andChesley began with practical applications of glasscapillaries in 1947. Synchrotron-radiation (SR)XRS was introduced in the late 1970s and Sparksdeveloped the first micro version at the StanfordSynchrotron Radiation Laboratory in 1980.So around 1990, there was a feeling thatradically new and stunning developments wereX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

2 CONSIDERING THE ROLE OF X-RAY SPECTROMETRY IN CHEMICAL ANALYSIS AND OUTLINING THE VOLUMElacking in XRS and scientists began to have someambivalent opinions regarding the future role ofXRS in analytical chemistry. One could wonderwhether, in spite of remarkably steady progress,both instrumental and methodological, XRS hadreached a state of saturation and consolidation,typical for a mature and routinely used analysistechnique.In the meantime, XRF had indeed developedinto a well-established and mature multi-elementtechnique. There are several well-known key reasonsfor this success: XRF is a universal techniquefor metal, powder and liquid samples; it is nondestructive;it is reliable; it can yield qualitative andquantitative results; it usually involves easy samplepreparation and handling; it has a high dynamicrange, from the ppm level to 100 % and it can, insome cases, cover most of the elements from fluorineto uranium. Accuracies of 1 % and better arepossible for most atomic numbers. Excellent datatreatment software is available allowing the rapidapplication of quantitative and semi-quantitativeprocedures. In the previous decades, somewhatnew forms of XRS, with e.g. better sensitivityand/or spectral resolution and/or spatial resolutionand/or portable character, had been developed.However, alternative and competitive more sensitiveanalytical techniques for trace analysis had, ofcourse, also been improved; we have seen the riseand subsequent fall of atomic absorption spectrometryand the success of inductively coupled plasmaatomic emission and mass spectrometry (ICP-AESand ICP-MS) in the last two decades.Since 1990, however, there has been dramaticprogress in several sub-fields of XRS, and inmany aspects: X-ray sources, optics, detectorsand configurations, and in computerisation andapplications as well. The aim of the followingchapters in this book is precisely to treat the latestand often spectacular developments in each ofthese areas. In principle, all references will pertainto the last 5–6 years. Many of the chapters willhave a high relevance for the future role of XRSin analytical chemistry, but certainly also for manyother fields of science where X-rays are of greatimportance. The following sections in this chapterwill give a flavour of the trends in the positionof different sub-fields of XRS based e.g. on therecent literature and will present the outline ofthis volume.1.1.2 THE ROLE AND POSITION OFXRS IN ANALYTICAL CHEMISTRYAn attempt has been made to assess the recenttrends in the role and position of XRS based on aliterature survey (see also Injuk and Van Grieken,2003) and partially on personal experience andviews. For the literature assessment, which coveredthe period from January 1990 till the end ofDecember 2000, a computer literature search onXRS was done in Chemical Abstracts, in orderto exclude (partially) the large number of XRSpublications on astronomy, etc.; still, it revealedan enormous number of publications. Figure 1.1.1shows that the volume of the annual literature onXRS, cited in Chemical Abstracts, including allarticles having ‘X-ray spectrometry/spectroscopy’in their title, is still growing enormously and exponentially.During the last decade, the number ofpublications on XRS in general has nearly doubled;in 2000, some 5000 articles were published,versus 120 annually some 30 years ago. As seenin Figure 1.1.2, XRS in general seems more alivethan ever nowadays.However, the growth of the literature on specificallyXRF is much less pronounced: from about500 articles per year in 1990 to about 700 in 2000,still a growth of 40 % in the last decade. While in1990 it looked like XRF had reached a state of saturationand consolidation, newer developments inthe 1990s, e.g. the often-spectacular ones describedin the other chapters of this volume, have somehowcountered such fears. It is a fact that WDXRFremains the method of choice for direct accuratemulti-element analysis in the worldwide mineraland metallurgy industry. For liquid samples, however,the competition of ICP-AES and ICP-MSremains formidable. It is striking that, while thereare still many more WDXRF units in operationaround the world than EDXRF instruments, thenumber of publications dealing with WDXRF isabout five times lower. This clearly reflects thepredominant use of the more expensive WDXRF

THE ROLE AND POSITION OF XRS IN ANALYTICAL CHEMISTRY 355005000number of articles450040003500300025001990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000yearFigure 1.1.1 Total annual number of articles on X-ray emission spectrometry in the period 1990–2000 (source of data: ChemicalAbstracts). Reproduced by permission of John Wiley & Sons, Ltd600054005000Number of articles4000300020001000120700277001970 1980 1990 2000yearFigure 1.1.2 Number of articles on X-ray emission spectrometry since 1970 (source of data: Chemical Abstracts). Reproducedby permission of John Wiley & Sons, Ltdin routine industrial analysis, where publishing isnot common, while EDXRF is mostly present inacademic and research institutions; there are manyapplications in environment-related fields whereultimate accuracies are not so mandatory.Also the number of publications on radioisotopeXRF has been increasing from 40 in 1990 to100 in 1998, reflecting the frequent use of thetechnique in many field and on-line applications.In Australia alone, more than 2000 portable XRFare employed in the mining and mineral industry.It is expected that the radioisotope-based on-lineinstallations will gradually be replaced by systemsbased on small X-ray tubes.The annual number of articles dealing with variousaspects of the PIXE technique (but excludingmicro-PIXE) is in the range of 30 to 70with very prominent peaks every 3 years. These

4 CONSIDERING THE ROLE OF X-RAY SPECTROMETRY IN CHEMICAL ANALYSIS AND OUTLINING THE VOLUMEare obviously related to the publication of theproceedings of the tri-annual PIXE Conferences(Figure 1.1.3), with many short articles. It is clear,and not only from the literature, that, of all X-rayemission techniques considered, PIXE is thrivingthe least; there is no clear growth in the literature,although PIXE might still be the method ofchoice for the trace analysis of large numbers ofrelatively small samples, like e.g. for particulateair pollution monitoring using impactor depositsof aerosols. The number of PIXE installations inthe world is probably decreasing, and the futureof PIXE seems to be exclusively in its micro version;some 30 institutes are active in this field atthe moment. The literature on micro-PIXE is stillgrowing; a search on Web of Science showed thatthe annual number of articles on micro-PIXE wasaround 10 at the beginning of the previous decadeand around 35 in the last few years.Since the early 1970s, SR-XRS has been experiencingremarkable growth, nowadays approachingalmost 350 articles per year, with a doubling seenover the last decade. Investment in SR facilitiescontinues to be strong and with the increasingavailability of SR X-ray beam lines, new researchfields and perspectives are open today. Most ofthe presently operational SR sources belong to theso-called second-generation facilities. A clear distinctionis made from the first generation, in whichthe SR was produced as a parasitic phenomenon inhigh-energy collision experiments with elementaryparticles. Of special interest for the future are newthird-generation storage rings, which are specificallydesigned to obtain unique intensity and brilliance.SR has a major impact on microprobe-typemethods with a high spatial resolution, like micro-XRF,andonX-rayabsorptionspectrometry(XAS)as well as on TXRF. For highly specific applications,SR-XRS will continue to grow. The costsof SR-XRS are usually not calculated, since inmost countries, SR facilities are free of charge forthose who have passed some screening procedure.Of course, such applications cannot be consideredas routine.There are nowadays some 100 publicationsannually on TXRF, and this number has more orless doubled since 1990. However, it may seemthat TXRF has stabilized as an analytical methodfor ultra-trace determination from solutions anddissolved solids due to the fierce competition fromICP-MS, in particular. There are now only a fewcompanies offering TXRF units. But mostly forsurface analysis directly on a flat solid sample,TXRF is still unique. SR-TXRF might be oneof the methods of choice in future wafer surfaceanalysis (in addition to e.g. secondary ion massspectrometry). In addition, by scanning around thetotal-reflection angle, TXRF allows measurementsof the density, roughness and layer thickness anddepth profiling, which are, of course, of muchinterest in material sciences. New possibilitiesfor improving the performance of TXRF are inusing polarised primary radiation. SR has almostideal features for employment in combination withnumber of articles300250200150100501990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000yearFigure 1.1.3 Annual number of articles on PIXE in the period 1990–2000 (source of data: Web of Science). Reproduced bypermission of John Wiley & Sons, Ltd

THE ROLE AND POSITION OF XRS IN ANALYTICAL CHEMISTRY 5TXRF. It is several orders (8–12) of magnitudehigher in brightness compared to X-ray tubes, hasa natural collimation in the vertical plane andis linearly polarised in the plane of the orbit ofthe high energy (GeV) electron or positrons. Thespectral distribution is continuous, so by propermonochromatisation, the performance of selectiveexcitation at best conditions is possible. SR offers asignificant reduction in TXRF detection limits anda remarkable improvement has been achieved overthe past 20 years from nanogram level in 1975 toattogram level in 1998.Until recently, evolution of XRF into the microanalyticalfield was hampered because of the difficultiesinvolved in focusing a divergent X-raybeam from an X-ray tube into a spot of smalldimensions. However, the development of SRsources and the recent advances in X-ray focusinghave changed the situation. Contemporary micro-XRF applications started only some 10 years agoon a significant scale, and it appears today to beone of the best microprobe methods for inorganicanalysis of various materials: it operates at ambientpressure and, in contrast to PIXE and EMPA,no charging occurs. In many instances, no samplepreparation is necessary. The field of micro-XRF is currently subject to a significant evolutionin instrumentation: lead-glass capillaries andpolycapillary X-ray lenses, air-cooled micro-focusX-ray tubes, compact ED detector systems witha good resolution even at a high-count rate andno longer requiring liquid-nitrogen cooling. Commerciallaboratory instrumentation using capillaryoptics combined with rapid scanning and compositionalmapping capability is expected to grow, andvarious systems are commercially available. Duringthe 1980s, SR facilities around the world beganto implement X-ray microbeam capabilities ontheir beam lines for localised elemental analysis.Recent trends in SR micro-XRF are towards optimisationof optics and smaller beam sizes down tothe submicrometer size.With respect to the general applications ofXRS, it appears that environmental, geological,biological and archaeological applications makeup a stunning 70 % contribution to the literature;undoubtedly this is far above their relative contributionsin actual number of analysis, since XRFis certainly still a working horse in many typesof industries, for all kinds of routine analyses,but the latter applications are published very seldom.The number of articles dealing with environmentalapplications of XRS, in the past decade,shows a steady growth. Interestingly, the relativecontributions for the different topics coveredin the environmental applications, like soils andgeological material (23 %), biological materials(19 %), water (19 %), air (17 %) and waste material(8 %) have not changed considerably duringthe last decade.Table 1.1.1 shows the relative share of laboratoriesin different countries to the literature onXRS generated in 1998 (according to AnalyticalAbstracts) and the language in which the publicationswere written. It appears that European countriesproduce almost one half of the total number ofpublications, while, of the non-European countries,China and Russia are leading. The low contributionof the USA is striking. There might be several reasonsfor this. Apparently, XRS is considered moreas a routine technique by the US industry and thereare almost no US academic centers working in thisfield. It is also true that in 1998, no volume ofAdvances in X-ray Analysis appeared and this coversthe proceedings of the popular Denver X-rayTable 1.1.1 The relative share of laboratories in differentcountries to the literature on XRS generated in the year 1998(as covered by Analytical Abstracts) and the language in whichthe publications were writtenCountry Relative contribution (%) LanguageChina 13.4 25 % English75 % ChineseRussia 10.2 70 % English30 % RussianJapan 8.0 55 % English45 % JapaneseOther Asian 4.8 100 % EnglishGermany 9.3 95 % EnglishItaly 6.3 100 % EnglishUK 4.8 100 % EnglishOther European 26.2 100 % EnglishUSA 5.4 100 % EnglishOther American 5.4 100 % EnglishAustralia 3.6 100 % EnglishAfrica 2.7 100 % English

6 CONSIDERING THE ROLE OF X-RAY SPECTROMETRY IN CHEMICAL ANALYSIS AND OUTLINING THE VOLUMEAnalysis Conference. Finally, the most advancedresearch (as described in the following chaptersin this volume) may still be published in physicsjournals rather than in journals covered by AnalyticalAbstracts. It also appeared from our literaturesearch that about one fourth of the XRS literatureis written in less accessible languages like Russian,Chinese and Japanese.In view of the enormous advances that are beingmade in XRS and that, hopefully, are coveredwell in the following chapters of this book, onecan expect that the applications of XRS willdramatically be changed over the next few years,and that, in the literature, the distribution overfundamental aspects (probably not fully reflectedyet in the literature covered by Chemical Abstractsand Analytical Abstracts discussed above) will beradically different as well.1.1.3 VOLUME OUTLINEAll of the chapters of this volume have beenwritten by acknowledged research and applicationleaders, the best that the editors could find in eachof the sub-fields. A relatively large fraction of themare Japanese scientists, and this may be a bonus forreaders elsewhere in the world, since only abouthalf of the advanced XRS research in Japan ispublished in English and hence it is not alwayssufficiently widely known, e.g. in the West.All the chapters or sets of subchapters covertopics in which remarkable progress has beenmade during the last decade and which offer goodperspective for drastically changing the power ofXRS in the near future.Chapter 2 deals with X-ray sources, which havebecome more powerful and diverse in the last fewyears. Significant improvements have been madeto the design and performances of conventionalX-ray tubes, and in their miniaturisation (whichis treated in a later chapter), but most impressivehas been the progress in micro-X-ray sources, thedevelopment of new synchrotron sources and thefirst steps towards X-ray laser and laser-inducedplasma X-ray sources applicable to XRS. Subchapter2.1 (by M. Taylor, R. Bytheway and B. K.Tanner of Bede plc, Durham, UK) describes howelectromagnetic rather than conventional electrostaticfocusing, for shaping and steering the electronbeam in the X-ray tube, allows the X-raysource dimensions to be controlled much betterthan in the past, to achieve a higher brilliance withouttarget damage, to tailor the X-ray spot dimensionsfor optimising the input coupling with subsequentgrazing-incidence X-ray optical elements,like ellipsoidal mirrors and polycapillaries (treatedin a later chapter), and hence to deliver high brilliancebeams of small dimension to the sample.These high-brightness micro-focus sources havebeen used mostly in X-ray diffraction (XRD) sofar, but they are likely to have a major impacton XRS in the near future as well. Subchapter 2.2on new synchrotron radiation sources was writtenby M. Watanabe (Institute of MultidisciplinaryResearch for Advanced Materials, Tohoku University,Japan) and G. Isoyama (Institute of Scientificand Industrial Research, Osaka University,Japan). In this subchapter, new synchrotron radiationsources are introduced and the characteristicsof synchrotron radiation are summarised. Newaspects and typical properties of the synchrotronradiation flux at the sample position are describedfor users of third-generation sources and candidatesfor fourth-generation sources are discussed.In Subchapter 2.3, C. Spielman (PhysikalischesInstitut EP1, University of Würzburg, Germany)treats a novel generation of laser-driven X-raysources, which could produce femtosecond pulsesof soft to hard X-rays, synchronisable to otherevents, and very high intensities, from compactlaboratory X-ray sources. This section describesrecent progress in the development of laser sourcesrelevant for X-ray generation and reviews the generationof laser-produced incoherent radiation, thedevelopment of X-ray lasers and high-harmonicgeneration. Applications of coherent laboratory X-ray sources are still in their infancy, but thesemight be intriguing in the future, in XRS, X-raymicroscopy, X-ray photoelectron spectroscopy andmaybe X-ray interferometry, all of which have hadto rely on large-scale synchrotron facilities thus far,and might open the way to attosecond science.

VOLUME OUTLINE 7The third chapter is all about X-ray optics,another field that has seen an explosive growthin the last decade, in various ways, resulting innew commercial instruments and new applicationlines. In Subchapter 3.1, M. Yanagihara (Instituteof Multidisciplinary Research for AdvancedMaterials, Tohoku University, Japan) and K.Yamashita (Department of Physics, Nagoya University,Japan) discuss advances in multilayer productiontechnology, due to the progress in thin-filmtechnology and polishing of super-smooth substratesto the sub-nanometer level, and in theirperformance and applications. For soft X-rays, thelatter include focusing, microscopy and polarimetry;for hard X-rays, obtaining microbeams formicroscopy, X-ray telescopes and multilayercoatedgratings are discussed. In Subchapter 3.2,Y. Hosokawa (X-ray Precision, Inc., Kyoto, Japan)presents the state-of-the-art for single capillaries,which make use of multiple external totalreflections. He shows how a very bright andnarrow X-ray microbeam can be realised usingsingle capillaries (or X-ray guide tubes), andhow this leads to a tabletop X-ray analyticalmicroscope. Several applications are presented. InSubchapter 3.3, N. Gao (X-ray Optical Systems,Albany, NY, USA) and K. Janssens (Universityof Antwerp, Belgium) give a detailed treatment ofthe fundamentals of multi-fiber polycapillaries andthe recent fused and heat-shaped monolithic versions.In the last decade, polycapillary optics havebecome widespread and successfully used as crucialcomponents in commercial X-ray microanalysisand low-power compact instruments. Novelanalytical applications are situated in elementalmicroanalysis in laboratory scale, portable andsynchrotron systems, micro-X-ray absorption nearedgespectroscopy (XANES), EMPA, etc. Futuredevelopments in performance and spot size arediscussed. Finally, the new compound refractivelenses, first fabricated in 1996, are presented inSubchapter 3.4 by A. Simionovici (European SynchrotronResearch Facility, Grenoble, France) andC. Schroer and B. Lengeler (Aachen University ofTechnology, Germany). Their theory, design andproperties are considered, as well as their use forimaging and microbeam production. Some focusis on parabolic refractive X-ray lenses that canbe used in e.g. a new hard X-ray microscope thatallows sub-micrometer resolution and for e.g. combinedfluorescence spectroscopy and tomography.Applications in the realms of biology, XRF computedmicro-tomography, geochemistry and environmentalresearch are given.The most dramatic and spectacular progress hascertainly been made recently in the field of X-raydetector technology, and all this is covered inChapter 4. In Subchapter 4.1, L. Strüder, G. Lutz,P. Lechner, H. Soltau and P. Holl (Max-Planck-Institute for Physics and Extraterrestrial Physics,pnSensor and/or the Semiconductor Lab of theMax Planck Institute, Munich, Germany) treatadvances in silicon detectors. After an introductionto the basic operation principles of semiconductorsand the electronics used, some importantnew detectors are discussed in detail and importantapplications in XRS and imaging are reviewed.The detectors include Silicon Drift Detectors forX-ray detection, Controlled Drift Detectors (CDD),fully depleted backside illuminated pn-CCD andActive Pixel Sensors (APS) for XRS. All thesequite sophisticated detectors have left their initialfields of applications in high-energy physics,astrophysics and SR research. They are now amature technology and open many new industrialapplications. These detectors exhibit now ahigh quantum efficiency, excellent energy resolution,high radiation tolerance, good position resolution,high speed, homogeneous response of the fullbandwidth of radiation and high background rejectionefficiency. In Subchapter 4.2, C. A. N. Conde(Department of Physics, University of Coimbra,Portugal) treats the role of new gas proportionalscintillation counters (GPSC) for XRS, after consideringthe physics of the absorption of X-rays ingases, the transport of electrons and the productionof electroluminescence in gases, and the basic conceptsof different types of GPSC. Their energy resolutionis only 8 % for 5.9 keV X-rays, but they canbe built with very large windows and be useful forvery soft X-rays like the K-lines of C and O. Differenttypes of cryogenic detectors, operating nearthe liquid helium temperature (implying sophisticatedcooling systems) and offering unseen energy

8 CONSIDERING THE ROLE OF X-RAY SPECTROMETRY IN CHEMICAL ANALYSIS AND OUTLINING THE VOLUMEresolutions, are truly a major development ofrecent years. However, their commercial availabilityand price range is still somewhat unclear at themoment. Both superconducting tunneling junctions(STJ) and microcalorimeters are treated in detailin this volume. In Subchapter 4.3, M. Kurakado(Department of Electronics and Applied Physics,Osaka Electro-Communication University, Japan)explains the unique working principles of STJ,which usually consist of two superconductor layersand a nanometer-thick insulator layer, which isa tunnel barrier between the superconductor layersthat can be passed by excited electrons or holes,i.e. quasiparticles, to give rise to a signal. Singlejunctiondetectors and two other types of STJdetectors are discussed. Fantastic energy resolutionsaround 10 eV are possible. New applicationsare emerging, including one- and two-dimensionalimaging. Other equally promising cryogenic detectorsare the cryogenic microcalorimeters, treatedin Subchapter 4.4 by M. Galeazzi (Department ofPhysics, University of Miami, Coral Gables, FL,USA) and E. Figueroa-Feliciano (NASA/GoddardSpace Flight Center, Greenbelt, MD, USA). Theidea of detecting the increase in temperature producedby incident photons instead of the ionisationof charged pairs, like in semiconductor detectors,was put forward almost 20 years ago, andthe operating principle is rather simple, but thepractical construction is quite challenging. Only inrecent years has the practical construction of adequatecryogenic microcalorimeters been realised.The required characteristics, parameters and nonidealbehavior of different components and types,including large arrays, detector multiplexing andposition-sensitive imaging detectors, are discussedin detail. Several expected future developmentsare outlined. In the last section of this chapteron detectors, W. Dabrowski and P. Gryboś (Facultyof Physics and Nuclear Techniques, Universityof Mining and Metallurgy, Krakow, Poland)treat position-sensitive semiconductor strip detectors,for which the manufacturing technologies andreadout electronics have matured recently. Siliconstrip detectors, of the same type as used fordetection of relativistic charged particles, can beapplied for the detection of low-energy X-rays,up to 20 keV. Regardless of some drawbacks dueto limited efficiency, silicon strip detectors aremost widely used for low-energy X-rays. Singlesided,double-sided and edge-on silicon strip detectorsand the associated electronics are treated ingreat detail.There are many special configurations andinstrumental approaches in XRS, which have beenaround for a while or have recently been developed.Eight of these are reviewed in Chapter 5.In Subchapter 5.1, K. Sakurai (National Institutefor Materials Science, Tsukuba, Japan) dealswith TXRF or grazing-incidence XRF (GI-XRF).Although TXRF may have been fading awaya bit recently for trace element analysis ofliquid or dissolved samples, there have stillbeen advances in combination with wavelengthdispersivespectrometers and for low atomic numberelement determinations. But mostly, there haverecently been interesting developments in surfaceand interface analysis of layered materials by angularand/or energy-resolved XRF measurements,and in their combination with X-ray reflectometry.Micro-XRF imaging without scans is a recentinnovation in GI-XRF as well. Future developmentsinclude e.g. combining GI-XRF with X-rayfree-electron laser sources. An approach that hasnot been used widely so far is grazing-exit XRS(GE-XRS), related in some ways to GI-XRF. GE-XRF is the subject of Subchapter 5.2, by K. Tsuji(Osaka City University, Japan). Since the X-rayemission from the sample is measured in GE-XRS,different types of excitation probes can be used,not only X-rays but also electrons and chargedparticles. In addition, the probes can be used toirradiate the sample at right angles. This subchapterdescribes the principles, methodological characteristics,GE-XRS instrumentation, and recent applicationsof GE-XRF, as well as GE-EPMA andGE-PIXE. At the end of this subchapter, the futureof GE-XRS is discussed, which implies the useof more suitable detectors and synchrotron radiationexcitation. One interesting aspect of XRFis the enormously increased recent (commercial)interest in portable EDXRF systems. This topicis treated in the next subchapter by R. Cesareoand A. Brunetti (Department of Mathematics and

VOLUME OUTLINE 9Physics, University of Sassari, Italy), A. Castellano(Department of Materials Science, Universityof Lecce, Italy) and M.A. Rosales Medina (University‘Las Americas’, Puebla, Mexico). Only inthe last few years, has technological progress producedminiature and dedicated X-ray tubes, thermoelectricallycooled X-ray detectors of small sizeand weight, small size multichannel analysers anddedicated software, allowing the construction ofcompletely portable small size EDXRF systemsthat have similar capabilities as the more elaboratelaboratory systems. Portable equipment maybe necessary when objects to be analysed cannotbe transported (typically works of art) or whenan area should be directly analysed (soil analysis,lead inspection testing, etc.) or when the mappingof the object would require too many samples.The advantages and limitations of different setups,including optics, are discussed. A focusedsubchapter on the important new technology ofmicroscopic XRF using SR radiation has been producedby F. Adams, L. Vincze and B. Vekemans(Department of Chemistry, University of Antwerp,Belgium). It describes the actual status with respectto lateral resolution and achievable detection limits,for high-energy, third-generation storage rings(particularly the European Synchrotron RadiationFacility, Grenoble, France), previous generationsources and other sources of recent construction.Related methods of analysis based on absorptionedge phenomena such as X-ray absorption spectroscopy(XAS), XANES, X-ray micro-computedtomography (MXCT) and XRD are briefly discussedas well. Particular attention is paid to theaccuracy of the XRF analyses. Subchapter 5.5 by I.Nakai (Department of Applied Chemistry, ScienceUniversity of Tokyo, Japan) deals with high-energyXRF. It considers SR sources and laboratory equipment,in particular a commercial instrument forhigh-energy XRF that has only recently becomeavailable. The characteristics of the techniqueinclude improved detection limits, chiefly for highatomic number elements. This makes it particularlysuitable for the determination of e.g. rare earthsvia their X-lines. Other interesting applicationexamples pertain to environmental, archaeological,geochemical and forensic research. Low-energyEMPA and scanning electron microscopy (SEM)are the topics of S. Kuypers (Flemish Institute forTechnological Research, Mol, Belgium). The fundamentaland practical possibilities and limitationsof using soft X-rays, as performed in the two separateinstruments, are discussed. The potential of thetwo techniques is illustrated with recent examplesrelated to the development of ultra-light-elementbased coatings for sliding wear applications, membranesfor ultrafiltration and packaging materialsfor meat. In Subchapter 5.7, E. Van Cappellen (FEICompany, Hillsboro, OR, USA) treats ED X-raymicroanalysis in transmission electron microscopy(TEM), for both the scanning and conventionalmode. The section describes how EDXRS in the(S)TEM can be made quantitative, accurate andprecise, and is nowadays an extremely powerfultechnique in materials science and has not vanishedin favor of electron energy loss spectrometry(EELS) as predicted 20 years ago. Severalexamples are given of quantitative chemical mapping,quantitative analysis of ionic compounds andother real-world applications. Finally, J. Kawai(Department of Materials Science and Engineering,Kyoto University, Japan) discusses in detail theadvances in XAS or X-ray absorption fine structurespectroscopy (XAFS), which include XANES(X-ray absorption near edge structure) and EXAFS(extended X-ray absorption fine structure). X-rayabsorption techniques are now used in commerciallyavailable film thickness process monitorsfor plating, printed circuit and magnetic disk processes,in various kinds of industries. But they areused, both in laboratories and synchrotron facilities,for basic science as well. The X-ray absorptiontechniques, described extensively in this subchapter,differ in probe type (electrons and X-rays,sometimes polarised or totally reflected), detectedsignals (transmitted X-rays, XRF, electrons, electriccurrents, and many others) and applicationfields (high temperature, high pressure, low temperature,in situ chemical reaction, strong magneticfield, applying an electric potential, short measurementtime, and plasma states). One shortcoming ofXAS techniques, that absorption spectra of all theelements were not measurable using one beamline,

10 CONSIDERING THE ROLE OF X-RAY SPECTROMETRY IN CHEMICAL ANALYSIS AND OUTLINING THE VOLUMEhas been overcome in many synchrotron facilitiesnowadays.Chapter 6 reviews some advances in computerisationconcerning XRS. The first subchapter, writtenby L. Vincze, K. Janssens, B. Vekemans andF. Adams (Department of Chemistry, Universityof Antwerp, Belgium) deals with modern MonteCarlo (MC) simulation as an aid for EDXRF.The use of MC simulation models is becomingmore and more viable due to the rapid increaseof inexpensive computing power and the availabilityof accurate atomic data for photon-matterinteractions. An MC simulation of the completeresponse of an EDXRF spectrometer is interestingfrom various points of view. A significantadvantage of the MC simulation based quantificationscheme compared to other methods, such asFP algorithms, is that the simulated spectrum canbe compared directly to the experimental data inits entirety, taking into account not only the fluorescenceline intensities, but also the scatteredbackground of the XRF spectra. This is linkedwith the fact that MC simulations are not limitedto first- or second-order approximations andto ideal geometries. Moreover, by considering thethree most important interaction types in the 1–100keV energy range (photoelectric effect followedby fluorescence emission, Compton and Rayleighscattering), such models can be used in a generalfashion to predict the achievable analytical characteristicsof e.g. future (SR)XRF spectrometersand to aid the optimisation/calibration of existinginstruments. The code illustrated in this subchapterhas experimentally been verified by comparisonsof simulated and experimental spectral distributionsof various samples. With respect to the simulationof heterogeneous samples, an example isgiven for the modeling of XRF tomography experiments.The simulation of such lengthy XRF imagingexperiments is important for performing feasibilitystudies and optimisation before the actualmeasurement is performed. Subchapter 6.2 by P.Lemberghe (Department of Chemistry, Universityof Antwerp, Belgium) describes progress in spectrumevaluation for EDXRF, where it remainsa crucial step, as important as sample preparationand quantification. Because of the increasedcount rate and hence better precision due to newdetectors, more details became apparent in thespectra; fortunately, the availability of inexpensiveand powerful PCs now enables the implementationof mature spectrum evaluation packages. In thissubchapter, the discussed mathematical techniquesgo from simple net peak area determinations, to themore robust least-squares fitting using referencespectra and to least-squares fitting using analyticalfunctions. The use of linear, exponential or orthogonalpolynomials for the continuum fitting, and of amodified Gaussian and Voigtian for the peak fittingis discussed. Most attention is paid to partial leastsquaresregression, and some illustrative analyticalexamples are presented.The final chapter, Chapter 7, deals with fivegrowing application fields of XRS. J. Börjesson(Lund University, Malmö and the Department ofDiagnostic Radiology, County Hospital, Halmstad,Sweden) and S. Mattsson (Department of DiagnosticRadiology, County Hospital, Halmstad Sweden)focus on applications in the medical sciences since1995, i.e. on recent advances in in vivo XRF methodsand their applications, and on examples of invitro use of the technique. The latter deals mostlywith the determination of heavy metals in tissues,in well-established ways. But there have beensignificant developments lately in in vivo analysiswith respect to sources, geometry, use of polarisedexciting radiation, MC simulations and calibration,and the analytical characteristics have beenimproved. Examples of novel in vivo determinationsof Pb, Cd, Hg, Fe, I, Pt, Au and U arediscussed. The next subchapter deals with novelapplications for semiconductors, thin films and surfaces,and is authored by Y. Mori (Wacker-NSCECorp., Hikari, Japan). Progress in the industrialapplication of TXRF in this field is first discussed.The use of TXRF for semiconductor analysis cameinto popular use in the 1990s; today, more than 300TXRF spectrometers are installed in this industryworldwide, meaning that almost all leading-edgesemiconductor factories have introduced TXRF.Since the main purpose of TXRF is trace contaminationanalysis, improvements in the elementalrange (including light elements), detection ability(e.g. by preconcentration) and standardisation

REFERENCE 11(versus other techniques) are discussed. In addition,XRF and X-ray reflectivity analysers forthe characterisation of thin films made from newmaterials are introduced. A. Zucchiatti (IstitutoNazionale di Fisica Nucleare, Genova, Italy) wrotethe next subchapter on the important applicationof XRS in archaeometry, covering instrumentationfrom portable units through PIXE and synchrotrons.Applications of the latter techniquesinclude e.g. the study of Renaissance glazed terracottasculptures, flint tools and Egyptian cosmetics.Also the XRF and XANES micro-mapping of corrodedglasses is described. Radiation damage isa constant major concern in this field. The muchlarger availability of facilities and several technologicaladvances have made archaeometry a verydynamic field for XRS today and an even greaterresearch opportunity for tomorrow. T. Ninomiya(Forensic Science Laboratory, Hyogo PrefecturalPolice Headquarters, Kobe, Japan) illustrates somerecent forensic applications of TXRF and SR-XRF.Trace element analysis by TXRF is used to fingerprintpoisoned food, liquor at crime scenes,counterfeit materials, seal inks and drugs. Forensicapplications of SR-XRF include identificationof fluorescent compounds sometimes usedin Japan to trace criminals, different kinds ofdrugs, paint chips and gunshot residues. Subchapter7.5 deals with developments in electroninducedXRS that have mainly an impact on environmentalresearch, namely the speciation andsurface analysis of individual particles, and is writtenby I. Szaloki (Physics Department, Universityof Debrecen, Hungary), C.-U. Ro (Departmentof Chemistry, Hallym University, Chun Cheon,Korea), J. Osan (Atomic Energy Research Institute,Budapest, Hungary) and J. De Hoog (Departmentof Chemistry, University of Antwerp, Belgium).In e.g. atmospheric aerosols, it is of interest toknow the major elements that occur together inone particle, i.e. to carry out chemical speciationat the single particle level. These major elementsare often of low atomic number, like C, N andO. In EDXRS, ultrathin-window solid-state detectorscan measure these elements but for such softX-rays, matrix effects are enormous and quantificationbecomes a problem. Therefore an inverse MCmethod has been developed which can determinelow atomic number elements with an unexpectedaccuracy. To reduce beam damage and volatilisationof some environmental particles, the useof liquid-nitrogen cooling of the sample stage inthe electron microprobe has been studied. Finally,irradiations with different electron beam energies,i.e. with different penetration power, have beenapplied, in combination with the MC simulation,to study the surface and core of individual particlesseparately and perform some depth profiling.The given examples pertain to water-insoluble elementsin/on individual so-called Asian dust aerosolparticles, nitrate enrichments in/on marine aerosolsand sediment particles from a contaminated river.REFERENCEJ. Injuk and R. Van Grieken, X-Ray Spectrometry, 32 (2003)35–39.

Chapter 2X-Ray Sources2.1 Micro X-ray SourcesM. TAYLOR, R. BYTHEWAY and B. K. TANNERBede plc, Durham, UK2.1.1 INTRODUCTIONA little over a century ago, X-rays were discoveredby Wilhelm Conrad Röntgen (Röntgen, 1995) asa result of the impact of a beam of electrons,accelerated through an electrostatic field, on ametallic target. Current commercial X-ray tubeswork on the self-same principle, heated cathodeshaving replaced the original cold cathodes andwater cooling enabling much higher power loadsto be sustained. Electrostatic focusing of theelectron beam is used in almost all tubes andof the incremental improvements in sealed tubeperformance over the past 50 years, the recentdevelopment of ceramic tubes (e.g. Bohler andStehle, 1998) by Philips is the only one of note.A discrete step in performance occurred inthe late 1950s with the development (Daviesand Hukins, 1984; Furnas, 1990) of the rotatinganode generator. Through rapid rotation (severalthousand revolutions per minute) of the target,the heat load and hence X-ray emission, couldbe increased as the heated region is allowed tocool in the period when away from the electronbeam. Rotating anode generators are manufacturedby a number of companies and provide the highestoverall power output of any electron impact device.It was recognized many years ago that forsome applications, in particular those involvingimaging, that a small source size was desirable.In the 1960s Hilger and Watts developed a demountable,continuously pumped X-ray tube thatfound use, for example, in X-ray diffractiontopography (Bowen and Tanner, 1998) of singlecrystals. One of the electron optical configurationsfor this generator gave a microfocus source butwith the demise of the company and the adventof synchrotron radiation, use of such very smallsources was unusual.The limitation of electron impact sources liesprincipally in the ability to conduct heat away fromthe region of electron impact, hence limiting thepower density on the target. Heat flow in solidsis governed by the heat diffusion equation, firstderived by Fourier in 1822. This describes thetemperature T at any point x, y, z in the solidand at time t. Assuming that there is a heat sourcedescribed by the function f(x,y,z,t) we have∂T /∂t = α 2 ∇ 2 T + f/cρ (2.1.1)where α = (K/cρ) 1/2 and K is the thermal conductivity,c is the heat capacity and ρ is the density.Thus under steady-state conditions, the key parameterin determining the temperature distributionX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

14 MICRO X-RAY SOURCESTable 2.1.1 Physical properties of target materialsMaterialMelting temperature,T m ( ◦ C)Thermal conductivity,K (W cm −1 K −1 )Heat capacity,c (J g −1 K −1 )Density,ρ (g cm −3 )Diffusivity,α (cm s −1/2 )Cu 1084 4.01 0.38 8.93 1.09Al 660 2.37 0.90 2.7 0.99Mo 2623 1.38 0.25 10.22 0.74W 3422 1.73 0.13 19.3 0.83Diamond(Type IIa)3500 23.2 0.51 3.52 3.60is the thermal conductivity. However, in transientconditions, it is the parameter α, often referred toas the diffusivity, that is the important in determiningthe maximum temperature at any point.Clearly, to avoid target damage, the maximum temperatureT must be significantly below the meltingpoint of the target material.Reference to Table 2.1.1 shows that the choiceof copper as the anode material is governed bymore than its ease of working and relatively lowcost. In rotating anode generators, even when theactual target material is tungsten or molybdenum,these materials are plated or brazed onto a copperbase. Calculations performed many years agoby Müller (Müller, 1931) and Oosterkamp (Oosterkamp,1948) showed that the maximum permissiblepower on a target was proportional to thediameter of the focal spot on the target. Relativelylittle is gained from such strategies as makingturbulent the flow of coolant on the rear surfaceof the target. As the power of the X-ray tube isincreased, there must be a corresponding increasein focal spot size and inspection of manufacturers’specifications will readily attest to this fundamentallimitation. Synchrotron radiation sources, wherethere is no such problem of heat conduction, haveproved the route past this obstacle.2.1.2 INTER-RELATIONSHIPBETWEEN SOURCE AND OPTICSNevertheless, there are many applications where itis either impossible or impractical to travel to asynchrotron radiation source and thus, driven bythe spectacular developments at the synchrotronradiation sources, there has been strong pressureto improve laboratory-based sources. As it is clearfrom the above impasse that increase in the rawpower output was not the solution, attention hasfocused on the exploitation of X-ray optics. Itwas realized that there was a prodigious waste ofX-ray photons associated with standard collimationtechniques and that the scientific community hadprogressed no further than the pinhole camera.(Of the photons emitted into 2π solid angle, acollimator diameter 1 mm placed 10 cm from thesource accepts only 8 × 10 −5 steradians. Only0.0013 % of the photons are used.)The huge developments in X-ray optics overthe past decade are described elsewhere in thisvolume. In this subchapter we confine ourselves todiscussion of only two optical elements, ellipsoidalmirrors and polycapillary optics. These devices aremirrors that rely on the total external reflectionof X-rays at very low incidence angles andthe figuring of the optic surfaces to achievefocusing. However, as is evident from Figure 2.1.1,Reflectivity1.00.80.60.40.20 Å r.m.s.5 Å r.m.s.10 Å r.m.s.15 Å r.m.s.20 Å r.m.s.1.54 Å wavelength00 0.2 0.4 0.6 0.8 1.0Incidence angle (degrees)Figure 2.1.1 Reflectivity of a gold surface as a function ofincidence angle and surface roughness (r.m.s. = root meansquare of the amplitude of surface displacement)

AMICROFOCUS GENERATOR WITH MAGNETIC FOCUSING 15because the refractive index for materials in theX-ray region of the spectrum is only smallerthan unity by a few parts in 10 5 , the rangeof total external reflection is very limited. As aconsequence of this grazing incidence limitationon total external reflection, to maximize the photoncollection, the optic needs to be placed very closeto the X-ray source. [Although parabolic multilayermirrors have been developed (Schuster and Göbel,1995; Gutman and Verman, 1996; Stommer et al.,1997) that significantly enhance the flux deliveredfrom rotating anode generators, the gains arerelatively modest due to the large source sizeand large source to optic distance. Nevertheless,the combination of high power and insertion gainresults in such devices delivering a huge intensityat the specimen.]A small optic to source distance has animmediate consequence in that, if the beamdivergence (or crossfire) at the sample is to besmall, the optic to sample distance must be large.The magnification of the source is therefore highand to maintain both a small beam size at thesample and low aberrations, the source size mustbe very small. Thus, to achieve a high insertiongain from a grazing incidence optic, it is essentialthat a microfocus X-ray source be used.2.1.3 A MICROFOCUS GENERATORWITH MAGNETIC FOCUSINGDespite the widespread use of X-ray fluorescenceanalysis from extremely small electron beam spotsin scanning electron microscopes, until recentlyall commercial X-ray generators used exclusivelyelectrostatic focusing. This is despite the factthat electron microscope manufacturers long agorealized that magnetic focusing was superiorin many ways. Electrostatically focused tubesgenerally exhibit side lobes to the electron beamspot and are relatively inefficient at deliveringelectrons to the target itself.The first electromagnetically focused microfocustube was described by Arndt, Long and Duncumb(Arndt et al., 1998a) in 1998. The designmaximized the solid angle of collection of theemitted X-rays and thus, in association with anellipsoidal mirror, achieved a high intensity at thesample. The observed intensity was in reasonableagreement with that calculated and compared withthat achieved with non-focusing X-ray optics usedwith conventional X-ray tubes operated at a powermore than 100 times as great.In the patented design (US Patent No. 6282263,2001), the electron beam, of circular cross-section,from the gun is focused by an axial magnetic lensand then drawn out by a quadrupole lens to forman elongated spot on the target. When viewed ata small take-off angle an elongated focus is seen,foreshortened to a diameter between 10 and 20 µm.Within the X-ray generator (Figure 2.1.2) the tubeis sealed and interchangeable. The electron opticsenable the beam to be steered and focused intoeither a spot or a line with a length to width ratioof 20:1. An electron mask of tungsten is includedto form an internal electron aperture. The electrongun consists of a Wehnelt electrode and cathode thatcan be either a rhenium–tungsten hairpin filamentor an indirectly heated activated dispenser cathode.The advantages of the dispenser cathode is that it ismechanically stable and, due to the lower powerconsumption and operating temperature, it has agreater lifetime than heated filament cathodes. It isalso simpler to align in the Wehnelt electrode. Thetube is run in a space-charge limited condition (asopposed to the conventional saturated, temperaturelimited condition), with the filament maintained at aconstant temperature. As a result, the tube current isdetermined almost exclusively by the bias voltagebetween the filament and the Wehnelt electrode.The electrons are accelerated from the cathode, heldat a high negative potential, towards the groundedanode. They pass through a hole in the anode beforeentering a long cylinder and subsequently collidingwith the target. An electron cross-over is formedbetween the Wehnelt and anode apertures and thisis imaged onto the target by the iron-cored axialsolenoid. So far Cu, Mo and Rh target tubes havebeen run successfully. The power loading that canbe achieved is such that a small amount of watercoolingproves essential.The ability to control the electron beam spotsize and shape by adjustment of the current in

16 MICRO X-RAY SOURCESF80GHESource dimension (µm)604020Vertical dimensionHorizontal dimensionD0−100 −50 0 50 100% of maximum stigmator currentFigure 2.1.3 Source dimension as a function of the maximumcurrent through the stigmator coilsCBAneeds to be increased to achieve the minimum spotsize. Increasing the tube current usually increasesthe spot size, due to space charge effects. Itis our standard practice to set up the focusingcoils with the stigmator coil current chosen toachieve an equiaxed beam. However, by adjustingthe stigmator coil current to draw the source outinto a line, a significant gain in intensity can beobtained without compromising on the couplinginto subsequent X-ray optical elements. The outputis limited by the maximum power at which targetdamage does not occur and Figure 2.1.4 showsFigure 2.1.2 Schematic drawing of an electromagneticallyfocused microfocus X-ray tube. (A) Cathode, (B) Wehneltgrid electrode, (C) anode, (D) electromagnetic axial focusinglens, (E) electromagnetic quadrupole lens, (F) target, (G) X-rayshutter, (H) direction of X-ray beamthe quadrupole stigmator coils is critical to theoptimum performance of the microfocus tube.Figure 2.1.3 shows the variation of the sourcedimensions as a function of the current in thestigmator coils. We note that there is a significantrange, close to the minimum in source area, whichis almost independent of the stigmator current andwhere the source is approximately equiaxed.As the tube accelerating voltage is increased,the value of the current in the focusing coilsPower/[spot area] ½ (W µm −1 )1.51.31.10.90.70.530 40 50Tube voltage (kV)Figure 2.1.4 Power divided by the square root of the spot areaunder conditions for achieving maximum output intensity atthree settings of tube voltage. The line is a least-squares linearfit to the data

SOURCE SIZE MEASUREMENT 17that the maximum permissible power divided bythe square root of the spot area remains constantwhether the tube is run at 30, 40 or 50 kV. Thisis in agreement with the results of Müller (Müller,1931) and Oosterkamp (Oosterkamp, 1948). Themaximum loading is a fortuitously close to aneasily remembered value, namely 1 W µm −1 .2.1.4 SOURCE SIZE MEASUREMENTMeasurement of the spot size, so crucial for theoperation of microfocus sources, is not trivial andcare needs to be taken in its definition. There aretwo measurement methods that can be adopted.The first is to use a small pinhole (5 µm) in a heavymetal substrate (e.g. platinum) to create a ‘pinholecamera’ image of the source on an imaging device.The second is to use a wire or knife-edge of heavymetal (e.g. platinum or tungsten) to cast a shadowon such an imaging device.In the former technique (Figure 2.1.5), a pinholeis used to project an image of the X-ray sourceonto an imaging device with source to specimendistance a and specimen to detector distance btypically, a = 12 mm, b = 250 mm.A source size can be measured directly from theimage that is collected, and scaled by a factor a/b.Resolution is affected by the size of the pinholeh, distances a and b, and the resolution of theimager. Each point of the source illuminates a spoton the imager of size h[(b + a)/a]. This gives aminimum distance to position the imager, wherethe illuminated spot is equal to the pixel size ofthe imager. For the Photonic Science X-Ray Eye2i imagers (17 µm pixel size) with a 5 µm pinhole,b min is 30 mm.Each point on the image corresponds to a finiteportion of the source of size h[(a + b)/b)]. Whenb ≫ a the size of this portion of the source isapproximately equal to the pinhole size h. Thislimits the minimum observable source size to thesize of the pinhole. In practice, the minimum sizefrom which useful measurements can be taken ismore nearly two to three times the pinhole size.In the second method (Figure 2.1.6), a finetungsten wire is used to cast a shadow when placedin the X-ray beam. It can be used to measure asource of size less than the wire diameter. The sizeof the source can be calculated from the intensityprofile in two ways:abFigure 2.1.5 Schematic diagram of the pinhole geometry for determination of source sizesdW 1 W 2 W 3abFigure 2.1.6 Shadow technique for source size measurement

18 MICRO X-RAY SOURCES(1) If the diameter of the wire d is accuratelyknown, the source size s is given by:s = W 3 − W 1. d (2.1.2)2 W 2Using a digital imager and image collectionsoftware, a very smooth curve can be obtainedby averaging many frames, and then averagingalong the shadow.(2) If the magnification is known, the source sizes is given by the width of the sloped part ofthe intensity profile (W 3 − W 1 )/2, divided bythe magnification.For both of these methods, it is necessary toidentify the corners of the intensity distribution,that is where to measure W 1 and W 3 . The simplestapproach is to fit straight lines to the penumbra(Figure 2.1.7) and measure directly.It is usual to quote the full width at halfmaximum(FWHM) of a source but unfortunately,the majority of the microfocus source shapes arenot simple statistical distributions. The standardMicrosource ® 80 W source is a very square shapewith more intensity in the corners than the centre.The shadow measurement gives a measurement ofthe source dimension perpendicular to the wireaxis, and integrates across the source parallel tothe wire axis. Assuming a Gaussian profile we cancalculate the shadow data (‘Cumulative Centre’line) as shown in Figure 2.1.8.The ‘Cumulative Centre’ line is a plot of theshadow that would be seen in a wire measurementand we note that the 12 % (and 88 %) pointscorrespond to the FWHM dimension of theGaussian distribution. The source dimension givenby these points corresponds to the size of spot thatincludes 76 % of the total energy. This is usefulwhen matching source size to an optic since theaim is to capture as much of the source powerwith the optic as possible. By using the 12 %corner points in the distribution for non-Gaussiandistributions, a ‘Gaussian equivalent FWHM’ canbe determined.2.1.5 APPLICATIONS IN PHASECONTRAST IMAGINGThere is a general perception that a monochromatic,coherent beam is necessary for phaseimaging. Such highly coherent beams are availableat synchrotron radiation sources and spectacular,high-resolution phase images have beenreported from third generation sources in recentyears (Cloetens et al., 1999, Elliot et al., 2002).However, it was demonstrated by Wilkins et al.40000350003000025000200001500010000500000 0.5 1 1.5 2 2.5 3Normalized positionFigure 2.1.7 Measured intensity as a function of normalized position across the image of a tungsten wire with linear interpolationto determine the shadow extent

FOCUSING OPTICS WITH MICROFOCUS SOURCES 19100%90%80%70%60%50%40%30%20%10%FWHM and 12% points605040302010CentreSumCumulative Centre0%0−100 −80 −60 −40 −20 0 20 40 60 80 100Figure 2.1.8 ‘Cumulative Centre’ line and Gaussian profile of a model source geometry(Wilkins et al., 1996) that even for a polychromaticsource, refractive index gradients distort thewavefront. The crucial insight of the Australiangroup was to recognize that the wavefront distortiondiverges at the edge of a circular objectfor all X-ray wavelengths present. As a result, ifthe imaging medium is placed a significant distancefrom the specimen, then the distortion of thewavefront results in interference and hence characteristicintensity changes. Thus, this very simplephase contrast imaging method reveals regions ofhigh electron density gradient. To avoid resolutionblurring destroying the effects, a microfocussource is needed. A detailed analysis of the contrastshows that, in the differential phase contrastthe wavelength appears only as a separable factor,the geometric features of the contrast being wavelengthindependent (Pogany et al., 1997). The techniquehas the benefit of ultimate simplicity in thatno monochromatization is thus strictly necessary.The dominance of characteristic X-ray lines givesmore than adequate monochromaticity for highcontrast at quite high spatial frequency. Recoveryof the phase and hence the quantitative determinationof the electron density is, however, muchmore difficult.Figure 2.1.9(a) shows an example of phasecontrast from a small fly. Very little absorptioncontrast is present, the image revealing the edgesof the body and organs. The phase contrast imagingtechnique presents an interesting application in thefood processing industry, where there is a need todetect and recognize low atomic number (organic)objects inside the products. Figure 2.1.9(b) showsan image of the same fly inside a tuna fishsandwich. The contrast from the sandwich isstrong, but against this slow contrast variation thesharp outline of the phase contrast image is readilyidentifiable.2.1.6 FOCUSING OPTICS WITHMICROFOCUS SOURCES2.1.6.1 ELLIPSOIDAL MIRRORSAs indicated above, the key potential of microfocussources lies in the ability to couple closely X-ray optical elements, thereby resulting in a verysubstantial insertion gain at the sample. The designof Arndt et al. (Arndt et al., 1998b) is such thatthe distance from source to optic can be less than10 mm. They reported a collection solid angle

20 MICRO X-RAY SOURCES(a)(b)Figure 2.1.9 (a) Phase contrast image of a small fly, length 3 mm. (b) Image of the same fly inside a tuna fish sandwichof 8 × 10 −4 steradians using an ellipsoidal mirror(Figure 2.1.10) and a resulting insertion gain ofover 100.The small ellipsoidal mirrors were developed inthe Czech Republic by Hudec and co-workers atthe Czech Academy. They can be produced by anelectroforming process (Hudec et al., 1988, 1993)in which a highly polished mandrel is first made asa negative of the final required shape. Followinglacquer polishing, the mandrel is coated with goldand then electroplated with nickel. The whole isthen surrounded with a carbon-fibre reinforcedepoxy to give structural strength. On withdrawal ofthe mandrel, the gold is left behind on the nickelshell (Arndt et al., 1998b). The complete assemblyis only a few centimetres in length and the innerdiameter of the ellipsoid is approximately 1 mm(Figure 2.1.11).Although the hole through the centre of theellipsoid does mean that there is a halo of diverging,non-reflected X-rays emerging in addition tothe focused beam (Figure 2.1.10) in practice thisdoes not prove a problem as the focus is typically30–60 cm from the mirror and the majority of theTargetMicromirrorSampleFigure 2.1.10 Ellipsoidal mirror for application in protein crystallography

FOCUSING OPTICS WITH MICROFOCUS SOURCES 217Intensity (arbitrary units)654320 1 2 3 4Time (years)Figure 2.1.11 Photograph of a Reflex MicromirrorX-rays in the diverging halo can be removed byan aperture. For X-ray diffraction applications, adivergence of less than a few milliradians is necessaryand to achieve this low level of crossfire atthe focus, the ellipsoidal mirrors must have highmagnification. As a result, the 10 µm source ismagnified to typically 300 µm at the specimen. Anexample of the focusing is shown in Figure 2.1.12,where for a 1 mrad divergence mirror, the FWHMof the beam at the sample is 300 µm inthiscase.There has been gradual improvement in theperformance of the ellipsoidal mirrors over time(Figure 2.1.13). As the roughness has only aFigure 2.1.13 Improvement in Reflex s.r.o. Micromirroroutput performance over time (1997–2000). (Intensity wasmeasured through a 500 µm pinhole at 150 mm from the mirrorin all cases)small effect on the efficiency in the total externalreflection regime, the principal improvement hascome from improved figuring.In the field of protein crystallography wherethere is a demand for a low divergence to matchcrystal perfection and small beam area to matchsmall crystal size, the results have been encouraging.Arndt and Bloomer (Arndt and Bloomer,1999a,b) note that diffracted intensities approachthat equivalent from a 5 kW rotating anode generatorwith X-ray mirrors, the microfocus sourceconsuming only 80 W, a fraction of the power of1 mmPinhole(a) (b) (c)Figure 2.1.12 Focal spot size as a function of distance from an ellipsoidal mirror: (a) 15 cm, (b) 20 cm and (c) 55 cm

22 MICRO X-RAY SOURCESthe rotating anode generator. Further the microfocussource is extremely small and compact comparedwith a rotating anode generator, which cantypically weigh up to 1 tonne. Microfocus sourcesfit in a suitcase and weigh typically a few kilograms.In terms of structure refinement with suchsources, very good agreements are found with anoverall R merge from 100 Åto1.8Åof3.2%.Protein data are visible out to 1.6 Å with very‘clean’ diffraction patterns. Rocking curve widthsare typically 0.15–0.18 ◦ .2.1.6.2 POLYCAPILLARY OPTICSPolycapillary optics provide an alternative methodfor collecting efficiently the output from a microfocustube. They consist (Figure 2.1.14) of a bundleof hollow borosilicate glass tubes stacked together,the X-rays being totally externally reflected fromthe internal surfaces of the capillary tubes. Byshaping the bundle appropriately, the spot size andbeam divergence can be varied over a wide range.As a capillary, like the ellipsoidal mirror, relieson total external reflection to guide the X-rays(much in the manner of an optical waveguide)the angular range of acceptance is small. Thus,as with the mirror, optimum coupling is achievedonly when the polycapillary optics is placed veryclose to the X-ray source, again presenting amajor challenge in the engineering design of themicrofocus source housing. Again, as with themirror, there is a requirement to minimize thesource size and maximize the brilliance in orderto maximize the intensity, as opposed to countrate, at the sample. Where the polycapillary opticgains over the ellipsoidal mirror is that by shapingthe bundle so that each capillary is oriented forgrazing incidence, the effective aperture angle ωcan be made quite large. Although care must betaken in such comparisons as the divergence oftendiffers, in practice there is a gain of about anorder of magnitude in intensity transmitted by apolycapillary optic compared with an ellipsoidalmirror.Over recent years the improvement in performanceof polycapillary optics has been dramatic.Configured for large crossfire but small beamdiameter at the sample, in combination with amicrofocus X-ray tube they have major potentialfor X-ray fluorescence analysis.2.1.7 APPLICATION OFMICROFOCUS TUBES AND OPTICSTO HIGH-RESOLUTION X-RAYDIFFRACTION (HRXRD)High-resolution X-ray diffraction (Bowen andTanner, 1998) has found a pivotal niche in thenondestructive characterization of the compoundsemiconductors that underpin high-speed opticalSourcewSampleFigure 2.1.14 Schematic diagram and photograph of a polycapillary focusing optic. (Reproduced with kind permission of XOSInc. USA)

HIGH-RESOLUTION X-RAY DIFFRACTION (HRXRD) 23communications systems. Since the pioneeringexperiments in the 1980s, the technique hasmoved from research laboratory to productionline within the most advanced semiconductorfabrication plants in the world. The key to highresolutionX-ray diffraction measurements is theuse of Bragg reflections from highly perfectcrystals to control the angular divergence andmonochromaticity of the beam hitting the sample.Such tailored beams can be used to measurethe relative lattice parameters of substrate andheteroepitaxial layers, enabling the composition,thickness, perfection, relaxation, and uniformity tobe determined without damage to the wafer.An example of a high-resolution diffraction configurationis shown in Figure 2.1.15, where a pairof asymmetric channel-cut silicon crystals are usedsuccessively to condition the angular spread andthen the wavelength spread of the X-ray beam.In this so-called DuMond arrangement, the combinationof Si 022 reflections gives a beam of11.5 arc seconds angular divergence and dispersionλ/λ = 1.3×10 −4 with CuKα radiation. With theresulting beam, the Bragg peaks from substrate andlayer having very closely matched lattice parameterscan be separated. Further, interference phenomena,giving a precise measurement of the layerthickness can be resolved. Using current generationpersonal computers, the diffraction profile (rockingcurve) can be simulated for a model structure,compared with the experimental data and iterativelyfitted by adjustment of the layer parametersin the model. The fitting is far from trivial, due tothe presence of multiple minima in the differencefunction between simulation and experiment, andonly with the introduction of genetic algorithmsby Wormington et al. (Wormington et al., 1999)in 1999 was the problem solved for anything otherthan the simplest cases.An example of a rocking curve from apsuedomorphic high electron mobility transistor(pHEMT) structure (commonly used in mobiletelecommunications), consisting of three layers ona GaAs (001) oriented substrate, is given in Figure2.1.16. The first layer is highly strained and is ofIn x Ga 1−x As, the second of Al x Ga 1−x As and thethird is a pure GaAs cap. Thickness and compositionsdeduced from fitting the X-ray data are givenin Table 2.1.2.In the application of high-resolution diffractionfor in-line process control there is a constant drivetowards reduction of the area of the probe beamon the sample. This must be achieved without lossof statistical accuracy or increase in measurementtime. With a microfocus source and associatedoptic Taylor et al. (Taylor et al., 2001) have shownthat not only can the beam footprint be reduced butalso the exposure time compared with larger focussources. In the experiments reported by Tayloret al., the standard air-cooled 80 W source in thecurrent generation Bede QC diffractometer (Loxleyet al., 1991) was replaced by an 80 W microfocussource and an ellipsoidal mirror (Figure 2.1.17).In this setting, the monochromating is done bythe aperture after the reference crystal ratherthan a second channel-cut crystal. Although aparaboloidal mirror would give the most efficientcoupling of the beam into the beam conditioningcrystal, the beam size would be large and the beamprofile annular. The focusing of the ellipsoidalmirror not only reduces the spot size but alsomakes adjustment extremely easy, albeit at theexpense of some intensity.Figure 2.1.16 shows an example of the order ofmagnitude gain in count rate as well as the overallFigure 2.1.15 Schematic diagram of the high resolution double axis diffraction setting with DuMond monochromator before thespecimen

24 MICRO X-RAY SOURCES10 5 −5000 −4000 −3000 −2000 −1000 0 1000 2000 300010 4Intensity (cps)10 310 210 110 0Theta/2Theta (arc seconds theta)Figure 2.1.16 Double axis X-ray rocking curve from a pHEMT structure on GaAs (Taylor et al., 2001). Upper curve: datacollected on a Bede QC200 diffractometer with microfocus source running at 50 W, plus micro-mirror. CuKα 1 wavelengthpresent only, beam footprint 1 mm diameter, total collection time 22 min. Lower curve: standard compact source (0.25 mm focalspot), no mirror, CuKα 1 and CuKα 2 wavelengths present. Beam footprint approximately 3 mm × 2 mm, collection time 53 min.The 10-fold increase in count rate and the beam footprint reduced by 85 % represent an increase in brightness of around 70times. Reprinted from Materials Science and Engineering B, Vol. 80, M. Taylor, J. Wall, N. Loxley, M. Wormington and T.Lafford, ‘High resolution X-ray diffraction using a high brilliance source, with rapid data analysis by auto-fitting’, pages 95–98,Copyright (2001), with permission from Elsevier ScienceTable 2.1.2 Thickness and composition of a pHEMT structureLayer Material Thickness (nm) Composition fraction x3 GaAs 35.07 (+0.52, −0.3) –2 Al x Ga 1−x As 41.57 (+0.52,−0.34) 0.286 (+0.024,−0.037)1 In x Ga 1−x As 15.75 (+0.42, −0.16) 0.117 (±0.001)Substrate GaAs – –ReflexmirrorReference crystalVariable apertureMicrosourceDetectorSampleFigure 2.1.17 Schematic diagram of the high resolution configuration for high throughput and small spot size

GRAZING INCIDENCE IN-PLANE X-RAY DIFFRACTION (GIIXD) 25reduction in beam area of a factor 7 between theoriginal configuration and that adopted in the BedeQC200 system. Similar enhanced performance inthe analysis of SiGe epitaxial layers has beenreportedbyZaumseilet al.(Zaumseilet al., 2001).Further intensity gain can be achieved by useof a polycapillary focusing optic, and it is nowstraightforward to locate automatically (with robothandling) a conditioned beam 300 µm diameteron a test window in a 300 mm wafer. Withoutthe microfocus X-ray tube, the development ofthe fully automated X-ray tools that are nowaccepted for key metrological functions in thesilicon industry would not have been possible.2.1.8 APPLICATION OFMICROFOCUS TUBES AND OPTICSTO GRAZING INCIDENCE IN-PLANEX-RAY DIFFRACTION (GIIXD)Grazing incidence in-plane X-ray diffraction is anX-ray scattering technique through which the inplanelattice parameter and lattice orientation ofvery thin surface and buried semiconductor layerscan be determined (Robinson and Tweet, 1992).With the incident beam close to or below thecritical angle for total external reflection, a Braggreflection is excited from planes perpendicularto the surface (Figure 2.1.18). As the depthpenetration of a wave incident below the criticalangle is only a few nanometres, the techniquehas become of major importance in studyingthe surface crystallography and, in particular, theconstruction of semiconductors. In this geometry,the simple Bragg condition for diffraction isnever quite satisfied and the scattering power istherefore weak. Further, at these very low angles ofincidence, much of the beam spills off the sample,not contributing to the scattering. Using normalX-ray generators, the intensity is generally so lowthat statistics are poor and data difficult to interpret.As a consequence, most of the developments haveoccurred at synchrotron radiation sources.However, the ability to focus the beam froma microfocus source to a spot typically 300 µmis diameter with a divergence of typically 2 mradopens up the possibility of performing theseexperiments in the laboratory on a realistic timescale.Goorsky and Tanner (Goorsky and Tanner,2002) have demonstrated extremely high intensitydiffracted beams from a microfocus X-ray tube andellipsoidal focusing optic.In the initial experiments, the Cu target microfocusX-ray generator was run at a power of 80 W,the beam being focused onto the sample using aReflex Micromirror TM ellipsoidal mirror of focallength 300 mm and divergence at the sample of2 mrad in both horizontal and vertical directions.The resulting spot diameter at the sample was0.3 mm FWHM. Even so, at the extremely lowangle of incidence (α f in Figure 2.1.18) of typically0.25 ◦ , the footprint on the sample was about70 mm. This resulted in substantial beam spill-offfor small samples. No further conditioning of theincidence beam was used. The sample was rotatedA planes}a fΘ B}a i2Θ BFigure 2.1.18 Geometry of GIIXD. θ B , Bragg angle; α f , angle of incidence of X-ray beam to surface

26 MICRO X-RAY SOURCESuntil it was horizontal, the vertical height beingadjusted to half-cut the incident beam. A smallrotation about the axis horizontal and perpendicularto the incident beam permitted the grazingangle to be tuned. The sample was rotated aboutthe axis normal to the sample surface. A 2 mraddivergence Soller slit limited the angular acceptanceof the scintillation detector in the horizontalplane in which the detector was scanned (2 Baxis). Over the small range of grazing incidenceangles used in GIIXD, the vertical aperture of thedetector was large enough to accept all beams.The technique has proved particularly powerfulfor the measurement of the in-plane mosaicof the GaN-based epitaxial films used for bluelight emitting devices. Measurement of the inplanemosaic is particularly difficult and involvesa model-dependent complex deconvolution of severaldata sets. The GIIXD technique enables thein-plane mosaic to be determined directly from asingle measurement, the total experimental time(including alignment) being 5 min. Figure 2.1.19shows an example of the measurement of the inplanemosaic of a (001) oriented epitaxial multilayerof Fe–Au on MgO carried out at the EuropeanSynchrotron Radiation Facility and in thelaboratory. The agreement is excellent. In bothcases a Voigt function was necessary to fit the tailsof the intensity distribution although a Gaussianwas a quite reasonable approximation. The noisebase of the laboratory measurements was proportionallyhigher than at the synchrotron radiationsource as there was little discrimination against Fefluorescence in the laboratory measurements. Useof a Si(Li) energy dispersive detector at the synchrotronsource eliminated the fluorescence almostcompletely.2.1.9 SUMMARYThe use of electromagnetic focusing to focusand steer the electron beam has enabled X-raysource dimensions to be controlled to a muchgreater tolerance than in the past. In particular theabsence of side lobes on the spot and controllableastigmatism permits the achievement of a higherbrilliance without target damage and the abilityof tailoring the spot dimensions to optimizethe input coupling to subsequent X-ray opticalelements. The result is the efficient use of grazingincidence optical elements such as mirrors andpolycapillaries to deliver high brilliance beams ofsmall dimension on the sample. While the greatestimpact has so far been in the field of diffraction,the availability of high brightness microfocussources is likely to have a major impact on X-rayspectroscopy in the near future.Normalized intensity1.00.80.60.40.20ESRF dataFit to ESRFdataLab dataFit to lab data−4 0 4Sample rotation angle (°)Figure 2.1.19 Comparison of GIIXD rocking curves takenat the European Synchrotron Radiation Facility and in thelaboratory using a microfocus X-ray generator. Fits are to aVoigt functionREFERENCESArndt, U. W. and Bloomer, A. C. Curr. Opin. Struct. Biol., 9,609 (1999a).Arndt, U. W. and Bloomer, A. C. Acta Cryst., Biol. Crystallogr.,D55, 1672, (1999b).Arndt, U. W., Long, J. V. P. and Duncumb, P. J. Appl. Cryst.,31, 936 (1998a).Arndt, U. W., Duncumb, P., Long, J. V. P., Pina, L. andInneman, A. J. Appl. Cryst., 31, 733 (1998b).Bohler, P. and Stehle, J. L. Phys. Status Solidi A, 170, 211(1998).Bowen, D. K. and Tanner, B. K. High Resolution X-rayDiffractometry and Topography, Taylor and Francis, London,1998.Cloetens, P., Ludwig, W., Baruchel, J., Guigay, J.-P., Pernot-Rejmánková, P., Salomé-Pateyron, M., Schlenker, M., Buffière,J.-Y., Maire, E. and Peix, G. J. Phys. D: Appl Phys.,32, A145 (1999).

REFERENCES 27Davies, K. E. and Hukins, D. W. L. J. Appl. Cryst., 17, 486(1984).Elliott, J. A., Windle, A. H., Hobdell, J. R., Eeckhaut, G.,Oldman, R. J., Ludwig, W., Boller, E., Cloetens, P. andBaruchel, J. J. Mater. Sci., 37, 1547 (2002).Furnas, T. C. Nucl. Instrum. Methods, , 299, 246 (1990).Goorsky, M. S. and Tanner, B. K. Crystal Res. Technol., 37,647 (2002).Gutman, G. and Verman, B. J. Phys D: Appl. Phys., 29, 1675(1996).Hudec, R., Valnicek, B., Ashenbach, B., Braeununger, H. andW. Burkart, Appl. Opt., 27, 1453 (1988).Hudec, R., Arndt, U. W., Inneman, A. and Pina, L. Inst. Phys.Conf. Ser., 130, 499 (1993).Loxley, N., Bowen, D. K. and Tanner, B. K. Mater. Res. Soc.Symp. Proc., 208, 119 (1991).Müller, A. Proc. R. Soc. London, 132, 646 (1931).Oosterkamp, W. J. Philips Res. Repts, 3, 303 (1948).Pogany, A., Gao, D. and Wilkins, S. W. Rev. Sci. Instrum., 68,2774 (1997).Robinson, I.K. and Tweet, D. J. Rept. Prog. Phys., 55, 599(1992).Röntgen Centennial, University of Würzburg, 1995.Schuster, M. and Göbel, H. J. Phys. D: Appl. Phys., 28, A270(1995).Stommer, R., Metzger, T., Schuster, M. and Göbel, H. NuovoCim. D, 19, 465 (1997).Taylor, M., Wall, J., Loxley, N., Wormington, M. and Lafford,T. Mater. Sci. Eng. B, 80, 95 (2001).US Patent No. 6282263 (2001).Wilkins, S. W., Gureyev, T. E., Gao, D., Pogany, A. andStevenson, A. W. Nature, 384, 335 (1996).Wormington, M., Panaccione, C., Matney, K. M. and Bowen,D. K. Philos. Trans. R. Soc., 357, 2827 (1999).Zaumseil, P., Lafford, T. A. and Taylor, M. J. Phys. D: Appl.Phys., 34, A52 (2001).

2.2 New Synchrotron Radiation SourcesM. WATANABEInstitute of Multidisciplinary Research for Advanced Materials, Tohoku University, JapanandG. ISOYAMAThe Institute of Scientific and Industrial Research, Osaka University, Japan2.2.1 INTRODUCTIONSynchrotron radiation is light emitted by highenergyelectrons moving on a circular orbit in auniform magnetic field. It has a continuous spectrumranging from the infrared, through the visible,the ultraviolet, and the soft X-ray, to the hard X-rayregions. 1–4 Experiments in the soft X-ray and thehard X-ray regions began in the 1960s using lightfrom bending magnets of synchrotrons operatedfor elementary particle physics. In the 1970s, synchrotronradiation users began to parasitically usestorage rings constructed for colliding beam experiments,instead of synchrotrons, as a light source,because the lifetime of the electron or positronbeam circulating in a storage ring is longer thana few hours and hence synchrotron radiation froma storage ring is spatially and temporally muchmore stable than that from a synchrotron. Thesesynchrotrons and storage rings used parasiticallyare called first generation sources.In the 1980s, synchrotron radiation usersacquired their storage rings dedicated to lightsources, which are called second generationsources. Figure 2.2.1 shows a schematic drawingof a storage ring as a light source. Various experiments,including spectroscopy, photoelectron spectroscopy,extended X-ray absorption fine structure(EXAFS), and X-ray diffraction, were extensivelyconducted with light from bending magnets ofthese dedicated machines. Time resolved experimentswere also conducted by making use ofthe pulsed time structure of synchrotron radiationfrom these storage rings. Insertion devices suchas superconducting wigglers, multipole wigglers,and undulators were developed in this decade inorder to obtain higher energy light, higher flux lightand brighter quasi-monochromatic light, respectively.These insertion devices consist of arraysof magnets with alternating fields and they areinstalled in straight sections of storage rings. Hereafterthe term ‘synchrotron radiation’ means lightnot only from bending magnets but also from insertiondevices.Several third generation sources were constructedin the 1990s, and even at present someare under construction and others are in the planningstages. They are storage rings optimized forutilizing insertion devices, especially undulators.In order not to deteriorate bright light from undulators,the size and the divergence of the electronbeam, the product of which is approximatelyequal to the emittance of the electron beam, has tobe reduced considerably. Third generation sourcesare, therefore, low emittance rings. The verticalemittance of an electron storage ring is muchsmaller than the horizontal one and the diffractionX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

30 NEW SYNCHROTRON RADIATION SOURCESBending magnetSRadiationySNSNNSNSN UndulatorRF (Radiofrequency)CavityElectronbunchs ys ls xre −qRadiationPre-mirrorFront endMonochromatorFigure 2.2.1 Schematic drawing of a storage ring as the synchrotron radiation source and a beamline. The angular coordinate isalso defined for synchrotron radiation from a bending magnetlimit is achieved in the longer wavelength regionof synchrotron radiation for the vertical direction.By making use of third generation sources,experiments requiring brighter light have progressed,such as microscopy, high resolution measurement,and two-color experiments using synchrotronradiation together with laser. In addition,it is noteworthy that other synchrotron radiationsources have been newly born and some areunder construction, which should be evaluated asan intermediate class between second and thirdgeneration sources. This means that the utilizationof synchrotron radiation grows rapidly andspreads worldwide. Stability of the electron beamin its cross-section and position has considerablyimproved compared with that in the 1980s,due to cures for collective instability and developmentof feedback systems, so that more precisemeasurements can be made. A new operationmode of storage rings was recently tested, whichis called top-up injection. Whenever the storedcurrent decreases slightly, electrons are repeatedlyinjected to keep the current almost constant.The synchrotron radiation sources open to outsideusers in the world are listed in Table 2.2.1. Theemittance of the storage rings indicates the horizontalemittance, as usual.On the other hand, efforts have been made todevelop free electron lasers (FEL). An FEL iscomprised of an undulator and an optical resonatorcomposed of two mirrors, and a high energyelectron beam is provided from a linac or a storagering. The first FEL was realized in 1977 in theinfrared region using a low energy linac. Thewavelength region is extended to the visible andthe ultraviolet with FEL based on storage rings.In 2000, lasing in the vacuum ultraviolet wasachieved with a special type of the linac-based FELwithout an optical resonator, called self-amplifiedspontaneous emission (SASE). Some SASE-FELsin the soft X-ray and the hard X-ray regions areunder construction or in the design stage.Fourth generation sources are expected toappear in the 2000s. 5 One candidate for such lightsources is SASE-FEL mentioned above. Othersare storage rings with ultra-low emittance andenergy recovery linacs recently proposed. In fourthgeneration sources, the emittance of the electronbeam will reach the diffraction limit even in thehorizontal direction and brilliance will be very

INTRODUCTION 31Table 2.2.1 Synchrotron radiation sourcesLocation Institute Ring Energy (GeV) ε c (keV) Emittance (π nm·rad)SpainBarcelona Catalonia SR Lab. 2.5–3UKDaresburyChiltonFranceOrsayGrenobleSwitzerlandVilligenItalyFrascatiTriesteGermanyKarlsruheBonnDortmundHamburgBerlinDenmarkAarhusSwedenLundUkraineKharkovKievRussiaMoscowSRCRALLURELUREESRFPaul Scherrer Inst.INFNSyn. TriesteFZKBonn Univ.Univ. DortmundHASYLABHASYLABBESSYISAISAUniv. of LundUniv. of LundUniv. of LundKPIUNSCSRC 2DIAMOND 3a 2.03DCI 21.85Super ACO 2 0.8SOLEIL 3a2.5ESRF 3 63.22.5 14.33.70.6720.61600353.03.9SLS 3 2.4 5.4 4.4DAFNE 1Elettra 3 0.512.0ANKA 22.5ELSA 1DELTADORIS III 1PETRA 1BESSY II 31.6–2.71.54.45121.7 (1.9)ASTRID 10.58ASTRID II 3a 0.6–1.4MAX I 20.55MAX II 31.5MAX III 3a 0.7Pulse Stretcher/SR 1ISI-8000.75–20.7–1.00.23.26.216202.610007.04111404256.10.38 160Kurchatov Inst.Siberia I 20.276INPVEPP-4 1 5–7DubnaJINRSiberia II 2DELSY 3b0.452.51.21.75, 7.11.1688010ZelenogradNovosibirskF. V. Lukin Inst.INPTNK 2VEPP-3 11.2–1.62.22.95JordanAllaan SESAME 2b 1.0 1.25 115 (50 c )IndiaIndore CAT INDUS-I 2ThailandNakhon0.45INDUS-II 2a 2.5NSRC Siam Photon Source 2 1.0 0.80 74RatchasimaSingaporeSingapore Nat. Univ. Singapore Helios 2 2 0.7 1.47 1370TaiwanHsinchu SRRC SRRC 3 1.3 (1.5) 1.4 19.2KoreaPohang POSTECH PLS 3 2 (2.5) 2.8 12.1ChinaBeijingHefeiShanghaiBSRLUSTCSSRFBEPC 1(1.55) 2.2HLS 20.8SSRF 3a 3.50.310.26.32.280.528.8137358.17653(continued overleaf )

32 NEW SYNCHROTRON RADIATION SOURCESTable 2.2.1 (continued)Location Institute Ring Energy (GeV) ε c (keV) Emittance (π nm·rad)JapanSendaiTsukubaKashiwaOkazakiKusatsuNishi-HarimaTohoku Univ.AISTKEKKEKUniv. TokyoIMSRitsumeikan Univ.JASRIHimeji Inst. Tech.Hiroshima Univ.Saga Pref.TSRF 2aTERAS 2PF 2AR 2Super-SOR 3aUVSOR 2AURORA 2SPring-8 3NewSUBARU 2HiSOR 22b1.50.62.56.51.80.750.57581.50.71.4Higashi-HiroshimaSagaAustraliaMelbourne Monash Univ. Boomerang 3a 3 12CanadaSaskatoon Canadian L. S. CLS 3a (2.5) 2.9 7.57 18.1USAStanfordBerkeleyStoughtonIthacaArgonneNewport NewsGaithersburgUptonBaton RougeBrazilCampinasSSRLLBNLSRCCHESSANLJefferson Lab.NISTBNLBNLLouisiana S. Univ.LNLSLNLSSPEAR 3 3b3ALS 3Aladdin 2CESR 1APS 3Helios 1 2bSURF III 2NSLS/VUV 2NSLS/X-Ray 2CAMD 21 First generation source; 2 second generation source; 3 third generation source.a In planning/design stage.b Under construction.c With two wigglers.(1.5) 1.9(0.8) 1.05.570.70.40.752.51.5LNLS-1 2LNLS-2 a 1.3721.870.564.026.42.420.430.8428.92.330.881.97.6(0.55) 1.111.019.50.4952.5626.93681275.96740025.5186.81088.22002.08 100high. Furthermore, the pulse duration will beshorter than that of third generation sources, so thatpeak brilliance will be much higher. Experimentsusing fourth generation sources will be directedto extensively utilize coherence, the time structureand peak brilliance.In this subchapter, new synchrotron radiationsources are introduced briefly and characteristicsof synchrotron radiation are summarized.New aspects of synchrotron radiation, most ofwhich were topics at the 6th and the 7th InternationalConferences on Synchrotron RadiationInstrumentation, 6,7 are described for users exploitingthird generation sources and typical propertiesof light at the sample position such asthe number of photons are briefly mentioned.Finally, candidates for fourth generation sourceswill be described.2.2.2 THIRD GENERATION SOURCESAND OTHER NEW SOURCESIn the world, there are about 45 synchrotronradiation sources in operation, including 10 thirdgeneration sources, as given in Table 2.2.1. Thirdgeneration sources are storage rings with thehorizontal emittance around or lower than 10 πnm·rad and with many long straight sections toinstall insertion devices, especially undulators witha large number of periods.Figure 2.2.2 shows a schematic drawing of aplanar undulator. Most of undulators are made

THIRD GENERATION SOURCES AND OTHER NEW SOURCES 33GapElectronsyqRadiationl uFigure 2.2.2 Electron bunch moving in a planar undulator. The angular coordinate is defined for synchrotron radiation fromthe undulatorwith permanent magnets. The peak energy ofquasi-monochromatic light from the undulator isinversely proportional to the period length, λ u .Toproduce high energy photons with an undulator,λ uhas to be made short and at the same timethe gap has to be reduced so as to keep themagnetic field high. The minimum gap determinesthe vertical physical aperture for the circulatingbeam in the storage ring, and the aperture hasto be large enough to make the lifetime of theelectron beam long. Another method is to usehigher order harmonics from a planar undulator.Brightness of higher harmonics above the 5th orderis, however, reduced due to errors in the magneticfield, so that light from the undulator covers only alower portion of the spectral region obtained withthat from bending magnets for the same electronenergy. In order to obtain high energy photonswith an undulator, the electron energy has to bemade high. This is the reason why energies ofthird generation sources are, in general, higher thanthose of second generation sources.The third generation sources are classified intotwo groups; those dedicated mainly to vacuumultraviolet and soft X-ray experiments, and thoseto hard X-ray experiments. Typical examples ofthe first group are ALS, BESSY II and Elettra.Energies of these storage rings are 1.6–2 GeV,circumferences are 180–250 m, and 6–10 undulatorsare installed. The members of the secondgroup are ESRF, APS and SPring-8. Their energiesare 6–8 GeV, circumferences are 0.84–1.4 km, and30–50 undulators are installed. Along with developmentof these third generation sources, undulatortechnologies have progressed significantly. 8 Oneof the novel undulators is an in-vacuum undulatorwith small λ u , which has no vacuum chamberin the magnet gap, so that the magnet gap canbe made extremely small. In addition, the storagerings can be operated in a special manner, whichensures a long lifetime even though the verticalaperture is small in straight sections for undulators.Magnetic field errors of undulators are, furthermore,reduced, so that higher harmonics up to the11th order can be used for experiments. By makingbest use of these achievements, storage ringsbelonging to a new group have been constructedor are under construction, which have intermediateenergies of 2.4–3 GeV but can provide bright lightin the hard X-ray region below 20 keV as well asthe vacuum ultraviolet and the soft X-ray regions.These sources in the third group of third generationsources are Swiss Light Source, DIAMOND,SOLEIL and CLS.Some of the other new storage rings arecompact synchrotron radiation sources, whichuse superconducting bending magnets or strongfieldnormal-conducting magnets to extend thephoton energy region toward the hard X-rayregion with relatively lower electron energies.They are AURORA, Helios 1 and 2, and HiSOR.It is remarkable that old soft X-ray rings withenergies of 1 GeV belonging to second generationsources are moved to other places and modifiedto add the ability to generate hard X-rays withsuperconducting wigglers. They are SESAMEtransformed from BESSY I (Berlin) and the SiamPhoton Source from SORTEC (Tsukuba). ANKAis an intermediate scale X-ray source with thecircumference of 110 m.

34 NEW SYNCHROTRON RADIATION SOURCES2.2.2.1 CHARACTERISTICS OFSYNCHROTRON RADIATIONThe motion of an electron in a storage ring isshown schematically in Figure 2.2.1, together withthe definition of the angular coordinate for lightfrom bending magnets. If electrons circulating inthe storage ring have the same energy E, theyoscillate incoherently around the central orbit withsmall amplitudes, which is called betatron oscillation.An electron with a different energy E + Ecirculates on a different orbit slightly away fromthe central orbit. The energy spread of the electronbeam σ E /E is typically 5 × 10 −4 − 1 × 10 −3 ,where σ stands for the standard deviation of theGaussian distribution. Owing to the betatron oscillationand the energy spread, the electron beamhas a finite beam size σ x and divergence σ x ′ inthe horizontal direction, and σ y and σ y ′ in the verticaldirection. If the contribution of the energyspread to the beam size is negligible, the emittance,defined as the phase space area occupied bythe electron beam, is approximately equal to πσ x σ x′or πσ y σ y ′ . The shape of the cross-section is usuallyelliptic, and sizes are σ x = 0.05 − 0.5mmandσ y = 0.01 − 0.05 mm and divergences are σ x ′ =0.01 − 0.05 mrad and σ y ′ = 0.005 − 0.01 mrad forthird generation sources. These values are one totwo orders of magnitude larger for second generationsources. Electrons form bunches due tothe radio frequency (RF, 100–500 MHz) acceleratingsystem used to compensate for the energyloss by emission of synchrotron radiation. Thebunch length σ l is 1–30 cm, depending mainlyon the RF and the momentum compaction factorα = (L/L)/(E/E), whereL is the circumferencefor an electron with the energy E. The pulseduration of the electron beam and accordingly thetime duration of light pulses is 30 ps–1 ns. Noveltechniques to make the light pulse duration considerablyshorter have been developed, which will bedescribed later. The time interval between bunchesis the inverse of the RF and it is 2–10 ns. When astorage ring is operated in the single bunch modeor in the several bunch mode with equal intervals,pulsed light with an interval of 0.1–1 µs, which isthe revolution time of the storage ring or a fraction,can be used for time resolved experiments.In many cases, recently, the intensity of synchrotronradiation is given by the number of photonsN ph per second for a nominal stored beamcurrent (100–500 mA), rather than for a unit current(mA), where synchrotron radiation from astorage ring is regarded as DC light. We definethree quantities, flux, angular flux and brilliance aswell as their practical units most frequently usedto measure the intensity of synchrotron radiation ata certain wavelength or photon energy as follows:flux = dN ph /[dt(dλ/λ)]→ phs/s/0.1%bwangular flux = dN ph /[dtdθ(dλ/λ)]→ phs/s/mrad/0.1%bwbrilliance = dN ph /[dtdθdψdxdy(dλ/λ)]→ phs/s/mrad 2 /mm 2 /0.1%bwwhere x and y are coordinates on the cross-sectionof the light source, phs and 0.1 %bw denote thenumber of photons and the fractional bandwidth ofλ/λ = ω/ω = 10 −3 , respectively. The angularflux defined above is the number of photonsper horizontal angular acceptance θ = 1mradintegrated over the vertical angle ψ. This quantityis useful only for light from bending magnets. Thebrilliance, which is often called brightness, is thenumber of photons per θ = 1mrad and ψ =1 mrad divided by the cross-sectional area of theelectron beam. The brilliance is useful for lightfrom undulators as well as from bending magnets.The peak brilliance is defined as the instantaneouspeak value obtained at peaks of light pulses.Light from bending magnets has a smooth andcontinuous spectrum characterized by the criticalphoton energy ε c , which is calculated in practicalunits as ε c (keV) = 2.22 × E 3 (GeV)/ρ(m), whereρ is the orbit radius in the bending magnet.Angular fluxes for several light sources are givenin Figure 2.2.3, where critical photon energiesare indicated by the arrows. The angular fluxspectrum has a broad maximum around the photonenergy 0.4 × ε c . When it is plotted in the double

THIRD GENERATION SOURCES AND OTHER NEW SOURCES 35SPring-8Angular flux (phs/s/mrad/0.1% bw)10 1310 12Helios2SPEAR3BESSYIIBendBESSYII10 11SW10 1010 −2 10 −1 110 10 2 10 3Photon energy (keV)Figure 2.2.3 Angular flux spectra of synchrotron radiation from bending magnets for some storage rings. The arrows indicatecritical photon energies. The angular flux spectrum is also shown for the superconducting wiggler SW of BESSY-IIlogarithmic scales, the angular flux decreasesgradually in the lower photon energy region, whileit drops sharply in the higher photon energy region,as can be seen in Figure 2.2.3. The flux, whichis the number of available photons, is given bythe product of the angular flux and the acceptanceangle θ.The magnetic field in bending magnets isgiven by B(T) = 3.34 × E(GeV)/ρ(m). The criticalphoton energy is, therefore, proportional tothe magnetic field for the same electron energy.The bending magnets of BESSY-II, SPEAR 3and SPring-8, angular flux spectra of which areshown in Figure 2.2.3, are conventional normalconductingmagnets with a magnetic field around1 T. Since a superconducting magnet can generatea magnetic field up to 4–10 T, it is possible toproduce synchrotron radiation in a photon energyregion several times higher than that from conventionalmagnets for the same electron energy,if superconducting magnets are used as bendingmagnets (Helios 2) or as a superconducting wiggler(BESSY-II SW).The angular divergence of light from bendingmagnets is small in the vertical direction andit is given typically by 1/γ around ε c , whereγ = E/mc 2 is the Lorentz factor with mc 2 =0.511 MeV being the rest energy of an electron.The vertical angular divergence depends on thephoton energy; it becomes larger as the photonenergy decreases. In second generation sources, theelectron beam divergence σ y′ is smaller than theangular divergence of light from bending magnetsin the photon energy region below ε c , while it iscomparable or larger above ε c . In third generationsources, however, σ y ′ is smaller than the angulardivergence in most of the photon energy region.Light from bending magnets is linearly polarizedwith the electric vector lying on the planeof the electron motion when it is observed on theplane, while it is, in general, elliptically polarizedwhen observed above or below the plane. Whenan angle of observation in the vertical directionis large, it is, not perfectly but practically, circularlypolarized.The undulator has a transverse magnetic field,which varies sinusoidally along the central axiswith a period length longer than 1 cm and thenumber of periods ranging from a few to hundreds.The angular coordinate for light from an undulator

36 NEW SYNCHROTRON RADIATION SOURCESis defined in Figure 2.2.2. Light from a planarundulator comprises a series of harmonic peaks.The wavelength λ of a peak is given byλ =λ ()u1 + K22nγ 2 2 + γ 2 2 (2.2.1)where n is an integer indicating the harmonicorder, 2 = θ 2 + ψ 2 , and K is the deflectionparameter given by K = 93.4 × λ u (m)B 0 (T) withB 0 being the peak magnetic field. When themagnetic field in a planar undulator is notvery high and the maximum deflection angle ofelectrons is of the order of 1/γ , for which Kis around one, quasi-monochromatic light withhigh brilliance can be obtained. The fractionalbandwidth of the nth harmonic peak is givenby λ/λ ≈ 1/nN , where N is the number ofperiods. To calculate the wavelength for a helicalundulator, the second term K 2 /2 in the parenthesesof Equation (2.2.1) should be replaced with K 2 .Light from a planar undulator is linearly polarized,while that from a helical undulator is circularlypolarized. If the electron energy is fixed, thedeflection parameter has to be varied to changepeak wavelengths. For an undulator made withpermanent magnets, the peak magnetic field B 0 isvaried by mechanically changing the magnet gap.The angular divergence of light for a singleelectron is approximately axially symmetric evenfor a planar undulator, and as small as the fractionof the vertical angular divergence of light froma bending magnet. Its standard deviation is σ r ′ ≈1/[γ(nN ) 1/2 ] ≈ (λ/L u ) 1/2 for K ≈ 1, where L uis the total length of the undulator. The effectivesource size for a single electron, originating fromthe depth of the light source along the undulatorlength and the angular divergence, is calculated atthe center of the undulator as σ r ≈ (λL u ) 1/2 /(4π).Overall source sizes and divergences of light froman undulator are denoted by x and x ′ in thehorizontal direction, respectively, and by y and y ′ in the vertical direction, where x = (σr 2 +σx 2)1/2 , y = (σr 2 + σ y 2)1/2 , x ′ ′2= (σ r + σ x ′2)1/2,and y ′ ′2= (σ r + σ y ′2)1/2.The intensity of light from undulators is usuallyexpressed in terms of the brilliance. The brillianceis proportional to N 2 in an ideal case. Figure 2.2.4shows examples of brilliance spectra of light at = 0 for K = 1 together with those from abending magnet and a multipole wiggler. The10 22Brilliance (phs/s/mrad 2 /mm 2 /0.1%bw)10 2110 2010 1910 1810 1710 1610 1510 14ALS HUn = 1SPring-8 PUn = 1n = 3n = 1 n = 3ESRF PUn = 5APS HUn = 1SPring-8 Bendn = 5ESRF MPW10 13 10 −1 1 1010 2Photon energy (keV)Figure 2.2.4 Brilliance spectra of synchrotron radiation from insertion devices and a bending magnet for some storage rings. PU,HU, MPW and Bend denote a planar undulator, a helical undulator, a multipole wiggler, and a bending magnet, respectively.The broken curves show envelopes of the brilliance for odd harmonics obtained by varying the undulator gap

THIRD GENERATION SOURCES AND OTHER NEW SOURCES 37broken curves show envelope of peak values of thebrilliance for odd harmonics obtained by varyingthe undulator gap. As can be seen in Figure 2.2.4,the odd harmonics appear stronger than the evenharmonics, and the fundamental peak with n = 1isthe strongest in a planar undulator, while only thefundamental peak is strong for a helical undulator.The brilliance of the fundamental peak is morethan 10 3 times as high as that of light frombending magnets. As N becomes considerablylarge, the brilliance increases, but not as muchas N 2 , because the energy spread of the electronbeam moderates the increase of the brilliance. Thelongest undulator for a storage ring is, at present,the 25 m long undulator at SPring-8. The undulatorcovers the photon energy range from 8 to 18 keVwith the first harmonic and the brilliance is higherthan 10 20 phs/s/mrad 2 /mm 2 /0.1 %bw.The flux for the undulator may be approximatelycalculated from the brilliance multiplied by2π x y and 2π x ′ ′ y . The flux increases linearlywith the period number N, even though beam sizesand divergences as well as the energy spread of theelectron beam are non-zero and finite. Figure 2.2.5shows flux spectra for two of the undulators andthe multipole wiggler appearing in Figure 2.2.4.The solid curves represent the flux spectra for theundulator with K = 1 and the multipole wiggler,while the broken curves show envelopes of the fluxpeak obtained for the undulators by changing K.When K is much larger than unity, light froman undulator turns to a continuous spectrum andit extends to the higher photon energy region.The angular divergence becomes large and itsproperties become similar to those of light frombending magnets. This undulator is called amultipole wiggler. The brilliance and the flux oflight from the multipole wiggler are proportionalto N. As can be seen in Figure 2.2.5, the flux fromthe multipole wiggler exceeds the flux from theundulator at ESRF.2.2.2.2 NEW ASPECTS OFSYNCHROTRON RADIATIONEnergy RangeThe third generation sources for X-rays, namelyESRF, APS and SPring-8, were designed and constructedto provide X-rays around 10 keV energywith the first harmonic light from undulators. Theirelectron energies are much higher than those of thesecond generation sources for X-rays. As a result,higher energy photons are available from bending10 16SPring-8 PUn = 1n = 3n = 5Flux (phs/s/0.1%bw)ESRF MPW10 15ESRF PUn = 1n = 310 13 APS HUn = 1n = 510 141 10 10 2Photon energy (keV)Figure 2.2.5 Flux spectra of synchrotron radiation from insertion devices. The broken curves show envelopes of the brilliancefor odd harmonics obtained by varying the undulator gap

38 NEW SYNCHROTRON RADIATION SOURCESmagnets of these storage rings and their criticalphoton energies are 20.6, 19.5 and 28.9 keV forESRF, APS and SPring-8, respectively. The angularflux of SPring-8 is shown in Figure 2.2.3. Ascan be seen, experiments can be conducted usinghigh-energy photons up to 100 keV or higher.This feature confers several advantages as follows.Materials containing heavy elements can be investigated,for instance, by means of the fluorescencetrace analysis of their K absorption edges withoutbeing disturbed by other lighter elements. Indiffraction experiments, it is possible to detect scatteredX-rays with large wave numbers, so thatthe Fourier transformation can be accurately madeeven for amorphous materials or liquids. Samplesbecome more transparent to the higher energy photons,so that images of thick samples can be takeneasily. Signals from Compton and other scatteringprocesses can be measured clearly, becausetheir cross-sections become larger and comparableto the cross-section for the photoelectric process.New elements with higher nuclear levels can beexcited for nuclear inelastic resonance.Flux and BrillianceIn the early stage of undulator usage, the magnetgap of an undulator was not allowed to changeduring the experiment, because the beam positionmoved with the gap. Technologies have beendeveloped to reduce magnetic field errors of undulatorscausing beam position movements and tocorrect beam positions precisely. As a result, thegap can be changed synchronously with scanning amonochromator during the experiment, so that thehighest brilliance at the peak can be used at anyphoton energy. Hereafter we call it ‘synchronoustuning’.The photon number within a required spot sizeand a divergence for a given fractional bandwidth,which is the intensity at the sample position, shouldbe as high as possible for the experiment. Theproduct of the size and the divergence of thelight beam at the source point is conserved at anyfocusing point in the optical system, which wetentatively call the optical invariant, provided theoptical system is ideal. In the following discussionon the light intensity, the efficiency of opticalelements is neglected. When the product of the sizeand the divergence of the light beam required at thesample position, which is the acceptance of lightat the sample, is smaller than the optical invariantof the synchrotron radiation, the available flux islimited by the acceptance at the sample position.The flux is reduced by the ratio of the acceptanceto the optical invariant. The high brilliance of thesource is, therefore, essential to obtain sufficientintensity in microbeam experiments of small areasand in high energy-resolution experiments withnarrow slits in the monochromators. When theacceptance at the sample position is larger thanthe optical invariant of the synchrotron radiation,the intensity is given by the flux and the fractionalbandwidth of a monochromator. The available fluxintroduced to an optical system is, for example,given in Figure 2.2.5. The typical value of theflux is 10 15 phs/s/0.1 %bw. If synchrotron radiationfrom a multipole wiggler is used, higher intensitylight can be obtained. When a high flux isrequired in a somewhat larger area, light from abending magnet is also useful. If light emitted ina horizontal angular region of 1 mrad is gatheredwith a mirror, the flux will be 10 14 phs/s/0.1 %bw.A large flux is required for investigation of dilutesystems, secondary processes and external fieldeffects. When undulator radiation is used with anappropriate filter but without a monochromator,intense light may be obtained though its bandwidthis not very small. This utilization was first appliedto photochemical reaction on solid surfaces and isoften used for fluorescence excitation.Coherence and Source DegeneracyThe coherence of light can be improved to a certainextent with optical devices at the expense ofthe flux. In practice, however, sufficient intensityis required, so that a light source should generatehighly coherent light by itself. Synchrotron radiationis partially coherent. Here coherent propertiesof synchrotron radiation will be briefly introduced.Light is transversely coherent when the opticalinvariant at a wavelength λ is nearly equal toλ/4π, which corresponds to the diffraction limit. If

THIRD GENERATION SOURCES AND OTHER NEW SOURCES 39the electron beam size and the angular divergenceat the source point are much smaller than thoseof the synchrotron radiation, σ r and σ ′ r ,whichisrealized in the vertical direction in third generationsources, synchrotron radiation from an undulator istransversely coherent. Light from bending magnetsis transversely coherent in the vertical direction inthe longer wavelength range even for second generationsources. The transverse coherence ensuresthat all the light coming from the source point caninterfere at dispersive elements in a monochromatorto obtain the highest spectral resolution withoutlosing intensity but also at the sample to obtainsharp diffraction or interference patterns. Longitudinalcoherence of light from an undulator isexpressed in terms of the coherence length definedas l c = λ 2 /λ, whereλ is the spectral width oflight. Since the fractional spectral width of the nthharmonic light from an undulator is approximatelyequal to 1/nN, the coherence length is given bynNλ. Interference experiments such as holographycan be done on a specimen, the thickness ofwhich is of the order of the coherent length. Thecoherence length can be done longer using a highresolution monochromator. By coherently illuminatingsurfaces with microstructures, interferencepatterns are generated by scattered light, which arecalled speckle patterns, and they give informationon the microstructures.The source degeneracy of synchrotron radiation,which is an index showing the intensity of coherentlight, is given as δ = B p λ 3 /4c, whereB p is thepeak brilliance expressed in mrad, and 100 %bw. 9For ordinary undulators, δ is less than unity contraryto lasers, for which δ is enormous. Free electronlasers, which can produce high power coherentlight with large δ in the shorter wavelength regions,are awaited for quantum optical experiments suchas nonlinear optics.PolarizationIf light from bending magnets is confined withan appropriate horizontal slit in the beamline, linearlypolarized light is obtained on the medianplane of the storage ring and elliptically polarizedlight is obtained off the plane. Linear polarizationexceeding 95 % is easily obtained, whilethe degree of circular polarization is around 80 %.Intense circularly polarized light recently becameavailable from an undulator, in which the electronbeam describes a helical motion. The switchingfrequency of the helicity is 0.1–100 Hz, dependingon the type of helical undulator used. Someundulators can generate not only circularly polarizedlight, but also linearly polarized light with theelectric vector lying even on the vertical plane aswell as elliptically polarized light. The degree ofpolarization of undulator radiation can be kept highwith synchronous tuning. Several kinds of dichroicexperiments such as magnetic circular dichroismhave been performed using polarized light.Higher Order Light RejectionLight from a bending magnet has a broad andcontinuous spectrum, while that from an ordinaryundulator consists of the fundamental peak accompaniedby its higher harmonics. Higher order lightfrom a monochromator, due to shorter wavelengthcomponents in the incident light, is rejected in thebeamline, using filters, mirrors and detuning ofa monochromatizing crystal. On the other hand,there are a few trials to construct novel undulators,magnetic periods of which are quasi-periodic,so that higher harmonics do not appear at integermultiples of the fundamental photon energy. Similarly,a quasi-periodic grating has been developed.Time StructureIn the vacuum ultraviolet region, two-color experimentssuch as two-photon absorption experimentsand pump-probe experiments have been conductedusing a synchrotron radiation pulse and a synchronizedlaser pulse. Some of them are experimentsusing a free electron laser in the ultravioletregion instead of a conventional laser. Recently,time resolved X-ray diffraction studies have beenconducted, in conjunction with synchrotron radiationand a laser pulse, to investigate instantaneousheat-up phenomena in solids by laser light. Suchtwo-color experiments will be conducted more inthehardX-rayregion.

40 NEW SYNCHROTRON RADIATION SOURCESIf synchrotron radiation is available with muchshorter pulse duration than ordinary values of30 ps–1 ns, many interesting fields, such as thedynamics of chemical reactions and structureanalysis on the timescale of lattice vibrationperiods would be opened. There are two methodsknown to obtain shorter pulses. One is isochronousoperation of the storage ring to shorten the bunchby reducing the momentum compaction factor.This operation mode has been attempted in afew rings. The storage ring called NewSUBARUhas been designed and constructed to reduce theelectron bunch to as short as a few picosecondsor even shorter. The other method is to sliceoff an extremely short electron pulse from anelectron bunch. When an electron bunch comesin an undulator, a femtosecond (fs) laser pulseis synchronously injected from outside to interactwith the electrons in the beam as they move sideby side in the undulator, which is tuned at the laserwavelength. Electrons within the fs laser pulseare slightly accelerated or decelerated due to theinteraction between them, which is the inverseprocess of free electron lasers to be described later.As the electron bunch moves in a downstreambending magnet, energy-modulated electrons moveaway from the central orbit and a fs electron pulseis produced. A fs light pulse is obtained in thebeamline by screening light from the main bunchin the central orbit.2.2.2.3 PHOTON INTENSITIESAVAILABLE AT BEAMLINEA beamline is composed of a front end, premirrors,a monochromator, refocusing mirrors,and an instrument for the measurement, whichis called the end station. Soft X-ray beamlinesare directly connected to storage rings withoutwindows, while hard X-ray beamlines are equippedwith Be windows separating high vacuum instorage rings and low vacuum in the beam lines.Even for hard X-rays, long beamlines have to beevacuated to suppress absorption of X-rays by theair and to prevent ionization of the air, whichmay react with or erode beam pipes and otherdevices. In beamlines for the photon energy regionbelow 20 keV, pre-mirrors are often used to gathersynchrotron radiation. These mirrors are coatedwith high reflectance materials as a monolayer oras multilayers and are used at grazing incidenceangles. Synchrotron radiation is monochromatizedwith gratings below 1.5 keV, while crystals areused above 1 keV.The available flux at the sample position isreduced by the efficiency of the optical elementsand performance of a beamline. It should be notedthat the polarization properties of the light sourceis not necessarily transferred to the end station dueto the polarization characteristics of the opticalelements. Figure 2.2.6 shows an example of thethroughput spectrum for the undulator beamlineBL39XU at SPring-8, which was obtained bysynchronous tuning. The intensity around 10 keVis 4×10 12 phs/s for a fractional bandwidth of0.02 % at 100 mA and the beam size at a sampleposition is 1.5 mm wide and 0.6 mm high withoutusing refocusing mirrors. In other energy regions,the following monochromatized photon beams areavailable at advanced beamlines. Around 0.4 keV,the bandwidth of light obtained is 40 meV andthe intensity is 5×10 8 phs/s. Around 14 keV, thebandwidth obtained is 2.5 meV and the intensityis 1.6×10 9 phs/s. The bandwidths will be reducedto one tenth of the present values before long.A microbeam, which has a diameter of about1 µm and a photon density of 10 13 phs/s/mm 2 ,isavailable around 20 keV using a zone plate and adouble-crystal monochromator.2.2.3 FOURTH GENERATIONSOURCESThere is no clear definition of fourth generationsources, but nevertheless it is widely accepted thatnext generation sources with much higher performancewill show up before long. The key wordsmay be much higher brilliance surpassing that ofthird generation sources and higher coherence. Inthe following, candidates for such light sourceswill be briefly introduced.

FOURTH GENERATION SOURCES 415Intensity (× 10 12 phs/s)432109.0 9.5 10.0 10.5Photon energy (keV)Figure 2.2.6 Throughput spectrum for the undulator beamline BL39XU at SPring-8 obtained by the synchronous tuning. Thestructures of the solid curve around 9.9 eV are due to monochromator glitches. The broken curve is the spectrum measured witha fixed undulator gap. The fractional bandwidth is 0.02 %. (Courtesy of M. Suzuki)2.2.3.1 SASE-FELA free electron laser (FEL) is a device thatproduces high power coherent light by meansof stimulated emission of radiation from therelativistic electron beam. This process involvesmany electrons interacting with coherent radiation.Let e i be the electric field of radiation emitted bythe ith electron in a bunch and E be the electricfield of coherent radiation. Since the radiationpower is proportional to the square of the electricfield, the total power may be given by( ) 2 n∑n∑P ∝ E + e i = E 2 + 2Ei=1e ii=1( n∑) 2+ e i (2.2.2)i=1where n is the number of electrons in the bunch.The electric field E of radiation propagating inthe z-direction with wave number k and frequencyω has such spatial and time dependences asexp[j(kz − ωt)]. The first term of the right-handside of Equation (2.2.2) is the power of coherentradiation, the second term is the stimulatedemission or absorption by an electron due to thecoherent radiation, and the third term is spontaneousradiation.When there is no coherent radiation, onlyspontaneous radiation given by the third termis emitted. Since wavelengths of synchrotronradiation in the X-ray region are much shorterthan the bunch length in a storage ring, phasesof electric fields produced by electrons will berandomly distributed and they cancel each otherout on the average, so that the third term becomes( n∑) 2 n∑ n∑ n∑P ∝ e i = e 2 + ei i e ji=1i=1 i=1≈j=1j̸=in∑e 2 = ne 2 (2.2.3)ii=1Thus an obvious result is derived that the intensityof synchrotron radiation is proportional tothe number of electrons, or the beam current.When a short electron bunch from a linac passesa bending magnet and emits light in the farinfrared and the sub-millimeter regions, the wavelengthis comparable to or longer than the electronbunch. Electric fields emitted by individual electronsadd up coherently and the radiation poweris proportional to the square of the electron number,which is called coherent synchrotron radiation.It has been also observed on the storagerings MAX II and BESSY II in isochronousoperation.

42 NEW SYNCHROTRON RADIATION SOURCESNext, we will look into the problem of emissionof light by an electron beam in an undulator whencoherent radiation exists. An electron oscillatestransversely in the undulator and consequentlyit moves along the electric field E, so that itexchanges energy with the coherent radiation.Whether the electron emits or absorbs radiationby stimulated emission or absorption, dependingon the phase of e i relative to that of E, as canbe seen in Equation (2.2.2). Since electrons arerandomly distributed longitudinally in a bunch,half of them in the acceleration phase with respectto coherent radiation gain energy and the otherhalf in the deceleration phase lose it, so that thetotal energy change will be zero on average, butthe energy of the electron beam is modulated inthe spatial period of the light wavelength. As theelectron beam moves in the undulator, the higherenergy electrons catch up with the lower energyones, so that the energy modulation is convertedto density modulation of the electron beam. Whenhigher density parts of the electron beam sit onthe deceleration phase, the number of deceleratedelectrons is larger than the number of acceleratedelectrons and hence a part of the kinetic energy ofthe electron beam is, on aggregate, transformed tocoherent light power. This is the principle of FELwith an optical resonator.The shortest wavelength realized with FEL withoptical resonators is, at present, slightly shorterthan 200 nm. In the shorter wavelength regions,however, reflectivity of mirrors used for opticalresonator falls off rapidly and hence conventionalFEL do not work in the vacuum ultraviolet and theX-ray regions. In order to realize FEL in shorterwavelength regions, a new type of FEL calledSASE has been proposed, 10 where noise componentsin spontaneous light are amplified as seedsup to the saturation level with a high-gain amplifierFEL. A schematic drawing of SASE is shown inFigure 2.2.7. SASE is, in principle, a simple systemconsisting of a linac and an undulator. A highintensity, low emittance electron beam is necessaryfor SASE in the short wavelength region andtherefore a laser photocathode RF electron gun isusually adopted. Photoelectrons emitted by irradiationof picosecond ultraviolet lasers are acceleratedby a very high electric field in the RF cavity to avelocity close to that of light and thereby increaseof the emittance due to space charge forces canbe reduced. This electron gun produces an electronbeam with a normalized emittance ε n of afew πµm·rad, a few picoseconds pulse durationand a peak current up to 100 A. The normalizedemittance is a constant of motion and doesnot change with energy. As the electron beam isaccelerated in a linac, the emittance ε decreasesinversely proportional to the electron energy dueto adiabatic damping as ε = ε n /γ , where γ isthe Lorentz factor. In a chicane type bunch compressorshown in Figure 2.2.7, electrons in thehead of a bunch are slightly decelerated comparedwith electrons in the central part and those inthe tail are accelerated, using an upstream accelerationpart. The lower energy electrons in thehead make a detour, while the higher energy electronstake a short cut and catch up with the head,so that the bunch becomes shorter and the peakcurrent is enhanced to a few kA. The high intensityand low emittance beam is then acceleratedin the main linac and produces high power SASELinac Linac Linac UndulatorBeam dumpSASEBunch compressorBunch compressorLaser photocathode RF gunBending magnetFigure 2.2.7 Schematic drawing of a typical SASE system

FOURTH GENERATION SOURCES 43Electron bunchP SASESAT ~ rP bSaturation regimeOutput power Log(P)Exponential gain regimeElectron bunchElectron bunchLethargy regime0 l u /rDistance from the undulator entrance zFigure 2.2.8 Evolution of the SASE power along the undulator. ρ, P b and P SATpower, and the saturation power of SASE, respectively 10SASEare the FEL parameter, the electron beamin a long undulator. The evolution of the radiationpower emitted by the electron beam passingthrough the undulator is shown schematically inFigure 2.2.8. At the entrance region of the undulator,where the electron distribution is uniform inthe bunch, spontaneous radiation dominates. Thepower increases linearly with the distance fromthe entrance, z. Note that the vertical axis is plottedusing a logarithmic scale. In this region calledlethargy regime, the incipient stage of SASE is inprogress though the power level is much lower.The startup of SASE is thought to develop asfollows. There are many electrons randomly distributedin a bunch and these electrons produceextremely short and randomly distributed electricfield spikes when they are transversely acceleratedin the magnetic field of an undulator. Thefrequency distribution of the noise power fluctuatesstatistically, but if the long-term averageis taken it will extend with a constant intensityto extremely high frequencies. Part of the noisewithin the bandwidth of the FEL gain, the center ofwhich is located around the fundamental frequencyof undulator radiation, is gradually amplified bybunching electrons at a single optical wavelength.The density modulation of the electron beam andthe phase of coherent radiation affect each otherto amplify the coherent radiation due to stimulatedemission, given by the second term of the righthandside of Equation (2.2.2), where the coherentradiation is provided by upstream electrons. Theelectron beam continues to interact with coherentlight, so that the density modulation of electronsis enhanced gradually, as shown schematically inFigure 2.2.8. Meantime, the interaction comes inthe exponential gain regime, where the gain perunit length is constant and the power of coherentlight is exponentially amplified with z. Theradiation power continues to be amplified exponentially,but eventually the power will saturatebecause the electron beam amplifying coherentlight gradually loses kinetic energy and at the sametime the energy spread increases in the amplificationprocess. Experimental studies on SASEhave been conducted progressively from the farinfraredregion to the shorter wavelength regionsand now SASE is successfully generated in thevacuum ultraviolet region between 80 and 180 nm

44 NEW SYNCHROTRON RADIATION SOURCESat DESY. 11 A wavelength spectrum of SASE measuredaround 109 nm is shown in Figure 2.2.9.A new SASE facility is in the course ofconstruction at SPring-8, which is named SPring-8 Compact SASE Source (SCSS), to extend theSASE wavelength down to 3.6 nm in a waterwindow. 12 The aim of this project is to blaze atrail in the short wavelength region important forbiology with a relatively small-sized facility. Theunique features of this facility are that C-bandlinacs operating at 5.7 GHz are used and an invacuumundulator with a period length of 15 mmis employed, in order to make the facility compact.The spectral range and the peak brilliance areshown in Figure 2.2.10.There are two proposals, one in the UnitedStates and one in Europe for constructing a userfacility for coherent X-rays based on SASE; 13 theLinac Coherent Light Source (LCLS) at the StanfordLinear Accelerator Center (SLAC) and theTeV Energy Superconducting Linear Accelerator-X-Ray Free Electron Laser (TESLA-XFEL) atDESY. The LCLS project is to construct aSASE-FEL facility in a wavelength region rangingfrom 0.15 to 1.5 nm using the SLAC linac.The electron beam is accelerated to 14.3 GeVwith the linac and led to a 111.8 m long undulator.The magnet gap of the undulator is fixedat 6 mm, but the wavelength can be tuned byvarying the electron energy. The peak powerof SASE at λ = 0.15 nm is 9 GW and energyin a pulse is 2.6 mJ. The peak brilliance runsup to 1.2 × 10 33 (phs/s/mrad 2 /mm 2 /0.1 %bw), asshown in Figure 2.2.10. Since the repetition rateof the linac is 120 Hz, the average power is0.31 W. The average brilliance is 4.2 × 10 22(phs/s/mrad 2 /mm 2 /0.1 %bw). It is not very differentfrom the brilliance of third generation lightsources, but the peak brilliance is extremely high.The TESLA-XFEL project is similar to theLCLS project, but a superconducting linac will beused. An electron beam is accelerated to 20–50GeV with the linac and led to a 323.5 m long undulator.The period length of the undulator is 60 mmand the magnet gap is variable between 12 and22 mm to scan the wavelength. The peak powerat λ = 0.1 nm is 37 GW and energy per pulse is3.7 mJ. The peak brilliance is comparable to thatof LCLS as shown in Figure 2.2.10. The averagepower is 210 W and the average brilliance is4.9 × 10 25 (phs/s/mrad 2 /mm 2 /0.1 %bw). The averagebrilliance of the X-ray beam is extremely high.140012001000Intensity (a.u.)800600SASESimulations4002000105 106 107 108 109Wavelength (nm)110 111 112Figure 2.2.9 Wavelength spectrum of SASE measured at the TESLA Test Facility in DESY. The central wavelength is around109 nm. 11 Reprinted from Rossbach, J. First observation of self-amplified spontaneous emission in a free-electron laser at 109nm wavelength. Physical Review Letters 85 (2000) 3285. Reproduced by permission of The American Physical Society

FOURTH GENERATION SOURCES 45Peak brilliance (phs/s/mrad 2 /mm 2 /0.1%bw)10 3610 3410 3210 3010 2810 2610 2410 2210 20DESYTTF-FELSPring-8SCSSSPring-8 undulatorALS undulator ESRF undulator APS undulatorNSLX X-Ray bendTESLA-XFELLCLSPERL 6 GeV undulator10 18 10 −2 10 −1 1 10Photon energy (keV)10 2 10 3Figure 2.2.10 Peak brilliance of synchrotron radiation for various light sources. NSLX X-ray bend is for a second generationsource, SPring-8 undulator, ESRF undulator, APS undulator, and ALS undulator are for third generation sources, RERL 6 GeVundulator is for an energy recovery linac, and TESLA-XFEL, LCLS, SPring-8 SCSS, and DESY TTF-FEL are for SASE2.2.3.2 FOURTH GENERATIONSTORAGE RINGS AND ENERGYRECOVERY LINACSA natural extension of the present technologyfor fourth generation sources would be higherperformance storage rings called fourth generationstorage rings. 14 The emittance of the electron beamwill be reduced to a fraction of 1 πnm·rad, whichis one tenth of the typical emittance of thirdgeneration light sources. Since the emittance ofthe electron beam in a storage ring is inverselyproportional to the third power of the number ofbending magnets, the circumference of the ringshould be doubled. A drawback of this method toreduce the emittance is that the dynamic apertureis considerably reduced and consequently thebeam lifetime becomes shorter. A countermeasuredevised for the problem is the top-up injection, sothat the electron beam is continuously injected tocompensate for beam loss due to the short lifetime.As the electron beam size becomes smaller, spatialand temporal stabilities of the stored beam arecrucial issues. These problems including short andlong term drifts of the beam position and fastbeam instability are, however, extensively studiedin third generation sources.Another candidate for fourth generation sourceswas recently proposed, which is called the energyrecovery linac (ERL). Several proposals for constructinga new synchrotron light source based onERL have been advanced throughout the world. 15A schematic drawing of the energy recovery linacis shown in Figure 2.2.11. The electron beamis accelerated with a superconducting linac toa final energy and then passes through bendingmagnets and undulators to produce synchrotronradiation. After making a round, it comes backto the entrance of the linac again 180 ◦ out ofphase with the accelerating RF field and deceleratedin the linac, thereby delivering the kineticenergy of the electron beam to the acceleratingbeam through the RF field. If the electron beamis injected continuously to the linac, this processwill be repeated successively, so that a continuousbeam can be obtained without supplying enormousRF power to accelerate the beam.If an electron beam with ε n = 1 πµm·rad isaccelerated to 5 GeV, the emittance will be reducedto 0.1 πnm·rad. The average beam current shouldbe comparable to that of third generation sources,

46 NEW SYNCHROTRON RADIATION SOURCESUndulatorsUndulatorsBending magnetsBending magnetsElectron gunSuperconducting linacBeam dumpFigure 2.2.11 Schematic drawing of an energy recovery linacso that superconducting linacs will be used toavoid RF power loss in acceleration structures. Theaccelerated beam produces high intensity and highbrilliance synchrotron radiation in all the bendingmagnets and undulators installed on the return passto the entrance of the linac for energy recovery.The outward appearance of ERL is not verydifferent from that of a third generation source,but it is not a storage ring and consequently itis free from various technical constraints imposedon storage rings for storing an electron beamin a circular pass for a long time. The electronbeam may be focused down to a few micrometersin diameter and bunches may be compressed to100 fs. The beam lifetime is not a critical issuebecause electrons are used only once to producesynchrotron radiation in the return pass, so that theundulator gap may be reduced to a few millimetersand accordingly its period length may be made asshort as some millimeters.ERL has many advantages over the conventionalsynchrotron radiation sources based on storagerings. To turn these advantages into reality,however, there are some technical issues to besolved, including the electron source and stabilityof the beam, because ERL is a dynamic acceleratorand there is no such built-in stabilizer as radiationdamping in a storage ring. ERL can provide synchrotronradiation with an average brilliance thatis two to three orders of magnitude higher thanin the case of third generation sources and theestimated peak brilliance is also extremely high.As an example, the peak brilliance of the PhotoinjectedEnergy Recover Linacs (PERL) proposedat Brookhaven National Laboratory is shown inFigure 2.2.10. Advantages of ERL compared withSASE are such that many undulators can be usedsimultaneously and higher energy photons can beobtained. ERL and SASE will play complementaryroles as fourth generation sources. Indeedthere is a proposal to combine both at DaresburyLaboratory. 5REFERENCES1. Spencer, J. E. and Winick, H. Properties of synchrotronradiation, in Synchrotron Radiation Research (EdsH. Winick and S. Doniach), Plenum Press, New York(1982).2. Krinsky, S., Perlman, M. L. and Watson, R. E., Characteristicsof synchrotron radiation and of its sources, inHandbook of Synchrotron Radiation Ia (Ed.E.E.Koch),North-Holland, Amsterdam (1983).3. Watanabe, M. and Isoyama, G. Synchrotron radiationand free electron lasers, in Dynamics during SpectroscopicTransitions (Eds E. Lippert and J. D. Macomber),Springer, New York (1995).4. Thompson, A. C. and Vaughan, D. (Eds) X-ray DATAbooklet, Center for X-ray Optics, Lawrence BerkeleyNational Laboratory (2001).5. Hasnain, S. S., Kamitsubo, H. and Mills, D. M. Newsynchrotron radiation sources and next generation lightsources. J. Synchrotron Rad., 8, 1171 (2001).6. Hasnain, S.S., Helliwell, J. R. and Kamitsubo, H. (Eds)Proc. of 6th Int. Conf. on Synchrotron Radiation Instrumentation.J. Synchrotron Rad., 5, Part 3 (1998).7. Gudat, W. and Zimmermann, P. (Eds) Proc. of 7th Int.Conf. on Synchrotron Radiation Instrumentation. Nucl.Instr. Meth. Phys. Res., A467–468 (2001).

REFERENCES 478. Walker, R. P. and Diviacco, B. Insertion devices–recentdevelopments and future trends. Synchrotron Rad. News,13(1), 33–42 (2000), and references therein.9. Gluskin, E., McNulty, I. and Viccaro, P. J. X-ray intensityinterferometer for undulator radiation, Nucl.Instr.Meth.Phys. Res., A319, 213–218 (1992).10. Kim, K. J. and Xie, M. Self-amplified spontaneous emissionfor short wavelength coherent radiation. Nucl. Instr.Meth. Phys. Res., A331, 359–364 (1993).11. Andruszkow, J. et al. First observation of self-amplifiedspontaneous emission in a free-electron laser at 109 nmwavelength. Phys. Rev. Lett., 85, 3825–3829 (2000).12. Shintake, T., Matsumoto, H., Ishikawa, T. and Kitamura,H. Proc. of SPIE Conf. 4500, Optics for Fourth-Generation X-ray Sources (2001) p. 12.13. Nuhn, H.-D. and Rossbach, J. LINAC-based short wavelengthFELs: The challenges to be overcome to produce theultimate X-ray source–the X-ray laser. Synchrotron Rad.News, 13(1), 18–32 (2000).14. Hofmann, A. and Rivkin, L. Fourth generation storage ringsources. Synchrotron Rad. News, 12(2), 6–15 (1999).15. Besn-Zvi, I. and Krinsky, S. Future light sources basedupon photo-injected energy recovery linacs. SynchrotronRad. News, 14(2), 20–24 (2001), and references therein.

2.3 Laser-driven X-ray SourcesC. SPIELMANNPhysikalisches Institut EP1, Universität Würzburg, Germany2.3.1 INTRODUCTIONSynchrotrons represent the major source of powerfulX-rays and will continue to play a dominantrole for X-ray science in the foreseeable future.Nevertheless, a wide range of X-ray applicationsin science, technology and medicine would greatlybenefit from (i) X-ray pulse durations much shorterthan routinely available from synchrotrons (fewhundred picoseconds), (ii) synchronizability ofultrashort pulses to other events, and (iii) availabilityof useful fluxes from compact laboratory X-raysources. Triggered by these demands a large numberof research groups made enormous efforts todevelop novel generation X-ray sources driven byhigh power lasers.Advances in ultrashort-pulse high-power lasertechnology over the last decade (Perry and Mourou,1994; Umstadter et al., 1998) paved the waytowards compact, versatile laboratory X-ray sourcesin a number of laboratories for spectroscopic aswell as other applications. Ultrashort-pulsed X-ray radiation became available from femtosecondlaser-producedplasmas (Gibbon and Förster, 1996;Giulietti and Gizzi, 1998; and references therein).These sources are now capable of converting upto several per cent of the driving laser pulse energyinto incoherent X-rays emitted in a solid angleof 2π –4π and delivering pulses with durationsdown to the subpicosecond regime. Femtosecondlaser produced plasma sources matured to a pointwhere a wide range of applications can be tackledin a wide spectral range extending from thesoft to the hard X-ray regime. Already demonstratedexamples include time-resolved X-raydiffraction and absorption spectroscopy (Helliwelland Rentzepis, 1997; Rousse et al., 2001b) aswell as medical radiology with improved contrastand resolution (Gordon III et al., 1995; Grätzet al., 1998).Many laboratory X-ray applications wouldgreatly benefit from or rely on (spatially) coherentsources with high average and/or peak power. Oneof the major approaches to laboratory productionof coherent X-rays is the development of X-raylasers. Whereas short-wavelength lasing has beensuccessfully demonstrated with compact, tabletopsetups using several promising schemes atλ>15 nm in the XUV range (Lemoff et al., 1995;Nickles et al., 1997; Korobkin et al., 1998; Rocca,1999), lasing at shorter (soft-X-ray) wavelengthscould only be achieved at large-scale facilities sofar (Zhang et al., 1997; Klisnick et al., 2002).Another promising route to developing compactcoherent X-ray sources is high-order harmonicgeneration (HHG) with ultrashort-pulselasers (L’Huillier and Balcou, 1993). Extensivetheoretical and experimental research providedvaluable insight into the microscopic (stronglydriven atomic dipole) and macroscopic (propagationeffects, e.g. phase mismatch) phenomenarelevant to HHG (for a recent review see Brabecand Krausz, 2000). Recent investigations revealedthat ultrashort drivers with pulse durations wellbelow 100 fs can produce HH conversion efficienciescomparable to XUV lasers in the 100–20 nmX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

50 LASER-DRIVEN X-RAY SOURCESrange (Rundquist et al., 1998; Sommerer et al.,1999; Constant et al., 1999).Recently, few-cycle, sub-10 fs laser pulses producedHH radiation at 13–10 nm with somewhatlower efficiencies and with pulse durations estimatedas

LASERS FOR X-RAY GENERATION 51Brilliance photons/(s mm 2 mrad 2 0.1% BW)10 2410 21Ti:S laser10 1810 1510 1210 9Discharge pumpedX-ray laserHigh harmonicsoft X-raysX-ray FEL(proposed)Undulator Bessy IILaser pumpedX-ray laserLaser plasmaX-ray line source10 61 10 100 1000 10 000(a)Photon energy (eV)Peak brilliance photons/(shot mm 2 mrad 2 0.1% BW)(b)10 32 X-ray FEL(proposed)10 29 Ti:S laserLaser pumped10 26X-ray laser10 23High harmonicLaser plasmasoft X-raysX-ray line source10 2010 17Undulator Bessy II1 10 100 1000 10 000Photon energy (eV)Figure 2.3.1 Average (a) and peak brilliance (b) as a function of photon energy for conventional and laser-driven X-ray sources.For the calculation of the peak brilliance the pulse duration as reported in the corresponding literature has been usedan energy of more than a few joules (Yamakawaand Barty, 2000). To further increase the pulseenergy hybrid systems consisting of a Ti:S preamplifierfollowed by Nd:glass power amplifier chainhave been developed. Pulse energies of up to 10 Jfor table top and 400 J have been achieved ina laboratory and a large scale facility (Dansonet al., 1998; Perry et al., 1999), by drawing onthis concept. Such a hybrid system offers alsothe possibility to generate synchronized energeticnano- and femtosecond pulses beneficial for realizinglaser-driven X-ray lasers.The other direction of current laser developmentsis towards higher repetition rates and shorter pulses.The development of powerful-kHz-repetition ratepump lasers and the excellent thermal properties ofTi:S opened the way to producing millijoule-energy20-fs pulses at kilohertz frequencies (Backus et al.,

52 LASER-DRIVEN X-RAY SOURCESTable 2.3.1 Parameters of state-of-the-art laser sources. In the far right column potential realizations of X-ray sources are listed:high harmonic generation (HHG), X-rays from a laser produced plasma (LPPX), and X-ray laser (XRL)Pulse energyPulse duration(fs)Repetition ratePeak intensity(W/cm 2 )X-ray sourceto be realizedOscillator nJ

HARD X-RAYS FROM LASER PRODUCED PLASMAS 53high yield hard X-ray pulses, and they have tobe treated relativistically. In addition to the highterminal velocity, the acceleration distance is alsovery short, of the order of less than several tens ofmicrons, the time spread of the electron packet isvery small when it interacts with the solid target.These electrons are then stopped in the solid withina few tens of microns. The combined effect resultsin X-ray pulse duration on the order of a few hundredfemtoseconds or less, determined mainly byhow quickly these electrons are stopped and bythe size of the emission volume. As a result, featuresof these sources include ultrashort hard X-raypulse duration (10 14 photons/s/4π sr)substantially higher than conventional X-ray tubes.High average flux is indispensable for detectingfemtogram low atomic number material impurities

54 LASER-DRIVEN X-RAY SOURCESin silicon wafers by X-ray fluorescence analysis,currently only feasible with synchrotron radiation(Streli et al., 2001). For some spectroscopicapplications the problem of debris has to beaddressed. Debris from the target can obscure ordamage samples in the vicinity of the plasma. Onesolution is the use of liquid target, which minimizesthe undesired effects of debris (Tompkinset al., 1998). A liquid source also ensures thateach laser pulse hits fresh material (Hemberget al., 2000).Time resolved X-ray spectroscopy requiresan X-ray source that is a spectrally, spatiallyand temporally well-characterized. Spectral andspatial measurements can be easily performedwith standard methods. Accurate measurementsof the duration of hard X-ray pulses representsa major challenge. The knowledge of the X-raypulse duration is crucial because it determinesthe temporal resolution of the envisaged timeresolved experiments. X-ray streak cameras havebeen built with resolutions in the range of apicosecond (Chang et al., 1997a). X-ray/opticalcross-correlation methods based on photoelectronspectroscopy successfully implemented for thecharacterization of soft X-rays cannot be extendedinto the hard X-ray range. Phase transitions can beextremely fast, and therefore call for an ultrashortX-ray pulse in a diffraction experiment. From thesemeasurements the upper limit of the hard X-raypulse duration has been estimated in the rangeof 100–300 fs (von der Linde et al., 2001; Feureret al., 2001).Based on these newly developed sub-picosecondX-ray sources, a series of proof-of-principle timeresolvedX-ray absorption (Raksi et al., 1996)and X-ray diffraction (Rischel et al., 1997; Rose-Petruck et al., 1999; Siders et al., 1999; Cavalleriet al., 2000; Rousse et al., 2001a) experimentshave been performed over the last few years. Inall these experiments the structural dynamics havebeen initiated by an ultrashort laser pulse. A typicalsetup as used for time-resolved X-ray spectroscopyis shown in Figure 2.3.2. Raksi et al.investigated the photodissociation of SF6 by studyingthe modifications of the X-ray absorption duringthe transition from the molecular to the atomicstate. Rischel et al. exposed a Langmuir–Blodgettfilm to a short laser pulse at an intensity well abovethe damage threshold, causing a disorder of thefilm. The transition between the ordered and disorderedstate was characterized by time-resolvedX-ray diffraction. This transition took place ona timescale of the order of a few hundred femtoseconds.Such a fast dynamic was not accessiblewith previously available X-ray sources. MoreTi:S terawattlaser systemR < 10%Laser producedplasma X-raysourceAdjustableoptical delayOptical pumpbeamX-ray generatinglaser pulseX-ray probebeamSampleFocusingmirrorDiffracted X-raysX-raydetectorTransmitted X-raysX-raydetectorFigure 2.3.2 Typical setup for time-resolved X-ray spectroscopy. A fraction of the output of a high power laser system is splitoff and after an adjustable delay focused onto the sample to initiate a structural change. The major fraction of the laser energyis focused onto a solid or liquid used to generate X-rays. The pulsed X-ray radiation is used to probe the structural changes in areflection or transmission geometry

HIGH HARMONIC GENERATION 55recently Rose-Petruck et al. used ultrashort X-raypulses to measure the response of a GaAs crystalto a sudden heating. The material is heatedup so rapidly that no notable expansion can takeplace. The impulsive heat deposition launches anacoustic wave that travels into the material formingregions of compression and expansion. Thelattice dynamics was characterized by observingthe temporal evolution of the Bragg diffractionline. In this experiment sub-picosecond temporaland sub-milliangstrom spatial resolution has beendemonstrated. After these first pioneering experimentstime-resolved X-ray diffraction has beenused to characterize non-thermal melting (Siderset al., 1999; Rousse et al., 2001a), acoustic transientsin solids (Sokolowski-Tinten et al., 2001),and solid–solid phase transitions (Cavalleri et al.,2001). These experiments clearly demonstrate theimpressive potential of table-top picosecond X-raysources and brings us closer to the goal of watching,on femtosecond time scales, so called molecularmovies.2.3.4 X-RAY LASERSMost lasers operate in the visible and infrared spectralregions along on an axis defined by a Fabry-Perot style of reflecting cavity. The lasing mediumis pumped to produce population inversion. Amplificationalong this axis is provided by stimulatedemission. The intensity exponentiates further witheach pass in the medium. A high degree of collimationand coherence is achieved with efficient cavities.In the X-ray region the reflectivity of availablecavity mirrors is relatively poor. Hence, X-raylasers to date have been based mainly on amplificationof inherent spontaneous emission (ASE)throughout the medium. This occurs in a singlepass along a particular direction. This requiresgain coefficients in the medium approximately100 times larger than those for more familiar lasersoperating with efficient resonators. X-Ray lasersoperate on electronic transitions from outer shellsto inner shells. To achieve population inversioninvolving these transitions is much more difficultthan for visible transitions, primarily because ofthe very short excited lifetimes of X-ray transitions(Rocca, 1999).Soft X-ray lasers operating at wavelengths of4 to 40 nm and sub-nanosecond pulse durationhave been demonstrated. The laser medium is aplasma of highly ionized atoms. The plasma isproduced by heating solid targets with energeticvisible laser pulses having an energy of severaljoules to kilojoules. Such high energies can only beachieved in a few large-scale laser facilities all overthe world. The major objective of current X-raylaser research is to reduce the driving laser pulseenergy. Using driver pulses of a few picosecond orthe combination of a nanosecond and femtosecondlaser pulse has reduced the required energy bynearly two orders of magnitude (Nickles et al.,1997; Lin et al., 1999). Further improvements inpimping efficiency resulting from optimized targetconfiguration and travelling wave excitation can beexpected to lead to soft X-ray lasers occupying asingle optical table (Korobkin et al., 1998). Up tothis time X-ray lasers, despite their unprecedentedpeak brilliance (Figure 2.3.1) (Burge et al., 1997),will play only a minor role in spectroscopy.2.3.5 HIGH HARMONICGENERATIONA bright laboratory soft X-ray source is expected tohave great impacts on physics, chemistry and biochemistrylikewise. Recently laboratory sources ofcoherent soft X-rays extending into the water windowhave been demonstrated (Spielmann et al.,1997; Chang et al., 1997b) by means of high harmonicgeneration in helium. The use of femtosecondnear-infrared pump pulses limits the effectiveinteraction time relevant for the generationof the highest harmonics to less than the driverpulse duration. Under specific conditions a singleattosecond X-ray pulse should be emitted. Theseextraordinarily short pulses are likely to open theway to the atomic timescale characterization ofthe quantum-mechanical evolution of the electronwave function in bound atomic states as well asfor electronic processes in chemical reactions. Furthermore,the concentration of the X-rays within an

56 LASER-DRIVEN X-RAY SOURCESextremely short time interval and the high degreeof spatial coherence of the femtosecond laserdrivenXUV source give rise to an unprecedentedpeak brightness, which paves the way towards anextension of nonlinear optics in the XUV regime.The availability of light pulses comprising justa few oscillation cycles at intensities well above10 14 W/cm 2 opens up new prospects for coherentshort-wavelength generation. Matter irradiatedat these intensity levels undergoes tunnel ionization(Brabec and Krausz, 2000). For pulses containingmany oscillations, the number of ionizedparticles (e.g. atoms, molecules, or clusters) accumulatesover many optical cycles, which mayresult in a depletion of the ground state wellbefore the peak of the incident pulse impingesupon the target. The consequences of the dramaticallyshortened exposure to the laser field arenumerous and far reaching. First, the peak electronemission (or ionization) rate is much higherthan in the multi-cycle regime. Secondly, the freedelectrons are released into significantly strongerfields as compared to the multi-cycle regime. Theseimplications suggest that coherent XUV generationresulting from a free-bound transition (highorderharmonic or continuum generation, henceforthHHG) (L’Huillier and Balcou, 1993) willexhibit improved efficiency and generate higherXUV frequencies. After ionization, the freed electrongains energy in the laser field. This is anessential process, because emission of high-energyphotons is the result of the interaction of theseelectrons with their parent ions.Following Corkum (Corkum, 1993), the electronmotion in the laser field can be describedby classical mechanics after tunnelling. The electronreencounters its parent ion if and only if thelaser field is linearly polarized and the electron isreleased at a suitable phase. The maximum kineticenergy is given by W kin,max ∼ 3.17U p (Corkum,1993), where U p is the ponderomotive energy. Inunits of electronvolts it can be expressed as U p =9.3 × 10 −14 I/λ 2 ,whereI is the (cycle-averaged)laser intensity and λ is the laser wavelength in unitsof W/cm 2 and µm, respectively. With some smallprobability the returning electron recombines in itsoriginal ground state upon emitting a photon withan energy equal to the sum of the ionization potentialI p and the electron kinetic energy W kin gainedin the laser field. Because the electron wavepacketevolution is driven by a spatially coherent laserfield, the emission of the high-energy XUV photonsfrom the particles in the ensemble also occursin a spatially coherent manner, leading to a wellcollimatedXUV beam collinear with the pumplaser beam. In the multi-cycle regime, the processis repeated quasi-periodically over many laserperiods, consequently the XUV emission spectrumis made up of discrete harmonics of the laserfrequency. In the photon energy range close tothe highest harmonics (cutoff region) the emissionperiod has been predicted to be confined toa small fraction of the laser oscillation cycle. Thisprediction implies that the temporal evolution ofthe XUV output in the cutoff region can be characterizedas a train of bursts of subfemtosecondduration (Brabec and Krausz, 2000). It is obviousfrom the above considerations that the use ofa quasi-single-cycle driver benefits HHG in severalrespects. First, higher photon energies (shorterwavelengths) can be achieved because the electronsare released into a stronger laser field. Second,the X-rays near cutoff can be emitted in a singleattosecond pulse, resulting in an unprecedentedconcentration of electromagnetic energy. Third,efficiency is increased due to the higher ionizationrate and an increased coherence length (Spielmannet al., 1998). Experimental results of these findingsare summarized in Figures 2.3.3 and 2.3.4.At first sight it looks as if soft X-rays (

HIGH HARMONIC GENERATION 57XUV spectral intensity (a.u.)10010∆t = 7 fs∆t = 30 fscut-off50 30 20 10Wavelength (nm)Figure 2.3.3 Typical HHG spectrum obtained with neon. The laser pulse duration was 7 and 30 fs, respectively, and the peakintensity was several times 10 14 W/cm 2 . The conversion efficiency is nearly constant over a wide range (plateau) followed by asharp cut-off. Reproduced by permission of M. SchnürerWavelength (nm)10 −5 30 20 10 5 3Conversion efficiency10 −610 −710 −810 −9ArNeHe10 −1020 30 50 100 200 300Harmonic orderFigure 2.3.4 Energy conversion efficiencies using sub-10 fs laser pulses and an optimized target geometry. The higher theionization potential of the noble gas the higher photon energies can be achieved via HHG. Reprinted from Schnürer, M.,Cheng, Z., Hentschel, M., Krausz, F., Wilhein, T., Hambach, D., Schmahl, G., Drescher, M., Lim, Y. and Heinzmann, U.Few-cycle-driven XUV laser harmonics: generation and focusing. Appl. Phys. B 70(suppl.), S227–S232, Figure 4 (2000).Reproduced by permission of Springer-Verlag GmbH & Co. KGand width of harmonic lines is controllable withthe intensity and duration of the driving laserpulses (Figure 2.3.3); (iii) the limited conversionefficiency from laser to soft X-ray radiation is compensatedby an emission in a well defined beam,allowing a very effective coupling between thesource and the experiment; (iv) the HHG radiationis polarized; and (v) last but not least, thenecessary driving laser pulses intensity is moderate,making rather simple high repetition rate lasersusable as pump sources.(i) Pulse duration. Using multi-TW scale lasersand solid targets, line or continuum radiationis emitted in pulses having a duration

58 LASER-DRIVEN X-RAY SOURCESclose to a picosecond. However, several processestake place on a much faster timescale;e.g. with LPPX source it was not possibleto study the dynamic of the chemical shiftof the silicon L-edge whilst excited withan intense femtosecond laser pulse (Nakanoet al., 1998). Pulses from a HHG sourceare short enough to follow the dynamic.Also very fast processes take place on surfaces.To understand the basic mechanismsof adsorbate–substrate interaction studyingthe charge transfer between the adsorbatestates and metal substrate is of fundamentalimportance. This process has been investigatedwith high spectral resolution X-rayspectroscopy (Wurth and Menzel, 2000) andrevealed time constants in the order of afew femtoseconds. Soft X-ray pulses fromHHG sources should allow the evolution ofthese reactions to be monitored in their fundamentaltimescale (Bauer et al., 2001; Siffalovicet al., 2001). Other experiments relyingon ultrashort X-ray pulses are studies ofthe dynamic of photodissociation, e.g. it wasfound Br 2 dissociates on a timescale of 40 fs(Nugent-Glandorf et al., 2001).(ii) Spectrum. Using few-cycle driving laserpulses the spectrum of HHG radiation hasbeen extended down to 2 nm or 500 eV(Chang et al., 1997b; Spielmann et al., 1997).Since this wavelength range covers not onlythe 2p (L edges) of most 3d transition metalsand 3d edges (M edges) of 4f rare earth metalsit is ideally suited for the study of magneticmaterials. In addition, carbon (Schnürer et al.,2000) and probably nitrogen and oxygen Kabsorption edge can also be covered, so thatmany interesting processes in biology, chemicaldynamics, polymers and catalysis can beinvestigated. By varying the laser and targetparameter the line width and position couldbe controlled. Even if it is a line spectrumthe whole wavelength range could be covered,because the lines could be shifted bymore than their initial separation by a moderatechange of the laser intensity (Shin et al.,1999; Riedel et al., 2001). The width of aspecific harmonic depends critically on theduration and intensity of the driving laserpulse. Very short laser pulses lead to linesbroad enough to monitor chemical shifts ofthe absorption edge. Somewhat longer laserpulses result in narrower lines better suitedfor high resolution X-ray photoelectron spectroscopy(Haight, 1996; Quere et al., 2000).(iii) Spatial properties. X-ray sources based onlaser plasma interaction can be very efficient.Conversion efficiencies in the order of apercent have been demonstrated. However,the X-rays are emitted into 4π. Due to thelack of large aperture condenser optics ina typical experimental arrangement only avery small fraction of the generated photonscan be used. In contrast, the coupling ofHHG radiation to the experiment is nearlyfree from losses because it is emitted in alaser like beam (Spielmann et al., 1997). Dueto the excellent spatial beam quality HHGradiation can be easily focused down to lessthan a micrometre spot size, paving the wayto high resolution X-ray spectro-microscopy.The spatial coherence of HHG radiationmakes also interferometry with soft X-rayradiation feasible (LeDeroff et al., 2000).(iv) Polarization. HHG radiation is the only laserbasedX-ray source which emits polarizedradiation. The study of surfaces and magneticmaterials will greatly benefit from this property(Schulze et al., 1998).(v) Laser requirement. With a laser pulse havingan energy of 1 mJ or less, enough softX-ray photons for spectroscopy can be generated.Further improvements of the generationscheme such as quasi-phase matching(Rundquist et al., 1998) or adaptive controlof the driving laser pulses (Bartels et al.,2000) will further increase the conversionefficiency. The relaxed energy requirementscan be easily fulfilled by compact kilohertzlaser systems which are already commerciallyavailable. The higher repetition rate results inhigher average X-ray flux and allows the useof e.g. lock-in techniques enhancing the signalto noise ratio of the collected data. Also,

REFERENCES 59the integration time in X-ray photoelectronspectroscopy based on time-of-flight detectionwill be substantially reduced by using a kilohertzsystem.The significance of intense ultrashort laserpulses is likely to go well beyond the frontiersof physical science. A laboratory-scale source ofcoherent X-rays will undoubtedly make a majorimpact on time-resolved X-ray spectroscopy. Furtheroptimization of the above described ultrashortpulse-driven harmonic generator (e.g. by theimplementation of quasi-phase matching) allowsthe development of the first laboratory tool suitablefor time-resolved spectro-microscopy. Thepredicted ‘concentration’ of the high-energy XUVphotons in a single burst of attosecond durationmay not only extend nonlinear optics into theX-ray regime and allow the study of the dynamicsof bound electrons, but provide a tool for studyingchemical reactions and wave packet dynamics ona previously inaccessible timescale. 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Chapter 3X-Ray Optics3.1 Multilayers for Soft and Hard X-raysM. YANAGIHARAInstitute of Multidisciplinary Research for Advanced Materials, Tohoku University, JapanandK. YAMASHITADepartment of Physics, Nagoya University, Japan3.1.1 INTRODUCTIONX-Rays have an advantage over visible light toachieve higher resolution in image formation. Furthermore,X-ray spectroscopy has an advantagethat near the absorption edges the spectra provideelement- and state-specific information. However,it has been difficult to handle X-rays using techniquessimilar to those applied in the longer wavelengthregion because grazing-incidence opticsbased on total reflection is essential for a reflectorof X-rays. Actually the X-ray reflectivity almostvanishes at incidence angles beyond the criticalangle of the total reflection. Therefore, grazingincidenceoptics needs a large-sized mirror.A multilayer coating consists of alternate layersof different materials with appropriate optical constants.Its periodic structure enhances the reflectivitydue to the constructive interference of themultiple reflections from the interfaces by analogywith Bragg reflection from a crystal. Soonafter the discovery of X-rays, it was proposedthat synthetic layered structures might extend thespectral region to long wavelengths. As the X-rayreflection from each layer is very small, a fewhundreds of layer pairs are needed to synthesizemultilayer structures. Besides, for the constructiveinterference among the partial waves, thelayer thickness should be controlled at the subnanometerlevel over large areas. Early attemptsto fabricate such structures were not successfuldue to technological limitations. Since the 1970s,fabrication of multilayer structures of sufficientquality for X-ray optics has been widely developeddue to the progress in thin-film technologyand polishing of supersmooth substrates to thesub-nanometer level. In the low energy region ofsoft X-rays, multilayer coatings are now practicallyapplicable at nongrazing-incidence angles.In particular, in the 13-nm wavelength region,a normal-incidence reflectivity of about 70 % isnow achieved using Mo/Si multilayers. Basedon these successful achievements, the multilayershave been applied as normal-incidence reflectorsto microscopy, telescopes, and lasers to advancesoft X-ray science. Also in the field of industryX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

64 MULTILAYERS FOR SOFT AND HARD X-RAYStheir application has been widely attempted as akey component of reductive projection lithographyfor next-generation large scale integrated circuit. Inthese applications, multilayers are coated on planeor figured substrates to form images of soft X-rays.For hard X-rays, multilayers have also been developedfor grazing-incidence optical systems. Themultilayer coating on a reflecting surface makes itpossible to enhance the reflectivity in the properenergy band beyond the critical angle. Furthermore,depth-graded multilayers, so called ‘multilayersupermirrors’, extend the reflection band inthe hard X-ray region of 10–100 keV. Such mirrorshave been used as focusing components not onlyin synchrotron radiation facilities but also in usualX-ray laboratories. Using multilayers, a hard X-ray telescope has been developed for balloon-borneobservations and will be put on board of futureX-ray astronomy missions. Furthermore, reflectionmultilayers are used as coating on gratingsto enhance the diffraction efficiency for soft andhard X-rays and as polarizers for soft X-rays. Onthe other hand, a transmission-type multilayer hasbeen fabricated by depositing a multilayer on avery thin transparent substrate. It has been appliedas a polarizer, a phase shifter, and a beam splitterin the soft X-ray region.3.1.2 DESIGN PRINCIPLEOptical properties of materials are closely relatedto the response of the electrons. By the Drudemodel, where a free electron oscillates with anouter electric field, the dielectric constant isgiven by2ω pε(ω) = 1 −(3.1.1)ω 2 + iƔωwhere ω p 2 = Ne 2 /ε 0 m is the squared plasmafrequency and Ɣ is a damping constant. The plasmaenergy ¯hω p of metals ranges below 20 eV. As wecan neglect Ɣ in Equation (3.1.1) we see that ε isslightly smaller than 1 when ω ≫ ω p ,thatis,inthe X-ray region. The index of refraction is relatedto the dielectric constant asn = √ ε (3.1.2)In the X-ray region, the index of refraction isusually denoted asn ≡ 1 − δ + iβ (3.1.3)From the above discussion δ and β are verysmall compared to 1. β is the same quantity asthe extinction coefficient and is related to theabsorption coefficient µ byβ = λµ(3.1.4)4πwhere λ is the wavelength. δ and β are given byδ ∼ = r eλ 2 ∑N j f 1j β2π∼ = r eλ 2 ∑N j f 2j2πjj(3.1.5)where the sum is taken over every atomic speciesof atomic density N j and atomic scattering factorf j = f 1j − if 2j .Thetermr e = e 2 /4πε 0 mc 2 is theclassical electron radius. The atomic scatteringfactor is a useful concept because the index ofrefraction of a material is calculated using theatomic scattering factors of its constituent atoms. 1This is a good approximation except for theabsorption edges where the near-edge structure isdominant in absorption spectra.Now an electromagnetic wave is incident froma medium 1 with an index of refraction n 1 onto aboundary with a medium 2 with n 2 at a grazingangle of incidence θ 1 . Snell’s law is presented byn 1 cos θ 1 = n 2 cos θ 2 (3.1.6)where θ 2 is the grazing angle of refraction. TheFresnel reflection and transmission coefficients, rand t, for s and p polarizations are formulated byandr s = t s − 1 = n 1 sin θ 1 − n 2 sin θ 2n 1 sin θ 1 + n 2 sin θ 2(3.1.7)r p = t p − 1 = n 2 sin θ 1 − n 1 sin θ 2n 2 sin θ 1 + n 1 sin θ 2(3.1.8)respectively. The reflectivity R is given by R =r ∗ r. Figure 3.1.1 shows the reflectivity for s and ppolarizations calculated for (δ 2 ,β 2 ) = (0.2, 0.1)and (0.01, 0.001) when n 1 = 1 (vacuum). The

DESIGN PRINCIPLE 6510 −1 110 −2d = 0.2, b = 0.1sp10 −3log R10 −4s10 −5p10 −6d = 0.01, b = 0.00110 −7 0 10 20 30 40 50 60 70 80 90Grazing angle of incidence (deg)Figure 3.1.1 Calculated reflectivities for s (solid line) and p (broken line) polarization as a function of grazing angle of incidencefor δ, β = 0.2, 0.1 and 0.01, 0.001, respectivelyformer is a typical example for the extremeultraviolet region, and the latter for the X-rayregion. For X-rays, the reflectivity for both s andp polarizations decreases rapidly at the criticalangle of the total reflection, which is obtainedfrom Snell’s law as sin θ c = √ 2δ. It is practicallycalculated for a wavelength λ (nm) assin θ c = √ 2δ = 2.325 × 10 −2√ ρf 1 /Aλ (3.1.9)where ρ (g/cm 3 ) is the mass density and A isthe atomic weight. The reflectivity becomes verylow at normal incidence. The reflectivity for ppolarization shows a minimum around 45 ◦ ,whichis the Brewster reflection. The result is confirmedfrom Fresnel’s and Snell’s equations as n ofevery material is very close to 1 in the X-rayregion.The Bragg angle θ m of the mth order reflectionfrom a multilayer with a d-spacing is given bymλ = 2d sin θ m√1 −2δ − δ2sin 2 θ m(3.1.10)It is reduced to the usual form mλ = 2d sin θ mwhen θ m is large. Figure 3.1.2 shows the boundaryof the total reflection (θ = θ c ) calculated for a Ptsingle layer mirror using Equation (3.1.9) and theBragg reflection in 1st and 5th order (θ = θ m ; m =1.5) calculated for a multilayer of d = 1.5 nmusing Equation (3.1.10) as a function of λ. Theright-hand side of each curve in the θ –λ plane isaccessible by X-ray optical systems. It is obviousthat multilayers enable the applicable region to beextended to five times shorter wavelengths than

66 MULTILAYERS FOR SOFT AND HARD X-RAYS90m = 5m = 1MultilayersGrazing angle (deg)101Total reflection0.1 0.01 0.1 110Wavelength (nm)Figure 3.1.2 Applicable boundaries shown in the θ –λ plane for the total reflection of a Pt mirror (solid line) and the Braggreflection of a multilayer with d = 1.5 nm in 1st (broken line) and 5th (dotted line) order. The right-hand side of each curve isaccessible for X-ray opticswithout them. Normal incidence optics becomeavailable in the wavelength region longer than3 nm. The bandwidth of the Bragg peak in mthorder is given asE = E/mN (3.1.11)where N is the number of total layer pairs.The X-ray energy (E) and the wavelength areconnected byE(keV) · λ(nm) = 1.23985 (3.1.12)The maximum number of layer pairs is estimatedfrom the ratio of the d-spacing to the penetrationdepth of the incident X-rays.A multilayer is designed so that all boundariesadd in phase to the reflected wave. Here the ‘layerby-layer’method 2 is presented. Let the overallreflectivity and transmissivity of a multilayer ber 0 and t 0 at the moment, and then a film witha thickness l be deposited onto the surface ofthe multilayer. The new amplitude reflectivityand transmissivity of the multilayer structure aregiven byr new = r(1 − rr 0) + (r 0 − r)exp(−iα)1 − rr 0 + r(r 0 − r)exp(−iα)t 0 (1 − r 2 ) exp(−iα/2)t new =1 − rr 0 + r(r 0 − r)exp(−iα)(3.1.13)where r is the Fresnel reflection coefficient of thedeposited film of an index of refraction n withrespect to the vacuum andα = 4π λ l√ n 2 − cos 2 θ (3.1.14)is the phase delay due to the propagation inside thedeposited layer. As the form of Equation (3.1.13)is the same for s and p polarizations, the subscriptsare omitted in it. Reflection loss due to the surfaceroughness is accounted for in r in the form of aDebye–Waller factorexp[−2(2πσ sin θ/λ) 2 ] (3.1.15)where σ is the root mean square surface roughness.In order to suppress σ , the thickness must be

SOFT X-RAY MULTILAYERS AND THEIR APPLICATIONS 67controlled within an accuracy of the atomicscale. The reflectivity of a multilayer structureis obtained by calculating r new layer by layer,starting from the Fresnel reflection coefficient ofa substrate. This method is useful not only tocalculate the multilayer reflectivity for a givenstructure, but also to optimize the thickness of eachlayer by monitoring the reflectivity to achieve thehighest value.Using the layer-by-layer method, the criterionfor selecting the optimal pair for a high-reflectivitymultilayer was established. That is, β of bothmaterials is small and the difference in δ betweenthe two is as large as possible. In other words,the multilayer has a periodic structure made ofalternately deposited heavy and light elements.In general, materials are used in the regionbelow their core absorption edges. Furthermore,material combinations have to be selected to formuniform layers and stable interfaces in physical andchemical aspects.A synthetic multilayer usually has a periodicstructure. Furthermore, multilayers with aperiodicstructure have been developed. The bandwidthof the reflection from an X-ray multilayer isquite narrow, so that X-ray supermirrors havebeen widely developed to achieve a wide energyband of high reflectivity beyond the critical angle.Generally, it consists of a top layer for totalreflection for long-wavelength light, a bottommultilayer with a periodic structure for shortwavelengthlight, and a middle multilayer withnonperiodic structure for middle-wavelength light.The number of layers has to be determined tominimize the attenuation of incident X-rays, butto maximize the reflectivity.3.1.3 SOFT X-RAY MULTILAYERSAND THEIR APPLICATIONSFor soft X-ray multilayers around 100 eV, Mo/Siand Mo/Be are the most successful combinations.For Mo/Si multilayers a normal-incidence reflectivityof about 71 % has been achieved at 12.8 nmusing magnetron sputtering. 3 The multilayer consistsof 50 layer pairs and contains B 4 C diffusionbarriers. Its measured reflectivity is shownin Figure 3.1.3, where a peak value of 70.0 % at13.5 nm for another multilayer is also shown. The706071.0%70.0%Reflectance (%)5040300.49 nm0.545 nm2010012.4 12.6 12.8 13 13.2 13.4 13.6 13.8 14Wavelength (nm)Figure 3.1.3 Normal-incidence reflectivity measured for magnetron-sputtered Mo/Si multilayers. They consist of 50 layer pairsand contain B 4 C diffusion barriers. 3 Reprinted from Opt. Eng. 41 (2002) 1797. Reproduced by permission of SPIE

68 MULTILAYERS FOR SOFT AND HARD X-RAYSbandwidths are reasonable from Equation (3.1.11).The ideal reflectivity is about 75 %. Using a magnetronsputtered Mo/Be multilayer of 70 layer pairsa normal-incidence reflectivity of 70.2 % has beenachieved at 11.34 nm. 4 The Mo-based multilayersare the basis for the development of the soft X-raylithography. 5,6Up to now, it has been difficult to achievehigh multilayer reflectivity below the 11-nm regiondue to the surface roughness in comparisonwith the incident wavelength. A normal-incidencereflectivity of 18.9 % has been achieved recentlyusing a magnetron sputtered Cr/C multilayer with150 layer pairs at a wavelength of 6.42 nm. 7A CoCr/C multilayer of 16.1 % has been alsofabricated at 6.1 nm. The motivation to developa highly reflective multilayer in this wavelengthregion is X-ray photoemission spectroscopy withinner-shell excitation using a multilayer-coatedSchwarzschild objective.It is a primary subject for soft X-ray microscopyto observe living cells under natural environmentin the water-window region between 4.4 nm (CK absorption edge) and 2.3 nm (O K absorptionedge). In this region the absorption coefficient ofC, N (K edge), and Ca (L edges) changes by a largeamount within a narrow wavelength region, whilethat of O in the water is very low, which providesgood contrast for living cells. Very recently areflectivity of 20.5 % has been achieved at θ = 73 ◦using a Cr/Sc multilayer of 600 layer pairs. 8 Itwas fabricated using an ion-assisted dual-targetmagnetron sputter system to avoid intermixing ofthe two metals.3.1.3.1 FOCUSING AND MICROSCOPYFigure 3.1.4 illustrates the Schwarzschild optics.It is a combination of a concave and a convexspherical mirror, where the centers of the twospheres are slightly shifted to eliminate the higherorder aberration. Multilayer-coated Schwarzschildobjectives have been installed at a beamline of asynchrotron radiation facility to carry out photoemissionexperiments with high spatial resolution. 9The objectives provide a small radiation spot of0.5 µm on the sample. Three objectives are currentlyavailable at E = 74, 95, and 110 eV. The74 and 95-eV objectives are made of Mo/Si multilayers,while the 110-eV one is made of Ru/B 4 C.The objective reflectivity of the 95-eV objective isabout 25 %, and that of the 110-eV one is 1.1 %.Figure 3.1.5 shows a cross-sectional image of amolecular-beam epitaxy-grown p-n GaAs superlatticewith different periods obtained by samplescanning. As can be seen, the spectromicroscopeallows layers as thin as 0.25 µm to be imaged.The contrast of the image is based on the shiftin energy between the Ga 3d level in p-type andn-type GaAs. A multilayer-coated Schwarzschildphotoelectron microscope with the use of He-I andHe-II resonance lines has been also developed. 10A transmission multilayer is available as abeam splitter in soft X-ray interferometry. A MirauFigure 3.1.4 A schematic drawing of the Schwarzschild optics. It is a combination of a concave and a convex spherical mirror

SOFT X-RAY MULTILAYERS AND THEIR APPLICATIONS 69Figure 3.1.5 Cross-sectional image of an MBE-grown p-nGaAs superlattice with different periods obtained by samplescanning. The two top images are obtained by tuning theenergy analyzer at the kinetic energy of the Ga 3d peak of (a)n-type GaAs and (b) p-type GaAs. The layers of n-type GaAsappear bright in (a) and dark in (b). Image (c) is the differencebetween the two top images. 9 Reprinted from Rev. Sci. Instrum.71 (2000) 5. Reproduced by permission of American Instituteof Physicsinterferometric microscope has been developedby combining a multilayer beam splitter withan imaging-type soft X-ray microscope basedon a multilayer-coated Schwarzschild objective. 11When using it, some stacking defects have beenobserved on a multilayer reflection mask withhigh contrast.The enhanced reflectivity of a multilayer isalso sufficiently powerful to collect soft X-rayfluorescence from low atomic number elementssuch as C, N, O, and F. Photon-in/photon-outsoft X-ray absorption measurements of catalytic Cchemistry have been possible by the developmentof a high-efficiency detection system for C Kfluorescence. A Cr/C multilayer was coated onthe concave collector. 12 Nearly background-freeC near edge X-ray absorption fine structure(NEXAFS) spectra have been obtained.3.1.3.2 POLARIMETRYThe ratio of multilayer reflectivity for s to p polarizationis usually three orders of magnitude ormore at the Brewster angle (θ ≈ 45 ◦ in the softX-ray region). Thus the multilayer works as a usefulpolarizer for soft X-rays. 13 Figure 3.1.6 showsthe polarizance calculated for a Mo/B 4 C multilayerwith d = 5.1 nm for photons of E = 175to 190 eV as a function of θ. The polarizanceis higher than 0.995 between θ = 44 ◦ and 47 ◦independent of the photon energy. A transmissionmultilayer is also available as a phase shifterlike a quarter-wave plate for visible light. Usingreflection and transmission multilayers, ellipsometricstudies have been performed in the soft X-rayregion. 14–16When a multilayer is coated on a grating, itsdiffraction efficiency is enhanced. 17 Moreover, itbecomes a hybrid of polarizer and grating whenused around θ = 45 ◦ , resulting in a polarizationspectrometer in the soft X-ray region. The polarizationspectrometer is applicable to investigationinto polarized soft X-ray fluorescence from solids,gas phases and astrophysical plasmas. A Rowlandcirclemount polarization spectrometer based ona grating coated with a Mo/B 4 C multilayer hasbeen constructed. 18 The polarizance of the gratingwas higher than 98.9 % at a wavelength of6.7 nm at θ ≈ 45 ◦ . CrB 2 has a layer structurelike MgB 2 , which becomes a superconductor at39 K. The B 1s emission from CrB 2 consists ofσ and π emission due to the B 2p xy and 2p zorbitals, respectively. The π emission cannot beseparately observed in any measurement geometryusing a traditional grazing-incidence spectrometer.Figure 3.1.7 shows the B 1s σ and π emissionspectra measured for a CrB 2 single crystal with anenergy width of 0.9 eV. The most notable feature isthat the π electron contributes to the upper valenceband as compared with the σ electron, which iscomparable with the band calculation.At the L 2,3 edges of transition metals, largemagnetic circular dichroism (MCD) has beenobserved. It has attracted much interest offering ameans to separate electron spin and orbital momentin contributions to magnetism. MCD measurementsin the soft X-ray region require incident lightwith high-degree circular polarization, while opticalrotation measurements need only linearly polarizedlight. For polarization methods (Faraday, Kerr

70 MULTILAYERS FOR SOFT AND HARD X-RAYS1.000.98Polarizance0.96Mo/B 4 Cd = 5.1 nmE = 175 eV1800.9418519042 44 46 48 50Grazing angle (deg)Figure 3.1.6 Calculated polarizance for a Mo/B 4 C multilayer with d = 5.1 nm for photons of E = 175 to 190 eV as a functionof θc-CrB 2E = 205 eVsIntensity (arb. unit)p0175 180 185 190Photon energy (eV)Figure 3.1.7 B1sσ and π emission spectra measured for a CrB 2 single crystal using the polarization spectrometer equippedwith a grating coated with a Mo/B 4 C multilayer. The excitation energy is 205 eV. (From ref. 18)

SOFT X-RAY MULTILAYERS AND THEIR APPLICATIONS 71Azimuthalrotation axisABABABABA45°Substrate(a)(b)Figure 3.1.8 A schematic setup of the rotation analyzer based on a multilayer polarizer (a) and a schematic cross-section of themultilayer polarizer with a lateral gradient in period (b)Rotation (deg)6420−2−4TransmissionsampleI 0HH parallel kH anti-parallel kNdFeBmagnets−6680 690 700 710hn (eV)720 730Figure 3.1.9 Faraday rotation observed for a Fe(2.0 nm)/Cr(1.9 nm) multilayer of 40 periods at the Fe L 2,3 edge region. A 3-kOefield was applied parallel or antiparallel along the beam direction and sample normal. (From ref. 19)rotation) in the soft X-ray region, measurementof optical rotation required the development of acontinuously tunable linear polarizer. The righthandside of Figure 3.1.8 shows a schematic crosssectionof the multilayer polarizer with a lateralgradient in period. R s = 0.01 and R s /R p∼ = 3 ×10 4 were estimated for a W/B 4 C multilayer around700 eV. 19 The left-hand side of Figure 3.1.8 showsa schematic of the rotation analyzer based onthe multilayer polarizer. The analyzer rotates themultilayer about the incident beam with fixedincidence angle while monitoring the reflectedintensity. Continuous tunability is achieved bytranslating the multilayer to position the Braggpeak at the desired energy. Figure 3.1.9 shows theresonance in the Faraday rotation, observed fora transmission sample of a Fe(2.0 nm)/Cr(1.9 nm)multilayer at the Fe L 2,3 edge region. A 3-kOefield was applied parallel or antiparallel along thebeam direction and sample normal as illustratedin Figure 3.1.9. The MCD absorption spectra werealso measured for the same sample. Analysis ofthe MCD data showed good agreement with themeasured Faraday rotation.

72 MULTILAYERS FOR SOFT AND HARD X-RAYS3.1.4 HARD X-RAY MULTILAYERSAND THEIR APPLICATIONSIn the 1–100 keV region, material combinationssuch as W/C, W/Si, W/B 4 C, Ni/C, Cr/C, Co/C,Ru/Si, Rh/C, Mo/C, Pt/C, Pt/Si, and Pt/Ti arepromising for high-reflectivity multilayers as grazing-incidencereflectors. Among them, a reflectivityof 68 % has been achieved using a Pt/C multilayer(d = 4.3 nm, N = 50) at λ = 0.154 nm andθ = 1.1 ◦ . 20 The interfacial roughness is estimatedto be 0.32 nm. There are many instrumentsusing such multilayers with periodic structure.Solid Fabry–Perot etalons for X-rays have beenconstructed. 21 Each etalon consists of two W/Cmultilayers separated by a carbon spacer. Thethick carbon spacer works as a resonant cavity.The structure was characterized at grazing incidencein reflection using Cu Kα radiation. Theobserved reflectivity was approximately 50 % ofthat calculated, which might result from the interfacialroughness. This interferometer is applicableto determine the absolute value of the thicknessand δ of the spacer or λ and θ.Figure 3.1.10 shows a spectral reflectivity curvecalculated for a Pt/C multilayer supermirror atθ = 0.3 ◦ . The cross-sectional view of the supermirrorstructure observed by transmission electronmicroscopy (TEM) is shown in Figure 3.1.11.Figure 3.1.10 shows, for comparison, reflectivitycurves calculated for a Pt single layer mirror anda Pt/C multilayer mirror with d = 4.0 nm and γ =0.4, where γ is the ratio of layer thickness ofheavy element to d-spacing. The great advantageof the supermirror for the wide band and practicalreflectivity is obvious. This supermirror has no toplayer for total reflection and the d-spacing graduallydecreases from the surface to the substrateas adjusted to match the energy band concerned.Figure 3.1.12 shows a measured spectral reflectivityfor a W/Si multilayer supermirror with N = 50at θ = 0.5 ◦ , 22 for an example. It can be seen thatthe experimental data fit the theoretical predictionsquite well. It provides a beam with uniform spectralintensity from 7 keV up to 20 keV.3.1.4.1 MICROBEAM ANDMICROSCOPYRecently, X-ray microbeams have been greatlyrequired for the determination of crystal structuresby diffraction, trace elements analysis and imaging,10.1Reflectivity0.0110 −310 −4 10 20 30Energy (keV)40 50Figure 3.1.10 Spectral reflectivity curve calculated for a Pt/C multilayer supermirror at θ = 0.3 ◦ . Reflectivity curves calculatedfor a Pt single layer mirror (broken line) and a Pt/C multilayer mirror with d = 4.0 nm (dotted line) are also shown for comparison

HARD X-RAY MULTILAYERS AND THEIR APPLICATIONS 73Figure 3.1.11 Cross-sectional view of a Pt/C multilayersupermirror observed by TEM. (Courtesy of N. Ohnishi, ChubuUniversity)Reflectance10 010 −110 −210 −3(2)W/Si multilayer, 50 periodsat grazing angle of 0.5°(1)10 −4 10 15 20Photon energy (keV)25 30Figure 3.1.12 Measured spectral reflectivity for a W/Si multilayersupermirror with N = 50 at θ = 0.5 ◦ . 22 Reported fromJ. Synchrotron Rad. 5 (1998) 239. Reproduced by permissionof IUCbecause new artificial materials just synthesizedare usually small powders or composed of smallgrains, or the inner materials in biological cells arevery small. The sizes are around 10 µm or less. Theoptical elements for imaging are grazing incidencemirrors, Fresnel zone plates, and Bragg–Fresnellens. By the use of single mirrors, such as toroidaland ellipsoidal mirrors, it is possible to obtainmicrobeams. However, it is desired to suppressthe aberration caused by the grazing incidenceoptics, by the use of double reflection. Suchan objective coated with a multilayer is theKirkpatrick–Baez type, as shown in Figure 3.1.13.The Kirkpatrick–Baez objective consists of twograzing spherical or nonspherical mirrors, each ofwhich focuses the light horizontally or verticallyindependently. In many cases, the surface of thegrazing incidence mirrors is used at the totalreflection condition of heavy metals, so thatlarge mirrors have been required. Therefore, themultilayers and the supermirrors are used forcoating materials to gather more flux.In Figure 3.1.14 is illustrated a graded W/B 4 Cmultilayer deposited on a flat substrate, whichwas bent to a parabola. 23 The d-spacing hasto be laterally graded because the angle ofincidence differs continuously from the edge ofthe surface. The obtained nonlinear lateral gradientdiffered from the theoretical calculations by lessthan 1 %. The vertical spot size was measuredby the use of 8 keV X-rays and was about7 µm, as shown in Figure 3.1.15. Recently, aspot size of 1 µm has been achieved. Manyefforts have been made to fabricate multilayer- orsupermirror-coated Kirkpatrick–Baez objectivesto obtain microbeams at synchrotron radiationfacilities and laboratories. 243.1.4.2 X-RAY TELESCOPEA normal-incidence telescope has been investigatedin the soft X-ray region. 25 On the other hand,grazing incidence X-ray optics have been wellinvestigated to construct X-ray telescopes. Usuallythe optical configuration of Wolter type I, asshown in Figure 3.1.16, is adopted for astronomicalobservations using the total reflection of singlemetal layer mirrors. The X-ray telescope on boardthe Einstein and ROSAT satellites revolutionizedX-ray astronomy by observing a number of objects

74 MULTILAYERS FOR SOFT AND HARD X-RAYSFigure 3.1.13 Schematic drawings of the Kirkpatrick–Baez opticsFocusa = 1.1°L-XXf = 285 mmL = 270 mmF4.5 mmScrewpoint spread function of this telescope. X-ray emissionsseem to originate from Bremsstrahlung orinverse Compton of non-thermal electrons arounda black hole. The telescope was of a multi-nestedthin foil type assembled with four quadrant unitsmade of 510 pieces of coaxially and confocallyaligned thin foils coated with Pt/C supermirrors.The inner and outer diameter and focal length aredetermined to be 12 cm, 40 cm and 8 m, respectively,which correspond to a grazing angle of0.105–0.356 ◦ . The design parameters, d and N,of supermirrors are divided into 13 groups correspondingto each grazing angle.Figure 3.1.14 Schematic of a mirror bent to a parabola. Alaterally graded W/B 4 C multilayer was deposited on a flatsubstrate. 23 Reported from Rev. Sci. Instrum. 70 (1999) 3227.Reproduced by permission of American Institute of Physics10.8with good image quality, though the energy regionwas limited to be 0.2–4.5 keV corresponding to agrazing angle of

HARD X-RAY MULTILAYERS AND THEIR APPLICATIONS 75ParaboloidHyperboloidOptical axisFocal lengthFigure 3.1.16 Schematic drawings of the Wolter type I optics302520Position (arcmin)15105005101520Position (arcmin)2530Figure 3.1.17 Hard X-ray image of the black hole candidate CygX-1 observed by a supermirror telescope on board a balloon.(From ref. 29)3.1.4.3 MULTILAYER-COATEDGRATINGMultilayer-coated gratings have been developedfor hard X-rays (

76 MULTILAYERS FOR SOFT AND HARD X-RAYSPixel1000p = 0Cu Kb8.91 keVm = 1p = +1p = +2 m = 2W La Cu KbContinuum8.40 KeV 8.04 keV W La Cu Kb(a)Intensity010 610 510 410 310 23000 4000 5000Pixel6000(b)10 1 0.5 1Exit angle q e (deg)1.5 2Figure 3.1.18 Raw diffraction image of a multilayer-coated grating at θ 1 = 0.66 ◦ (a) and the projected profile (b). X-Rayswere generated from a Cu target contaminated with W. Cu Kα, WLα, andCuKβ peaks (m = 1,p =+1) are found aroundθ e = 1.29 ◦ . (From ref. 30)This type of grating has to satisfy the Braggcondition and grating rule expressed by2d(sin θ i + sin θ e ) = mλ2D(cos θ i − cos θ e ) = pλ(3.1.16)where D is the period of grooves, θ i grazingangle of incidence, θ e exit angle, m and p thespectral order of the Bragg reflection and gratingdiffraction. A laminar grating with a 1200grooves/mm and a 39-nm groove depth coated witha Pt/C (d = 5nm, N = 10) multilayer was fabricatedand evaluated with characteristic X-rays. 30The dispersion measurement was performed witha charge-coupled device detector. The first orderpeak reflectivity and resolution were obtained to be30 % and more than 100 for Cu Kα respectively,as shown in Figure 3.1.18.3.1.4.4 DOUBLE-MULTILAYERMONOCHROMATORA double-multilayer monochromator was proposedfrom analogy with a double-crystal monochromator.This novel technique uses an identical pairof multilayers. A double-multilayer monochromatorhas been installed on a soft X-ray beamline. 31Also, a hard X-ray beamline has been installed.In this case, a W/Si double-multilayer monochromatorwas used to suppress higher order harmonicsfrom the synchrotron X-rays of a bendingmagnet. 32 It enabled suppression of all higher orderharmonics to less than six orders of magnitudewith a ∼30 % throughput in the first Bragg peak(8 keV). The use of such a multilayer monochromatorin tandem with a crystal monochromator hasa great advantage over the traditional method using

REFERENCES 77a large grazing-incidence mirror with respect tosize and cost.REFERENCES1. Henke, B.L., Gullikson, E.M. and Davis, J.C. X-ray interactions:photoabsorption, scattering, transmission, andreflection at E = 50–30,000 eV, Z = 1–92, At. DataNucl. Data Tables, 54, 181–342 (1993). These data areavailable at http://www-cxro.lbl.gov/optical constants/.2. Yamamoto, M. and Namioka, T. Layer-by-layer designmethod for soft-x-ray multilayers. Appl. Opt., 31,1622–1630 (1992).3. Bajt, S., Alameda, J.B., Barbee Jr, T.W., Clift, W.M.,Folta, J.A., Kaufmann, B. and Spiller, E.A. Improvedreflectance and stability of Mo–Si multilayers. Opt. Eng.,41, 1797–1804 (2002).4. Bajt, S., Behymer, R.D., Mirkarimi, P.B., Montcalm, C.,Wall, M.A., Wedowski, M. and Folta, J.A. Experimentalinvestigation of beryllium-based multilayer coatings forextreme ultraviolet lithography. SPIE, 3767, 259–270(1999).5. Kinoshita, H. and Watanabe, T. Experimental results obtainedusing EUV laboratory tool at New Suraru. Jpn. 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78 MULTILAYERS FOR SOFT AND HARD X-RAYS27. Turner, M.J.L., Briel, U., Ferrando, P., Griffiths, R.G.,Villa, G. and the EPIC Team. Science Highlights, Calibration,and Performance of EPIC on Newton-XMM: theMOS cameras. SPIE, 4851, 169–180 (2003).28. Serlemitsos, P.J., Jalota, L., Soong, Y., Kunieda, H.,Tawara, Y., Tsusaka, Y., Suzuki, H., Sakima, Y., Yamazaki,T., Yoshioka, H., Furuzawa, A., Yamashita, K.,Awaki, H., Itoh, M., Ogasaka, Y., Honda, H. and Uchibori,Y. The X-ray telescope on board ASCA. Publ.Astron. Soc. Japan. 47, 105–114 (1995).29. Ogasaka, Y., Tamura, K., Okajima, T., Tawara, Y., Yamashita,K., Furuzawa, A., Haga, K., Ichimaru, S., Takahashi,S., Fukuda, S., Kitou, H., Gotou, A., Kato, S.,Satake, H., Nomoto, K., Hamada, N., Serlemitsos, P.J.,Tueller, J., Soong, Y., Chan, K.-W., Owens, S., Brendse,F., Krimm, H., Baumgartner, W., Barthelmy, S.D., Kunieda,H., Misaki, K., Shibata, R., Mori, H., Itoh, K. andNamba, Y. Supermirror hard x-ray telescope and theresults of first observation flight of InFOCuS. SPIE, 4851,619–630 (2003).30. Tamura, K., Yamashita, K., Kunieda, H., Yoshioka, T.,Watanabe, M. and Haga, K. Development of multilayercoated gratings for high-energy x-ray spectroscopy. SPIE,3766, 371–379 (1999).31. Mekaru, H., Tsusaka, Y., Miyamae, T., Kinoshita, T.,Urisu, T., Masui, S., Toyota, E. and Takenaka, H. Constructionof the multilayered-mirror monochromator beamlinefor the study of synchrotron radiation stimulated process.Rev. Sci. Instrum., 70, 2601–2605 (1999).32. Lingham, M., Ziegler, E., Luken, E., Loeffen, P., Mullender,S. and Goulon, J. Double multilayer monochromatorfor harmonic rejection in the 5–60 keV range. SPIE, 2805,158–168 (1996).

3.2 Single Capillaries X-ray OpticsY. HOSOKAWAX-ray Precision, Inc., Kyoto, Japan3.2.1 INTRODUCTIONIn general, it is not easy to apply X-ray spectrometryto the characterization of small areas ofelectronic materials, semiconductors, tissues, etc.because the interactions between X-rays and thosesamples are relatively low compared with those oflight or electron beams. However, X-ray spectrometry,in principle, gives us a variety of informationnot only about the surface but also about the insideof a sample, without destruction. These advantagesof the technique encourage us to expand its limitsin spite of many difficulties. Especially, forsamples to be measured under atmospheric conditionsit is very interesting and challenging for usto perform research and development in the field ofanalysis techniques based on X-ray spectrometry.X-rays commonly used for analysis are:(1) transmitted and absorbed X-rays; (2) A fluorescentX-rays; (3) scattered X-rays; (4) diffractedX-rays; (5) totally reflected X-rays; and (6) refractedX-rays. Basically, either discrete intensities ofthese X-rays or the entire spectrum is measured.Since Wilhelm Röentgen discovered X-rays,research and application development based onX-rays have proceeded and advanced independently.So far, research and development have notproduced any measuring instruments that integratethe use of the various X-rays mentioned above.It can be said that this is mainly due to geometricalconstraints imposed by X-ray irradiation. It hasbeen difficult to obtain X-ray microbeams becauseX-rays do not interact with electromagnetic fieldsin the way electron beams do and because nosuitable and small lenses are available for X-rayoptics as is the case for light due to the fact thatthe refractive index of X-rays is smaller than one.It can be expected that an integrated X-ray analyticalinstrument can only be realized if a very brightX-ray microbeam is available.This subchapter will give a description of howa very bright and narrow X-ray microbeam can berealized using single capillaries (or X-ray GuideTubes, XGT). In addition, a tabletop X-ray analyticalmicroscope based on the use of an XGT andapplications thereof are shown.3.2.2 FORMING OF X-RAYMICROBEAMThere are many methods to obtain a micrometersizedX-ray beam as shown in Table 3.2.1. In thecase of imaging systems, narrow beams of about0.1 µm diameter can be achieved in a relativelylow energy area but only monochromatic X-raysare available. Non-imaging systems can transportX-rays over longer distances over a wide rangeof energies although relatively small in size. Inlaboratories, X-ray tubes are most widely used togenerate X-rays to obtain an X-ray microbeam.Commercially available X-ray generators are relativelysmall in size and easy to use, but often theirX-ray intensities are not sufficient. Therefore, inorder to ensure higher X-ray intensities, it is necessaryto get optimum X-ray taking solid angleand to expand the spectral range. XGTs (singleX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

80 SINGLE CAPILLARIES X-RAY OPTICSTable 3.2.1 Methods to obtain X-ray microbeamsX-ray microbeamforming systemsImagingsystemNon-imagingsystemMethods Designation Features Remarks(1) Grazingincidence methodKirkpatrick–Baez mirror Two-dimensional totalreflection mirrorLong focusingdistanceWolter–MirrorRotating non-spherical totalreflection mirrorMultichanneling plate Multi-bundle single-totalreflection capillaryKumakov–Lens(Polycapillary)Multi-bundle poly-totalreflection capillary(2) DiffractionmethodZone plate Soft X-ray, 0.1 µm φ Short focusingdistanceSchwartzchildSoft–hard X-rayJohnson CrystalSoft X-rayMultilayerSoft–hard X-rayBragg–Fresnel Zone Plate Soft X-ray(3) RefractionmethodRefractive lens Hard X-ray, 10 µm φ Long focusingdistance(1) Slit method Slit/collimator Continuous X-raySimple50–500 µm φ(2) GrazingXGT (single capillary) Wide area continuous X-ray Fine beamincidence method1–10µm φPolycapillaryContinuous X-ray, low pass High brightness30–100 µm φ(3) Diffraction Asymmetry reflection Single colormethodcrystalX-ray – 100 µm φcapillaries) and polycapillaries used in a grazingincidenceconfiguration in non-imaging systemsare expected to meet the above requirements ratherthan the conventional combination of a slit anda collimator.3.2.3 X-RAY MICROBEAMS USINGA SINGLE CAPILLARYIn the case of a single capillary, X-rays aretotally reflected on the inside surface if X-raysare emitted with an incident angle of less thanθ c (radian) = 0.02 × √ ρ (g/cm 3 )/E(keV). In thisway, parallel, focused or diverging X-rays aregenerated depending on the geometry of thehollow tube. More elaborate discussion aboutthe fundamental theory and applications of totalreflection can be found elsewhere. 1–3Different morphologies of a single capillary areshown in Figure 3.2.1. Studies on the shape ofthese capillaries are described elsewhere. 4–8References 9 and 10 deal with studies andexperiments on the relation between the intensityof totally reflected X-rays and the shape andsmoothness of the internal surface. Reference 11describes a study on the reduction of the X-raybackground signal obtained by using capillaryoptics. Reference 12 deals with studies on extremeultraviolet rays.At present, single capillaries are produced usingeither the pulling method or the gas pressuremethod. Reference 6 describes the pulling method.In the case of the pulling method, the pullingshould be controlled in such a way that themiddle part of the hollow tube is expanded towardthe outside.The gas pressure method forces a gas flowthrough a preformed capillary which is therebypressed against a press mold in an electric furnace.In this case, care should be taken on how tonarrow both ends of the capillary. At present,efforts are being undertaken to develop betterproduction processes.Different X-ray output diameters are requireddepending on the type of measurement. A combinationof various optically prealigned capillarieswith different output diameters can be installed

X-RAY MICROBEAMS USING A SINGLE CAPILLARY 81(a)(b)(c)(d)(e)Figure 3.2.1 Single capillary shapes. (a) Cylindrical capillary: easy to make using the pulling method. Brightness and straightnessof the X-ray beam are low. (b) Tapered capillary: relatively easy to make using the pulling method. Straightness of the X-raybeam is good. When used reversed, it is possible to get a fine beam but working distance is as short as several millimeters.(c) Rotated parabolic capillary: possible to obtain a long working distance beam. (d) Rotated ellipsoid capillary: if a pinpointX-ray source is available, it is possible to get a fine and very long distance reaching beam. (e) Walter–Mirror single capillary:most efficient usage of the X-ray source is achieved with the possibility to get a fine beam. Difficult to produce using the normalpulling methodto ease the change between output diameters.Figure 3.2.2 shows two single capillaries withdifferent output diameters (100 µm and 10 µm),which are mounted together and can be installedas such in an instrument.3.2.3.1 AN INSTRUMENT FOR THEMEASUREMENT OF TWO-DIMEN-SIONAL DISTRIBUTIONS BY X-RAYSCANNING USING A SINGLECAPILLARYAs an example of an actual application of asingle capillary, a tabletop type X-ray analyticalmicroscope that can make two-dimensional surfacedistribution measurements by X-ray scanning isshown in Figure 3.2.3(a).A small-sized instrument, which can be used ina normal laboratory is realized by a combination ofsingle capillaries and a low power X-ray generatorof 50 W. An X-ray microbeam is emitted verticallythrough a single capillary and reaches the sample.The sample is placed on an X-Y stage and can thusbe scanned in two dimensions. Both transmittedX-rays and fluorescent X-rays are detected, and atwo-dimensional image is obtained by computingsignals from these detectors.

82 SINGLE CAPILLARIES X-RAY OPTICSDetails of this setup are described in reference4. Reference 5 deals with an archetype ofthis kind of instrument, which uses a conventionalcollimator.Figure 3.2.3(b) shows an example of a softX-ray transmitting window consisting of Mylarfilm with a thickness of several micrometers, whichis installed so that the sensitivity for soft X-raysis improved.3.2.4 AN EXAMPLE OF THEAPPLICATION OF A TABLETOP TYPEX-RAY ANALYTICAL MICROSCOPEFigure 3.2.2 An example of two XGTs (single capillaries)mounted together. The XGT on the left has a nominal diameterof 100 µm and the one on the right has a nominal diameter of10 µm. Both are optically aligned in parallel. Input diametersare 100 and 60 µm, respectively. Output diameters are about100 and about 8 µm. Both overall lengths are 130 mm. Theupper end is the X-ray input side and the lower end is thecapillary outputFigure 3.2.4 shows the transmitted X-ray intensitymeasurement of the press groove of a pull-tabof a soft drink can by means of a microbeamscanned over its surface. Figure 3.2.4(a) showsa two-dimensional distribution of the intensityof transmitted X-rays. Figure 3.2.4(b) shows anintensity histogram that corresponds to (a). Thehorizontal axis is the intensity of transmittedX-rays and the vertical axis is the number of pixelsin (a). The X-ray intensity in the gray colored areaX-raygeneratorXGTOpticalmicroscopeMotorSample stageSampleX,Y ZTransmittedX-ray detectorLNdewarFluorescentX-raydetectorCRTPulseprocesserCPUfor operatingcontroller( )Optical microscopeXGTFluorescentIrradiated X-ray X-ray detectorX-Y stagecontrollerCPU(MCA)

AN EXAMPLE OF THE APPLICATION OF A TABLETOP TYPE X-RAY ANALYTICAL MICROSCOPE 835.75 mm(a)(b)Figure 3.2.4 An example of measurement of the depth of a pull-tab of a soft drink canTransmitted Image Cl Distribution Fe DistributionK DistributionCa DistributionSr DistributionFigure 3.2.5 Mapping images of a cultured pearl obtained with an X-ray analytical microscope. The distribution of ironcompounds has swirly shape. The shadow in the lower part of the mappings is due to the shadow of X-ray absorption caused bythe spherical shape of the pearlcorresponds to the thickness of the pull-tab. Thedepth of the pull-tab groove can be measured withthis technique.Figure 3.2.5 shows the results of a nondestructivedirect observation of a cultured pearl by fluorescentand transmitted X-rays. It has been saidthat the structure of a pearl is made up of morethan 1000 layers of organic and inorganic secretionsof a shellfish piled up alternately around aninorganic nucleus.The theory that trace amounts of iron compoundsare reversed in the nucleus was proven.

84 SINGLE CAPILLARIES X-RAY OPTICS(a)(b)Figure 3.2.6 Scanned image of transmitted X-rays of FRP (a) and the distribution of filler on the surface obtained from thefluorescent X-rays (b)Sample:Optical ImageTransmitted X-ray ImageAl-Ka ImageAl (purity 99.99%)Sample treatment:8 mm thickness form ingotrolled out to a thickness of1 mm and no annealingObservation images:Optical image,Transmitted X-ray imageFluorescence X-ray image(Al Ka),Diffracted X-ray imageMeasurement conditions:XGT diameter 100 µmTube voltage 50 kVTube current 1 mA5.25 mmDiffraction X-ray Images5.25 mm 5.25 mm2.88 keV [1 1 1] 4.69 keV [2 2 0] 5.50 keV [3 1 1] 5.75 keV [2 2 2]5.25 mm 5.25 mm 5.25 mm5.25 mm7.24 keV [3 3 1] 8.63 keV [3 3 3] [5 1 1] 9.82 keV [5 3 1] 12.43 keV [6 4 2]5.25 mm 5.25 mm 5.25 mm5.25 mmFigure 3.2.7 Distribution of aluminum crystal grains in cool rolled aluminum samples (no annealing) as observed with an X-rayanalytical microscope. The horizontal bands indicate small crystals being oriented in the rolling direction

AN EXAMPLE OF THE APPLICATION OF A TABLETOP TYPE X-RAY ANALYTICAL MICROSCOPE 85Sample:Al (purity 99.99%)Optical ImageTransmitted X-ray Image Al-Ka ImageCrystal directiondistribution imageSample treatment:8 mm thickness form ingotrolled out to a thickness of1 mm and annealing 400 °C1 h2.56 mm2.56 mm2.56 mm 2.56 mmDiffraction X-ray Images2.88 keV [1 1 1] 4.76 keV [2 2 0] 5.40 keV [3 1 1] 5.80 keV [2 2 2]Observation images:Optical image,Transmitted X-ray imageFluorescence X-ray image(Al Ka),Diffracted X-ray image2.56 mm 2.56 mm 2.56 mm 2.56 mm7.32 keV [3 3 1] 8.76 keV [3 3 3] [5 1 1] 9.80 keV [5 3 1] 12.44 keV [6 4 2]Measurement conditions:XGT diameter 100 µmTube voltage 50 kVTube current 1 mA2.56 mm 2.56 mm 2.56 mm 2.56 mmFigure 3.2.8 Distribution of aluminum crystals observed with an X-ray analytical microscope (annealing at 400 ◦ Cfor1h)Sample:Al (purity 99.99%)Optical ImageTransmitted X-ray ImageAl-Ka ImageCrystal directiondistribution imageSample treatment:8 mm thickness form ingotrolled out to a thickness of1 mm and annealing 600 °C1 hObservation images:Optical image,Transmitted X-ray imageFluorescence X-ray image(Al Ka),Diffracted X-ray imageMeasurement conditions:XGT diameter 100 µmTube voltage 50 kVTube current 1 mA2.56 mm2.56 mm 2.56 mm2.56 mmDiffraction X-ray Images2.88 keV [1 1 1] 4.68 keV [2 2 0] 5.40 keV [3 1 1] 5.80 keV [2 2 2]2.56 mm 2.56 mm 2.56 mm 2.56 mm7.12 keV [ 3 3 1 ] 8.76 keV [3 3 3] [5 1 1 ] 9.80 keV [5 3 1] 12.44 keV [6 4 2]2.56 mm 2.56 mm 2.56 mm 2.56 mmFigure 3.2.9 Distribution of aluminum crystals observed with an X-ray analytical microscope (annealing at 600 ◦ C for 1 h). Size,orientation, and distribution of crystals can clearly be observed with X-ray analytical microscopy

86 SINGLE CAPILLARIES X-RAY OPTICSFigure 3.2.6 shows an example of the applicationof X-ray analytical microscopy to the study ofFRP (Filler Reinforced Plastics), which is a kindof the engineering plastic. A scanned image of thetransmitted X-rays shows the distribution of fillersthroughout the whole thickness, and a scanned fluorescentX-ray image of Ca corresponds to thetwo-dimensional distribution of filler in a surfacelayer of about 10 µm of the FRP. Fillers are commonlyadded in the process of injection moldingto increase mechanical strength of the FRP. Unlessthe distribution of the fillers are uniform in theFRP, it is likely to be damaged due to stress concentration.3.2.5 X-RAY ANALYTICALMICROSCOPY APPLIED FOR DIRECTOBSERVATION OF ALUMINUMCRYSTAL GROWTHFigure 3.2.7 shows images of a rolled aluminumsample obtained with X-ray analytical microscopy.It can be observed that crystal grains are small andoriented in the rolling direction.These samples were annealed at a temperatureof 400 ◦ C and 600 ◦ C for 1 h and observed with anX-ray analytical microscope. The results are shownin Figures 3.2.8 and 3.2.9. It can be clearly seenthat the size of the crystal grains increased withincreasing temperature.Figure 3.2.10 shows the damage to an aluminumtest piece submitted to repeated fatigue testcycles.3.2.6 MULTIDIMENSIONALANALYSIS WITH X-RAYMICROBEAMSBy two-dimensionally scanning a sample withX-ray microbeams, various kinds of distributionanalysis techniques can be proposed as shown inTable 3.2.2.It is expected that an integrated X-ray analysisinstrument can be realized that enables4-f7.0R25818306590t = 5RDN = 0 N = 1.8 × 10 4 N = 3.0 × 10 4Figure 3.2.10 Images of an aluminum plate obtained with an X-ray analytical microscope. The slip bands resulting from byrepeated fatigue test cycles can be seen. N corresponds to the number of cycles, pulling was done at test plane (311) or effectivedepth (t e = 11.81 µm)

REFERENCES 87Table 3.2.2 Multidimensional analysis by means of X-raymicrobeamsDistributionanalyzing probe1 Irradiated X-ray beaminduced currentdistribution2 X-ray beam induced samplecurrent distribution3 Transmitted X-rayintensities distribution4 Fluorescent X-rayintensities distribution5 Diffracted X-ray intensitiesdistribution6 Scattered X-ray intensitiesdistribution7 Refracted X-ray IntensitiesdistributionAbbreviationIXBCDXBICDTXIDFXIDDXIDSXIDRXIDNature of theinteractionsSurfaceelectricchargeInner electricchargeElectrondensityAtomicCrystallizationElectrondensityElectrondensitymultidimensional X-ray analysis by visualizing thedetected X-ray signals shown in Table 3.2.2.ACKNOWLEDGEMENTSIn this subchapter, the descriptions regardingIXBCD are based on suggestions made byDr Yoichi Ghoshi of The Japan National Institutefor Environmental Studies. The topographicobservations of aluminum crystals are the resultsof a cooperation with Professor Yoshio Miyoshiet al., at the School of Engineering, Shiga PrefectureUniversity. The author also wishes to thankthe Japanese Scientific and Technological Agencyand Horiba, Ltd for their support.REFERENCES1. A.H. Compton and S.K. Allison. X-rays in Theory andExperiment, Braunworth and Company, Inc., New York,1936.2. V.E. Cosslett and W.C. Nixon. X-Ray Microscopy, CambridgeUniversity Press, London, 1960.3. T. Namioka and K. Yamashita. X-Ray Imaging Optics,Baifukan, Japan 1999.4. D.H. Bilderback. Microbeam generation with capillaryoptics. Rev. Sci. Instrum., 2059–2063, 66(2), 1995.5. Y. Shuzuki and Y. Chikaura. Characterization of metalorganicchemical vapor deposition grown GaAs on Si bymeans of X-ray scattering radiography. J. Appl. Phys.,1290, 70, 1991.6. Y. Hosokawa, S. Ozawa, H. Nakazawa and Y. Nakayama.An X-ray guide tube and a desktop scanning X-rayanalytical microscope. X-Ray Spectrom., 380–387, 26,1997.7. C. Liu and J.A. Golovchenko. Surface trapped X-ray:whispering-gallery modes at λ = 0.7 Å. Phy. Rev. Lett.,788–791, 79(5), 1997.8. Yu.I. Dudchik, et al. Formation of X-ray beams with theaid of a tapered micro capillary. Tech. Phys. 562–564,43(5), 1998.9. S.V. Kuhlevsky, et al. Wave-optics treatment of X-rayspassing through tapered capillary guides. X-Ray Spectrom.,354–359, 29, 2000.10. B. Chen. Theoretical consideration of X-ray transmissionthrough cylinder capillaries. Rev. Sci. Instrum.,1350–1353, 72(2), 2001.11. P. Engstrom and C. Riekel. Background reduction inexperiments with X-ray glass capillary optics. Rev. Sci.Instrum., 4061–4063, 67(12), 1996.12. R. Bruch, H. Merabet, M. Bailey, S. Showers and D. Schneider.Development of X-ray and extreme ultraviolet opticaldevices for diagnostics and instrumentation for varioussurface applications. Surf. Interface Anal., 236–246, 27,1999.

3.3 Polycapillary X-ray OpticsN. GAOX-ray Optical Systems, Albany, NY, USAandK. JANSSENSUniversity of Antwerp, Antwerp Belgium3.3.1 INTRODUCTIONA polycapillary X-ray optic consists of an arrayof a large number of small hollow glass tubesformed into a certain shape. The optic collectsX-rays that emerge from an X-ray source withina large solid angle and redirects them, by multipleexternal total reflections, to form either afocused beam or a parallel beam, as illustrated inFigure 3.3.1.The use of polycapillary optics has becomewidespread in various X-ray analysis applicationsafter more than a decade of extensive researchand development work led by a few groupsaround the world. 1–4 These optical devices havealso been successfully used as crucial componentsin commercial X-ray analysis instrumentsand have dramatically enhanced the system performance.The rapid development of polycapillaryoptics also triggered the development ofrelated X-ray equipment such as microfocus X-ray sources and compact X-ray spectrometers.As a result, the development of analytical X-rayinstruments is being driven towards compact, lowpowerinstruments that can be used in-line. Thisopens opportunities for an even larger variety ofapplications in different fields of science and technology,both in academic laboratories and industrialinstitutions.3.3.2 FUNDAMENTALS OFPOLYCAPILLARY OPTICSThe fundamental mechanism with which X-raystransmit through a curved capillary tube hasbeen described in detail on many occasions inthe literature. 5–7 As shown in Figure 3.3.2, thedirection of X-ray radiation can be changed whenX-rays undergo multiple total reflections within abent capillary, as long as the incident angle at eachreflection is less than a critical angle θ c .Asthiscritical angle is very small [of the order of a fewmrad for X-rays in the 5–30 keV range: θ c (mrad)∼30/E (keV) for reflection on glass surfaces],the bending curvature of the capillary has to begentle and the capillary diameter has to be small tomaintain the total reflection condition. The typicalradius of curvature of the individual hollow glasstubes within a polycapillary optic is about a fewhundreds of millimeters and the channel diameteris anywhere from a few micrometers to a few tensof micrometers. The optimal curvature and channelsize are usually determined by the particularapplication and the energy range the optic willbe used in. The first practical use of polycapillaryfocusing device, reported in 1990, 5 was a multifiberpolycapillary optic that consisted of an arrayof curved fiber bundles guided through supportingthin metal screens, successfully assembled byX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

90 POLYCAPILLARY X-RAY OPTICSFocusing optics(a)X-raysource(b)Collimating optic(c)Figure 3.3.1 Polycapillary X-ray optics that produce a focused (a,b) or parallel beam (c), starting from a X-ray point source(micro-focus X-ray tube (a, c)) or a quasi-parallel X-ray source (synchrotron (b))AirGlassq cq c≈30E[keV](mrad)Straight capillaryBent capillaryFigure 3.3.2 Schematic representation of the principles of capillary optics. θ c is the critical angle for total reflectionKumakhov et al. 8 A photograph of a multi-fiberoptic and a cross section of a single fiber are shownin Figure 3.3.3. The total number of capillarychannels can be as many as a few millions. Thecapture angle can be as large as 30 ◦ and the outputbeam size can be up to 50–100 mm.A new generation of polycapillary devices,referred to as monolithic polycapillary optics, wasannounced in 1992. 8 Instead of using supportingmetal screens, as employed in multi-fiber optics,the polycapillary fibers were closely packed andthen fused together and formed into the desiredshape through a heating process. One of the mostdistinguishing properties of a monolithic optic isthat the cross-section of an individual channelchanges along the length of the optic so thateach individual channel points to the focus ofthe optic. As a result, the transmission efficiencyof the optic is significantly increased and otherbeam properties, such as the focal spot size (fora focusing optic see Figure 3.3.1a and 3.3.1b)and beam divergence (for a collimating opticsee Figure 3.3.1c), are improved. Photographs ofmonolithic optics and their cross sections areshown in Figure 3.3.4. Although a monolithicpolycapillary optic is superior to a multi-fiber opticin general, a multi-fiber optic is still a better optionfor some applications such as large beam X-raydiffraction 9 and X-ray lithography 10 in which ahigh uniformity of the output beam is required.

FUNDAMENTALS OF POLYCAPILLARY OPTICS 91Figure 3.3.3 Photograph of multi-fiber optics and the polycapillary fiber (right)Figure 3.3.4 Photographs and SEM images showing the typical size of monolithic polycapillary optics and their cross-sectionThe transmission efficiency of a polycapillaryoptic, defined as the ratio of the number ofX-rays exiting at the output end of the optic tothose entering the input end of the optic, is afunction of energy because of the dependencyof the critical angle on the energy. Figure 3.3.5shows simulation results for a typical focusingoptic. The drop of the transmission efficiency onthe high-energy end results from the decreasingcritical angle θ c and the more strict conditionsfor total reflection that are associated with thisdecrease. The particular transmission-energy curvewill be determined by the particular optic design.For example, an optic designed for high-energy

92 POLYCAPILLARY X-RAY OPTICSTransmission efficency (%)30252015105Optic parameters:Input focal distance: 52 mmOutput focal distance: 10 mmLength: 60 mmCollecting angle: 3.3°Channel diameter: 10 µm00 5 10 15 20 25 30Energy (keV)Figure 3.3.5 Transmission efficiency of a polycapillary optic as a function of the X-ray energyX-rays can have a more favorable high-energy tolow-energy transmission efficiency ratio. However,this does not necessarily mean that the absolutetransmission efficiency at the high energies ishigher than that at the low energies. The bandpassproperty shown in Figure 3.3.5 can be veryuseful in many applications where the high-energyradiation generates an undesired background.allows to produce bundles of tubes with smalltaper angles on the size that faces the X-ray source(Figure 3.3.1). On the focusing side (part nearestto the sample), the taper angles are larger. One ofthe future challenges is to make the focal spot sizemore constant with energy so that probe sizes donot vary by as much as a factor of two over a broadX-ray energy range.3.3.3 FABRICATION AND SHAPEOPTIMIZATION3.3.3.1 FABRICATION TECHNIQUESPolycapillary optics are made by heating bundlesof glass tubes in a furnace and pulling themto a particular shape. Today’s technology allowscontrol of the diameter vs length profile to betterthan 5 µm. 11 One of the recent developmentsis the ability to produce lenses with a nonconstantcurvature vs length profile; previously,the capillary tubes in focusing lenses featured aconstant curvature over the entire length of thelens. In one particular example, the experimentalflux density observed was 79 % higher than for aconstant curvature optic at 8 keV and the focal spotsize decreased from 52 to 40 µm. The development3.3.3.2 SIMULATION TOOLSSeveral Monte Carlo ray-tracing simulation programsare available that are able to calculatethe trajectory of individual X-ray photons withina particular hollow glass tube that form partof a polycapillary lens. 7,12,13 Each of them hasunique features that greatly help researchers to betterunderstand the properties of the polycapillaryoptics and their potential application capabilities.In one of the pioneering simulation tools developedby Xiao et al., 7 the trajectory of an X-rayphoton was described as a classically acceleratedparticle undergoing collisions with wallsdefined by the capillary. Using the small incidentangle approximation, the motion of a particlewas divided into the one along the capillary axiswith a constant velocity and the one transverse

FOCUSING OPTICS 93to the axis, which has acceleration associatedwith the curvature of the capillary. The modelsimplified a complicated ray-tracing problem inthree-dimensional space to a much more manageabletwo-dimensional problem, which significantlyreduced the simulation time, and consequentlymade it possible to perform large numbersof simulations to optimize the optic design for agiven application. The results generated from thesimulation were compared to the experimental dataand excellent agreement has been achieved for differenttypes of polycapillary optics.State-of-the-art simulation programs can handlevarious optic profiles, including circular, parabolic,elliptical, and polynomial shapes. The photon positionand angular distributions can be obtained atany image plane, so the dimensions and divergenceof the output beam can be calculated. Differentsource distributions can be handled, includingGaussian and line sources. The simulation hasbecome an essential tool to provide information forthe optic design, performance analysis and evaluationof potential applications.3.3.4 FOCUSING OPTICSA polycapillary focusing optic collects a largesolid angle of X-rays from an X-ray source andfocuses them to a small spot (see Figure 3.3.1a).The X-ray flux density obtained at the focus canbe more than three orders of magnitude higherthan that from a conventional pinhole aperturethat provides the same beam size. Importantperformance specifications for a polycapillaryfocusing optic include the focal spot size, theoutput focal distance (working distance), and theintensity gain.3.3.4.1 FOCAL SPOT SIZEThe best way to estimate the focal spot sizeis to use one of the simulation tools describedearlier, because it is usually determined by anumber of factors such as the focal distance, thechannel diameter, the optic profile and the X-raysource. On the other hand, it is also possible toestimate the focal spot size with the followingempirical relation:S ≈ a · f · θ max + d out (3.3.1)where S is the full width at half-maximum (FWHM) of the spot, d out is the channel diameter ofthe capillary at the output end of the optic, andθ max is the maximum angle with which the X-rays exit from the individual capillary tubes at thegiven energy. In many cases, the approximationθ max = θ c is valid; d out is usually very small comparedto S and can be neglected. a is an adjustmentparameter determined by the optic design and theX-ray source property, and typically ranges from1.0 to 1.5. Since the focal spot size is proportionalto the focal distance, a smaller spot size can beobtained by using lenses with shorter focal distance.The trade-off is the loss of the working spacebetween the optic and the sample.Equation (3.3.1) applies to both the input andthe output of the optic. The input focal spot sizewill determine the area of the X-ray source that canbe ‘seen’ by the optic and therefore the optimalsource size for the optic. This is important indesigning an optic for an existing X-ray source,or choosing the right X-ray source for an existingoptic. Equation (3.3.1) indicates that the focal spotsize will change with the critical angle, i.e. thatit is dependent on the X-ray energy. Figure 3.3.6shows the simulation result of the output focal spotsize of a focusing optic as a function of the X-rayenergy. The spot size change with energy canbe a problem in some applications where highlyaccurate quantitative analysis is needed for a widerange of elements.Simulation results also indicate that, to a certainextent, the output focal spot size of a polycapillaryoptic is a function of the source size. When theX-ray source size is much less than the inputfocal spot size of the optic, the output focalspot size can be much less than predicted byEquation (3.3.1). This is because, when the sourcesize is small enough, the maximum incident angleθ max , predominated by the source size, will be lessthan the critical angle θ c . Consequently the X-raysexiting the optic will have a divergent angle less

94 POLYCAPILLARY X-RAY OPTICS60Focal spot size (micron, FWHM)50403020Optic parameters:Input focal distance: 52 mmOutput focal distance: 10 mmLength: 60 mmCollecting angle: 3.3°Channel diameter: 10 µmSource size: 0.15 mm × 0.15 mm100 5 10 15 20 25 30Energy (keV)Figure 3.3.6 Focal spot size of a polycapillary focusing optic as a function of the X-ray energyFocal spot size (micron, FWHM)2624222018161412Optic parameters:Input focal distance: 20 mmOutput focal distance: 10 mmLength: 75 mmCollecting angle: 5.4°Channel diameter: 5 µmSource size: 0.03 mm × 0.03 mm100 5 10 15 20 25 30Energy (keV)Figure 3.3.7 Focal spot size of a polycapillary focusing optic as a function of the X-ray energy with a small X-ray sourcethan the critical angle, and a smaller output focalspot size is obtained.As an example, Figure 3.3.7 shows the simulationresult for an X-ray source with 30 µm anodefocal spot diameter. Clearly, the change of thespot size with the energy is much less than inFigure 3.3.6, where a 150 µm focal spot sourcewas used. Other factors contributing to the resultin Figure 3.3.7 include the small channel size andthe optic design. It is shown that the use of very

FOCUSING OPTICS 95small X-ray source provides one possible solutionfor the problem of the spot size change with theenergy that was mentioned earlier.The most commonly used method to measurethe beam size is the knife-edge scan, where asharp knife edge is moved across the beam andthe derivative of the knife-edge scan profile isused to determine the beam size. Figure 3.3.8shows a typical knife-edge scan profile and itsderivative for a polycapillary focusing optic with5 mm output focal distance. The focal spot sizes(FWHM) of 13.8 and 23.2 µm were obtained at17.4 and 8.0 keV, respectively.In another often-used method, a thin wire ismoved across the beam and the intensity of thefluorescent X-rays is recorded as a function ofthe wire position. The obtained scan curve is theconvolution of the wire thickness and the beamsize S b . The latter can be estimated by means ofthe following formula:√S b ≈ S 2 − Twire2where S is the FWHM of the measured scan curve(see Figure 3.3.8) and T wire the thickness of thewire. The result obtained is dependent upon thematerial the wire is made of. It must be recognized,however, that the result obtained with this methoddoes not represent the spot size at any particularenergy. Instead, the result is the beam size at aneffective average energy 〈E〉 of all the X-raysthat can excite the fluorescence of the elementthe wire is made of. Usually, 〈E〉 is close to theadsorption edge energy of the element considered.The result is also dependent upon the geometryof the X-ray tube such as take-off angle and itsoperating conditions.3.3.4.2 FLUX DENSITY GAINThe combination of the large collecting angle andsmall focal spot size of a focusing optic resultsin a high flux density, defined as the number ofphotons passing through a unit area per unit time.The flux density gain of an optic is defined asthe ratio of the X-ray flux density obtained atthe focus of the optic to that obtained with apinhole aperture placed at a certain distance tothe source. Usually the distance is the smallestone that can practically be employed for theapplication/X-ray source under consideration. Thereason for using the term flux density rather thanintensity is because the latter has been widelyaccepted in the X-ray analysis community to referto the photon counting rate (detected number ofphotons per unit time), although this is a misuse ofthe term based upon the strict classical definition,as pointed out by Jenkins et al. 14 It is thereforeless confusing to use the flux density gain ratherthan the intensity gain for a polycapillary optic.The gain clearly depends upon how far the pinholeE = 8.0 keVE = 17.4 keV600050004000Knife-edge scanDerivative of scan curve40003000Knife-edge scanDerivative of scan curveCounts300020001000FWHM = 22.7 µmCounts20001000FWHM = 13.8 µm00−1.30 −1.28 −1.26 −1.24 −1.22Knife-edge position (mm)−1.24 −1.22 −1.20 −1.18Knife-edge position (mm)Figure 3.3.8 Focal spot size of a polycapillary focusing optic at different energies. The focal distance of the optic is 5 mm

96 POLYCAPILLARY X-RAY OPTICSis placed from the X-ray source. It is thereforeimportant to specify the source-to-sample distancewhen reporting the intensity gain data.The experimental result given in Figure 3.3.9shows the typical level of the flux density gainof a polycapillary focusing optic, which is morethan three orders of magnitude for W L lineX-rays (8–12 keV). The polycapillary optic hasan output focal distance of 10 mm and producesa spot of 40 µm (FWHM)attheWLα energy.The data for the pinhole case were obtained usinga 2 mm pinhole aperture and then scaled down tothe equivalent of a pinhole of 40 µm diameter.The flux density gain is also a function of thesource size because of the dependency of the opticperformance on the source size (Figure 3.3.10).The rapid decrease of the intensity with theincreasing source size indicates the importance ofusing microfocus X-ray sources in applicationswhere polycapillary optics are employed.Polycapillary optics can also provide ‘gain’ inspecial cases. In the above discussion for the pinholeaperture case, we assume the sample is placedright after the aperture. In practice, however, a10 8 Fe and Cr from the aperture material10 710 610 5W L aW L bW L gPolycapillary focusing optic0.04 mm aperture, 100 mm from the sourceCounts10 410 310 210 110 0Ar in air0 5 10 15 20 25 30Energy (keV)Figure 3.3.9 Scatter X-ray spectra taken from a polycapillary optic and from a 0.04 mm pinhole. The optic has an output focaldistance of 10 mm. The pinhole data were acquired with a 2 mm pinhole aperture and the optic data were then rescaled. Thepinhole was placed 100 mm to the X-ray source that has a tungsten target and 10 µm spot sizeFlux density gain1000E = 8.0 keV (Cu K a )Flux density gain1000100E = 17.4 keV (Mo K a )1000.0 0.1 0.2 0.3 0.4Source diameter (mm)100.0 0.1 0.2 0.3 0.4Source diameter (mm)Figure 3.3.10 Flux density gain of a polycapillary focusing as a function of the X-ray source size at different energies

COLLIMATING OPTICS 97minimal working distance is indispensable in mostapplications. When a very small beam size isrequired and a large X-ray source is to be used, theX-ray source has to be far enough from the pinholeaperture to ensure the ‘image’ of the source on thesample plane matches with the desired beam size.This will dramatically reduce the collecting angleof the pinhole aperture and thereby the efficiencyof the system. Using a polycapillary optic, however,can be beneficial in this case, as illustrated inFigure 3.3.8. Despite the relatively low transmissionefficiency with the large X-ray source, it stillprovides a reasonable intensity gain. The successfulapplication of a focusing polycapillary optictogether with neutron sources 15 is a good exampleof this type of application.The absolute X-ray intensity or flux densityachievable with polycapillary optics stronglydepends upon the characteristics of the X-raysource used. Haller et al. 16 reported havingachieved a Cu Kα intensity of 5.4 × 10 9 photon/sin a spot of 30 µm (FWHM) corresponding to aflux density of 7.6 × 10 12 photons/s/mm 2 .3.3.5 COLLIMATING OPTICSA polycapillary collimating optic converts divergentX-rays from the X-ray source into a quasiparallelbeam (see Figure 3.3.1c). Although acollimating optic can be made such that all capillarychannels are perfectly parallel to each otherat the output end of the optic, the output X-rayshave a certain divergent angle, which is determinedby the critical angle and thereby the X-ray energy.The performance specifications for a collimatingoptic include the intensity gain, the output beamdimensions and the output beam divergent angle,which is a critical parameter for applications suchas X-ray diffraction (XRD) wavelength dispersivespectrometer. The intensity gain is defined as theratio of the output beam intensity obtained withthe optic to the beam intensity obtained withoutthe optic. Unlike in the case of focusing opticswhere the term flux density is used to describethe performance of the optic, the term intensity,referring to the number of photons per unit time,is used for characterizing collimating optics. Usuallythe total number of X-ray photons is the mostimportant for the applications in this field. The basecase (without the optic), however, must be definedcarefully for collimating optics. It is a commonpractice to define the geometry of the base caseas of a conventional aperture collimator providinga beam with the same dimension and divergentangle θ d as delivered by the optic. The collectionangle of the aperture collimator in the base caseis therefore equal to the divergent angle, which isapproximately twice the critical angle at a givenenergy. The intensity gain is then determined bythe following formula:Gain = o · Tθ 2 d= o · T(2 · θ c ) 2where o and T are the collection solid angleand the transmission efficiency, respectively, ofthe optic. It is follows from the above expressionthat the larger the output beam size, the higherintensity gain will be obtained. For example, apolycapillary collimating optic with 5 ◦ collectionangle, 30 % transmission efficiency and 6 mmoutput beam diameter will provide an intensitygain of approximately 200 at Cu Kα (8.04 keV,θ c = 3.75 mrad). If the output beam diameter isdoubled, the corresponding collecting solid angleof the optic will be four times larger. Although thetransmission efficiency of the optic will decrease toabout 18 % due to the greater bending curvature ofouter capillaries, the intensity gain of the optic willincrease by a factor of 2.4 to approximately 100.Besides the intensity gain, another criticalparameter to be considered in the design ofcollimating optics is the divergent angle θ d ,whichis usually determined by the requirement of theapplication. For example, when a collimating opticis used for wavelength-dispersive spectroscopy(WDS), the most efficient coupling with thediffracting crystal is obtained when the beamdivergence of the optic is matched to the mosaicityof the crystal. In this case, an optic providing themaximum intensity may not be the optimal for theapplication. Figure 3.3.11 shows simulation resultson how the intensity and divergent angle of the

98 POLYCAPILLARY X-RAY OPTICS26005.2Intensity (arbitrary unit)24002200200018001600140012001000IntensityDivergent angle4.84.44.03.63.22.82.42.0Divergent angle (mrad., FWHM)80020 30 40 50 60Optic length (mm)1.6Figure 3.3.11 Simulation result of the output beam intensity and divergent angle of a collimating optic as a function of theoptic lengthoutput beam changes with the optic length at giveninput focal distance and energy.The conclusion that the beam divergent angleθ d is determined by the critical angle θ c onlyholds when the maximal incident angle of theX-rays at the entrance of the optic is larger thanthe critical angle. This is generally true becausethe optic will have the maximal collecting angleunder such conditions. In some cases where themaximal incident angle is less than the criticalangle, however, θ d will be smaller than θ c becausethe incident angle of X-rays decreases slightlyafter each reflection in a collimating optic. Thiscondition can be achieved when a very smallX-ray source is used. Figure 3.3.12 show results ofexperimental determinations of θ d of a collimatingoptic when coupled to a 20 µm X-ray source. Thedivergent angle was measured by acquiring therocking curve of the beam using a highly orientedsingle crystal such as silicon or germanium.Figure 3.3.12(a) is the result at Cu Kα (8.04 keV),where the obtained divergent angle of 2.4 mrad(FWHM) was much less than the critical angleat Cu Kα, which is 3.8 mrad. In Figure 3.3.12(b)the result for Mo Kα (17.4 keV) are shown, whereθ d = 1.1 mrad is also smaller than the critical angleat Mo Kα (θ c = 1.7 mrad). A Si (400) crystal wasused in both measurements as a Bragg reflector.3.3.6 ANALYTICAL APPLICATIONSOF POLYCAPILLARY OPTICS3.3.6.1 ELEMENTAL ANALYSISPolycapillary lenses are currently being used indifferent forms of X-ray microanalysis: in micro-XRF instruments of various kinds, they are usedto focus the primary radiation emitted by a (microfocus)X-ray tube (see Figure 3.3.1a) or by asynchrotron storage ring (see Figure 3.3.1b). Thus,only a small spot on the sample surface isirradiated and the local composition can be derivedby using an energy-dispersive detector to collectthe emitted fluorescent radiation. Focal spots in therange 10–20 µm diameter at an energy of 17.4 keVhave recently been obtained.In electron probe X-ray microanalysis, polycapillaryoptics are used to collect fluorescentX-rays from the sample and redirect them tothe detector. Such applications include, but arenot limited to: (1) superconducting microcalorimeterdetectors 17,18 or tunnel-junction detectors, 19 inwhich polycapillary optics are used to increase the

ANALYTICAL APPLICATIONS OF POLYCAPILLARY OPTICS 99E = 8.04 keV (Cu Ka)1600014000Experimental dataGauss fitDetails of the double Gauss fitFWHM(Ka1) = FWHM(Ka2) = 0.136°(2.4 mrad.)Diffracted beam intensity (cps)120001000080006000400020000(a)34.2 34.4 34.6 34.8 35.0Angle (degree)E = 17.4 keV (Mo Ka)1200010000Experimental data, E = 17.4 keVGauss fitGauss fit peak 1FWHM = 0.062° (1.1 mrad.)Gauss fit peak 2FWHM = 0.058° (1.0 mrad.)8000Counts600040002000(b)015.0 15.1 15.2 15.3 15.4 15.5Angle (degree)Figure 3.3.12 Measurement of the divergent angle of a collimating optic using a Si(400) crystaleffective collection solid angle; (2) environmentalscanning electron microscopy (ESEM) or lowvacuumscanning electron microscopy (LV-SEM)where the use of polycapillary optics improves thecontrast of X-ray imaging; 20 and (3) wavelengthdispersive spectrometer, where polycapillary collimatinglenses (see Figure 3.3.1c) are nowbeing used to replace soller-slit assemblies, thusincreasing the throughput of the wavelengthdispersive detection system. 21

100 POLYCAPILLARY X-RAY OPTICSMicro-XRFLaboratory micro-XRFInitially, custom-designed polycapillary lenseshave been used by various groups to extend thecapabilities (both in terms of absolute sensitivityand in terms of lateral resolution) of existing(i.e. commercially available) micro- and mini-XRF instruments. 22 Usually, the geometry of thesesystems imposes rather severe constraints on thedimensions of the polycapillary optics that maybe used, so that lenses with optimal performancecould not always be used effectively.In situations were there are no or not so strictgeometric constraints, Bichlmeier et al. 23 testedout several combinations of low-power microfocustubes, polycapillary lenses and Peltier-cooledenergy-dispersive detectors and measured relativeDL (detection limit) values for typical laboratorysystems situated in the 20–50 ppm range fortransition elements in a glass matrix. The sameauthors used this system for quantitative analysisof historical glass beads and gold coins and variousindustrial materials. 24 A detailed comparison ofthe performance of polycapillary lenses offered bythree commercial manufacturers for use in micro-XRF spectrometers was performed by Haschke andHaller. 25 Next to an examination of the primaryparameters of the lenses (spot size and gain), alsosecondary characteristics such as the variation ofthe spot size with working distance and energy,the halo-effect and the reproducibility with whichlenses can be produced, were considered.Worley et al. 26 have used a combination of twopolycapillary lenses, one between X-ray tube andsample and another between sample and detectorfor improving the detection power of a micro-XRFinstrument for analysis of radioactive samples.During XRF analysis of highly radioactive samplesusually problems are encountered since thespontaneous radiation from the radioactive materialscan affect the analysis in different ways. First,the energies of the radiation may overlap with thatof the characteristic lines of the elements of interest.Second, the high-intensity of the radiation fromthe radioactive materials can increase the backgroundand reduce the energy resolution of thedetection system, reducing the detection sensitivityof the system. In some cases, the radiation canbe so strong that the X-ray detector is saturated.The problem becomes more severe in the case ofmicro-XRF. Here the fluorescence signal is usuallysmaller in magnitude because it originates from asmall area while the spontaneous radiation backgroundremains unchanged.This low peak-to-background situation can beimproved in two ways: (1) a focusing X-rayoptic can be used to provide a higher primarybeam intensity in a small area so that the signalwill be enhanced while the background remainsunchanged; and (2) a spatial filter can be placedbetween the sample and the detector so the detectorwill only collect X-rays from a particular area.In this case, the net fluorescent signals will remainunchanged or become lower, but the backgroundwill be significantly reduced. Monolithic polycapillaryfocusing optics can be used for both purposes;Figure 3.3.13(a) shows the arrangement used ina proof-of-principle experiment involving an 55 Fesource in which the local Fe concentration wasdetermined; in Figure 3.3.13(b) spectra obtainedfrom this source with and without a polycapillarylens between the sample and detector arecompared. In the case where an optic is usedto preferentially guide the fluorescent X-rays tothe detector, the Mn Kα signal (mainly arisingfrom the radioactive decay of 55 Fe via the electroncapture mechanism) is significantly reduced.Similarly, Fiorini et al. 27 have used a polycapillaryconical collimator to manufacture a micro-XRFsystem that employs an unfocused beam and usesa conical polycapillary waveguide to restrict thearea on the sample surface to a small spot fromwhich fluorescent X-rays can reach the detector.Portable micro-XRFIn Figure 3.3.14, a scheme of a transportablemicro-XRF instrument suitable for in situ analysisof large paintings at a museum, etc. is shown.This figure details how polycapillary optics canbe coupled to a compact X-ray tube to createa small focal spot (ca. 100 µm diameter inthis case) on a large painting. This arrangement

ANALYTICAL APPLICATIONS OF POLYCAPILLARY OPTICS 101ComputerSi(Li) detectorMotion controllerX-ray sourceXYZ stagesOptic #2XYZ stagesXYZ stages(a)Optic #1SampleCounts (normalized)10000100010010With collection opticWithout collection opticMn KaFe Ka & Mn KbFe KbCu (scatter)(b)10 1 2 3 4 5 6 7 8 9 10Energy (keV)Figure 3.3.13 (a) Diagram of the experimental setup of the double-optic micro-XRF system. (b) Comparison of XRF spectra of55 Fe radioisotope sample, with and without the collecting optic between the sample and the detectoris sufficiently stable to allow transport of theentire instrument between the laboratory and themuseum without significant loss of lens alignmentoccurring. Other polycapillary-based instrumentswith a geometry and lay-out specifically optimizedfor in situ analyses have been described. 28 Theuse of the focusing optics has two advantages: onthe one hand a larger number of photons fromthe X-ray source is captured by the optic thanwould be done by a pinhole of ca. 1 mm 2 , therebyreducing spectrum acquisition times. On the otherhand, this higher photon flux is focussed into asmaller spot, permitting the selective irradiation ofsmall features. The use of the optic does preventthe use of tube voltage settings above 30 kVwhich is sometimes useful for demonstrating thepresence of high atomic number elements suchas Sn or Sb in pigmented materials by means oftheir K lines. Figure 3.3.15 illustrates how thisspectrometer is useful for making the distinctionbetween original vs restored painted areas of thesame color, when the pigments originally used aresignificantly different in composition from thoseused in later periods.

102 POLYCAPILLARY X-RAY OPTICSX-ray tubeMo anodeSi-PINdetector125 µm Mo filterPolycapillaryX-ray lens100−150 µmspotObjectFigure 3.3.14 A portable X-ray tube with Mo target is focusedto a spot size of 100–150 µm by means of a polycapillary lens.The X-ray fluorescence lines emitted by an object under studyare observed with a silicon PIN diode detectorSynchrotron micro-XRFPolycapillary optics (of the type shown inFigure 3.3.1b) are also used at bending magnetbeamline L of HASYLAB (Hamburg, Germany)for focusing of monochromatic synchrotronradiation. The experimental scheme of the beamlineis shown in Figure 3.3.16. Previously, atthis beamline, straight or elliptical monocapillarytubes were used to collimate/concentrate the polychromaticwhite radiation for trace-level micro-XRF experiments. 29 Monochromatic radiation wasnever used since the intensity of the resultingmicrobeam was insufficient to allow trace-levelmeasurements within reasonable spectrum collectiontimes. Using lenses manufactured at BeijingNormal University (BNU, Beijing, P.R. China)and X-ray Optical Systems (XOS, Albany, NY,US), beams of, respectively, 34–53 µm and10–40µm were produced in the energy range5–24 keV. The observed transmission of about40 % at 10 keV for the BNU lens comparedwell with a simulation where the assumed surfaceroughness of the glass is 5 Å. 30 Gain factorsin the range 100–400 (for the BNU lens) and1000–2500 (for the XOS lens) 31 were obtained.Above 17 keV, however, a significant ‘halo’ surroundsthe focal spot of focussed X-rays. Thehalo is due to two effects: at very high energy(>30 keV), X-ray photons can penetrate through10 6Intensity (arbitrary units)10 510 410 310 210 1 1PbTiCrPbFe Co Energy (keV)PbPbRestoredPbOriginal5 1015(a)(b)Figure 3.3.15 (a) Micro-XRF analysis of a baroque painting (attributed to P. Thys). The area marked ‘1’ shows Fe, Pb but noCo or Cu, suggesting the use of indigo (an organic pigment), the area marked ‘2’ contains Fe, Hg, Sr, Pb (vermillion), area ‘3’Ca, Mn, Zn, Pb (umber), and area ‘4’ contains Ca, Mn, Fe, Zn, Pb (umber). (b) Two XRF spectra from adjacent spots in the areamarked ‘1’ in (a). Positions where more recent paint (containing Ti, Cr and Co) was applied during past restoration activitiescan clearly be distinguished from positions with original seventeenth century paint

ANALYTICAL APPLICATIONS OF POLYCAPILLARY OPTICS 103DORIS-IIICross -slitsSi(III)monochromatorSR ∆E ∆ZCross -slitsPolycapillarySampleI o -chamberMicroscopeFluorescenceHPGedetectorFigure 3.3.16 Polycapillary optics from Beijing Normal University installed at Hasylab beamline L for fluorescence mode X-raynear edge structure (XANES) studies. The use of polycapillary optics makes it possible to obtain a small spot with a highly stableposition on the sample while the incident X-ray energy is scanned over the elemental absorption edges of interest. In this way aninexpensive Si(111) channel-cut monochromator could be used for micro-XANES instead of a costly fixed-exit monochromatorthe entire body of the X-ray lens; at lower energies,they are partially transported along the capillarytubes, but near the front tip of the lens theyare no longer are totally reflected and ‘escape’through the remaining glass material near the lenstip. Despite these unwanted phenomena, in thefocussed part of the beam, however, a significantincrease of flux density is observed, as gain factorsin the range 300–2500 were obtained. Thisincrease implies that monochromatic microbeamsof sufficient intensity can be produced for usein monochromatic micro-XRF and related experiments(see below). In Figure 3.3.17, the relativedetection limits obtained by means of a17.4 keV focussed X-ray microbeam from a NISTSRM1577a Bovine Liver standard sample areshown, indicating that for the transition elements,determinations down to the 10–100 ppb levelare possible.Electron Probe X-ray MicroanalysisVarious types of high-resolution energy-dispersiveX-ray spectrometer (EDS) are now being developedfor use in X-ray microanalysis. Newburyet al. 32,33 have described the use of cryogenicmicrocalorimeter X-ray detectors with an energyresolution of 3 eV at 1.5 keV and count rates of upto 500 cps. Since the active area of the detectorDetection limit (µg/g)10001001010.10.010.00110 20 30 40Atomic numberFigure 3.3.17 Relative detection limits (in µg/g) derived froma µ-XRF spectrum obtained by irradiation during 1000 s ofa 1 mm thick NIST SRM 1577a bovine liver sample using aprimary energy of 17.5 keVis relatively small (0.05 – 0.2 mm 2 ) polycapillaryoptics was used to increase the effective collectionsolid angle by a factor of 300. Thus, one of themost significant disadvantages of the small activearea detection system could be overcome, leadingto a microcalorimeter energy-dispersive detectorthat combines many of the favorable qualitiesof commercially available wavelength dispersivespectrometers (WDS) and semiconductor (EDS)detectors. Also a few applications are describedin these papers.A polycapillary optic can also be used asa spatial filter to eliminate background X-raysgenerated by the scattered electrons hitting the

104 POLYCAPILLARY X-RAY OPTICSsample outside the area of interest. Such electronspreading is commonly seen in ESEM or LV-SEMsystems where the pressure in the sample chamberneeds to be raised to up to a few Torrs toaccommodate non-conductive or wet samples,e.g. biological samples. Gao and Rohde 34 havedemonstrated that the contrast of X-ray images wassignificantly improved by coupling a polycapillaryfocusing optic between the sample and the EDSdetector in a LV-SEM.Wavelength Dispersion of X-raysAn alternative approach for wavelength-dispersiveX-ray fluorescence (WDXRF) analysis was proposedby Ebel et al. in 1983 35 where an analyzercrystal collected a divergent X-ray fluorescencebeam from a small area of the sample andthe lateral intensity profile of the diffracted beamwas detected by means of a position-sensitivewire detector. This approach was trying to combinethe high-energy resolution of the wavelengthdispersivespectrometer and the high detection efficiencyof the energy-dispersive spectrometer. Itsdisadvantage was the low count rate, which wasestimated to be an order of magnitude lower thanthat of an EDS. When a polycapillary lens is usedto focus the primary beam into small spot, so thatthe fluorescent X-rays originate from a quasi-pointsource on the sample surface, the dispersive systemwill function better than when the same number ofprimary X-rays irradiate the sample over a largearea. The principal arrangement of the experimentalsetup is shown in Figure 3.3.18(a). The anodefocal spot of the X-ray source was placed at theinput focus of the polycapillary optic. Irradiationof the sample with the focussed beam results influorescence X-rays that are diffracted by the crystalaccording to Bragg’s law. The diffracted X-rayswere detected by a position sensitive proportionalcounter (PSPC). The resulting signals were registeredand amplified by the electronic system andprocessed by a multichannel analyzer. After propercalibration, a position on the detector correspondsto a specific energy: via Bragg’s law, the angularrange θ 1 –θ 2 captured by the detector correspondsto an specific energy range E 1 –E 2 . The energyresolution of the PSXS system is determined bythe X-ray energy, the spacing of the crystal used inthe experiment, the spatial resolution of the PSPC,and the preamplifier noise. Effective energy resolutionsfrom several eV (for energy below 1 keV)to several tens of eV at ∼10 keV were obtained, asillustrated in Figure 3.3.18(b) where a 70 mm wideLiF(200) crystal (2d = 4.027 Å) was used under anangle of 43 ◦ . 24In electron microprobes equipped with wavelength-dispersivespectrometers, a polycapillarycollimating optic can be used to collect emittedX-rays from the sample and efficiently convertthem into a quasi-parallel beam that was thendiffracted by a flat crystal. In comparison withthe curved crystal geometry, which is commonlyused in most commercial instruments, the parallelbeam geometry provided by the polycapillary opticoffers a much simpler scanning mechanism, moreflexibility and a larger freedom of selection amonganalyzing crystals. Agnello et al. 21 also reportedthe combination of a polycapillary optic with areflect mirror to improve the collection efficiencyof a capillary-based WD spectrometer over a wideenergy range. Details of this work will be describedin the Detector section of this book.3.3.6.2 STRUCTURAL ANALYSISIn contract to X-ray fluorescence analysis whereprimary beams of either polychromatic andmonochromatic nature can be used and wherethe initial divergence of these beams is of nogreat concern, X-ray based methods that providestructural information such as X-ray diffraction(XRD) or X-ray absorption spectroscopy (XAS)place more restrictions on the properties ofthe primary X-ray beams. In XRD instruments,preferably a quasi-parallel beam is used toirradiate the materials under study, in order topreserve the angular resolution in the resulting2θ-patterns. Usually also a near-monochromaticbeam is used, either by using a so-called ‘Kβfilter’ (e.g., a Zr foil in combination with a Moanode X-ray tube) or a single-bounce graphite

ANALYTICAL APPLICATIONS OF POLYCAPILLARY OPTICS 105PSPCMultichannelanalyzerbased onPC computerElectronicsL2q iq cCrystalqI1 zShield(a)Cu anodeShieldX-ray lensSample(b)Counts200180160PSXS with X-ray lens30 kV 30 mA 350 s140120100TiKaFWHM=16.8eV806040TiKb2004.3 4.5 4.7Energy (keV)4.9 5.1Figure 3.3.18 (a) Principal arrangement of the position-sensitive X-ray spectrometer. (b) Spectral separation in a Tispectrum bymeans of the system in (a)monochromator. In XAS, highly monochromaticsynchrotron radiation (E/E ∼ 10 −4 ) is employedthat is usually obtained by employing a channelcutor double-crystal monochromator. In both typesof spectrometers, and especially in those seekingto employ X-ray beams with small cross-sections,polycapillary lenses can be employed to modifyeither the spatial or angular or both characteristicsof the primary X-ray beams.Micro-XANESThe experimental setup shown in Figure 3.3.16can also be used for performing micro X-raynear edge structure (XANES) experiments. DuringXANES experiments, the energy of the primary,monochromatic beam is changed in small (eV)increments in a range straddling the absorptionedge of an element of interest. During the energychange, the primary beam impinging on thecapillary optic gradually changes height as aresult of the rotation of the Si(111) reflectorinside the monochromator; in view of the largecollection area (of the order of 0.5–1 cm 2 ) ofthe polycapillary lens, no loss of alignment wasobserved during energy changes in the 5–25 keVrange while also the change in position of thefocused beam was kept to a minimum.The absorption profile can be recorded eitherdirectly (by measuring the intensities that impingeon and are transmitted by the sample at each

106 POLYCAPILLARY X-RAY OPTICSenergy) or indirectly by recording the variation ofthe fluorescent intensity with energy, as illustratedin Figure 3.3.19. The shape and shift of the absorptionprofile contains information on the valenceof the atomic species in question. In fluorescentmode, the valence information can be derivedfrom trace elements down to the 50 ppm level.In Figure 3.3.19(b) an XRF spectrum of a 70 µmdiameter fly-ash sample is shown containing ca.40 ppm of Se; Figure 3.3.19(a) compares theK-edge XANES profile derived from this particle 23to that of Sereference compounds. Most of the Sein the fly-ash particle appears to be present in the+IV (selenite) form. Other studies using this facilityinvolve the determination of the ferric iron contentin Ultra-High-Pressure eclogitic minerals, 36the measurement of the oxidation state of U inindividual particles of depleted uranium recoveredfrom Kosovo soil 37 and the study of the Fe 2+ /Fe 3+redox-equilibrium in ferro-gallic inks employed forwriting documents in previous centuries. 38XAFS (X-ray absorption fine structure) measurementsmostly are performed at synchrotronradiation facilities, in view of the fact that primaryX-ray beams of a high degree of monochromaticityare required. Nevertheless, in a limited numberof cases, also instruments based on laboratorysources are employed for this purpose. For inlaboratoryEXAFS apparatus, usually linear spectrometerswith bent crystals are used: here themonochromator crystals have to be aligned veryaccurately along a Rowland circle, so that thegoniometer movement becomes very complicated.The mechanism of the monochromator can be verymuch simplified when parallel X-rays are used.Taguchi et al. 39 have used polycapillary optics toobtain a quasi-parallel X-ray beam from a conventionalX-ray source and measure EXAFS spectraby a simple system utilizing an ordinary powderdiffractometer.X-ray Diffraction and Related Types ofInvestigationsAn overview of the use of polycapillary opticsin X-ray diffraction is provided by Schieldset al. 40 Gubarev et al. 41 have described the designand performance of a high flux X-ray systemfor macromolecular crystallography that combinesa microfocus X-ray generator having a 40 mmFWHM spot size at a power level of 46.5 W and acollimating polycapillary optic (see Figure 3.3.1c).The Cu Kα X-ray flux produced by this optimizedRelative intensity (a.u.)4Particle3H 2 SeO 32CdSe1Na 2 SeO 4012.65 12.70 12.75 12.80 12.85Energy (keV)(a)(b)Intensity (counts)10 610 510 4Ar10 310 210 110 0CaKTiV CrMnFeFeNi0 5 10 15CuZnEnergy (keV)GaAsSeScatterpeaksFigure 3.3.19 (a) Measured XANES spectra corresponding to various Se standard compounds and the XANES spectrum fromthe unknown fly ash particle of 70 µm. The concentration of Se in the particle is approximately 40 ppm. (b) The quantitativedata for Se were derived from a series of XRF spectra similar to the one shown here

ANALYTICAL APPLICATIONS OF POLYCAPILLARY OPTICS 107system through a 500 µm diameter orifice was7.0 times greater than the X-ray flux previouslyreported by Gubarev. 42 The X-ray flux from themicrofocus system was also 2.6 times higherthan that produced by a rotating anode generatorequipped with a graded multilayer monochromatorand 40 % less than that produced by arotating anode generator with the newest design ofgraded multilayer. Both rotating anode generatorsoperated at a power level of 5000 W, dissipatingmore than 100 times the power of the microfocusX-ray system. Diffraction data collected fromsmall test crystals are of high quality. By usingthe setup shown in Figure 3.3.20, the lyzozymecrystal diffraction patterns shown in Figure 3.3.21could be obtained. 42 540 reflections collectedat ambient temperature yielded a R-sym value of5.0 % for data extending to 1.70 Å, and 4.8 % forthe complete set of data to 1.85 Å. Amplitudesof the observed reflections were used to calculatedifference electron density maps that revealedpositions of structurally important ions and waterImageplate12 µmNi filterCrystalSourceωOpticMetal tube withtwo aperturesHeBeamstopFigure 3.3.20 A microfocus source of X-rays from Oxford Instruments, Inc. is collimated by a polycapillary semilens followedby a metal tube with two apertures. A protein single crystal is then placed between the collimator and the image plate detectorfor oscillation photography of the diffraction pattern(a)(b)Figure 3.3.21 Lysozyme diffraction images taken with source-collimating optic combination (a) and with source-slightly focusingoptic combination (b) with Cu Kα radiation. Note: the collimating lens characteristics and collimator dimensions are slightlydifferent for these two images

108 POLYCAPILLARY X-RAY OPTICSmolecules in the crystal of lysozyme using thephases calculated from the protein model. 43Other applications of collimating polycapillaryoptics are wafer size strain measurements 44 andX-ray lithography. 10,45 These greatly benefit fromthe increased intensity on the sample. Because ofthe higher flux, polycapillary collimating lensesallow monochromatic medical imaging to bedeveloped for potential clinical applications. 46Medical imaging applications will also potentiallybenefit from large area angular filters, which canbe used to reject Compton scattered radiationoriginating in the patient, and thus increase thecontrast of the resultant image. 47 Progress is beingmade in developing multi-optic large area devices.Angular filters can also be used to image diffusesources, as high resolution gamma cameras innuclear medicine. 483.3.7 FUTURE OF THETECHNOLOGYIt is expected that the requirements for X-raybeam with higher intensity, smaller spot, lowerdivergence and better uniformity will push theoptic manufacturing technology towards the followingdirections:• Use of polycapillary bundles with large outerdiameter (10–20 mm) and small channel diameter(1–5 µm). A polycapillary optic with largeouter diameter and small channel size will havea large collecting solid angle and high transmissionefficiency, and thereby provide higherbeam intensity. The increase of the outer diameterwhile keeping the channel size small impliesa significant increase of the total number ofchannels. For example, a polycapillary bundlewith 4 mm diameter and 10 µm channeldiameter will have approximately 100 000 channels.This number will go up to approximately2 600 000 for a polycapillary bundle with 10 mmdiameter and 5 µm channel diameter. This isa considerable challenge for the polycapillarybundle manufacturing technology when a largeopen area and a smooth inner surface need tobe maintained.• Optics with varying channel size or open area.The fact that the transmission efficiency of thecenter channels of a polycapillary optic is higherthan that of the outer channels causes the profileof the output beam to become non-uniformacross the optic. This non-uniformity, which isalso energy dependent, is unacceptable in X-ray lithography and some XRD applications. Byusing a varying channel size or open area itwill become possible to adjust the output X-ray distribution For the design of such type ofoptics, simulation tools will again play a criticalrole. The approach will also allow one to choosethe desired energy distribution of the outputbeam, which is of great importance in manyapplications.• Use of improved materials and manufacturingprocesses to reduce the halo effect. The‘halo effect’ has become a major obstacle fora polycapillary focusing optic to achieve small(i.e.

REFERENCES 109working space between the optic and the sampleis needed to place other components such as adetector and a video camera. With the rapid andcontinuous development on the polycapillarybundle and optic manufacturing technology, webelieve that achieving a 5–10 µm focal spot sizeis viable in the near future.• Focusing optics producing consistent spot sizeat different energies. The fact that the focalspot size of the focusing optic is dependentupon the X-ray energy can cause noticeableerrors in quantitative XRF analysis requiringhigh precision. Preliminary simulation resultsshow that polycapillary optics having a constantspot size can be realized in the energy range1–25 keV. The optic profile, channel size andthe X-ray source size all play an important rolein obtaining such property. The manufacturingrequirement is also very challenging.Polycapillary X-ray optics has been widelyaccepted in the X-ray analysis community andhave been successfully used in commercialinstruments. The development of optics and theperformance enhancement will further extendthe application area and the capability of theexisting instruments. The large collecting solidangle and high efficiency of polycapillary opticsalso allows a system to achieve the samelevel of performance as conventional systemsbut with a much less powerful X-ray source.The significantly reduced power requirementmakes it possible to build a compact and highperformancesystem that does not need intensivemaintenance. Such systems have great potentialsfor in-line monitoring and in situ analysis in awide range of areas of science and technology.REFERENCES1. Yan, Y. and Ding, X. Nucl. Instrum. Meth., An investigationof X-ray fluorescence analysis with an X-ray focusingsystem. B82, 121–124 (1993).2. Gao, N., Ponomarev, I., Xiao, Q. F., Gibson, W. M. andCarpenter, D. A. Monolithic polycapillary focusing opticsand their applications in microbeam X-ray fluorescence.Appl. Phys. Lett., 69, 1529–1531 (1996).3. MacDonald, C. A. Applications and measurements ofpolycapillary X-ray optics. J. Sci. Technol., 6, 32–47(1996).4. Arkadiev, V. A., Beloglazov, V. I., Bjeoumikhov, A. A.,Gorny, H. E., Langhoff, N. and Wedell, R. Poverkhnost.,1, 48–54 (2000).5. Arkadiev, V. A., Kolomitsev, A. I., Kumakhov, M. A.,Ponomarev, I. Y., Khodeev, I. A., Chertov, Y. P. andShakparonov, I. M. Wide-band X-ray optics with a largeangular aperture. Sov. Phys. Usp., 32, 271 (1989).6. Ullrich, J. B., Kovantsev, V. and MacDonald, C. A. Measurementsof polycapillary X-ray optics. J. Appl. Phys., 74,5933–5939 (1993).7. Xiao, Q. F., Ponomarev, I., Kolomitsev, A. I. and Kimball,J. C. Numerical simulation for capillary-based X-rayoptics. SPIE Proc., 1736, 227–238 (1992).8. Kumakhov, M. A., Nucl. Instrum. Meth., B48, 283 (1990).9. Kardiawarman, York, B. R., Qian, C., Xiao, Q. F., Gibson,W. M. and MacDonald, C. A. X-Ray and ultravioletsensors and applications. SPIE Proc., 2519, 197–201(1995).10. Klotzko, I., Xiao, Q. F., Gibson, D. M., Downing, R. G.,Gibson, W. M., Karnaukhov, A. and Jezewsky, C. J.Investigation of glass polycapillary collimator for use inproximity based X-ray lithography. SPIE Proc., 2523,175–182 (1995).11. Gao, N. and Ponomarev, I. Y., Polycapillary X-ray optics:manufacturing status, characterization and the future of thetechnology. X-ray Spectrom., 32, 186–194 (2003).12. Vincze, L., Janssens, K., Adams, F., Rindby, A. and Engström,P., Rev. Sci. Instrum., 69, 3494–3503 (1998).13. Balaic, D. X. and Nugent, K. A., Appl. Opt., 34, 7263(1995).14. Jenkins, R., Gould, R. W. and Gedcke, D., Quantitative X-ray Spectrometry, 199–201, Marcel Dekker, New York,1995.15. Xiao, Q. F., Chen, H., Sharov, V. A., Mildner, D. F. R.,Downing, R. G., Gao, N. and Gibson, D. M., Rev. Sci.Instrum., 65, 3399–3402 (1994).16. Haller, M., Gao, N., Fraser, G., Loxley, N., Taylor, M.and Wall, J., Enhancement of X-ray analysis by closecoupling of polycapillary optics with X-ray microsource.Poster presentation at 48th Annual Denver X-ray Conference(2000).17. Hohne, J., Buhler, M., von Hentig, R., Hertrich, T.,Hess, U., Phelan, K., Wernicke, D., Redfern, D. andNicolosi, J. Design features of a high resolutionmicrocalorimeter EDX system. Mikrochim. Acta, 138,259–264 (2002).18. Newbury, D. E., Wollman, D. A., Hilton, G. C., Irwin,K.D.,Bergren,N.F.,Rudman,D.A.andMartinis,J.M.The approaching revolution in X-ray microanalysis:the microcalorimeter energy dispersive spectrometer. J.Radioanal. Nucl. Chem., 244, 627–635 (2000).19. Frunzio, L., Li, L. and Prober, D. E. Detection of singleX-ray photons by an annular superconducting tunneljunction. Appl. Phys. Lett., 79, 2103–2105 (2001).20. Gao, N. and Rohde, D. Using a polycapillary optic asa spatial filter to improve micro X-ray analysis in

110 POLYCAPILLARY X-RAY OPTICSlow-vacuum and environmental SEM systems. Microsc.Microanal. Proc., 7(Suppl. 2), 700–701 (2001).21. Agnello, R., Howard, J. McCarthy, J. and O’Hara, D. Theuse of collimating X-ray optics for wavelength dispersivespectrometry. Microsc. Microanal. Proc., 3(Suppl. 2),889–890 (1997).22. Worley, C. G., Colletti, L. P. and Havrilla, G. J. Optimizingthe focal spot size and elemental sensitivity of a monolithicpolycapillary optic. Paper F-29 presented at the 1998Denver X-ray Conference (1999).23. Bichlmeier, S. Janssens, K., Heckel, J., Gibson, D., Hoffmann,P. and Ortner, H. M. Component selection for acompact micro-XRF spectrometer. X-ray Spectrom., 30,8–14 (2001).24. Bichlmeier, S., Janssens, K., Heckel, J., Hoffmann, P. andOrtner, H. M. Comparative material characterization ofhistorical and industrial samples by using a compact micro-XRF spectrometer. X-ray Spectrom., 31, 87–91 (2002).25. Haschke, M. and Haller, M. Examination of polycapillarylenses for their use in micro-XRF spectrometers. X-raySpectrom., 32, 239–247 (2003).26. Worley, C. G., Collett, L. P. and Havrilla, S. Quantitativeanalysis of radioactive materials by X-ray fluorescence.Abstracts of Papers of the American Chemical Society, 223,042-NUCL, Part 2, 7 April 2002.27. Fiorini, C., Longoni, A. and Bjeoumikhov, A. A newdetection system with polycapillary conic collimator forhigh-localized analysis of X-ray fluorescence emission.IEEE Trans. Nucl. Sci., 48, 268–271 (2001).28. Bronk, H., Rohrs, S., Bjeoumikhov, A., Langhoff, N.,Schmalz, J., Wedell, R., Gorny, H. E., Herold, A. andWaldschlager, U. ArtTAX – a new mobile spectrometerfor energy-dispersive micro X-ray fluorescence spectrometryon art and archaeological objects. Fres.J.Anal.Chem.,371, 307–316 (2001).29. Janssens, K., Vincze, L., Vekemans, B., Williams, C. T.,Radtke, M., Haller, M. and Knöchel, A. The nondestructivedetermination of REE in fossilized boneusing synchrotron radiation induced K-line X-raymicrofluorescence analysis. Fres. J. Anal. Chem., 363,413–420 (1998).30. Vincze, L., Wei, F., Proost, K., Vekemans, B., Janssens, K.,He, Y., Yan, Y. and Falkenberg, G. Suitability of polycapillaryoptics for focusing of monochromatic synchrotronradiation as used in trace level micro-XANES measurements.J. Anal. At. Spectrom., 17, 177–182 (2002).31. Proost, K., Vincze, L., Janssens, K., Gao, N. and Falkenberg,G. Characterization of a polycapillary lens for use inmicro-XANES experiments. X-ray Spectrom., 32, 215–222(2003).32. Newbury, D., Wollman, D., Nam et al., Energy-dispersiveX-ray spectrometry by microcalorimetry for the SEM.Microchim. Acta, 138, 265–274 (2002).33. Wollman, D. A., Irwin, K. D., Hilton, G. C., Dulcie, L. L.,Newbury, D. E. and Martinis, J. M. J. Microsc., 188,196–223 (1997).34. Gao, N. and Rohde, D. Using a polycapillary optic asa spatial filter to improve micro X-ray analysis inlow-vacuum and environmental SEM systems. Microsc.Microanal. Proc., 7(Suppl. 2), 700–701 (2001).35. Ebel, H., Mantler, M., Gurker, N. and Wernisch, J. X-RaySpectrom., An X-ray spectrometer with a position sensitivewave detector (PSD). 12, 47 (1983).36. Schmid, R., Wilke, M., Ober, R., Dong, S., Janssens, K.,Falkenberg, G., Franz, L. and Gaab, A. Micro-XANESdetermination of ferric iron and its application in thermobarometry.Lithos, 70, 381–392 (2003).37. Salbu, B., Janssens, K., Lind, O. C., Proost, K. andDanesi, P. R. Oxidation states of uranium in DU particlesfrom Kosovo. J. Environ. Radioact., 64, 167–173 (2003).38. Janssens, K. H., Proost, K., De Raedt, I., Bulska, E., Wagner,B. and Schreiner, M. The use of focussed X-ray beamsfor non-destructive characterization of historical materials.In Proceedings of the NATO Advanced Institute on MolecularArchaeology, NATO Science Series, Vol. 117, Kluwer,Dordrecht, 2003, pp. 193–200.39. Taguchi, T., Xiao, Q. F. and Harada, J. A new approachfor in-laboratory XAFS equipment. J. Synchr. Rad., 6,170–171 (1999).40. Schields, P. J., Gibson, D. M., Gibson, W. M., Gao, N.,Huang, H. P. and Ponomarev, I. Y. Overview of polycapillaryX-ray optics. Powder Diffraction, 17, 70–80 (2002).41. Gubarev, M., Ciszak, E., Ponomarev, I., Gibson, W. andJoy, M. A compact x-ray system for macromolecularcrystallography. Rev. Sci. Instrum., 71, 3900–3904 (2000).42. Gubarev, M. J. Appl. Crystallogr., First result from amacromolecular crystallography system with a polycapillarycollimating optic and a microfocus X-ray generator,33, 882 (2000).43. Huang, H., Hofmann, F. A., MacDonald, C. A., Gibson,W. M., Carter, D. C., Ho, J. X., Ruble, J. R. andPonomarev, I. Proc. SPIE., 4144, 100–109 (2000).44. Hofmann, F. A., Gibson, W. M., Lee, S. M. and MacDonald,C. A. Polycapillary X-ray optics for thin film strainand texture analysis. In Thin Film Stresses and MechanicalProperties VII, R.C.Cammarata, M.A.Nastasi,E. P. Busso, W. C. Oliver, eds, Materials Research SocietyProceedings, vol. 505, pp. 3–14, 1998.45. Turcu, I. C. E., Forber, R., Grygier, R., Rieger, H., Powers,M., Campeau, S., French, G., Foster, R., Mitchell, P.,Gaeta, C., Cheng, Z., Burdett, J., Gibson, D., Lane, S.,Barbee, T., Mrowka, S. and Maldonado, J. R. High powerX-ray point source for next generation lithography. SPIEProc., 3767, 21–32 (1999).46. Sugiro, F. R. and MacDonald, C. A. Monochromatic imagingwith a conventional source using polycapillary X-rayoptics. SPIE Proc., 4320, 427–435 (2001).47. Abreu, C. C. and MacDonald, C. A. Beam collimation,focusing, filtering and imaging with polycapillary X-rayand neutron optics. Phys. Med., XIII, 79–89 (1997).48. MacDonald, C. A., Gibson, W. M. and Peppler, W. W.X-Ray optics for better diagnostic imaging: In Technologyin Cancer Research and Treatment, 1, 111–123 (2002).

3.4 Parabolic Compound Refractive X-ray LensesA. SIMIONOVICIESRF, Grenoble, FranceC. SCHROER, and B. LENGELERAachen University, Aachen, Germany3.4.1 INTRODUCTIONIn his early experiments, W. C. Röntgen could notfind any noticeable refraction of X-rays by variousmaterials nor was he able to focus X-rayswith a rubber lens. He concluded that is wasnot possible to concentrate X-rays by refraction. 1Today, it is well known that refraction of hardX-rays in matter – although not zero – is weakerthan that of visible light by several orders ofmagnitude. While this is a great advantage forradiography, where an X-ray image can be interpretedas a straight projection through a nonrefractingbody, it led to the belief that refractivelenses for hard X-rays could not be made. 2Therefore, a great variety of X-ray optical elementsrelying on other physical effects were developed,such as mirrors 3–5 and capillaries 6,7 basedon external total reflection, multilayer mirrors, 8,9Fresnel zone plates, 10 Bragg–Fresnel optics, 11,12and bent crystal optics 13–15 based on diffraction.While all these X-ray optical elements can beused to produce a focused X-ray beam, onlysome of them have been shown to work as imagingdevices.While refractive optics are most common forvisible light, the interplay between weak refractionand strong absorption is what makes the designof refractive lenses for hard X-rays difficult. In1996 it was first demonstrated that refractive lensescould be fabricated despite these difficulties. 16They were made by drilling a linear array of smallholes into a lens material, such as aluminium orberyllium, focusing the X-rays in one direction.By crossing two such lenses or by crossingconsecutive holes in one lens, focusing in twodirections is possible. 16–18 The spherical aberrationintroduced by their shape prohibits their use ashigh quality imaging optics. Today, they arecommonly used for beam conditioning at variousbeamlines at the European Synchrotron RadiationFacility (ESRF) in Grenoble, France.Since then, several refractive lens designshave been developed by different groups. 16–26In this subchapter we will focus on parabolicrefractive X-ray lenses that have been designed anddeveloped at Aachen University in collaborationwith the ESRF in Grenoble. 19,20 They are highqualityimaging optics for hard X-rays, withapplications in imaging and microanalysis andare routinely used at beamline ID22, ID18F andseveral other beamlines of the ESRF. They areused in a new hard X-ray microscope 19 that allowssub-micrometer resolution. More transparent lensmaterials, such as beryllium, boron, or carbon,are expected to push the resolution limit wellbelow 100 nm.To obtain an intense hard X-ray microprobe, asynchrotron radiation source can be imaged ontoX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

112 PARABOLIC COMPOUND REFRACTIVE X-RAY LENSESthe sample by a refractive lens in the stronglydemagnifying setup. This allows performing hardX-ray analytical techniques, such as fluorescencespectroscopy, diffraction, small angle scattering,and absorption spectroscopy, with lateral resolutionsin the micrometer and sub-micrometerrange. 27 A combination of fluorescence spectroscopyand tomography allows the determinationof the spatial distribution of elements inside asample. 28–35m/r (cm 2 /g)1010.11Li BeB C Al Ni10 100 1000Energy (keV)3.4.2 PHYSICS OF REFRACTIVEX-RAY LENSES3.4.2.1 REFRACTION ANDABSORPTION IN MATTERThe refractive index for hard X-rays in matter istypically expressed in the form n = 1 − δ + iβ,where δ is the refractive index decrement thatdescribes the refraction. For a given atomic speciesit isδ = N A2π r 0λ 2 ρ Z + f ′ (E)(3.4.1)Awhere N A is Avogadro’s constant, r 0 is theclassical electron radius, λ and E the wavelengthand energy of the X-rays, respectively, ρ is themass density, Z + f ′ (E) the real part of the atomicform factor in forward direction, and A is theatomic mass. Away from absorption edges, f ′ (E)is small and δ is proportional to E −2 and ρ. SinceZ/A is almost constant for all elements, δ/ρ variesvery little as a function of the atomic species awayfrom absorption edges.Absorption inside the material is described by βthat is related to the linear attenuation coefficientµ byβ = µλ(3.4.2)4πβ includes photoabsorption as well as the attenuationof the incident beam by inelastic (Compton)scattering. The dependence of µ/ρ as a functionof the X-ray energy is shown in Figure 3.4.1.While at low energies, photoabsorption dominatesFigure 3.4.1 Mass absorption coefficient µ/ρ for Li, Be, B,C, Al, and Ni. Compton scattering dominates the attenuationbelow 0.2 cm 2 /g. (Reproduced from ref. 19)µ/ρ, Compton scattering becomes the most importantcontribution to µ/ρ at higher energies (below0.2 cm 2 /g).3.4.2.2 LENS DESIGNSince the refractive index for any lens material issmaller than one (n

PHYSICS OF REFRACTIVE X-RAY LENSES 113dOptical axis 2R 0ROptical axis(a)(b)Figure 3.4.2 Design of the parabolic refractive X-ray lenses. A large number of single lenses (a) are stacked behind each otherto form a refractive lens (b). (Reproduced from ref. 32)requiring a careful choice of the lens material.As µ/ρ increases strongly with increasing atomicnumber Z (µ/ρ ∝ Z 3 for X-ray energies awayfrom absorption edges), atomic species with lowZ are good lens materials, such as Li, Be, B, C,and compounds thereof. Other important materialproperties are stability in the X-ray beam, lowsmall angle scattering, and the machinability. 18,19Although the attenuation inside aluminium issignificantly higher than that for the other lensmaterials, it is particularly easy to machineand has therefore been very useful for thedevelopment of the lenses. As manufacturingtechniques for more transparent lens materials,such as beryllium, have become available, theimportance of aluminium as a lens materialwill decrease. However, all experimental resultsin this subchapter have been obtained withaluminium lenses. The energy range of operationfor aluminium lenses lies between about 10 keVand 120 keV. For more transparent lens materials,such as beryllium, the energy range has beenextended toward lower energies down to about5 keV. Beryllium parabolic refractive lenses ofhigh quality have been fabricated recently. 36As the radius of curvature R has to be as smallas possible to limit the number of single lenses, thespherical lens approximation that is successfullyapplied in classical optics does not apply to mostX-ray lens designs. It requires the aperture R 0 ofthe lens to be much smaller than the radius ofcurvature R. For most lens designs this wouldrequire the lens aperture to be prohibitively small.Unless the radius of curvature is made excessivelylarge requiring a large number of single lenses,spherical aberration is very pronounced in the X-ray regime (see ref. 20 for experimental resultson effects of spherical aberration). By choosinga parabolic lens shape, spherical aberration canbe avoided. In the design described here, thelens surfaces are two rotational paraboloids asshown in Figure 3.4.2(a). The surface may bedescribed byy = r2(3.4.3)2Rwhere r is the radial coordinate (r

114 PARABOLIC COMPOUND REFRACTIVE X-RAY LENSESet al. 20 Here, we review the most important properties,such as the focal length f , the transmissionT p , and the effective aperture D eff .Using the lens maker formula, the focal distanceof a single lens is f s = R/2δ. Assuming the stackof lenses to be thin compared to the focal distance(thin lens approximation), the focal length f 0 isgiven byf 0 =R(3.4.4)2Nδwhere N is the number of single lenses in thestack. The thin lens approximation no longer holdsfor lenses whose focal distance is short comparedto their overall thickness. In that case, the focaldistance is given by 271f = f 01 − 1 (3.4.5)l6 f 0where l is the overall length of the lens. Thetwo principal planes of the thick lens are slightlyshifted at its centre.Since the attenuation in a refractive lens isalways significant, the transmission T p , i.e. thefraction of the photons (homogeneously) incidenton the geometric aperture that is transmittedthrough the lens, is an important quantity, limitingthe flux behind the lens. It is given byT p = exp(−µNd) 12a p[1 − exp(−2a p )],a p = µNR2 02R + Nδ2 k 2 1 σ 2 R 2 0R 2 (3.4.6)where k 1 is the wave number of the incidentradiation, and σ the root mean square (rms)roughness of the lens surfaces. 20 The first term ina p describes the attenuation inside the lens. Thesecond term accounts for the surface roughnessof the lenses. The aluminium lenses consideredhere have a roughness σ below 100 nm, 20,37 Thesecond term in a p is negligible compared to thefirst one for aluminium lenses, and we can neglectthe roughness in the following.As the attenuation increases towards the outerparts of the lens, the effective aperture D effdescribing the diffraction at the lens is smaller thanthe geometric aperture R 0 .Itisgivenby 20√1D eff = 2R 0 [1 − exp(−a p )] (3.4.7)a pA sufficiently large geometric aperture R 0 loses itsinfluence on D eff . In that case, D eff is governedonly by attenuation inside the lens material:D eff = 2√2RµN(3.4.8)For a fixed focal distance f 0 , the effective aperture√ √D eff = 2 4 δ ( ) µ −1µ f 0 = 2 C f 0ρC = 4 N a2π r 0λ 2 Z (3.4.9)Adepends on the lens material only through µ/ρ(C is approximately independent of the lens material).This emphasizes the fact that the major figureof merit for the lens material is µ/ρ shown inFigure 3.4.1.3.4.2.4 IMAGING USING PARABOLICREFRACTIVE X-RAY LENSESA parabolic refractive X-ray lens can be usedin analogy to a glass lens for visible light andhas a wide range of applications. Two importantapplications are the microbeam production for X-ray microanalysis and the magnified imaging of asample in a new hard X-ray microscope. For bothapplications, the aberration-free image transferis crucial for the success of the method. Theimage quality strongly influences the microbeamcharacteristics, such as the lateral beam size,the depth of focus, the gain of the flux in themicrobeam, and the absence of a low intensitybackground. For microscopy, the magnification,lateral resolution, the absence of distortion, anddepth of field all depend on the quality ofthe optics.As in classical optics, the parabolic refractiveX-ray lenses can be used to image an object

PHYSICS OF REFRACTIVE X-RAY LENSES 115that is located a distance L 1 before the lens intoan image plane at a distance L 2 = L 1 f/(L 1 − f )behind the lens. The image is magnified by afactor m = L 2 /L 1 = f/(L 1 − f ). The parabolicshape is crucial to obtaining a high quality image.Magnified imaging using refractive lenses canimprove the resolution in hard X-ray microscopyto well below the sub-micrometer level. So far,using aluminium lenses, a resolution of 350 nmhas been demonstrated. 19 Using more transparentlens materials, such as beryllium, the effectiveaperture can be significantly increased. This hasincreased the resolution to well below 100 nm,and a resolution of 50 nm is expected in thenear future. Taking advantage of the large penetrationdepth of hard X-rays, magnified imaging canbe combined with tomographic techniques. 38–42This allows the non-destructive reconstruction ofthe three-dimensional structure of a sample withhighest resolution. The possibility to demagnifyan X-ray lithography mask may allow the transferof finer lateral structures into thick resists,e.g. for MEMS (Microelectromechanical Systems)applications. 413.4.2.5 MICROBEAM PRODUCTIONTo obtain a small intense microbeam for microanalysis,the X-ray source is imaged onto the sampleposition in a strongly demagnifying geometry.This requires the distance L 1 from the source tobe large compared to the focal distance f .Themicrobeam is then formed at a distance L 2 =L 1 f/(L 1 − f) slightly larger than f behind thelens. The lateral beam size is determined by thesource size, the geometric demagnification m of thesource and diffraction effects at the aperture of thelens. To obtain an intense and small microbeam,the source should be as small as possible, emittinga high intensity into the solid angle that isspanned by the effective aperture of the lens atthe distance L 1 . This requires highly brilliant X-ray sources, such as undulator sources at thirdgeneration storage rings. For a source with a Gaussianintensity profile, such as an ESRF undulatorsource, the lateral beam size (full width at halfmaximum(FWHM)) is 20B v,h = 2 √ √σv,h2 2ln2L 2L 2 + a12k1 2R2a = µNR + 2Nk 2 1 δ2 σ 2 (3.4.10)where σ v,h are the rms electron beam source sizein vertical and horizontal direction, respectively.Note that σ in a is the rms roughness of thelens surfaces. For an ESRF U42 high β undulatorsource, the source is well described by σ v =13 µm and σ h = 300 µm. The first term underthe square root in Equation (3.4.10) describes thegeometric demagnification of the source whilethe second term is the broadening of the beamdue to diffraction at the lens aperture and theroughness of the lens surfaces. At distances of40 m to 60 m from an ESRF undulator sourceand with a focal distance in the metre range,beam sizes of several micrometres horizontallyand several hundred nanometres vertically areachieved. While diffraction at the lens aperturebecomes relevant for the vertical direction, it doesnot significantly contribute to the relatively largehorizontal beam size.As the focal distance f is typically three tofour orders of magnitude larger than the effectiveaperture D eff , the depth of focusd long = 4 min(B v,B h )/(2 √ 2ln2) · L 2D eff(3.4.11)is larger than the lateral beam size by the same factor.This allows scanning samples with a thicknessin the millimetre range with a beam of constant lateralextension (‘pencil beam’). This is particularlyimportant for scanning microtomography techniquessuch as fluorescence microtomography. 31–35For scattering experiments it is also important, thatthe wave vector k of the incident radiation is sufficientlywell defined, i.e. the beam divergencek/k ≈ D eff /L 2 is small enough. In most scatteringexperiments, a k/k in the range from 10 −3to 10 −4 is sufficient.The gain in intensity in the microbeam comparedto the intensity behind a pinhole of equal

116 PARABOLIC COMPOUND REFRACTIVE X-RAY LENSESGain10 510 410 310 210 1AlBeIntensity (a.u.)100806040FWHM = 0.480 µm10 020(a)10 −112 4 6 8 102 4 6 8 1002 4Energy (keV)(b)0−2−1 0 1 2Position (µm)Figure 3.4.3 (a) Gain of a microbeam setup using an aluminium and beryllium lens (f = 500 mm, L 1 = 60 m, rms source size13 × 300 µm 2 ). (b) Vertical profile through a microbeam measured by a fluorescence knife edge technique. An error function isfitted to the measured data (crosses). Its derivative gives the vertical profile of the microbeam. (Reproduced from ref. 26)size is 20 g p = T p4R 2 0B v B h, (3.4.12)It depends on the transmission T p and on thelateral beam size that is determined by the imaginggeometry. Figure 3.4.3(a) shows the gain as afunction of photon energy for aluminium andberyllium lenses in a fixed geometry.For illustration purposes, the properties ofa microbeam (energy 18.2 keV) produced byaluminium lenses (N = 220) at the ID22 high βundulator beamline of the ESRF are discussed. Fora source to lens distance L 1 = 41.7 m, the minimalmicrobeam size was found L 2 = 335 mm behindthe lens. From this, a focal distance of f = 333 mcan be extracted. Using the radius of curvature R =209 µm ± 5 µm measured by profilometry and thethin lens approximation, 4 a focal length of f 0 =291 mm ± 7 mm would be expected. However,the lens with 220 individual lenses has a length ofl = 220 mm that is comparable to f 0 . The thin lensapproximation does not hold in this situation andthe focal distance must be calculated according toEquation 3.4.5 that yields f = 332.6mm ± 7mmin excellent agreement with the measured value.Here, the thick lens character adds about 14 % tothe focal distance.The horizontal and vertical microbeam sizeswere measured, using a fluorescence knife-edgetechnique. As knife-edge a gold strip (thickness100 nm, width 5 mm, length several centimetres)deposited on a silicon wafer (thickness 550 µm)was used. The gold Lα radiation (E = 9.71 keV)was measured by an energy dispersive detector(Si(Li)) as the gold edge was scanned throughthe beam. Figure 3.4.3(b) shows the scan throughthe microbeam in the vertical direction. A verticalbeam width of 480 nm was measured. Includingdiffraction and roughness, a beam size of 450 nmis expected. The horizontal microbeam size isone order of magnitude larger due to the largersource size. It was measured to be 5.17 µm(FWHM) as compared to the theoretical valueof 5.7 µm (FWHM). The measured transmissionT p = 0.114 % yields an average lens thickness ofd = 5 µm on the optical axis. The measured gainis 367 as compared to the theoretical value of 340that is slightly smaller due to the discrepancy inthe horizontal beam size.The background of the microbeam contributesto the signal obtained in microprobe applications.In principle, a deconvolution with the point-spreadfunction is necessary to remove the contributionof the background. Although the intensity ofthe background radiation is generally small, itmay contribute significantly to the signal, sincethe area over which it is integrated is severalorders of magnitude larger than the lateral areaof the microbeam. The background is therefore animportant characteristic of the microbeam.

APPLICATIONS 117As the dimensions of the knife-edge are largecompared to the beam size, the knife-edge techniquemeasures the integral flux over the half-planecovered by the gold knife. This allows the integralflux outside the microbeam to be measuredand to compare it to that in the beam spot. 27The knife-edge scan shown in Figure 3.4.3(b) canbe evaluated in view of the background. Theintegral flux that falls outside a vertical interval[−2 µm, 2 µm] around the spot is about 3.4 %, theflux falling outside the interval [−1 µm, 1 µm] is4.6 % and that falling outside [−0.5 µm, 0.5 µm] is10.4 %. Therefore, the monochromatic microbeamproduced by the refractive lens has a low backgroundand is well suited for clean microprobeexperiments. No additional pinholes are needed infront of the sample, which is an exceptional advantageover focusing devices (such as the FZP lenses)which feature a zero order transmitted beam andthus require an OSA (Order Sorting Aperture).Using beryllium as the lens material, a gainin flux of one order of magnitude was obtainedin the microbeam. 36 Recently we developednanofocusing lenses (NFL) with focal lengths ofaround 10 mm at X-ray energies in the range of10–100 keV. 43 These lenses are particularly usefulfor creating small microbeams at a short distancefrom the source, e.g. at 25 keV, a lateral beam sizeof 330 nm by 110 mm (FWHM) was achieved at adistance of 42 m from the source at ID22.3.4.3 APPLICATIONSFollowing the presentation of the characteristicsof refractive lenses, we would like to present theresults obtained at the ID22 beamline of the ESRF.ID22 41 is a beamline dedicated to microspectroscopy,micro-imaging and microdiffraction inthe range 6–70 keV. Although the CRL applicationsspan all three probes employed at ID22, wewill present here only the microspectroscopy applications,obtained using X-ray fluorescence (XRF)spectroscopy. The microprobe setup of ID22 isused for performing fluorescence spectroscopy,which is the probe used in collecting data for threedifferent techniques: direct XRF mapping, X-rayfluorescence computed tomography (XFCMT) andX-ray absorption spectroscopy (XAS).3.4.3.1 EXPERIMENTAL SETUPThe ID22 beamline is optimized for performingmicro-X-ray fluorescence (µ-XRF) and XAS withmicron resolution at high energy. The basicconcept in the design of this beamline wasthe simplicity of the optics guaranteeing thehigh flux/brilliance necessary for achieving asensitive X-ray fluorescence microprobe setup,while conserving the high degree of coherencerequired for phase-sensitive imaging. The requiredoptical quality of the beam was achieved by usinghighly polished and optically flat materials in thebeam path.The beam from the high β U42 undulator passesthrough polished Be and diamond windows toimpinge onto a highly flat horizontally deflectingmirror with ≤1.5 µrad slope error and 1.5 Årmsmicro-roughness, thus suppressing higher energyharmonics and lowering the transmitted heat load.A double crystal fixed-exit monochromator is usedwith Si crystals in either the 111 or 113 orientations.The setup includes several normalizationdetectors (photodiodes, ionization chambers)and a few focusing devices such as Fresnelzone plates (FZP), CRL lenses or bent mirrorKirkpatrick–Baez assemblies. Hereafter, the CRLlenses are exclusively used for focusing the beam.The sample environment comprises a pinholeassembly serving to define the horizontal size ofthe beam. A high precision sample stage with sevendegrees of freedom is used for positioning the sampleand rotating the sample axis perpendicular tothe beam. A few solid state detectors (SSD) such asSi(Li), HpGe and Si drift diodes can be included inthe setup either individually horizontally/verticallyor in pairs, on either side of the sample in the horizontalplane. An X-ray intensified charge-coupleddevice (CCD) camera (≥1 µm resolution) is usedin transmission behind the sample for direct imagingand/or alignment purposes. A typical setup withthe drift diode positioned vertically and exclusivelyused for XFCMT is shown in Figure 3.4.4. Asthe U42 undulator is in a high ß section of the

118 PARABOLIC COMPOUND REFRACTIVE X-RAY LENSESFlat mirrorBeamFixed-exitmonochromatorCRLPINdiodeSi driftdiodeVideoscope2DslitsPINdiodeSamplestageCCDFigure 3.4.4 Experimental setup of the microprobe dedicatedto fluorescence spectroscopy on beamline ID22 at the ESRF.(Reproduced from ref. 32)storage ring lattice, the source size is 900 × 30 µm 2FWHM horizontal × vertical, which puts greatstress on the focusing optics. At 15 keV, for a 1 mfocal distance and 45 lenses, this yields beamspotsof roughly 18 × 0.75 µm 2 (H × V). However, storagering electron beam average motions convolutedwith the mechanical instabilities of the double crystalmonochromator and mirror and diffraction atthe lens combine into an effective spot size of18 × 1.3 µm 2 as measured by knife-edge fluorescenceof a thin Au-plated Si wafer.Depending on the energy and number of lenses,one can focus down to 0.5 µm in vertical sizeand use a 10 µm diameter pinhole to definethe horizontal size. Alternatively, closing down thehorizontal slits located at 13 m upstream from thelens to define a secondary source of 30 µm, one canfocus down to about 2.5 µm in horizontal size. Themonochromatic flux obtained in these conditionsvaries from 10 9 to 10 10 ph/s in the beamspot,depending on the energy in the range 14–25 keV.A very interesting capability of ID22 is thePINK beam mode of operation, whereby one usesthe full undulator beam, after a mirror reflectionwhich serves as a low pass filter, and transmissionthrough a selected attenuator foil, which servesas a high pass filter. This combination is directlyused, without monochromatization, as incidentbeam on the CRLs, yielding a medium resolution(E/E ≈ 10 −2 ) highly focused, high flux beamwith intensities as high as 10 12 photons/s. Recently,ID22 was extended by adding an in vacuum highflux, high energy U23 undulator, which covers theenergy range 7–100 keV.3.4.3.2 MICRO XRF: HIGH FLUX PINKBEAM SPECTROSCOPY OF SINGLECELLSIn this work, 45 we aimed to achieve SXRF microanalysisof single cells by imaging the intracellulardistribution of trace elements and pharmacologicaldoses of the anticancer drug, 4 ′ -iodo-4 ′ -deoxydoxorubicin (IDX). Spatial distribution andconcentration of trace elements in tissues areimportant, as they are involved in some pathologicalconditions and in many biological functionsof living organisms like metabolism and nutrition.Llabador and Moretto 46 have reviewed theimportance of microprobes in biology and emphasizedtheir future use in cell physiology, pharmacology,and toxicology. CRLs used in a ‘PINK’(polychromatic) excitation provide a fast acquisitionrate and sub-ppm limits of detection. Additionally,the CRLs are currently the only focusingdevices capable of sustaining the high flux,high heatload of a PINK beam without noticeabledamage.A human ovarian adenocarcinoma (IGROV1)cell line prepared using a previously publishedprotocol 47 was used for this study. The cells,grown directly on 0.2 µm Formvarfilmwereincubatedwith complete culture medium and exponentiallygrowing cells were exposed to 5 µM IDX.Cell monolayers were rinsed, then cryofixed intoliquid nitrogen chilled isopentane and freeze-driedat −30 ◦ C. Analyses were performed at 14 keVusing either PINK or monochromatic excitation.PINK excitation is produced by direct, high intensity,medium bandwidth beams from the undulatorimpinging onto a flat mirror. The multi-stripmirror spans several full undulator harmonics anddecreases the beam heatload by a horizontal deflectionat a grazing angle of 2.6 mrad which gives anenergy cutoff of 24 keV for the Pd strip. In orderto remove the contribution of lower energy harmonics,a 2 mm Al filter was used. In the PINKbeam, CRLs produce a flux of about 5 × 10 10photons/s/µm 2 and a beam spot of 10 µm horizontallyby 1 µm vertically for 50 Al lenses, focaldistance 713 mm. For the same spot size, CRLswith monochromatic excitation give a flux about

APPLICATIONS 11910 times less. The minimal detection limits (MDL)evaluated using a NIST standard reference material(SRM 1833) yielded about 50 ppb for elementssuch as Zn. Data analysis was performed using theWinAxil software 48 in order to correct for X-rayphoton background and fit elemental X-ray linesdetected in the sample.In the case of a cell monolayer, the thin sampleapproximation can be applied. Previous Rutherfordbackscattering spectrometry (RBS) analyses 49 havedetermined a mean surface mass for freeze-driedcells around 260 µg/cm 2 . With polychromaticPINK beam a close look at the undulator spectrumreveals a contribution of photons of higher energyharmonics at 16.9, 19.7, and 22.4 keV, which aregreatly reduced by the lens and 10 µm pinholeassembly installed before the sample. Taking intoconsideration only maxima of each contributingharmonic, the k ratio of the number of photonsrelative to the 14 keV harmonic is obtained fromthe undulator spectrum calculated using the ESRFSynchrotron Radiation Workshop (SRW) code. 50Then, the effective ratio through the pinhole iscalculated according to CRL formulas that give theintensity distribution in the plane of the sample.Only the 14 keV harmonic is effectively focusedinside the 10 µm pinhole; the other three higherenergy harmonics before the mirror cutoff at24 keV spread out over a large area and givea reduced contribution through the pinhole. ThePIN diode placed before the sample and used fornormalization, generates a total current I 0 for agiven flux of N 0 photons/s of energy E 0 as:I 0 ∝ N 0 (1 − e −µ 0d ) (3.4.13)with µ 0 the energy deposition coefficient for Si,and d the Si PIN-diode thickness. For a given PINdiode, the current will always be a function of theincident energy of the photons through µ(E), asdis constant. So the measured current is in fact:I = I 0 (1 + k 1 f 1 + k 2 f 2 + k 3 f 3 ) (3.4.14)with k ratios previously calculated and f i obtainedaccording to PIN-diode calculations using theenergy deposition coefficient for each contributingharmonics of energy E i . Since I measured inpA is known, the number of 14 keV photonsN 0 is estimated, then those of higher and lowerenergy harmonics. From these values and thoseof fluorescence cross-sections σ F (E i ,Z), correctedquantitative elemental maps were generated. Thefollowing equation was used for quantization,based on the thin sample approximation:N Z = N 0tC Z σ F exp(−µ air (E F )ρ air d)ε det 4π sin α∫ T( µs (E 0 ) µ× exp[−xρ S0sin α + s (E F ))]dxsin β(3.4.15)where N Z is the number of counts in the characteristicline of element Z, N 0 is the incidentphotons/s, t is the integration time, C Z is the concentrationof element Z, σ F is the fluorescencecross-section in cm 2 /g, µ is the mass absorptioncoefficients of air or sample for the respectiveenergies, ρ is the density (g/cm 3 ) ofairorsample,ε det the detector efficiency, the detectionsolid angle, α and β the incident and take-offangles, x the sample depth coordinate, integratedfrom 0 to T (sample thickness). Spectra takenfrom single-cells treated with 5 µM ofIDXareshown in Figure 3.4.5. The spectrum taken usingmonochromatic beam with 120 s acquisition time(Figure 3.4.5a) is still of poor quality while the onefrom PINK-beam (Figure 3.4.5b) 100 s countingtime shows well-defined X-ray peaks of intracellularelements P, S, Cl, Ca, K, Mn, Fe, Cu, Zn, andI from drug treatment.Potassium is the major element in cells andgives elemental maps with the highest countingstatistics. Compared to light microscopy cell visualization,potassium maps depict the cell boundariesroughly, particularly in the nuclear region.Iodine imaging of cells treated with 5 µM ofIDXcould be performed in this study and yielded intracellulardistributions of trace elements comparableto previous results obtained by micro-PIXE (protoninduced X-ray emission) for higher doses of IDXof about 20 µM. 51 Particularly, the co-localizationof iron and iodine within the cell nucleus is stillobserved. The results obtained on the iodine distribution,in comparison with potassium and ironare presented in Figure 3.4.6. This was also found

120 PARABOLIC COMPOUND REFRACTIVE X-RAY LENSES180016001400120010008006004002000(a)P SClArK + CaI-LMn FeCu ZnCounts1600014000120001000080006000400020000P S ClK + CaArFeMn2 4 6 8 10 2 4 6 8 10Energy (keV)(b)I-LCuZnFigure 3.4.5 Spectra obtained from a IGROV1 cell treated with 5 µM of iododeoxydoxorubicin and freeze-dried. (a) Spectrumobtained using a 14 keV monochromatic focused beam, acquisition time 120 s. (b) Spectrum obtained using a focused 14 keVpolychromatic PINK excitation, acquisition time 100 s. (Reproduced from ref. 45)0.250.200.150.100.0518160.25140.20 12100.1580.10640.0518161412108640.150.100.050.150.100.05(a)402051015(b)402051015(c)402051015Figure 3.4.6 Two-dimensional elemental distribution of a freeze-dried cancer cell treated with 5 µM of iododeoxydoxorubicin.Cell was mapped with a 14 keV polychromatic PINK excitation, stepsize 1 × 3 µm 2 (V × H) and 2.5 s acquisition time/step,scan size: 60 × 60 µm 2 , around 2 h total acquisition time. (a) Potassium distribution (Kα X-ray line), (b) iron (Kα X-ray line),(c) iodine (L β X-ray line). (Reproduced from ref. 45)using monochromatic excitation (data not shown),but more than 12 h of mapping were necessary.From quantitative analysis, the surface concentrationsdisplayed a maximum of 0.02 µg/cm 2for iron and 0.15 µg/cm 2 for iodine in thenuclear region. Using a mean value of freezedriedcells surface mass of 260 µg/cm 2 obtainedby RBS, maximum concentrations for cells treatedwith 5 µM IDX were 10340 ppm for potassium,274 ppm for zinc, 76 ppm for iron, and 580 ppmfor iodine. These results are in agreement withpreviously published data on IGROV1 cells traceelement content. 47,52 Values concerning detectorefficiency and the K/L partial photoionizationcross-sections, fluorescence yields and branchingratios are determined within 10 % accuracy. 53–55When estimating error propagation the main contributingsource of error on the calculated concentrationC will be given by the standard deviationon the cell thickness T . The use of appropriate

APPLICATIONS 121certified standards simulating such thin biologicalmatrices should reduce uncertainty on quantitativeresults from 30–40 % estimation to 10–15 %. Theradiation dose deposited within a pixel is roughlyabout 10 6 G with PINK excitation and can bedownto10 4 G using monochromatic excitationwhich is several orders of magnitude less thanscanning ion microprobe, and still acceptable forfreeze-dried samples. A compromise is requiredbetween the desired resolution, mapping time, andthe dose that the sample can sustain. Improvementsin limits of detection can be reached workingabove the K edge of iodine B K ≈ 33.2keVwith micron-sized beams of high energy. Alternatively,using the newly commissioned setup atID22, the samples can be raster-scanned using apiezo YZ assembly, spreading out the heatloadover several successive scans. This experimentopens a new way toward possibilities of mappingintracellular distribution of drugs used at pharmacologicaldoses. SXRF is complementary to confocalmicroscopy or nuclear microprobe analysis,and brings missing information not accessible byany other technique. Finally, simultaneous chemicalspeciation by XAS and microanalysis of livingcells are exciting perspectives under investigationthat will soon be reached routinely with SXRFmicroprobes.3.4.3.3 MICRO XFCMTX-Ray fluorescence computed Microtomography(XFCMT) is a nondestructive, noninvasive imagingmethod which was introduced over 15 yearsago 56 and started to play an increasing role inmicroanalysis. 28–35 XFCMT is an excellent complementarytechnique to phase contrast imagingin that it offers the much-needed elemental sensitivitydown to trace element concentrations withthe same micron-sized spatial resolution. In orderto retrieve the quantitative two-dimensional/threedimensional(2D/3D) elemental information at theend of the tomographic scan, reconstruction techniquesare used as opposed to the direct imagingmethods associated with 2D mapping. As itrequires a pencil beam as its probe, synchrotronradiation fluorescence tomography expanded andbecame a precise and relatively straightforwardmethod of microanalysis only with the advent ofthird generation synchrotron sources such as theESRF, APS and SPRING 8 that provide beamswith high energy/high flux/high coherence characteristics.In the following, we describe high precisionexperiments performed at the ID22 beamline of theESRF on real samples featuring inhomogeneouselemental distributions, from the fields of plantphysiology and astrophysics.Depending on the desired resolution, either ofthe vertical or horizontal scanning geometries areused, with the associated detectors positioned vertically,respectively horizontally at 90 ◦ with respectto the beam. The horizontal focusing/scanninggeometry exhibits a significant decrease in fluxnecessary to demagnify the rather large horizontalsource size by closing down the beamlinehorizontal slits but has a better spectral purity,as it features Rayleigh and Compton scatteringa few tens of times less than the vertical geometry,thanks to the 90 ◦ angle between incidentand outgoing photons in the orbit plane and thehigh degree of linear polarization in the horizontalplane.The two movements used for the tomographicscans are Z/X (vertical/horizontal, precision0.1 µm) and R X /R Z (rotation around a horizontal/verticalaxis, precision 0.001 ◦ ). The othermovements (Y, R Y ,x) are used to align the samplerotation axis in the beam. The sample is mountedon a Huber goniometer head which is pre-alignedon a visible microscope setup in order to bringits rotation axis perpendicular to the beam and toreduce precession of the tomographic rotation axisat the beam position.Long Range Ion Transport in Higher PlantsIn order to study the impact of certain genes andtheir mutual interaction on the phenotype of higherplants, plant physiologists investigate the longrange transport of ions such as K + ,Ca 2+ or Cl − . 57The long range transport and uptake of heavy

122 PARABOLIC COMPOUND REFRACTIVE X-RAY LENSESmetals is an important issue in environmentalstudies. 58 The elements under investigation arehighly diffusive in the complex matrix of the plant,and the sample preparation required for standardanalytical methods, such as EDX or SIMS, requiresthe preparation of cryosections or fracture surfacesof the plant samples. While this kind of samplepreparation is difficult to achieve for certain plants,it is nearly impossible for others. In addition,there is always the danger of introducing artefactschanging the element distribution. Hard X-rayfluorescence microtomography can avoid thesedifficulties. It allows one to determine the elementdistribution on a virtual section through a bulk ofan opaque sample. The region of interest does notneed to be laid open. A detailed description of theexperimental method can be found elsewhere. 31–33To illustrate the strength of this method, thedistribution of potassium, iron, and zinc is determinedinside a mycorrhizal root of a tomato plantgrown on heavy metal polluted soil. Prior to theexperiment, the sample was shock frozen andfreeze dried. These two steps of sample preparationwere required to avoid diffusion of the elementsof interest and to reduce the attenuationof the low energy fluorescence radiation, respectively.The tomographic scan was performed usinga microbeam with a flux of 4.8 × 10 9 photons/s atan energy of about 19.8 keV (5th harmonic of theundulator source at beamline ID22 of the ESRFtuned to 19.8 keV, filtered using a molybdenumfoil with a thickness of 250 µm and a Pd coatedtotal reflection mirror with a reflection angle of0.15 ◦ ). The lateral beam extension was 1.9 µmhorizontally and 0.9 µm vertically (FWHM). Themicrobeam was generated by imaging the undulatoronto the sample using an aluminium refractiveX-ray lens with N = 220 single lenses (L 1 =41.7 m, f = 385 mm, L 2 = 388 mm). To reducethe effective source size horizontally, a horizontalpair of slits located 13 m upstream from the lenswith a gap of 0.1 mm was introduced into the opticalpath. In order to reduce scattering, the samplewas placed in a helium-filled chamber.For each projection, the sample was scanned in105 translational steps of 1 µm. At each point ofthe scan, the fluorescence radiation and the incidentand transmitted beam intensity were recorded for2 s. 132 projections were acquired at equidistantsteps over a full rotation of the sample. The datafor potassium normalized to the incident flux andthe attenuation (negative logarithm of the quotientof the transmitted and incident flux) are shown inFigure. 3.4.7 as a function of translational positionand rotation angle in a so-called sinogram.(a)(b)Figure 3.4.7 Tomographic data from a mycorrhizal root of the tomato plant. (a) K Kα fluorescence signal (E = 3.31 keV) and(b) attenuation at the energy of the incident radiation (19.8 keV). The fluorescence signal and the negative logarithm of the ratioof the transmitted and incident flux are plotted in shades of grey as a function of the translational position (horizontal axis) androtation (vertical axis) in so-called sinograms

APPLICATIONS 123The attenuation signal in Figure. 3.4.7(b)can be reconstructed by standard tomographictechniques such as filtered back projection,since the underlying tomographic model is thestandard radon transform. 59 The fluorescencesignal (Figure 3.4.7a), however, is generated ina more complicated way. The incoming beam isattenuated along its path. At each point along thepath, fluorescence is excited and radiated into thefull solid angle. The part of the radiation that fallsinto the solid angle of the fluorescence detectoris attenuated by an a priori unknown attenuationof the sample before it reaches the detector. If,as in this case, the sample has low density,secondary fluorescence and scattering effects canbe neglected. The attenuation effects of thefluorescence become apparent in Figure 3.4.7(a),where the fluorescence signal is slightly weakeron the left side (far side of the detector) than onthe right. This asymmetry in the sinogram can beused to estimate the attenuation inside the sampleself-consistently. 34 The results of such a selfconsistentreconstruction are shown in Figure 3.4.8for potassium, iron, and zinc.In Figure 3.4.8 the element distributions arereconstructed with subcellular resolution (

124 PARABOLIC COMPOUND REFRACTIVE X-RAY LENSESorder to mount it on the goniometer head. Thisway, the cleanliness and nondestructiveness ofthe measurement was guaranteed – all the moresince we wanted to perform infrared (IR) spectroscopyon it afterwards. The tomography wasdone in the vertical scanning geometry, makinguse of the good spatial resolution available (2 µm).The stronger scattering which this geometry producedwas evident in the energy spectra, wherelow-energy tails of the Rayleigh and Comptonpeaks at 14 and 13.6 keV, respectively produceda non-negligible background. The Axil 48 line fittingprogram was used to deconvolute individualelementary lines.The biological study of this meteorite 61 was ableto reveal bacteriomorphs with sizes between 0.1and 0.6 µm, which were obtained by cultures of thesoil surrounding the grains. These were observed inSEM and TEM and presumed to be real bacteria ortheir remnants. It was postulated that these bacteriaappear at the fracture sites of the grain, followingfluid circulation of carbonates from the soil due toterrestrial weathering. Therefore, our study aimedto identify and locate non-invasively carbonatephases as well as pyroxenes and chromites specificto the grain. The grain was analyzed throughthe quartz walls of the capillary which posed noproblem for the imaging of any elements with theexception of Si which was the main constituent ofthe capillary walls. In Figure 3.4.9 the distributionof Fe, Cr and Ca particular to the phases isshown, with a resolution of 2 µm usingtheARTreconstruction algorithm.The tomographic set of data collected complementsthe 3D transmission tomography, electronmicroscopy and IR data, allowing a rich imageof the grain to be obtained and to characterizein detail its morphology and structure nondestructively,prior to the other analyses which requiresample preparation and possibly alteration of thegrain. This study is part of a benchmark 62 to establishthe feasibility of such detailed analyses onMartian meteorites in the quarantine phase throughthe walls of a mini-P4 sample holder.ReconstructionIn this work the samples were exclusively imagedusing our modified version 32,63 of the algebraicreconstruction technique (ART) as described byKak and Slaney. 59 This technique requires severalsimplifications and assumptions to reduce thecomplexity of the problem and the requiredcalculation time. The sample is divided into aseries of ‘voxels’ (volume pixels) of width andheight equal to the beam size.The following approximations are made throughoutthe calculation:• The scattering from sample and surrounding airis neglected, as well as ‘enhancement effects’due to secondary/ternary fluorescence or toCompton-excited fluorescence.• The correction for the finite horizontal size(respectively vertical for horizontal scans) of thebeam is not applied, i.e. the sample is consideredFeSiCrSiCa100 mFeFigure 3.4.9 Fluorescence tomograms of a micrometeorite grain inside a quartz capillary. Reconstructions (using ART) of theKα lines for Si (capillary), Fe, Cr and Ca are shown. Resolution ≈2 µm. (Reproduced from ref. 57)

APPLICATIONS 125to be a 2D slice of thickness equal to the widthof the detector and equal to the horizontal sizeof the beam (respectively vertical for horizontalscans).• The detector to sample distance is constantas well as the detector efficiency taken as100 %, regardless of the photon energy or angleof incidence.We are continuously developing the ART method,since by its phenomenological character whichclosely mimics the physical interaction and by itsopen frame, it offers possibilities of adding the necessaryprocedures for direct quantitative interpretationof the reconstructed images including the fullbattery of appropriate corrections (self-absorption,enhancement, detector response function) seen influorescence spectroscopy.DiscussionWhen planning an experiment, the question wehave to answer is: How would the estimatedresolution change for a given change in thescanning parameters, such as number of translations/rotationsand counting time per step? Specifically,what is the smallest number of rotationswhich allow the realization of a resolution closeto the scanning step. The resolution function Rshould be sought in the form:R = R(N t ,N θ ,Ɣ t ) (3.4.16)with N t /N θ number of translations/rotations andƔ t the beamsize FWHM in the direction of thetranslation. Rayleigh’s criterion would impose atranslation step of about 1.22 times the FWHMof the beam. However, non-negligible contrast isobtained for steps well below the beamsize butitiscustomarytouseanoversamplingofupto30 % of the beamsize in order to obtain the smallestachievable modulation.In transmission tomography, based on reconstructiontechniques derived from Fourier transforms,it has been proved 59 that the number ofrotations N θ necessary is such that:N θ∼π =2 N t (3.4.17)That sampling follows the Fourier space requirementsfor obtaining an even resolution in the 2D(xy) space. However, when using algebraic reconstructiontechniques, one deals only with the passagefrom the rotating referential attached to thesample (s, t) to the referential attached to thebeam (xy) which is done by nearest-neighbourinterpolation.PerspectivesFor the next few years, part of the activity of theID22 group will be centered around the developmentsof XFCMT and its applications, bothhardware and software. The hardware efforts willconcentrate onto rendering the acquisition fromboth EDX and WDX spectrometers fast and userfriendly.We are implementing digital signal processing(DSP) systems to record the MCA spectraand lower the processing time in order to acceptcount rates of a few tens of kcps. Where necessary,a WDX spectrometer will be used to either recordhigh-resolution spectra of otherwise-overlappinglines, or to eliminate saturation effects producedby the matrix or major elements. The overheadtime of the acquisition system will allow countingtimes of 50–100 ms/pt thus opening the wayto obtaining full tomographic scans in less thanan hour. We are implementing a symmetric doubleEDX detector setup, in conjunction with asimultaneous WDX acquisition. This will effectivelyhalve the scan duration to 180 ◦ instead of the360 ◦ needed in regular tomographic scans and willallow tackling the 3D imaging by acquiring severaladjacent slices, of thickness equal to the beamsizein the other dimension. Fully quantitative imagingrequires well qualified and calibrated normalizationmonitors – photodiode detectors and ionizationchambers in our case which we are currentlyimplementing. We will also implement apolarization monitor, as fluorescence signals arestrongly dependent on the incoming beam polarizationwhich even at an undulator beam varies bya few percent as a function of the photon energyor the sample position with respect to the electronbeam orbit.

126 PARABOLIC COMPOUND REFRACTIVE X-RAY LENSESSoftware-wise, we have already implementedthe online spectrum fitting based on the AXILpackage and we are also using Monte-Carlosimulations 64 in order to check the validity of ourreconstruction and quantization.The ART reconstruction package we use correctsfor incident beam absorption and selfabsorptioneffects from the matrix and is underdevelopment to include self-absorption effects dueto the elements imaged. Besides the absorption signalwhich serves to generate a transmission tomogram,we are planning to exploit the Rayleigh andCompton scattering signals to obtain an ‘effective’Z image useful in ascertaining the matrix. Finally,we will couple image processing capabilities suchas Principal Component Analysis (PCA) and clusteringin order to treat the correlation patterns inthe reconstructed images.Our aim is to deliver a fast and accurate methodof 2D/3D characterization of the internal elementalstructure of various samples, with quantitativecapabilities, in a nondestructive, non-invasive wayand without a priori knowledge of the sampleconstituents.3.4.3.4 X-RAY ABSORPTION:CADMIUM SPECIATION IN MUNICIPALSOLID WASTE FLY ASHESThis work 65 is part of a collaboration betweenthe Chalmers University in Göteborg, Swedenand ID22, ESRF. Incineration of Municipal SolidWaste (MSW) has two main advantages: reducingthe waste volume by about 90 % and reducingreactivity by destruction of organic compounds.As in combustion of other fuels, the potentiallytoxic trace metals are concentrated in the fine ashfractions, i.e. the fly ash. The content of thesemetals (i.e. Pb, Ni, Cu, but mainly Cd) makesthis residue ecologically harmful. An effective andsafe handling of such ash requires a thoroughknowledge of its chemical properties, in particular,their potential for dissolution and leaching. Thedissolution and transport of metal ions from the ashmatrix to soil water are key steps since dissolvedions are available for biological uptake andground water contamination. As a consequence,knowledge of the total concentrations of heavymetals in ashes provides only limited information,as it does not show how strongly the metalsare bound to ash constituent. Thus, the riskassociated with the presence of heavy metalsdepends primarily on their speciation which isa difficult task because of their relatively highdilution and the structural and chemical complexityof the host material.This work describes a method for the determinationof Cd speciation and its possible quantitationin single MSW fly ash particles. Cd distributionwithin single particles was investigated bysynchrotron radiation induced micro-X-ray fluorescence(µ-SRXRF) spectrometry and its speciationon single spots by synchrotron radiation inducedmicro-X-ray absorption spectroscopy (µ-SRXAS).Both techniques can be used in air and they areusually nondestructive, due to the lower energydeposition compared to charged particle excitation.The high brightness of the 3rd generationsynchrotron radiation sources and the developmentof X-ray focusing optical elements make it possibleto create beams of micrometer size with highintensity making µ-XRF and µ-XAS appropriatetools for the analysis of individual particles withdiameters of several tens of micrometers. Elementalmaps, showing the 2D projection of the 3Delemental distribution of a particle, are created byscanning the particle in a regular grid pattern bythe X-ray microbeam and detecting the inducedfluorescent intensities at each position (xy-µ-XRFscan). µ-XAS spectroscopy was used for the directdetermination of the chemical forms of Cd in particularmicro-sized areas of high Cd concentrations,by measuring the absorption of the excitationbeam or the intensity of the Cd Kα X-ray line asa function of the excitation energy in the vicinityof the K absorption edge (E K = 26.711 keV)of Cd (−100 eV

APPLICATIONS 127with the penetrating capability of X-rays, it makesµ-XAS ideal for complex or difficult samples, likefly ashes.The study has been performed on fly ashesfrom a bubbling fluidised bed (BFB) combustionunit of 2×15 MW fired with MSW. Only textilefilter ashes were investigated here. Eleven singleparticles of different dimensions (varying fromca. 30 to 200 µm in diameter) were selected andeach of them was glued on a 100 µm diameterquartz capillary before the µ-XRF analysis. µ-XAS experiments were performed only on theparticles presenting high Cd concentrations (threeparticles) and only on those spots where Cd waspredominantly accumulated (four spots totally), asshown by the XRF maps.Both µ-SRXRF and µ-SRXAS measurementswere performed in the 1st experimental hutch ofthe ID22 beamline (EH1) of the ESRF. For thedemagnification of the synchrotron source andcreating the microbeam, a compound refractivelens (CRL) consisting of 94 individual Al lenseswas employed. A Au knife-edge sample wasused to determine the size of the focused beam.The beam size was H × V = 10 × 8 µm 2 duringfluorescence experiments and 12 × 3 µm 2 duringthe absorption experiments. The NIST-SRM1832thin glass and Cu and Au thin metal foils(Goodfellow, UK) were measured in order toestimate the number of incident photons. All theµ-XRF experiments were performed by usingmonochromatic radiation at an excitation energyof 27 keV.Cd K-edge µ-XAS experiments were performedon pure Cd compounds and fly ash particles aswell. The reference compounds used in this study(Cd, CdCl 2 , CdO, CdSO 4 , CdS, CdBr 2 ) were chosendue to their probability to be found in theash material. A small amount (0.5 mg) of eachreference material was crushed and mixed with0.3 mg of boron nitride and pressed to form pelletsof 1 mm thickness. The reference XAS spectrawere recorded in transmission mode. Due to thelow Cd concentration and the small dimensionsof the fly ash particles, their XAS spectra wererecorded in fluorescence mode. Due to the relativelysmall thickness of the fly ash particles,no self-absorption correction was necessary forthese spectra, as evidenced by the good agreementbetween the fluorescence and transmissionXAS spectra integrated for longer. All the µ-XASspectra were obtained by scanning the energy inthe 26.65–26.95 keV range in 1 eV steps maintainingthe same setup used for the microfluorescenceexperiments. Each energy scan was repeated fourtimes with 2 s live time/energy point. The higherintensity Si [111] reflex was used, yielding a resolutionof about 3.5 eV, to be compared with theCd core-hole width of 7.8 eV.The command view (CMDV) data analysispackage by Ansell 66 was used to fit the dataobtained on the fly ashes by linear combinationsof the measured standards. Initially, factor analysiswas performed in order to roughly estimatethe dominant standards for further fitting the flyashes. Then a discrete fit of the fly ashes by linearcombinations of the interpolated standards wasmade, using the three most representative candidatesevidenced by the factor analysis: CdSO 4 ,CdCl 2 and CdO.Results and DiscussionThe concentrations of the major and minor componentsin each measured voxel of the single fly ashparticles were determined from scanning µ-XRFexperiments as detailed in Camerani et al. 67 Thelarge differences between the average and maximumconcentrations within individual particlesindicate a considerable variation in concentrationswith ‘hot-spots’ containing about 10–100 timeshigher amount of a given element than the average.This finding supports the idea that the trace metalshave special affinity to some ash minerals locatednear the particle surface. This can occur as a resultof particle interactions, 68 or as a result of the variableswhich determine the transfer of elements tothe raw gas in the furnace, such as: (i) occurrenceand distribution of the elements in the inputwaste; (ii) physical and chemical conditions in thefurnace bed, e.g. temperature, redox conditions,chlorine and oxygen content; and (iii) the kineticsin the furnace bed, e.g. residence time and mixingconditions. 69 The inhomogeneous distribution

128 PARABOLIC COMPOUND REFRACTIVE X-RAY LENSESCdCuClZnKPbBrCaFigure 3.4.10 µ-XRF maps of various elements obtained fromparticle 6 (diameter ca. 160 µm), showing self-absorption ofthe lightest elements. Image size: 20 × 20 pixels, pixel size:10 × 8 µm, spectrum collection time per pixel: 6 s. Darkertones indicate a higher elemental abundance; light tonesindicate lower concentrations. (Reproduced from ref. 65)of heavy metals among and within individual particlesis illustrated, as an example, in Figure 3.4.10,where the spatial metal distributions of particle 6(ca. 200 µm diameter) are shown.Inside each of those particles, the enrichmentof Cu, Zn, Pb and Cd (at the 3600, 29700,11800 and 200 ppm level, respectively) in somewell-defined hot-spots relative to the surroundingareas is clearly visible, suggesting that a partof these metals might be arranged in inorganicprecipitates. Around the boundaries of those spots,zones with intermediate concentration levels arepresent, probably caused by diffusion of the heavymetals during the condensation process or bybinding to ion exchange sites. The right-hand lowerand upper quarters of particle 6 show, for example,a zone with a high abundance of Cd, possiblycorresponding to the nucleation area.Despite its low concentration, Cd could bedetected by µ-SRXRF in each single particle. Dueto the penetration depth of the high energeticprimary and characteristic photons (few hundredmicrometers range), the elemental signals originatingfrom the whole excited depth of the particleare detected simultaneously. This makes the µ-XRF maps, shown in Figure 3.4.10, become 2Dprojections of the 3D distribution of these traceelements throughout the fly ash particles. So, fromSrFethe µ-XRF maps alone, it is not possible to judgewhether the spots of accumulation of the heavymetals are situated on the particle surface (i.e. mostprone to leaching) or are present at some depthwithin the particle (where they might be moreshielded from chemical attack by water).To further understand the speciation of Cd insingle fly ash particles, the oxidation state and thechemical surroundings of Cd ions were studiedby µ-XAS in the areas of the particles showinga higher Cd concentration. µ-XAS spectra ofpure Cd compounds such as Cd, CdO, CdSO 4 ,CdS, CdCl 2 ,CdBr 2 pellets were measured priorto the single particle analysis, normalized andreported in Figure 3.4.11(a). Comparisons of XASspectra for fly ashes and for reference compoundsshow that in all the particles studied Cd ispresent in oxidation state +2 instead of metallicform. This can be explained by the oxidizingconditions experimented by the toxic metals aftervolatilization during combustion.The µ-XAS spectra of the ‘hot-spots’ of theparticles were also expressed mathematically asa Linear Combination (LC) of XAS fit vectors,using the measured absorption data of the Cdreference compounds. The µ-XAS spectra of oneof the two ‘hot-spots’, within particle 6, is shownin Figure 3.4.11(b). The comparison between thelinear combinations of the standard spectra and themeasured XAS-spectra of the Cd hot-spots allowthe concentrations to be estimated of the possibleCd compounds in those spots, e.g. in the case of thespot a in particle 6, Cd is present as an admixture ofCdSO 4 (70 %), CdO (19 %) and CdCl 2 (11 %) withover 90 % confidence level in the fitting process.In all the spots analysed, Cd was always presentas a combination of just CdSO 4 ,CdCl 2 and CdO.Thus, it can be seen that the Cd in MSW flyashes is present as water soluble species (CdCl 2and CdSO 4 ) up to 86 % and 76 %, respectively.These results confirm what was found by µ-XRF mapping and agree with earlier studies. 70,71Such metal speciation would make the managementof this filter ash problematic with respect totheir possible leaching. On the other hand this isnot a conclusive identification because the spectra

REFERENCES 1292CdCl 2Absorbance (arb. units)1.50.51CdBr 2CdCdOCdSO 4CdS0(a)26.726.75 26.8 26.85Energy (keV)26.9 26.952.5Absorbance (arb. units)2STD: 70% CdSO 4 +19% CdSO+11% CdCl 226.91.5(b)26.65 26.7 26.75 26.8 26.85Energy (keV)Figure 3.4.11 (a) XAS spectra of pure Cd compounds. The spectra are vertically offset to allow comparisons and were taken influorescence mode. (b) XAS fitted spectrum of a fly ash particle, using linear combinations of the previously measured standards.(Reproduced from ref. 65)of other Cd sulfates and some other possibly significantcompounds, like Cd silicates, were not examineddue to the lack of standard materials. Theseinvestigations are planned during future work.ACKNOWLEDGEMENTSWe would like to thank W. H. Schröder (ResearchCenter Jülich, Germany) for the ongoing fruitfulcollaboration to develop X-ray fluorescence microtomographyof plant samples.The authors gratefully acknowledge supportfrom J.M. Rigal, and A. Homs during the experiments.The financial support of the Swedish NaturalScience Research Council (NFR) for the work ofM.C. Camerani is gratefully acknowledged.REFERENCES1. W. C. Röntgen. Sitzungsber. physikal.-medizin. Gesellschaft,132, 1895.2. A. Michette. Nature (London) 353, 510, 1991.

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Chapter 4X-Ray Detectors4.1 Semiconductor Detectors for (Imaging) X-raySpectroscopyL. STRÜDER 1,3 ,G.LUTZ 1,3 , P. LECHNER 2,3 ,H.SOLTAU 2,3 and P. HOLL 2,31 Max-Planck-Institute für Physik und extraterrestrische Physik, München and Garching, Germany,2 PNSensor, München, Germany and 3 MPI Halbleiterlabor, München, Germany4.1.1 INTRODUCTIONLarge scale use of semiconductor detectors inX-ray spectroscopy is a recent development whichwas prompted by their success in particle physicsbased on technological developments in silicondetectors and in microelectronics. Applying theplanar technology first used in electronics alsoto detector production 1 allowed the fabrication ofhigh granularity fast detectors. This made it possibleto perform extremely precise particle positionmeasurements at a high event rate. Simultaneouslythe small energy needed for creating an electronholepair (a minimum of 1.12 eV and an averageof 3.65 eV as compared to 30 eV for ionizationof gases) created the potential for precise spectroscopicmeasurements. This aspect came to its fulluse when semiconductor detectors were applied toX-rays.This subchapter will concentrate on present useof silicon detectors which has culminated in imagingspectroscopic detectors in X-ray astronomy.Here the use of silicon charge-coupled device(CCD) detectors with their extended energy rangeand vastly improved spectroscopic capabilitiescompared to the previously used gas detectors haslead to many new important discoveries.Before proceeding to this subject, however,an introduction to the basic operation principlesof semiconductors and the electronics used fordigesting the fairly small electronic signals willbe given. Furthermore detectors aimed only atspectroscopy will be treated. These, as well asthe focal-plane imaging X-ray detectors, rely onoperating principles developed during the periodof rapid developments since the first introductionof position sensitive detectors into particle physicsin 1980. 2Now semiconductor detectors have spread toother fields of science and technology. Partsof those developments are described in thissubchapter. The presentation will be done in twoparts. The first part will deal with general aspectsof semiconductors when used as X-ray and particledetectors and describes the functional principlesof detector structures including the readout of thesignals. The second part describes some importantdetectors in more detail and deals also withimportant applications in X-ray spectroscopy andimaging.X-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

134 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYPART 1: SEMICONDUCTORPROPERTIES AND DETECTIONPRINCIPLES4.1.2 DETECTOR RELATEDPROPERTIES OF SEMICONDUCTORSCompared with other materials, semiconductorshave unique properties that make them verysuitable for the detection of ionizing radiation.Furthermore, semiconductors – especially silicon– are the most widely used basic materialsfor electronic amplifying elements (transistors) andmore recently for complete microelectronics circuits.Thus, part of the process technology thatalready existed in (micro) electronics could betaken or adapted for detector production. 1 Integrationof detector and electronics could be envisaged.In the following, the properties of important semiconductormaterials will be discussed.The uniqueness of semiconductor material propertiescan best be appreciated by comparing themwith the most widely used radiation detectors thatare based on ionization in gas. Values for siliconwill be used in this comparison.• The small band gap (1.12 eV at room temperature)leads to a large number of charge carriersper unit energy loss of the ionizing particlesto be detected. The average energy for creatingan electron–hole pair (3.65 eV) is an orderof magnitude smaller than the ionization energyof gases (30 eV).• Therefore the energy of X-rays can be measuredwith much higher precision and down to lowerenergies than is possible with gas detectors.• The high density (2.33 g/cm 3 ) leads to a shortabsorption length of low and medium energyX-rays and to a large energy loss per traversedlength of the ionizing particle (3.8 MeV/cm fora minimum ionizing particle). Therefore it ispossible to build thin detectors that still producelarge enough signals to be measured. In addition,the very small range of delta-electrons preventslarge shifts of the centre of gravity of theprimary ionization from the position of the track.Thus an extremely precise position measurement(of a few micrometres) is possible.• Despite the high material density, electronsand holes can move almost freely in thesemiconductor. The mobility of electrons (µ n =1450 cm 2 /V s) and holes (µ p = 450 cm 2 /V s) isat room temperature only moderately influencedby doping. Thus charge can be rapidly collected(several ns) and detectors can be used in highrateenvironments.• The excellent mechanical rigidity makes the useof foils for containment of the gas superfluousand allows the construction of self-supportingstructures. Therefore very thin radiation entrancewindows can be constructed and high quantumefficiency can be reached down to very lowenergies.• An aspect completely absent in gas detectors isthe possibility of creating fixed space chargesby doping the crystals used. It is thus possibleto create rather sophisticated field configurationswithout obstructing the movement of signalcharges. This allows the creation of detectorstructures with new properties that have noanalogy in gas detectors.• As detectors and electronics can both be builtout of silicon, their integration into a singledevice is possible.The most commonly used semiconductor detectormaterials are germanium and silicon but also othercompound materials are used, such as GaAs CdTeand CdZnT. Germanium and silicon are indirectsemiconductors, their most important differencebeing a factor of almost 2 in the band gap andthe much shorter photon absorption length for germaniumdue to its high Z-value. Therefore Ge issuitable for measurements of fairly high energyX-rays while direct conversion in silicon detectorswith reasonable efficiency is limited to X-raysenergies of a few tens of keV. Due to the smallband gap and the corresponding thermal generationof electron–hole pairs germanium detectors haveto be operated at cryogenic temperatures while silicondetectors can work at room temperature. HighZ-semiconductors with sufficiently large band gapfor room temperature operation are available ascompound semiconductors. These materials arehowever not available with the perfection of Si

THE MEASUREMENT OF SIGNAL CHARGE 135and Ge, instead the large concentration of crystaldefects dominates the properties of the devices.As silicon is the most commonly used materialin the electronics industry, it has one big advantagewith respect to other materials, namely a highlydeveloped fabrication technology. For X-ray detectionone problem is the limit in thickness that canbe depleted with the application of reasonably lowvoltages, as intrinsic material cannot be manufactured.This limits the maximum energy which canbe detected with reasonable efficiency.4.1.3 THE SIMPLESTSEMICONDUCTOR DETECTORSTRUCTURE: THE DIODEThe most basic semiconductor structure is a diode,a combination between n- and p-doped semiconductors.It has electrically rectifying properties andmay also serve as sensor for ionizing radiation. Inthat case it will usually be very asymmetricallydoped similar to the case shown in Figure 4.1.1where a lowly doped n-type substrate is connectedto a highly doped thin p-layer. Such a devicecan be operated in partial depletion (partial depletionoccurs already without application of a bias)or fully depleted by applying a sufficiently highreverse bias. In the latter case a highly doped n-layer has to be provided on the surface oppositeto the diode in order to prevent charge injection(holes) from the backside electrode.Width of the depletion region, charge density,electric field and potential can be calculatedstraightforwardly from simple electrostatics. Oneresult useful to remember is that the bias voltage,V bias , grows linearly with the doping density of thebulk and quadratic with the depletion depth:V bias = qN Dd 2 (4.1.1)2εε 0where N D is the donor concentration, d thedepleted thickness, q the charge of one electron,and εε 0 the dielectric constants of silicon. Signalcharge is collected not only from the space chargeregion where electrons and holes are separatedand driven to the electrodes by the electric field,but also incompletely from the nondepleted region.Here partial collection is due to diffusion into thespace charge region.The simple diode by itself is already a usefulX-ray detector providing spectroscopic informationwith limited precision due to the large capacitiveload it presents to the electronics measuringthe signal charge. The precision of charge measurementis a central subject for all types of detectorsand will be treated in the next section.4.1.4 THE MEASUREMENTOF SIGNAL CHARGESignal charge is measured with a charge sensitiveamplifier, an inverting amplifier with a capacitancein its feedback loop (Figure 4.1.2). The detector ispresented by its capacitance C D , the noise of theamplifier by a noise voltage U n at its input. We willconsider only the case of very high amplification.In that case the voltage at the amplifier input hasto remain zero when a charge Q s is deposited atthe amplifier input. One can then read immediatelyoff the figure that the output voltage has to beV out = Q s /C f (4.1.2)All charge is transferred from the detector onto thefeedback capacitance C f . Similar consideration canbe made for the effect of amplifier noise U n .Whenconsidering the charge required at the input inorder to compensate the effect of the noise voltageso as to keep the output voltage at zero. One findsas noise chargeQ n = U n (C D + C f + C i ) (4.1.3)with C i the amplifier input capacitance. The noisecharge equals the product of serial noise voltagetimes the total, ‘cold’ capacitance.These results hold in the limit of infinitely largeand fast amplification. They are good approximationsfor realistic situations. The latter resultdemonstrates the importance of keeping the detectorcapacitance low in order to contain serial noiseat a low level.The signal to noise ratio can be improved bysignal shaping when signal and noise have differentfrequency spectra. This is the case for (white)thermal noise which exhibits a flat frequencyspectrum. Here the signal to noise ratio improves

136 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYAlP + Dn +AlElectronHoleDonorAcceptorVDepletedInculatorNon depletedNoninculatorPEYFigure 4.1.1 Schematic structure of a semiconductor diode with charge density, electric field and potential for partial (solid line)and full (dashed) depletionC fQ in−U out = 0A+C D C in~ U nFigure 4.1.2 Schematics of a charge sensitive amplifierconnected to a detector represented by its capacitance C D .Thesum of all noise sources inside the amplifier is represented bya single noise voltage source at the amplifier inputwith the square root of the shaping time constant.Unfortunately all amplifying devices exhibit alsolow frequency (1/f ) noise with a noise frequencyspectrum corresponding to that generated by ashort current pulse in the detector. Therefore thesignal to noise ratio cannot be improved by shapingfor this type of noise.Besides serial noise, parallel noise has to beconsidered. The principal source of this noise isthe detector leakage current which flows into theinput of the amplifier. Integrating this current overthe signal shaping time gives a ‘dark charge’to be added to the signal. This added chargeis subject to statistical fluctuations which inthe simplest condition is described by Poisson

OTHER SEMICONDUCTOR DETECTOR STRUCTURES 137statistics according to the number of elementarycharges in this ‘dark charge’. Signal shaping resultsin a noise rising with the square root of the shapingtime.Taking these three noise sources into accountone arrives at the assumption that the dominantsource of amplifier noise is due to the inputtransistor whereENC 2 =(4kT 2 )C 2 1tot A 13g m τ + (2πa fCtot 2 )A 2white series noise(+ qI l + 2kT )A 3 τR fparallel noiselow frequencynoise(4.1.4)A detailed derivation is given in Pinotti et al. 3ENC is the equivalent noise charge, g m thetransconductance of the FET, A 1 ,A 2 and A 3 areconstants depending on the shaper’s filter function,a f is a constant, which parameterizes the amount oflow frequency noise, I l is the total leakage currentand R f is the equivalent resistor of the feedback.Additional sources of noise contributing tospectroscopic performance degradation come fromstatistical fluctuations in the ionization (electron–holecreation) process itself (Fano noise willbe described in the section on interaction of radiationwith semiconductors) and in imperfectionsin the charge collection of the detector which canhave several origins (to be described in the contextof these detectors).4.1.5 OTHER SEMICONDUCTORDETECTOR STRUCTURESThe diode described previously is capable of measuringthe energy of X-rays – although with moderateresolution and/or at low rate. Based on thisstructure position sensitivity can be reached bysplitting the diode into small units and readingthem out individually. Strip or pad-like structuresare commonly used. This development was drivenby particle physics where emphasis was on precisionposition measurement while ionization energyloss measurement was of minor interest.Most effort went into strip detectors where alarge degree of sophistication has been reached:single- and double-sided strip detectors with integratedcapacitive coupled readout, integrated biasingcircuits of various kinds have been developed.The detectors are able to withstand radiation fluencesin the range of 10 14 cm −2 hadronic particles. 4In principle they can also be used as X-ray detectors,however, due to the large capacitance of strips(typically 1 pF/cm length) the energy resolutionwill be moderate. A breakthrough for X-rays hasbeen reached with the invention of the semiconductordrift chamber by Gatti and Rehak in 1984. 5This device, originally aimed at position measurementwith the help of the drift time, has revolutionizedX-ray spectroscopy; in particular, throughthe invention of single-sided structured devices ofcircular geometry 6 which in addition had the inputtransistor integrated in the device. 7The semiconductor drift chamber also initiatedthe development of the pn-CCD which in X-raydetection has very important advantages comparedto standard CCDs which are based on MOS(metal–oxide–semiconductor) structures workingin deep depletion mode. These earlier, still widelyused types of CCDs are not discussed in detailhere. Controlled drift detectors (CDDs) representa combination of silicon drift detectors and pn-CDDs. They can be operated rapidly with simultaneousgood position and energy measurements.The DEPFET (depleted p-channel field effecttransistor), a new device invented in 1985 byKemmer and Lutz, 6 combines the function ofdetector and amplifier. It is the base structure ofa new type of pixel detector under developmentfor X-ray telescopes in astronomy.In the following, the working principles ofthe devices will be described while detaileddescriptions and applications are postponed to latersections.4.1.5.1 SILICON STRIP DETECTORSThe basic principle of a strip detector is shown inFigure 4.1.3. The diode of Figure 4.1.1 is split intomany strips each of which in the simplest case is

138 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYpSiO 2Alp +n −n +Figure 4.1.3 Cross-section of a silicon diode strip detectorSiO 2RAlp +C 3n −n +Figure 4.1.4 Strip detector with charge division readoutconnected to its own amplifier. The position of thestrip hit provides a coordinate, the signal heightthe energy of the X-rays. For a fraction of eventsthe signal will be split between neighbouring stripsdue to the size of the charge cloud caused byelectrostatic repulsion and diffusion on their waytowards the strips. For low energy X-rays thepreferred radiation entrance side is the unstructuredn + backside. This is due to the bad chargecollection properties in the gap regions between thestrips where electrons experience no drift towardsthe backside but have to cross a potential barrierwith the help of diffusion.Typical strip pitches p are in the range of 20to a few hundred micrometres. This may require alarge number of readout channels. This number canbe decreased by using capacitive charge divisionreadout as shown in Figure 4.1.4. Here only everyfourth strip is connected to an electronics channeland the charge collected at non-connected stripscouples capacitively through the naturally presentinter-strip capacitances to those strips connected tothe electronics. The ratio of signals in neighbouringreadout strips is used for position interpolation.For proper charge collection the potential of theintermediate strips have to be held at the samepotential as the readout strips. This is accomplishedby high resistive connections between strips. Acomplication arises in the extraction of energyfrom the data as part of the signal collectedin intermediate strips is lost to strip-backsidecapacitances. Corrections for this loss have to beapplied.Two-dimensional position measurement can beobtained by having (crossed) strips on both sidesof the wafer and using simultaneously holes andelectrons which are collected on opposite sides ofthe wafer. Figure 4.1.5 shows a double-sided stripdetector with holes being collected on the lowerside and electrons at the top side. This drawing isincomplete in the sense as it does not show thecomplications with n-strip isolation. The alwayspresent positive charge in the silicon oxide givesrise to an electron accumulation layer right belowthe oxide which shortens neighbouring n-strips. Itcan be interrupted with boron implantation. Thisimplantation can either be strip like or, simpler andwith better behaviour, uniformly over the whole

OTHER SEMICONDUCTOR DETECTOR STRUCTURES 139nn +np +Figure 4.1.5 Schematics of double-sided strip detectors. The figure does not address the complications of electrical shorteningbetween neighbouring n-strips due to the electron accumulation layer induced by the positive oxide chargeStripBiasAlSiO 2p +Undepletedn −AlSiO 2p +Undepletedn −AlSiO 2p +n −UndepletedFigure 4.1.6 Strip-biasing by punch-through of capacitively coupled strip detector. When applying the bias voltage the depletionregion around the bias-electrode grows and after touching that of the strip draws the strip potential along with itsurface. In the latter case the doping density hasto be much smaller than that of the n-strips androughly match that of the oxide charge so as toavoid breakdown due to large electric fields.Capacitively coupled readout 8 shields the electronicsfrom the dark current of the detector, nothowever, from the noise due to fluctuations of thiscurrent. It requires additional biasing circuitry tosupply the potential to the strips. Both features canbe simply integrated into the detector as shown inFigure 4.1.6. The capacitances are formed by theseparation by an oxide layer between a doped strip

140 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYand an aluminium strip. Biasing is performed withthe help of a punch-through mechanism from onebiasing strip running next to the ends of the stripelectrodes. The potential of the implanted stripsfollows that of the bias strip within several volts.This and similar biasing methods also workingfor n-strips 9 are considerably simpler than biasingwith polysilicon resistors, still the most widelyused method.U+ −n + p +(a) Undepleted n - siliconDepleted n - siliconUdd4.1.5.2 DRIFT DETECTORSThe semiconductor drift chamber was invented byGatti and Rehak in 1984. 5 It is based on the sidewarddepletion principle shown in Figure 4.1.7.The basic structure is a double-sided diode withdiodes on both wafer surfaces and a small n + bulkcontact on the side which is capable of depletingthe complete wafer.Space charge regions around the diodes arealready present before applying any bias (Figure4.1.7a). Leaving the n + contact at ground andapplying a negative bias to the diodes makes thedepletion region grow from both wafer surfacessimultaneously until they join (Figure 4.1.7b) at aquarter of the bias voltage needed for a standarddiode (compare Equation.4.1.1 in Section 4.1.3).Further increase does not change the form of thepotential in the diode region, only the electronsare retracted all the way towards the n + contact(Figure 4.1.7c).If electron–hole pairs are created by radiationthe holes will move toward one of the two p + contactsand the electrons towards the middle plane.Those are only very slowly removed by diffusion.Controlled drift of these electrons towards the n +anode can be achieved by superposition of an electricfield parallel to the wafer surface. This can bedone by dividing the diode into strips as shownin Figure 4.1.8 and applying potentials which risecontinuously from strip to strip. Thus one arrivesat the basic semiconductor drift chamber structure.The position of impinging radiation can be derivedfrom the drift time (if the entrance time of theradiation is known), the energy from the signalheight measured at the n + anode. The device hasremarkable properties which make it very suitable(b)(c)Figure 4.1.7 The principle of sideward depletion. In (a) noreverse voltage is applied, only the intrinsic depletion zoneshave developed. When applying a negative bias to the p +electrodes electrons are pushed towards the n + contact and thedepletion voltages grow. (b) shows the full depletion, startingfrom the rectifying junctions on both wafer surfaces. (c) showsthe configuration of ‘over-depletion’for X-ray spectroscopy. Those and many variationsof the device will be described in a later section.The most important features of such devices are• fast signal detection within a timing precision ofnanoseconds• law read node capacitance for low noise and fastsignal detection.4.1.5.3 CHARGE-COUPLED DEVICESStandard CCDs are based on MOS structureswhich operate in the deep depletion mode, i.e.in thermal non-equilibrium. The principle of athree-phase MOS CCD is shown in Figure 4.1.9.Signal electrons created by ionization assemble inpotential maxima at the Si–SiO 2 interface createdby the transfer gates. Periodic variation of theirpotential drives the charge towards the readoutanode. In the simple form shown in Figure 4.1.9UUd

OTHER SEMICONDUCTOR DETECTOR STRUCTURES 141n + p + p + p + p +− ++− − +− +− +p + p + p + p + p +Figure 4.1.8 Semiconductor drift chamber structure derived from sideward depletion structure of Figure 4.1.7. Dividing the diodeinto strips and applying a continuously rising potential superimposes a horizontal field that drives the signal electron towards then + anode which is connected to the readout electronics. Upon arrival of the signal charge at the n + anode the amount of chargeand the arrival time can be measuredf 3f 2f 1SiO 2UndepletedReadoutanodeAlN +P −transferred in a depth of almost 1 µm. For X-raysthere remains, however, at energies below 1 KeV,the disadvantage of the thick radiation entrancewindow and at high energy that of the fairly thinsensitive depleted region.P +4.1.5.4 THE pn-CCDFigure 4.1.9 Principle of a three-phase MOS CCDsuch a device will work badly due to the presenceof potential maxima in the regions between thenon-overlapping gates and because of the trappingof signal electrons in defects at the Si–SiO 2boundary. These problems could be alleviatedby designing modified structures, for example,buried channel CCDs in which the electrons areA pn-CCD works on a different principle (Figure4.1.10) from the previously described MOSbaseddevices (Figure 4.1.9), resulting in somerather interesting properties. While in MOS-baseddevices minority carriers are collected, thesedevices use the majority carriers, which are producedin the completely depleted and thereforealso radiation-sensitive bulk material. The workingprinciples can be explained from the silicon driftchamber. The possibility of using the drift-detectorprinciple for the CCD has been mentioned alreadyin the first publication by its inventors. 5Looking at the sideward depletion structure(Figure 4.1.7) we notice that the electron potentialvalley can be moved towards the top surface bybiasing the lower diode negatively with respect tothe top diode. Applying to the strips a periodicallyvarying potential rather than a continuously risingone, the valley will be structured in depth. Thelower diode may be formed as a single large-area

142 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYj 1n + - contactreadout for e −+Uj 2j 3p + - back contactSiO 2p + - transferregisterPotentialminimum for e −−−−Transfer Direction−−−n - bulk−UFigure 4.1.10 The fully depleted pn-CCD: cross-section along the channelstructure, and from that one arrives at the deviceshown diagrammatically in Figure 4.1.10. Thisdevice however still has some problems. In orderto obtain sufficient modulation of the potentialvalley depth, the valley has to be not more than adistance of the order of the strip pitch away fromthe surface. This reduces (with reasonable bulkdoping) the for potential barrier the holes betweenthe top gates themselves and between the top gatesand the back diode, thus enabling the thermionicinjection of holes. Furthermore, spread of thesignal charges along the gates is not prevented.Both problems can be solved simultaneously withan increase of doping in the surface region ifthis is done in a strip-like fashion, with stripsperpendicular to the gate direction. These stripsmay be called ‘channel guides’, the narrow gapsbetween the strips have the function of channelstops.Compared with standard CCDs, the fullydepleted pn-CCDs have several important advantageswhenusedasanX-raydetector:• Enhanced sensitivity as the full volume isdepleted. This is especially important for themeasurement of X-rays at higher energies andfor high energy charged particles.• Uniform response with backside illumination asthe backside consists of a unstructured large-areadiode.• High speed of operation due to charge transferat a moderate distance from the surface.• The possibility of building larger cell structures.• Increased radiation hardness because radiationsensitiveMOS structures do not play an essentialrole in the function of the device.4.1.5.5 THE DEPFETDETECTOR–AMPLIFIER STRUCTUREThe DEPFET structure which simultaneously possessesdetector and amplification properties wasproposed by Kemmer and Lutz 6 in 1987 and hassubsequently been confirmed experimentally. 10 Itis based on the combination of the sideward depletionmethod (Figure 4.1.7) – as used in a semiconductordrift chamber shown in Figure 4.1.8 – andthe field effect transistor principle.In Figure 4.1.11 a p-channel transistor is locatedon a fully depleted n-type bulk. As was donein the pn-CCD the potential valley has beenmoved close to the top side. Signal electronsgenerated in the fully depleted bulk assemble ina potential maximum (‘internal gate’) and increasethe transistor channel conductivity by induction.The device can be reset by applying a large positivevoltage on the clear electrode.

INTERACTION OF RADIATION WITH SEMICONDUCTORS 143SourceGateAlDrainClearSiO 2NP + P + N + X xxxSClearG xxx G xxxDP + BiasFigure 4.1.11 The DEPFET detector–amplifier principleThe DEPFET has several interesting properties:• combined function of sensor and amplifier;• full sensitivity over complete wafer;• low capacitance and low noise;• nondestructive repeated readout;• complete clearing of signal charge: no resetnoise.These properties make it an ideal building blockfor an active X-ray pixel detector, or an electronicamplifying device for other silicon detectors.4.1.6 INTERACTION OF RADIATIONWITH SEMICONDUCTORSThe interaction of radiation with semiconductormaterials causes the creation of electron–holepairs that can be detected as electric signals.For charged particles, ionization may occur alongthe path of flight by many low-recoil collisionswith the electrons. Photons have first to undergoan interaction with a target electron (photo orCompton effect) or with the semiconductor nucleus(e.g. pair conversion of photons). In any case,part of the energy absorbed in the semiconductorwill be converted into ionization (the creation ofelectron–hole pairs), the rest into phonons (latticevibrations), which means finally into thermalenergy.The fraction of energy converted into electron–holepair creation is a property of the detectormaterial. It is only weakly dependent on the typeand energy of the radiation except at very low energiesthat are comparable with the band gap. Fora given radiation energy, the signal will fluctuatearound a mean value N given byN = E (4.1.5)wwith E the energy absorbed in the detectorand w the mean energy spent for creating anelectron–hole pair (3.65 eV for silicon). Thevariance in the number of signal electrons (orholes) N is given byN 2 = FN (4.1.6)with F the Fano factor (F = 0.115 for silicon). 11Fano arrived at this expression by consideringthe probabilities of ionizing and non-ionizingcollisions of charged particles in gases, makingsome rather arbitrary assumptions in his model.His approach has been adapted to semiconductorsby Shockley. 12Very important aspects of the detector materialin spectroscopic applications are the penetrationdepth of charged particles and the absorptionlength of photons. A very small absorption lengthwill result in a high probability of generatingthe signal close to the surface, where signalcharge may only be partially collected becauseof surface treatment (e.g. doping), coverage withinsensitive material (e.g. a naturally or artificiallygrown insulation layer) or deterioration in thesemiconductor properties, which usually appearsclose to the surface due to distortion of thelattice. A very large absorption length leads

144 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPY10 −310 −4Absorption length (m)10 −510 −610 −710 −810 −9 1 10 100 1000 10000Energy (ev)Figure 4.1.12 Energy dependence of the photon absorption length in silicon (*) and in silicon dioxide (⋄)to inefficiencies as radiation may traverse thedetector without interaction. The dependence of theabsorption length on photon energy for silicon isgiven in Figure 4.1.12.Looking into the photon absorption process inmore detail one discovers additional importantaspects. Ejecting for example an electron fromthe K-shell will in some cases be followed bythe capture of an electron from the L-shell, thisprocess being accompanied by the emission ofa photon with an energy of 1.74 keV. As seenfrom Figure 4.1.12, this photon has an averagerange of 10 µm and therefore a reasonable chanceto be emitted from the detector without beingdetected. This ‘missing energy’ is responsible forthe occurrence of secondary ‘escape’ peaks shifteddownwards by this energy in the X-ray spectra.4.1.7 THE RADIATION ENTRANCEWINDOWThe quality of the radiation entrance window isof great importance for spectroscopic detectors,and in particular for radiation with short penetrationdepth as for example low energy X-rays.In the ideal case all energy should be convertedinto signal charge which then should reach withoutloss the collecting electrode. Unfortunatelythere are always absorbing layers present at thesurface or a region in which part of the chargegets lost by recombination or other processes. Allthe devices to be described in the second partof this paper have a homogeneous unstructuredlarge area entrance window which is optimized forspectroscopy. In the following the physical processesdetermining the spectroscopic performanceare discussed. 13,14Figure 4.1.13 shows the situation for a p + -ndiode window which is covered with a thin layer ofoxide. Photons interacting in the centre bulk (c) arecompletely converted and produce the proper peakin the spectrum. Photons with high energy (d) maytraverse the detector without interaction. Photonsinteracting near the p + contact (b) will lose partof the signal by recombination and give rise to theshoulder on the left of the peak. Photons interactingin the oxide (a) will emit part of the charge intothe silicon and create the ‘flat shelf’ on the left.It remains to emphasize that both quantities,the spectral resolution as well as the background,strongly determine the usefulness of a

THE RADIATION ENTRANCE WINDOW 14510 510 410 310 210 110 010 -10 100 200 300Energy (adu)400500−−(a)n + -Si(b)(c)SiO 2p + -Si(d)1.000.90CCK (g)0.800.700.600.500 200 400 600Depth (nm)800Figure 4.1.13 Schematic diagram of the physical processes responsible for the charge loss in the radiation entrance window.The spectrum is from the Cu L line (930 eV). The shape of the spectrum can be fitted with a model 13 which leads to the chargecollection efficiency as a function of the depth of interaction (shown in the bottom part of the figure)spectrometer. Beside the energy resolution thepeak to background (or peak to valley, P/V) ratiois the most important performance figure since itdefines the ability of the instrument to separateweak X-ray lines from the dominant lines.The good performance of a thin optimizedradiation entrance window manifests itself in ahigh quantum efficiency as shown in Figure 4.1.14and in excellent spectroscopic properties (to beshown together with the respective detectors inPart 2 of this subchapter).PART 2: SEMICONDUCTORDETECTORS IN X-RAYSPECTROSCOPY AND IMAGINGHaving given an overview of the basic detectiontechniques for X-rays in semiconductors we willnow look at the subject from the standpoint of possibleapplications. X-ray astronomy has been pushingfor several years the instrumentation for broadbandimaging non-dispersive X-ray spectrometers:Since the launch of the European XMM-Newton

146 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPY1.00.80.60.40.2Quantum efficiency1.000.980.960.941.830 1.840 1.850 1.860 1.870Energy (keV)0.0 0.15 1 10 30Figure 4.1.14 Quantum efficiency for X-rays in the range of 150 eV to 30 keV energy of a pn-CC of 300 µm thickness(measurements and solid line) equipped with a thin optimized radiation entrance window. Close to 100 % quantum efficiencyis reached over most of the range. Remarkable is the high efficiency at low energies. The falloff at high energy is due to thelimited thickness. The dotted line represents an extrapolation to 500 µm thick sensitive volumesatellite in December 1999, reliably operatingX-ray CCDs have been delivering extraordinaryimages, recorded in a single photon countingmode, imaged through the largest X-ray telescopeever built. Related applications in other fields ofbasic and applied science will equally be mentioned.State of the art X-ray detectors with energy,time and/or position resolution at high quantumefficiency from the near infrared up to 30 keV aredescribed in detail. They are all based on the conceptof sideward depletion, the underlying principleof silicon drift detectors. They have beenprimarily developed for astrophysics experimentsin space, for material analysis and for experimentsat synchrotron radiation facilities. The functionalprinciples of the silicon devices, i.e. detectors andon-chip electronics, are derived from basic solidstate device physics. The spatial resolution, thespectroscopic performance of the systems, the longterm stability and the limitations of the detectorsare described in detail. Field applications show theunique usefulness of state of the art silicon radiationdetectors.4.1.8 THE DETECTION OF OPTICALPHOTONS AND X-RAYSImaging of photons is best known in the visibledomain, ranging from a wavelength of 3.500 Åup to 6.000 Å. For those applications optics anddetectors are equally well developed. However, allthose imaging systems do not count the incomingphotons individually to measure their position,energy and arrival time.The photon information is either integratedin the grains of a photographic film that isafterwards developed chemically or the photonsare collected in individual picture cells (pixels)and after a given time sequentially read out. Thephotonic or electronic content of each grain orpixel is then ‘counted’ to measure the intensityof the incident photon flux. Traditionally, the

THE DETECTION OF OPTICAL PHOTONS AND X-RAYS 147energy of the photons is determined by anarrangement of various filters, transparent onlyfor a narrow, well defined bandwidth of theincoming photons. In this sense, the image is astatic, integrated reconstruction of a local photonintensity distribution.Single ‘optical’ photons cannot be counted upto now in a practical manner, i.e. with reasonablylarge arrays. The energy of the photons is too smallto detect them individually with non-cryogenicdetectors: it is a fraction of 1 eV in the nearinfrared and up to 4 eV for the violet part ofthe visible spectrum. [1] In gas detectors morethan 20 eV are needed for the ionization of adetector gas atom, and room temperature silicondetectors need at least 1 eV for the generation of anelectron–hole pair in the optical range and 3.65 eVfor ionizing particles with sufficiently large energy.For a proper electronic extraction of the very weaksignal of one optical photon, read out electronicsshould operate below 0.1electrons equivalent noisecharge (ENC). This has not yet been reached instate of the art silicon sensor systems. The bestnoise values obtained so far are 0.9 e − (rms).From approximately 11.000 Å to 3.000 Å only oneelectron-hole pair per photon is generated due tothe ionization process and its statistics in silicon.In this sense, direct spectroscopic information inthe optical range is physically not available fromsilicon detectors.The X-ray imaging detector systems which aredescribed below record simultaneously the energy,position and arrival time of each individual X-rayphoton without using selective absorbers. Thephysical reasons for being able to make trulyenergy-dispersive X-ray detectors are the low electron–holepair creation energy (average) of about3.65 eV in silicon at room temperature and the verythin radiation entrance windows of only a few tensof partially insensitive atomic layers of silicon andnative SiO 2 which can be penetrated by the (evensoft) X-rays. For a good quantum efficiency athigher X-ray energies only the depleted thickness[1] Cryogenic detectors are able to perform single photon countingin the near infrared, visible and soft X-ray domain. 20 The band gap forthis kind of detectors is in the mV range as compared to 1.1 eV for Si.But they require cooling down to the order of 100 mK.of silicon (signal interaction depth) is relevant. At500 µm sensitive detector thickness, for example,25 % of 25 keV X-rays are converted in electron–holepairs and can be collected and detected(see Figure 4.1.14). For two-dimensional silicondetectors with high position and energy resolution,the fabrication by a planar process – comparableto the fabrication in state of the art microelectronics– is obligatory. Depletion thicknesses of1000 µm are technically a limit for the detectorfabrication in planar processes.In the energy band between 0.1 keV and 30 keVstate of the art imaging silicon detector systems areideal for the direct detection with high quantumefficiency, position and energy resolution.The astrophysical requirements have driven thedevelopments of the high resolution X-ray detectorsfrom 100 eV to 10 keV in the last 10 years.The X-ray Multi Mirror Mission (XMM) of theEuropean Space Agency (ESA) was successfullylaunched in a highly eccentric orbit on10 December 1999 with three large X-ray telescopesand reflecting grating spectrometers all havingspecially designed X-ray CCDs in their focalplanes. 15,16 The wavelength dispersive gratings areread out with the more conventional back illuminated25 µm deep depleted MOS CCDs for energiesup to 4 keV. 17The review of silicon detectors and applicationsis based on basic principles and discusses physicallimitations. As limiting factors the electronicnoise in physical systems and the effect of theradiation entrance window will be treated. Devicesimulations will serve as an intuitive approachto understand the collection and motion of signalelectrons in the detectors. Various types of silicondrift detectors (SDDs) will be introduced, amongthose circular, linear and multi-cell devices. Applicationswill demonstrate the broad use of SDDs.The controlled drift detector (CDD) will highlightthe large variety of silicon drift devices. pn-CCDsas high resolution X-ray imagers will introducethe field of position resolved spectroscopy. Theexcellent properties of pn-CCDs will demonstratethe progress in the field. The conceptually mostadvanced device in spectroscopic X-ray imagingis represented by the backside illuminated active

148 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYpixel sensor (APS) DEPFET detector. The concept,functional principles, measured and expectedproperties will be described in detail.All experimental results shown here are fromdevices which have been designed, fabricated andtested at the MPI semiconductor laboratory.4.1.8.1 X-RAY DETECTIONThe absorption depth of photons in silicon oxideand silicon varies over five orders of magnitudes inthe bandwidth of 1 eV to 20 keV, as can be seen inFigure 4.1.12. The average range of the photon inthe silicon varies from several millimetres in thenear infrared to a few tens of ångstrøm only for UVlight and then increases again for higher energies to1 mm for approximately 20 keV. The absorption ismost efficient at the silicon M-, L- and K-edges atapproximately 20 eV, 100 to 150 eV and 1830 eV,respectively.The X-ray detectors should be able to absorb allincident radiation and transfer a variation of fiveorders of magnitude of absorption lengths into aquantum efficiency over the whole range of interestwith high homogeneity and an efficiency close to100 %. This should be independent of the photoninteraction location in the detector body, where thephoton to electron–hole conversion occurred.The primary conversion process of the incidentradiation into a detectable quantity can go intolight, heat and electrical charges. The incident photonscan be directly converted into light, e.g. inscintillators, which will then be analysed with thehelp of light sensitive detectors, i.e. photomultipliersor photodiodes to finally yield an electronic signal.Another technique makes use of the increaseof temperature caused by the absorption of the photonenergy. The temperature increase is then usedto break up Cooper pairs in a superconductor or tomake a current or voltage change in a microthermometer,resulting in an electronically detectablequantity. The last possibility is to convert the incidentradiation directly into electrical charges. Thegeneration of electron–hole or electron–ion pairsin semiconductors and gas counters can be directlyamplified to generate an electronic pulse, proportionalto the energy of the incoming photons. Upto now all three types of techniques have beenused to realize two-dimensional, X-ray sensitivedetector systems. 18Scintillators with photodiode or photomultiplierreadout can go to the highest energies; cryogenicdetectors as bolometers or superconducting tunneljunctions can achieve to date the best energyresolution; 19 avalanche photodiodes can achievea time resolution for individual events of severalpicoseconds; with proportional gas counters sensitiveareas without insensitive gaps in the orderof several hundred cm 2 have been built; operationat high temperatures has been achieved withHgI detectors, but there is no detector combiningall the needed properties in one single detectorsystem with highest quality. Up to now, onlystate of the art X-ray CCDs and APS unify thebroad band properties, with some compromises inthe above list of desired physical parameters. Themost advanced systems are all made on silicon asabsorbing detector material and with integrated onchipelectronics.The availability of very good starting silicon,the highly elaborated fabrication techniquesand the well matched physical properties of silicon,makes silicon microsystems – detector andelectronics, monolithically unified – a good candidatefor satisfactory performance figures for manyapplication scenarios. [2]4.1.9 SILICON DRIFT DETECTORSTo obtain the lowest possible noise in radiationmeasurements, the total capacitance of the signalcharge collecting node must be minimized. Inconventional structures the sensitive area alwayscorrelates with the readout capacitance. Either thesensitive area is made very small or the sensitivethickness very large to reduce capacitance. Thesilicon drift-type detectors decouple collection areafrom the readout node size, since an electric fieldparallel to the wafer surface transports the signal[2] Simple silicon pad and strip detectors, as well as hybrid pixeldetectors (detectors and electronics on different chips, then bumpbonded to form a hybrid detector) will not be treated, because theiruse is restricted to count X-rays. They are unable to reach Fano-limitedenergy resolution, mainly because of their high electronic readout noise.

SILICON DRIFT DETECTORS 149charge to a small output node, whose size isindependent of the sensitive area.Other silicon drift-type detectors like pn-CCDs 15,20 and APS 10,21,22 also make use ofthe so-called principle of sideward depletion(Figure 4.1.7). The functional principles of SDDsand CCDs are related. The SDD could be calleda phaseless pn-CCD (see Section 4.1.12), becausethe charge is continuously drifted out, or a pn-CCD could be called a discrete SDD, since a CCDdrifts the charge packets in clocked time intervals,discretely, to the readout node.4.1.9.1 OPERATION PRINCIPLEThe basic concept of semiconductor drift detectorshas already been presented in Section 4.1.5.Here we go into more detail and consider its consequenceson detector properties.The silicon drift chamber is derived from theprinciple of sideward depletion (see Figure 4.1.7)by adding an electric field, which forces theelectrons to the n + readout anode. This is simplyachieved by implanting a parallel p + strip pattern atboth sides of a semiconductor wafer (instead of thehomogeneous implant on both surfaces shown inFigure 4.1.8) and superimposing a voltage gradientat both strip systems. The direction of the voltagegradient is such that the n + readout anode hasthe highest (positive) potential, therefore collectingall the signal electrons accumulated in the localpotential minimum (bottom of the parabola inFigure 4.1.15) and drifting them to the absolutepotential minimum for electrons at the n + readoutnode (Figure 4.1.16). The holes from the ionizationprocess disappear directly in their local potentialminimum in the p + strips. From the Poissonequation it can be easily derived that in the case offull depletion with the depletion voltage U D and ina one-dimensional approximation across the siliconwafer (y) and with a linear superimposed driftfield parallel (x) to the wafer surface, the electricpotential (x,y) is with d the wafer thickness andthe depth:(x,y) = U D −ρ2ε 0 ε Si(y 2 − yd) − out − inx out − x in(4.1.7)7060Potential (−V)50403020100300250200150xxx1005000 100 200 300 400xxxFigure 4.1.15 Simulation of the electric potential of a silicon drift detector in the bulk of the detector far from the readout node

150 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPY8060Potential (−V)40200300250200xxx1501005000 100 200xxx300 400Figure 4.1.16 Simulation of the electric potential of a silicon drift detector in the vicinity of the readout nodeThe drift field E d is usually applied betweenthe outer p + drift structures ( out ) and the innerp + drift strips (field strips) or rings ( in ) inthe vicinity of the readout node. Neglecting thepotential perturbations close to the n + anode, thex component of the drift field can be written asE D = out − inx out − x in(4.1.8)The drift speed for practical drift fields variesbetween 1 µm/ns and 10 µm/ns. The maximumdrift length realized up to now is about 4 cm. 234.1.9.2 ENERGY RESOLUTIONThe measurement of the total energy of theincident radiation is achieved by a careful, lownoise‘counting’ of all electrons arriving at the n +readout node. The number of created electron–holepairs is proportional to the energy of the incidentX-ray and that the average energy required tocreate one electron–hole pair is 3.65 eV at roomtemperature. For the following considerations, weassume to operate the first amplifying stage in anideal source follower configuration. The detector’sanode, collecting all signal charges can in principlebe made very small, limited only by technologicalparameters. If this readout node is then directlycoupled to the gate of an on-chip pre-amplifyingfirst transistor, the total read-node capacitance canbe kept as low as 100 fF (or lower), translatingin a high sensitivity of the on-chip amplifier, i.e.the increase of the readout node voltage with thearrival of one electron. WithU out = Q inj(4.1.9)C totwhere U out is the increase of the output voltage,Q inj the injected charge and C tot the total readoutnode capacitance, an X-ray of 6 keV stimulates avoltage change of 2.6 mV. This corresponds to asensitivity of 1.6 µV/electron. The noise of the onchipamplifier in such configurations can be keptas low as 5 electrons rms at temperatures around−30 ◦ C.For optimum noise and speed performance theimplementation of the first amplifying stage on thedetector is essential to the use of SDDs.The anode is connected to an amplifyingjunction field effect transistor (JFET) integrateddirectly on the detector chip (Figure 4.1.17). Thisway the capacitance of the detector–amplifier

SILICON DRIFT DETECTORS 151Resetn-JFET GuardringDGSn' SIAnodeBackRing #1Path ofelectronsFigure 4.1.17 On-chip single-sided junction FET coupled tothe readout node of a SDDsystem is minimized by eliminating bond wiresbetween detector and amplifier, thus avoiding allkinds of stray capacitances between the readoutnode and ground, making the system again fasterand less noisy. Further advantages are evidentas the effect of electrical pickup is significantlyreduced and problems of microphony, i.e. noiseintroduced by mechanical vibration, are excluded.With the help of Figure 4.1.17, the basics ofthe amplification and resetting process of theintegrated JFET can be easily understood. In thecentre of the schematic drawing, a single sidedn-channel JFET is shown. Let us assume thatelectrons, generated by ionizing radiation, drifttowards the readout anode. The voltage change,generated at the readout node is directly coupledto the p + gate of the n-channel transistor (sourceand drain are n + implants, the transistor channelis a deep n implant). The negative voltage on thep + gate reverse biases the junction, thus depletinginto the transistor channel, resulting in a currentdrop through the transistor. This change of currentcan be precisely measured.As it collects more and more electrons the JFETgate gets increasingly reverse biased relative to thetransistor channel. At a given potential differencethe gate is discharged by impact ionization in thetransistor channel close to the junction of the p +gate and the drain at the end of the channel. 24During detector operation the gate adjusts itspotential in a way that all signal electrons andleakage current are compensated by the breakdownmechanism. In other words, the integrated JFETresets itself automatically, there is no need foran externally clocked reset pulse, and the SDDand integrated electronics are operated with directcurrent voltages only.The energy resolution is limited by the fluctuationsin the generation of electron–hole pairs inthe conversion process and the electronic noisegenerated by the input amplifier and the detectorleakage current. The electronic noise has beenconsidered in Section 4.1.4, the fluctuations in theionization process in Section 4.1.8. The followingresults have been obtained for the ENC:ENC 2 =(4kT 2 )C 2 1tot A 13g m τ + (2πa fCtot 2 )A 2white series noise(+ qI l + 2kT )A 3 τR fparallel noiseand for the Fano noiselow frequencynoise(4.1.4)N 2 = FN (4.1.6)The white serial noise that is due to thermalfluctuations in the transistor channel scales with1/ √ τ, the 1/f low frequency noise due to trappingof charge carriers in the vicinity of the channel isindependent of shaping and the parallel noise dueto detector and gate leakage current as well as thefeedback resistor contribution grows with √ τ.The leakage current has its physical originin the thermal generation of electron–hole pairsin the semiconductor through energy levels inthe forbidden band gap. Those levels may arisefrom (mainly) metal contamination in the siliconor imperfections in the silicon lattice. In thecase of ‘mid-band-gap’ traps, the leakage currentattenuates approximately a factor of two every7 K in temperature reduction. In the case of thelow frequency, or 1/f noise, electrically activetraps capture and release the charge carriers inthe transistor channel and therefore give rise to

152 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYa change of the electric field in the channel,influencing the current flow. The perturbations ofthe electric field are described by the density oftraps and their capture and emission time constants.If the detector leakage current could be madeinfinitely small (e.g. by cooling the detector andfront-end electronics) the time shaping constantshould be made as long as possible to obtainthe lowest ENC, up to the moment, when theshaping time constant independent 1/f noise setsa lower limit for the noise. Of course, again,this conflicts with the requirement of high countrate capabilities; long shaping times, i.e. longsignal processing times lead to signal pile-upand therefore degrade the system performance.To beat pile-up, again, the only possibility is tolower the total input capacitance C tot and thuslower τ to achieve the same ENC. The 1/fnoise contribution is independent of τ, whichcannot easily be overcome by operational means.This technologically intrinsic limitation of thenoise level has its origins in the nonperfectcrystal properties of the starting material and thefabrication process.The achievable energy resolution E FWHM of aSDD can be as good as√E FWHM = 2.355 w ENC 2 + FE (4.1.10)wF is the Fano factor, 25,26 E the total X-ray energy,w the pair creation energy, ENC the rms fluctuationof the readout noise and 2.355 the conversionfactor between the standard deviation σ (rms)of a Gaussian and the FWHM ln(2 √ 2) = 2.355.With F = 0.115, w = 3.65, for E = 6 keV and areadout noise of 10 electrons (e.g. close to roomtemperature), the best achievable energy resolutionis 150 eV FWHM. Values of 140 eV to 150 eV arenow routinely achieved at −10 ◦ C with SDDs. Byfurther reduction of the temperature, i.e. reductionof the detector leakage current, i.e. reduction ofENC from 10 to 5 electrons, the energy resolutionimproves to 125 eV FWHM at 6 keV. State of theart SDD systems operate very close to the abovevalues. 7,27 For ENC = 0, the Fano limit can bederived, which is 119 eV (FWHM) for 6 keV X-rays(see also Figure 4.1.45).4.1.9.3 POSITION RESOLUTIONIn standard applications of SDDs in high energyphysics experiments the position resolution ofSDDs is obtained by a precise measurement of thedrift time. The ‘start’ signal could be delivered bythe bunch crossing time mark and the ‘stop’ timeby the SDD. In our short consideration we restrictourselves to minimum ionizing particles, traversingthe SDD perpendicular to the detector’s surface.According tox drift = µ n E d t drift (4.1.11)the position x drift can be obtained easily with theelectron mobility µ n , the electrical drift field E dand the measured drift time t drift . If the readoutanode is segmented in many individual nodes,the position is measured in two dimensions, withthe help of the drift time (x) and the position ofthe anode (y) as indicated in Figure 4.1.18.The position resolution of a SDD was derivedfor minimum ionizing radiation by Rehak 28 includingthe effects of charge spreading during the collectionand drift time. For realistic assumptionsin high energy physics experiments, the limit forFigure 4.1.18 Sketch of a two-dimensional silicon driftdetector. The n + readout nodes are indicated as black squaresin the vertical direction on the left-hand side (y-direction). Thedrift of the signal charges is perpendicular to the p + field strips(x-direction)

SILICON DRIFT DETECTORS FOR X-RAY DETECTION 153the position measurement precision of SDDs isapproximately 2 µm rms.With the SDD principle in mind, the designerhas great flexibility in the choice of anodeconfigurations and drift directions. For instanceat the semiconductor laboratory of the Max-Planck-Institutes (MPI-HLL) large SDDs havebeen fabricated with linear drift geometry, i.e.parallel strips, 29 up to 4.2 × 3.6, 4.2 cm 2 and a55 cm 2 cylindrical geometry on 4 ′′ wafers, in whichelectrons drift along the radial direction to oneof 360 anodes placed at the wafer edge. 30 Bothsystems have been used as particle trackers.For the use in imaging X-ray spectroscopy thisstraightforward use of SDDs is not practical. TheCDD in Section 4.1.11 shows alternatives for thesimultaneous measurement of position and energywith SDDs.4.1.10 SILICON DRIFT DETECTORSFOR X-RAY DETECTIONTo make the detectors suitable for spectroscopicX-ray applications, the strip system on both surfacesis replaced by a large area pn-junctionon one side, which is used as a very homogeneousthin entrance window for the radiation 6,7,31(Figure 4.1.19). A further improvement is the useof circular drift electrodes, which force the signalelectrons to a very small anode in the centre of thedevice, from where they are transferred to the gateof an integrated JFET.The radiation entrance window, denoted as‘back contact’ in Figure 4.1.19 and 4.1.20, playsan important role in X-ray spectroscopy for thedetection of light elements, i.e. for X-ray radiationbetween 100 eV and 1 keV and for the detectionof trace elements in the presence of additional(strong) continuous and X-ray line emission: 13,14X-ray absorbing layers on top of the radiationentrance window as e.g. SiO 2 or Si 3 N 4 in SDDswould significantly lower the quantum efficiencyfor low energy X-rays. Depending on the photonenergy, a fraction of the X-rays would be stoppedin the insensitive layers.Figure 4.1.21 shows a typical low energy(900 eV) X-ray spectrum obtained with a detectorhaving a homogeneous entrance window. Theorigin of the low energy background (shoulderand flat shelf) has been discussed in Section 4.1.7.This background extending from zero to the X-rayenergy is of extreme importance in spectroscopyas it will hide weak lower energy lines. It canbe reduced by technological means by suppressionof SiO 2 –Si interface recombination. This isaccomplished by soothing the interface states at theboundary by technological means, e.g. hydrogenAnodeAmplifierField strips−vp +n − SI−−−−Path ofelectronsBack contactFigure 4.1.19 Cylindrical silicon drift chamber with an integrated amplifier for spectroscopic applications. The entire siliconwafer is sensitive to radiation. Electrons are guided by an electric field towards the small-sized collecting anode in the centre ofthe device

154 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPY−150Back contactElectron potential (V)−100−50Field strips0300250Depth (µm)20015010050Anode0−1.5−1.0−0.50.0Radius (mm)0.5 1.0 1.5Figure 4.1.20 Simulated potential energy distribution in a circular silicon drift chamber with homogeneous radiation entrancewindow. The simulation includes the whole detector shown in Figure 4.1.19 including the electron collecting readout node. Thearrows indicate the paths of the electrons drifting to the anode10 210 110 5 100 200 300 400 50010 4Noise peakGaussian peak10 3CountsFlat shelfShoulder10 010 −10Energy (adu)Figure 4.1.21 Typical low energy X-ray spectrum at 900 eV, showing the different components of the detector background. The‘noise peak’ arises from the detector, signal processors and digitization circuits. As can be seen here, the trigger threshold isabout 50 eV. The flat shelf arises from ionization in the layers above the sensitive silicon (see also Figure 4.1.13). The shoulderhas its origin in interaction areas close to the p + back diode. The p/v ratio of this measurement is approximately 2000:1

SILICON DRIFT DETECTORS FOR X-RAY DETECTION 155termination of bonds. Recombination processes atthe silicon surface region are controlled by appropriatedoping and annealing procedures.If the recombination is prevented or suppresseddue to proper thermal treatments, the signalcharges diffuse in the field free region of the p +implant until they eventually reach the edge of thespace charge region. At that moment, the charge isswept away to the n + readout node.The low energy background strongly determinesthe usefulness of a spectrometer. Beside theenergy resolution the peak to background (orpeak to valley, P/V) ratio is the most importantperformance figure since it defines the ability ofthe instrument to separate weak X-ray lines fromthe dominant lines.Within the cylindrical area no charge splittingis possible, [3] resulting in a single reading of agiven charge package. The low energy responsedown to 100 eV can be made as good as in anyother semiconductor detector, by keeping all fasttiming capabilities of the SDD system. In additionto the above mentioned features an electron sinkelectrode at the structured surface is implementedas well as an integrated voltage divider. Theelectron sink takes out all surface generated currentcomponents, reducing the leakage current to thepure bulk contribution of less than 1 nA per cm 2for a depletion depth of 500 µm. The integratedvoltage divider supplies all voltages for the driftrings. Only the innermost and outermost p +ring needs to be contacted. The details of thesetechniques are described elsewhere. 21 For a SDDof 5 mm 2 active area the maximum drift time fromthe edge of the detector is about 150 ns, while thetime spread of the signal charges of one photonevent is approximately 5 ns. As we have usually noevent trigger signal in the field of X-ray detection,the device has no position resolution within thesensitive area of 5 mm 2 .The electric potential of the cylindrical silicondrift chamber is shown in Figure 4.1.20 in atwo-dimensional cut perpendicular to the surfacethrough the silicon wafer. It shows the potential[3] In the vicinity of the on-chip FET, charge losses were observed.These are avoided by operating the FET outside the sensitive area (seeSection 4.1.10.1).energy for electrons of the SDD of Figure 4.1.19,including all field strips and the central electroncollecting anode. The equipotential of the homogeneouslydoped radiation entrance window can beseen on the back, the field strips (rings) with theirdecreasing (negative) potential on the front side.There is no field free region in the device and allelectrons in the sensitive area are guided withinless than 150 ns towards the readout node. Howeverthe time spread of the charge cloud is only inthe order of 5 ns. Overlapping charge clouds limitthe single photon counting capability to about 10 6X-rays per detector element.The cylindrical SDD has outstanding properties:at moderate temperatures of about −10 ◦ C(achievable by Peltier cooling), the devices havealready good spectroscopic properties, 32 comparableto state of the art Si(Li) detectors, but withcount rate capabilities up to 10 6 counts per second(cps) to be compared to the order of 10 4 cps with a70 ns shaping of the classical Si(Li) detector concept,without the need of liquid nitrogen cooling(Figure 4.1.22). The energy resolution at two differentshaping times and temperatures are shownin Figure 4.1.23. If the incident photons are correctlycollimated within the sensitive area, the P/Vratio,i.e.the 55 Fe peak count rate divided by theaverage number of counts around 1 keV, can beas large as 7000:1. The P/V ratio determines thesensitivity limit for weak X-ray intensities, as itdescribes the extraction of an X-ray line from thedetector background.Very recently a 10 mm 2 large SDD based on thesame layout was fabricated and tested. At −10 ◦ Cithas shown a similar energy resolution as the abovedescribed 5 mm 2 large SDD. This is an importantstep towards the use of SDDs in applications wherelarger areas must be covered.4.1.10.1 THE SILICON DRIFTDETECTOR DROP (SD 3 )The previously described ‘conventional’ cylindricalSDD with the on-chip amplifier located inthe middle of the detector exhibits partial events,i.e. events whose signal charge is partially correctlycollected and partially drained by the positivepotential of the first SSJFET on the SDD. An

156 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPY300280FWHM (eV) @ 5.9 keV -15°C2602402202001801601400200 400 600 800 1000Incoming rate (kcps)Shaping time1.0 µs0.75 µs0.46 µs0.22 µs0.15 µsFigure 4.1.22 Silicon drift detector energy resolution as a function of the X-ray ( 55 Fe source) count rate. The measurement wasdone close to room temperature. The signal processing time (here peaking time) ranged from 150 ns to 1 µs20002500Counts/channel15001000500exp. datagauss fitCounts/channel200015001000500exp. datagauss fit011001200 13001400 1500 1600012001300 14001500 1600 1700(a)Channel #(b)Channel #Figure 4.1.23 (a) Manganese spectrum recorded with a circular SDC at 25 ◦ C. The shaping time was 0.25 µs, the FWHM is178 eV. Typical values at room temperature scatter from 170 eV to 190 eV. (b) Manganese spectrum recorded with a SDC at−10 ◦ C. The shaping time was 1 µs, the FWHM is 144 eV. The p/v ratio is as good as 7000. In this case routinely obtainedenergy resolutions are in between 140 eV and 150 eV (FWHM) for the circular SDDsarea with a diameter of 300 µm around the on-chipFET can be affected by this partial signal collectionmechanism, leading to a decreased P/V ratio. Inaddition, if X-rays of higher energies are used e.g.15 keV to 25 keV, the X-rays eventually traversethe sensitive thickness of 300 µm to 500 µm andmay be converted into electron–hole pairs closeto the SiO 2 – silicon interface in the FET vicinity.In case the conversion cascade of electronsand holes is close enough to the border of the

SILICON DRIFT DETECTORS FOR X-RAY DETECTION 157on-chip FET, they may increase the number ofinterface traps and give rise to an increase of fixedpositive oxide charges or interface states. The lattereffects degrade the performance of the on-chipSSJFET.The following three reasons, namely, partialsignal collection, increased radiation hardness andreduced output node capacitance, have led us tothe design of a SDD with eccentric readout FET 33as shown in Figure 4.1.24. Energy resolutions atthe MnKα line of an 55 Fe source were measureddown to 124 eV at −20 ◦ C with count rates around1000 cps. Typical values scatter around 128 eVFWHM (Figure 4.1.25), being confirmed by manyother users, both scientific and industrial. TheSD 3 under test had a sensitive area of 5 mm 2 .The electronic noise contribution at −15 ◦ Cwas5 electrons (rms).The SD 3 detector now has the potential todirectly compete with Si(Li) detectors in thedetection of light elements. Cryogenics are notlonger needed and microphonics is completelyavoided. The SD 3 will shortly be also availablein larger formats up to 30 mm 2 .4.1.10.2 WORKS OF ARTINVESTIGATIONS WITH SILICONDRIFT DETECTORSIn archeometry different kinds of investigationsare used for the characterization of art objects. Inparticular, XRF (X-ray fluorescence) spectroscopyis a nondestructive technique widely used for theidentification of chemical elements in pigments,metal alloys, and other materials. The classicalhigh resolution cryogenic detectors, like Si(Li) andHP(Ge) detectors (whose energy resolution is ofthe order of 130 eV FWHM at the Mn Kα line),are not completely suitable for the realization ofportable instrumentation because of the need ofliquid nitrogen in the cooling system.Recently new silicon PIN diodes simply cooledby a Peltier element have been introduced. Theirenergy resolution (of the order of 200 eV FWHMat the Mn Kα line at −30 ◦ C) is in some casesunsatisfactory (especially for the analysis of lightchemical elements). At low energy, the maincontribution to the FWHM is due to the electronicnoise of the detector front-end system, which isDrift ringsIrradiated areaSignal electronsIntegrated FETFigure 4.1.24 Silicon drift detector ‘drop’ with asymmetric JFET location. The drift of the electrons is shaped by adequate fieldstructures on one of the surfaces. The read node capacitance was reduced by more than a factor of 2. In a practical applicationthe on-chip FET will be excluded from direct X-rays by a collimator

158 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYEnergy (eV)100001000 2000 3000 40005000 60001000Shaping time 1.0 µsTemperature −18°CEnergy resolution 128 eV (Mn Ka)Counts100101500 1000 1500 2000 2500 3000ChannelFigure 4.1.25 Measured Mn Kα and Mn Kβ spectrum with an SD 3 from an 55 Fe source. The peak-to-background ratio is about9000:1, the FWHM 128 eV at a shaping time of 1 µs. The electronic noise (ENC) was 6 electrons onlyassociated with the detector–capacitance, directlydependent on the detection area. In addition thisperformance is only obtained with a PIN typedetector at very low output count rates, typicallybelow 1000 cps.The possibility to operate the SDD at non cryogenictemperatures, i.e. at or close to room temperatureand the good energy resolution (in theorder of 140 eV FWHM at 6 keV) makes thesedetectors suitable for the realization of high resolutionportable instrumentation. Recently a portablehigh resolution X-ray spectrometer – based on theSDD, cooled by a Peltier element – was realizedat the research laboratories of Politecnico diMilano. 34 A commercial miniaturized X-ray tubewas utilized as an excitation source.The measurements on different kinds of artobjects confirmed the ease of use combined withthe high class performance, in particular the highenergy resolution. Figure 4.1.26 shows a spectrumof an orange pigment recorded with the abovedescribed system. The almost background-freedetection of the individual chemical elements helpsto identify the composition of complex materialsdirectly at the location of the work of art. Manymeasurements were carried out in museums andcathedrals in Italy, Germany and France.4.1.10.3 ELEMENT IMAGING INELECTRON MICROSCOPES WITHSILICON DRIFT DETECTORSSilicon drift detectors have been tailored touse them as energy dispersive spectrometers inscanning electron microscopes. The RÖNTEC-XFlash TM system was developed to record at temperaturesachievable with a single stage Peltiercooler, X-ray fluorescence spectra at about 10 timeshigher count rates than conventional energy dispersiveX-ray spectrometers. 35 This results in spatiallyresolved element mapping with a high dynamicrange, i.e. several hundred grey levels within shortmeasurement times. Figures 4.1.27 and 4.1.28 showthe analysis of a damaged pressure sensor with aspatial resolution of 1024 × 768 pixels. The measuringtime was 8 min and the average X-ray countrate was 500 000 cps. The detector system used

SILICON DRIFT DETECTORS FOR X-RAY DETECTION 159220020001800KCounts16001400SeK1200BaCd1000 LHg800CdL 1Sr600LLL K400K KL200 S2KZr K1FeKK200 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30Energy (keV)Figure 4.1.26 Spectrum of an orange pigment acquired with the XRF spectrometer based on a SDDFigure 4.1.27 Scanning electron microscope image of a damaged micropressure sensor. This image shows the topological structureof the electron channel. A 20 keV acceleration voltage was used (photo: RÖNTEC)

160 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYFigure 4.1.28 Element imaging with a SDD of the damage pressure sensor shown in Figure 4.1.27. This Al plated componentwas destroyed through electrical overload. The local power dissipation melted the Al layer such that the Si underneath appeared.Because of their nearly identical atomic mass, these elements can hardly be distinguished in the electron image (Figure 4.1.27),but the chemical components can clearly be identified in the SDD image. The spatial resolution is 1024 × 768 pixels, themeasuring time was 8 min and the average count rate was 500 000 cps (photo: RÖNTEC)is the ROENTEC XFlash TM operated at −10 ◦ C.The RÖNTEC-ColorSEM TM system was used forthe data acquisition, signal and image processing.Figure 4.1.27 shows the conventional imagerecorded with the electron detector. Figure 4.1.28shows the spectroscopic SDD image with Al, Siand SiO 2 as the main chemical components of thepressure sensor. Compared to conventional energydispersive X-ray systems, a factor of 10 is gainedin the number of grey steps for comparable measurementtimes. In total, 90 different elements canbe resolved.4.1.10.4 SILICON DRIFT DETECTORARRAYSAnother concept for (coarse) position resolvedX-ray spectroscopy with SDDs, for ultra highcount rates is shown in Figure 4.1.29. 7 The wholesensitive surface is segmented in relatively smalldrift detectors, each having its own amplifyingchain. 36 Every channel is connected to an individualsignal processor, producing its own positionresolved X-ray spectrum with count rates around100 000 cps at a temperature of 0 ◦ C with a resolutionof better than 160 eV for the MnKα lineof an 55 Fe source (see Figure 4.1.30). This correspondsto a count rate capability of 2 × 10 6 cpsper cm 2 , which is just right for the X-ray holographyapplications planned at HASYLAB (seeSection 4.1.10.6).Silicon drift detector arrays have also been usedfor the scintillation light readout of CsI(Tl) crystalsin γ -ray cameras. The high quantum efficiency ata wavelength around 4500 Å and the low noisereadout have led to an energy resolution in thedetection of γ -rays better than the conventionalphotomultiplier readout of the scintillator 37 (seeSection 4.1.10).

SILICON DRIFT DETECTORS FOR X-RAY DETECTION 161(a) (b) (c)Figure 4.1.29 Examples of multicell drift detector layouts: (a) large area detector 19 cells, 95 mm 2 , exists equally as a 39 celldetector unit with 195 mm 2 and as a 61 cell detector having 305 mm 2 ; (b) linear chain, 6 cells, 30 mm 2 ; and (c) closed ringwith a hole in the centre, 12 cells, 60 mm 2 . All plots show the layout of the detectors structured front side with the field stripsystem and the readout transistor in each cell’s centre. The hexagonal cell shape has be chosen for an optimum ratio of area andborder lengthΣSUM160 eVFigure 4.1.30 Spectroscopic performance of the seven-channel SDD. The sum of seven simultaneously recorded 55 Fe spectrayields an energy resolution of 160 eV (FWHM at 5.9 keV) at a temperature of −20 ◦ C. The detector was irradiated withoutcollimator. The low energy background is therefore dominated by split events, i.e. charge sharing between neighboring detectorcells when an X-ray hits the border4.1.10.5 COMPACT X-RAYFLUORESCENCE SPECTROMETERThe 12-channel ring detector of Figure 4.1.29 witha hole in its centre is the basic component of acompact X-ray fluorescence (XRF) spectrometer(Figure 4.1.31).The sample is excited by X-rays passingthrough the central hole of the detector chip, andthe SDD ring device receives the characteristicfluorescence photons emitted by the sample coveringa large fraction of the solid angle around thesample. The X-rays from the source may be intensifiedand focused by a capillary fibre as shownin Figure 4.1.31. This compact XRF spectrometerhas been implemented in a table-top system formaterial analysis.4.1.10.6 X-RAY HOLOGRAPHYX-Ray holography is a new experimental methodto reveal the crystal structure of solids. The sampleis irradiated by an intense beam of monochromatizedsynchrotron radiation X-rays under differentangles. The variation of the emitted fluorescenceintensity with the direction of the incident photonsallows the direct three-dimensional reconstruction

162 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYSample Ring detector X-ray sourcewith capillary fibreFigure 4.1.31 Principle of a compact XRF spectrometer using the SDD ring structureof the sample’s electron density distribution. Thistechnique requires the energy-dispersive detectionof an enormous number of scattered and fluorescentX-ray photons to gain sufficient statistics.Therefore it depends on a large area and fast detectorsystem. Single cell SDDs and small multicelldrift chips like the one shown in Figure 4.1.29have already been used in X-ray holography. Anew system currently in production aims towardsthe complete detection of all photons emitted bythe sample (Figure 4.1.32). More than 1000 SDDcells grouped in 61-channel multicell drift chipsand arranged in a football-like configuration coveralmost the complete sphere around the sample. Thepixelation of the detector allows the channels to bediscarded in the direction of intense Bragg reflectionsthat do not carry useful information.4.1.10.7 A γ -RAY CAMERA USINGMULTICHANNEL DRIFT DETECTORSThe use of SDDs for the detection and spectroscopyof photons is on the high energy endrestricted to 20 to 30 keV, limited by the lowatomic number of silicon and the detector thickness,which is 500 µm. For hard X-rays and γ -rays either direct converting detectors of high-ZmaterialslikeCd(Zn)Tehavetobeusedorindirectconverting systems like scintillators coupledto photomultiplier tubes (PMTs). Recently, scintillationdetectors experienced a step forward inperformance by replacing the PMT by a SDDX-ray beamFigure 4.1.32 Experimental setup for X-ray holography. Theirradiated sample is surrounded by an almost complete sphereof detectors. Each hexagon of the football-like configuration isa 61-channel SDD. The whole detector consists of more than1000 channelsused as a low-capacitance photon detector for thescintillation light. That way not only the knownpractical problems of PMTs like requirement ofspace, incompatibility with magnetic fields, andthe necessity of a high voltage are avoided, butalso the quantum efficiency and energy resolutionof the system are improved. The transmittanceof the SDD entrance window can be tuned bydeposition of anti-reflective coatings to the emittedwavelengths of a wide range of scintillators. For122 keV X-rays a position resolution of 300 µm

THE CONTROLLED DRIFT DETECTOR (CDD) 163was measured and simultaneously an energy resolutionof 15 %. 38Compared to direct converting pixelatedCd(Zn)Te detectors with equal position resolutionthe scintillator–SDD combination requires aconsiderably lower number of readout channels.In addition it has the advantages of comprehensivematerial experience, existing technologies, provedlong term stability, and practically unlimitedavailability of high quality material.For the readout of multichannel drift (Mc drift)chips the amplifier chip ROTOR (rotational trapezoidalreadout) based on JFET-CMOS technologyhas been developed. ROTOR includes a preamplifier,a filter amplifier, and a peak stretcher for eachdetector channel, as well as one analogue multiplexerthat sends the series of data of all channelsto an external flash ADC. The system is able tohandle the random asynchronous event occurrenceof a large number of SDDs with low read noiseat count rates exceeding 10 5 cps per channel. Atpresent 165 eV (FWHM) have been achieved withan 55 Fe source.4.1.11 THE CONTROLLED DRIFTDETECTOR (CDD)For X-ray imaging purposes, a detection schemewhich needs the time mark of the X-ray tobe detected is disadvantageous. A new readoutscheme was invented recently. 39,40 In addition tothe drift field for the transport of charges parallel tothe wafer surface, a potential barrier for electronsis implemented which provides a channel guide forelectrons, 41 thus the lateral spread of the chargesis prevented (Figure 4.1.33). This technique isvery similar to the channel stop configurations forthe pn-CCDs to be described in Section 4.1.12.In order to keep the generated electrons at theirposition for a well defined time, i.e. in theintegration time for the incoming photons, anadditional electron potential barrier is formedperpendicular to the channel stop implants. Thisadditional control of the electrons in the directionof the readout node can be made by means ofclocking the drift strips. At a given, externallydetermined moment, the potential barriers arereleased, defining the start signal for the drift timen + anodes p + field strips Deep p-implants (channel stops)Epitaxial layerSubstrateBack contactV backFigure 4.1.33 Cut through a CDD perpendicular to the wafer surface, and parallel to the electron drift direction

164 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYmeasurement. Upon arrival at the readout node,the stop mark is measured, and thus the positionof the generated signal charge cloud according toEquation (4.1.11) calculated. No external triggeris needed, the trigger signal is generated by thedetector system itself.The pn-CCD as well as this concept use ahomogeneous large rectifying p + implant for thecomplete depletion of the detector (Figure 4.1.33).The large p + (backside) contact is the radiationentrance window for the photons. As discussedalready in Section 4.1.7 (Figure 4.1.13), astructured surface would lead to (a) an inhomogeneousresponse as a function of the incident photonenergy and position and (b) incomplete chargecollection of the signal charge package when producedclose to the gaps of p + field strips.The simulation of the CDD intuitively showsthe functional principle: Figure 4.1.34 shows theelectric potential during the photon integrationtime, which must be long compared to the signaldrift and readout time. Figure 4.1.35 shows thepotential distribution once the drift strips have beenclocked to remove the electron potential barrier toallow the electron drift towards the read nodes.The time measurement of the arriving electronswith a precision of 10 ns would yield a positionmeasurement precision of 50 µm for standarddrift fields, depending on the pixel size. Theread out system has a ‘fast channel’ for thetime measurement and a ‘slow channel’ for thecharge measurement. This scheme makes the CDDextremely interesting for X-ray measurements forhigh photon rates and fast, low noise readout. Asthe SDD and the pn-CCD, the CDD has on-chipamplifiers integrated on the detector, one for eachindividual readout node.Concerning the readout speed and count ratecapability, the CDD is a real alternative to theCCDs (pn-CCDs). The drift towards the readoutnode happens with a velocity which is onlycontrolled by the externally applied drift field. Thetransfer is not interrupted by a pixel wise readingof the charge content, as in the case of CCDs. Fora 1 cm long drift distance a CDD typically needs5 µs, while a pn-CCD type detector requires about500 µs.The development status of the CDD is progressingtowards a detector system, which is showingall performance parameters as designed. To date,the CDD is existing in a prototype version. 42Figure 4.1.36 shows the position and energyresolved X-rays from a 55 Fe source recorded at100 kHz frame rate. The same set-up was used3231Potential (V)302928680660Drift coordinate (µm)640620600700 800 900 1000 1100Lateral coordinate (µm)Figure 4.1.34 Simulation of the two-dimensional controlled SDD in the signal accumulation mode. The generated signal chargesare confined in their local potential minima

THE CONTROLLED DRIFT DETECTOR (CDD) 1652827Potential (V)26252423685Drift coordinate (µm)640615590700 800 900 1000 1100Lateral coordinate (µm)Figure 4.1.35 Potential simulation of the two-dimensional controlled SDD in the signal drift mode. The signal charges in thepixels drift towards the readout nodes4000 ∆t = 55 nsFWHM = 11 nsEnergy (eV) Counts2000090008000700060005000277.5 eV FHWM(29.6 el. rms)400030000.00.1 0.2 0.3Time (µs)0.4 0.5 0.6 0E + 0 5E + 3Counts1E + 4Figure 4.1.36 Position and energy resolved image of a CDD detector recorded at a frame rate of 100 kHz. At room temperaturean energy resolution of 277 eV was measured

166 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYto take first images at the synchrotron in Trieste(Figure 4.1.37). In the meantime, CDDs have beenproduced in larger formats. They are foreseen asscattering detectors for small animal analysis inCompton camera systems.4.1.12 FULLY DEPLETED BACKSIDEILLUMINATED pn-CCDsConceptually the pn-CCD is a derivative of theSDD. 5 The development of the pn-CCDs startedin 1985. In the following years the basic conceptwas simulated, modified and designed in detail. 43n-channel JFET electronics was integrated in1992, 3,44 and the first reasonably fine workingdevices were produced in 1993. Up to then, allpresented devices were ‘small’ devices, i.e. 3 cm 2in sensitive area. 15The flight type large area detectors for X-rayastronomy (6 × 6cm 2 ) were produced from 1995to 1997, with a sufficiently high yield toequip the X-ray satellite missions ABRIXASand XMM 20,45,46 with defect-free focal plane pn-CCDs.XMM was launched on 10 December 1999from Kourou in French-Guiana. Commissioningof the scientific payload was completed in themiddle of March 2000. In this overview, the basicinstrument features as measured on the ground andin orbit will be shown.1.2 mm4.1.12.1 THE CONCEPT OF FULLYDEPLETED, BACKSIDE ILLUMINATED,RADIATION HARD pn-CCDsFor ESA’s X-ray Multi Mirror Mission (XMM),we have developed a 6 × 6cm 2 large monolithicX-ray CCD 47 with high detection efficiency upto 15 keV, low noise level (ENC≈5e(rms) at anoperating temperature of −90 ◦ C) and an ultra-fastreadout time of 4.6 ms per 3 × 1cm 2 large subunit(Figure 4.1.38). A schematic cross-section, alreadyshowing some of the advantages of the concept isdisplayed in Figure 4.1.39.The pn-CCD concept and the fabrication technologyallow for an optimum adaptation of thepixel size to the X-ray optics, varying from 30 µmup to 300 µm pixel size. Up to now systems with50 µm to 200 µm have been produced. The XMMtelescope performance of 13 arcsec half energywidth (HEW) translates to 470 µm position resolutionin the focal plane. The FWHM of the pointspread function (PSF) is about 7 arcsec. A pixelsize of 150 × 150 µm 2 was chosen, with a position3 cm (200 pixels)Channel stop1 cm (64 pixels)Shift registersf 3 f2 f1airreflon64 n +readoutanodesV aV aM8 boltS DgateresetSDgateresetFigure 4.1.37 X-ray image of an iron bolt in a Teflon nut.The image was recorded at the synchrotron in Trieste with anenergy of 15 keV. The frame rate was 100 kHzFigure 4.1.38 One pn-CCD subunit with 64 on-chip amplifiersand a size of 3 × 1cm 2 . Each column is terminated by anon-chip JFET amplifier

FULLY DEPLETED BACKSIDE ILLUMINATED pn-CCDs 167f 3f 2Pulse for signal transferOn-chipamplifierf 1285 mm 12 mmp + p + p + p + p + p + −n - epitaxial layer transfer direction(40 Wcm) − − −−−signal chargeFully depleted detector volume (n-Si, 2 - 5 k Wcm)n + anodeDetectordepthpotential minimumEntrance window (p + back diode)Depletion voltageElectron potentialFigure 4.1.39 Schematic cross-section through the pn-CCD along a transfer channel. The device is back illuminated and fullydepleted over 300µm thickness. The electron potential perpendicular to the wafer surface is shown on the right-hand sideresolution of 120 µm, resulting in an equivalentspatial resolving capability of 3.3 arcsec.This is sufficient to fully conserve the positionalinformation from the X-rays from the mirrors.The quantum efficiency is higher than 90 %at 10 keV because of the sensitive thickness of300 µm.The low energy response is given by the veryshallow implant of the p + back contact; theeffective ‘dead’ layer is smaller than 200 Å. 14The good time resolution is given by the parallelreadout of 64 channels per subunit, 768 channelsfor the entire camera. A high radiation hardness isbuilt in by avoiding active MOS structures and bythe fast transfer of the charge in a depth of morethan 10 µm.The spatially uniform detector quality over theentire field of view is realized by the monolithicfabrication of the pn-CCD on a single wafer. Forreasons of redundancy 12 individually operated3 × 1cm 2 large pn-CCDs subunits were defined.Non-homogeneities were not observed over thewhole sensitive area in the energy band from500 eV up to 8 keV, the precision of the measurementswas always limited by Poisson statistics.The insensitive gap in the vertical separation ofthe pn-CCDs is about 40 µm, neighbouring CCDsin horizontal direction have insensitive regions of190 µm.The basic concept of the pn-CCD is shownin Figure 4.1.39 and is closely related to thefunctional principle of the SDDs. A double-sidedpolished high resistivity n-type silicon wafer hasboth surfaces covered with a rectifying p + -boronimplant. On the edge of the schematic devicestructure (Figure 4.1.39) a n + -phosphorus implant(readout anode) still keeps an ohmic connectionto the nondepleted bulk of the silicon. A reversebias is now applied to both p + junctions, i.e. anegative voltage is applied with respect to the n +anode. For simplicity let us assume, that the siliconbulk is homogeneously doped with phosphoruswith a concentration of 1.0 × 10 12 per cm 3 .Thedepletion in the high ohmic substrate, with aresistivity of about 4 kcm, develops from bothsurfaces, until the depletion zones touch in themiddle of the wafer in the case of homogeneousdoping of the wafer. The potential minimum forelectrons is now located in the middle of the wafer.An additional negative voltage on the p + backdiode shifts the potential minimum for electronsout from the centre towards the surface havingthe pixel structure. Typical depletion voltages onthe backside are −150 V. To make a CCD-typedetector, the upper p + implant must be divided

168 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYShift ofsignal chargesf 3f 2f 1Transferregisters 1 pixel(150 × 150 nm 2 )On-chip readout electronicsSensitive thickness(280 mm)Back contactFigure 4.1.40 Inside the pn-CCD. The X-rays hit the device from the backside (bottom). The charges are collected in the pixelwell close to the surface having the pixel structure. After integration, they are transferred to the on-chip amplifierin p + strips as shown in Figure 4.1.39 and 4.1.40.Adequate voltages should now be applied tothe three shift registers, such that they formlocal electron potential minima at a distance ofapproximately 10 µm from the surface. Three p +strips (shift registers) with the potentials ( 1 , 2and 3 ) comprise one pixel. Charges are collectedunder 3 , the potential minimum for electrons.A reasonable change with time of the appliedvoltages transfers the charges in the local electronpotential minimum in a discrete way towards then + readout node. In reality the side having the p +shift registers has an additional phosphorus dopedepitaxial layer, 12 µm thick, with a concentrationof approximately 10 14 donors per cm 3 . Theinterface of the epi-layer and the high resistivitybulk silicon fixes the electron potential minimumto a distance of about 10 µm below the surface.As can be seen in Figure 4.1.38, one pn-CCDsubunit consists of 64 individual transfer channelseach terminated by an on-chip JFET amplifier.Figures 4.1.41, 4.1.42 and 1.4.43 show the chargetransfer mechanism in a depth of approximately10 µm below the shift registers. The p + backsidecontact is not shown: it expands quite uniformlyan additional 260 µm towards a negative potentialof −150 V. The sequence of changing potentialsshows nicely the controlled transfer from register 3 to register 2 , one-third of a pixel.This concept is seen from a different point ofview in Figure 4.1.40, seen from the inside of apn-CCD: X-rays hit the detector from the rear side(back contact). The positively charged holes moveto the negatively biased back side, electrons to theirlocal potential minimum in the transfer channel,located about 10 µm below the surface having thepixel structure. The electrons are fully collected inthe pixels after 5 ns at most, the collection of holesiscompletedinnomorethan15nsbecauseoftheirreduced mobility. As can be seen in Figure 4.1.40,each CCD line is terminated by a readout amplifier.The on-chip single sided JFET has already beendescribed in Section 4.1.4 as the first amplifyingelement in the SDD.The focal plane layout of XMM is depictedin Figure 4.1.44. Four individual quadrants eachhaving three pn-CCD subunits are operated inparallel. The camera housing and its mechanical,thermal and electrical properties are describedelsewhere. 48

FULLY DEPLETED BACKSIDE ILLUMINATED pn-CCDs 169Φ1Φ2Φ320AnodeU (volts)151050403020Y (microns)10050100X (microns)150 2000Figure 4.1.41 Negative potential of a pn CCD shift register. In this operating condition the signal charges are stored under theregister 3 only. The p + backside potential is only shown up to the depth of 40µm for clarity. It expands to −150 V at 300µmdistance from the pixel surfaceΦ1Φ2Φ320AnodeU (volts)151050403020Y (microns)10050100 150 200X (microns)0Figure 4.1.42 Negative potential of a pn-CCD shift register. In this operating condition the signal charges are stored under theregisters 2 and 3 . The electrons now share a larger volume for a short time. Note that the electrons are still nicely confinedin the potential well4.1.12.2 LIMITATIONS OF THE CCDPERFORMANCEThe performance of the CCDs is subject toseveral limitations: physical and technical. Someof these limitations, which are subject to mostdetectors described in this subchapter, have alreadybeen discussed in Sections 4.1.6 and 4.1.7. Asa result, a distortion of the spectrum to lowerenergies has been found (Figure 4.1.13 and 4.1.21;

170 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYΦ1Φ2Φ320AnodeU (volts)151050403020Y (microns)10050100X (microns)150 2000Figure 4.1.43 Negative potential of a pn-CCD shift register. In this operating condition the signal charges are stored under theregister 2 only. The charge was transferred by one-third of the pixel length in approximately 150 nsthe quantum efficiency as function of energyis presented in Figure 4.1.14). The low energytail in the spectrum (p/V ratio) and the dropin quantum efficiency at low energy is due topartial charge collection of photons converting inor near the entrance window. This drop is stillmuchlowerthaninother(MOS)CCDs.Thelossat high energy is due to the limited thicknessof the silicon wafer. Figure 4.1.14 also indicatesthe improvement achievable by increasing thesensitive thickness to 500 µm.As the bias voltage required for depletiongrows with the square of the thickness butonly linearly with doping density (Equation 4.1.1)the maximum depletable thickness achievablethickness at reasonable bias is limited. As anexample, 4.5 kcm n-type silicon (N D = 10 12donors per cm 3 ) and a bias voltage of 500 V resultin a depletion depth of 800 µm.Important aspects on the subject of energy resolutionwere also treated in Sections 4.1.4 and4.1.6 and for drift detectors in Section 4.1.9. Theseaspects concern electronic noise (Section 4.1.4),ionization statistics (Section 4.1.6) and their combinedeffect (Section 4.1.9). Those results applyalso to CCDs. According to Figure 4.1.45, the64 mm7 mmCAMEXtransferalong 200 pixel61 mmpixel0.150.15768readoutchannels4 inch wafer(FZ-Epi-Si)Figure 4.1.44 The focal plane of the pn-CCD camera on XMMand ABRIXAS consist of 12 independent, monolithicallyintegrated pn-CCDs with a total area of 6 × 6cm 2 .Intotal768 on-chip amplifiers process the signals and transfer themto a VLSI JFET-CMOS amplifier array. 12 output nodesof the CAMEX arrays are fed into 4 ADCs, i.e. one ADCper quadrantFano noise is dominant for energies above1 keV for an electronic ENC of 5 electrons. For1 electron noise (ENC) this threshold is loweredto 50 eV only.

FULLY DEPLETED BACKSIDE ILLUMINATED pn-CCDs 171100FWHM (eV)105 ENC1 ENCFano noise10 1001000 10000Energy (eV)Figure 4.1.45 Energy resolution as a function of the photon energy. The Fano noise is taken into account as well as a 5 electronand 1 electron electronics ENC, respectivelyAdded to these contributions is an essentialproperty of CCDs, the loss of charge duringtransfer from the place of origin towards thereadout node.Charge Transfer NoiseIn CCDs, where the signal electrons are transferredover many pixels, the charge shifting mechanismfrom pixel to pixel must be excellent. Leavingcharges behind during the transfer means reducingsignal amplitude. This loss can be corrected, butadds noise to the signal amplitude measurement.ENC 2 trans = n lost = q E w (1 − CTE)N trans (4.1.12)In a simple model the lost charges n lost canbe parameterized according to Equation (4.1.12),where the left behinds can be considered as abackward flow loss of electrons. As the lossprocess is of statistical nature, it is treated similarto a signal leakage current. N trans denotes thenumber of transfers in the CCD and CTE isthe charge transfer efficiency, a number close toone, of the order 10 −5 , depending on CCD type,radiation damage, temperature, etc.For the pn-CCD (as for any other SDD-typesystem) the electronic noise can be reduced byreducing the read node capacitance, by loweringthe leakage current and the 1/f noise constantsand by optimizing the shaping time constant τ.The total read noise, if not correlated, can be addedquadraticallyENC 2 tot = ENC2 el + ENC2 fano + ENC2 trans + ...(4.1.13)and delivers the total ENC. State of the artsystems of today exhibit electronic noise figuresaround 3 electrons and a readout speed per pixelbelow 1 µs and operating temperatures higher than−90 ◦ C.In pixelated detectors not all the signal chargesof one single X-ray photon will be collected in asingle pixel, so the electronic content of severalpixels must be added. This increases, for the socalledsplit events, the noise floor by √ N, with Nas the number of pixels affected.

172 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPY4.1.12.3 DETECTOR PERFORMANCE(ON GROUND AND IN ORBIT)The best values for the readout noise of the onchipelectronics is 3 electrons rms at 180 K forthe most recent devices; typical values scatteraround 5 electrons rms for the XMM system.This includes all noise contributions described inEquation (4.1.4). The charge transfer properties ofthe pn-CCDs on XMM are reasonably good, in theorder of a several percent signal loss from the lastto the first pixel over a distance of 3 cm chargetransfer. As the charge transfer losses describethe position dependent energy resolution, it isone of the key parameters for the spectroscopicperformance, especially after radiation damagemay have occurred.Figure 4.1.46 shows a 55 Fe spectrum of a pn-CCD in a flat field measurement resulting in atypical energy resolution of 130 eV at an operatingtemperature of −120 ◦ C. 15 The XMM flightcamera was operated at −90 ◦ C during calibrationon the ground with a resolution of about145 eV (FWHM) over the entire area of 36 cm 2 .The main effect on the degradation of energy resolutionwas the reduction of the charge transferefficiency (CTE) at warmer temperatures. Leakagecurrents and on-chip JFET properties only playeda minor role. The impact of the material propertiesof silicon and related impurities and their consequencesfor the operation of scientific grade X-raypn-CCDs including the effects of radiation damage,is treated in detail in the literature. 49,50The equivalent dose of 10 MeV protons overthe expected life time of XMM is 4 × 10 8 p/cm 2 .Figures 4.1.47 and 4.1.48 show the results of theirradiation tests with 10 MeV protons: the expecteddecrease of energy resolution over the 10 yeardose is from 145 eV to 158 eV at an operatingtemperature of −100 ◦ C. At the actual operatingtemperature of −90 ◦ C the expected effect oftrapping and detrapping at A-centres, generated bythe radiation, is even more reduced.In a single photon counting mode the quantumefficiency was measured with respect to a calibratedsolid state detector. Figure 4.1.14 showsmeasurements from the synchrotron radiation facilitiesin Berlin and Orsay. At 525 eV a 5 % dip canbe seen from the absorption at the oxygen edge in400300Counts20010005600 5800 6000 6200 6400 6600Energy (eV)Figure 4.1.46 Mn Kα spectrum of an 55 Fe source. The measured FWHM is 130 eV at −120 ◦ C

FULLY DEPLETED BACKSIDE ILLUMINATED pn-CCDs 1731.00.80.60.40.20.05000 5500 6000Energy (eV)6500 7000Figure 4.1.47 55 Fe energy spectrum after different 10 MeV proton fluencies of 0 p/cm 2 (dotted line), 4.1 × 10 8 p/cm 2 (solid line),6.1 × 10 8 p/cm 2 (dashed line), measured at the low (and after irradiation unfavourable) temperature of 142 K. The expected doseover a life time of 10 years is 4.0 × 10 8 MeV p/cm 2the SiO 2 layers. The same happens at the SiK-edgeat 1840 eV showing the fine structure of a typicalXAFS spectrum (see inset of Figure 4.1.14).For all energies the quantum efficiency is nicelyrepresented by a model using the photoabsorptioncoefficients from the atomic data tables. Thequantum efficiency on the low energy side canbe further improved with respect to the measurementsshown in Figure 4.1.14 by increasing thedrift field at the p + junction entrance window 14 andby using silicon instead of silicon.The useful dynamic range of the pn-CCD cameraon XMM was adjusted from 100 eV to 15 keV(Figure 4.1.49).Split events, i.e. events with electrons in morethan one pixel, originating from one single photon,were reconstructed and summed to one photonevent. In total, about 70 % of all events are singlepixel events, 28 % are two pixel events and 2 %are events with three and four pixels involved. Inthe case of the XMM pn-CCDs one single X-rayphoton never spreads the generated signal chargeover more than four pixels.The readout electronics of the pn-CCD systemis described in the literature. 47,51 A chargesensing amplifier followed by a multicorrelatedsampling stage, multiplexer and output amplifier(CAMEX64B JFET/CMOS chip) guide the

174 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPY260240XMMFWHM(Mn Ka = 5894 eV) (eV)220200180160T = 174 KT = 140 K1400 5.0 × 10 8 1.0 × 10 9Proton fluence (p/cm 2 )1.5 × 10 9 2.0 × 10 9Figure 4.1.48 FWHM of the Mn Kα spectrum (5894 eV) with dependence on proton fluence and temperature. Before protonexposure the lower operating temperature of 140 K gains better results. After a 10-MeV proton fluence of more than2.0 × 10 8 cm −2 the higher temperature of 174 K results in a better energy resolution. The FWHM is degraded from 135 eV(140 K) to 160 eV and 175 eV (174 K) after 4.1 × 10 8 p/cm 2 and 1.9 × 10 9 p/cm 2 , respectively. A FWHM of 160 eV is expectedafter the 10 year XMM missionpn-CCD pixel content as a voltage signal to a10 MHz 12-bit flash ADC system. The whole system,i.e. CCD and CAMEX64B amplifier arraydissipate a power of 0.7 W for the entire camera(768 readout channels), a value which is acceptablein terms of thermal budget on XMM realizedthrough passive cooling. A further increase of thereadout speed can be made only at the expense offurther increase of power, or a degradation of thenoise performance.The charge handling capacity of the individualpixels was tested with the 5.5 MeV α particlesfrom a radioactive 241 Am source. Around 10 6electrons can be properly transferred in every pixel.The spatial resolution of the camera system wasintensively tested in the PANTER facility with theflight mirror module in front of the focal plane. Thefirst light image of the Large Magellanic Cloud in(Figure 4.1.50), as well as the quantitative analysisof the point spread function have shown a perfectalignment of the telescope system on the ground:the spatial resolution of the entire telescope systemmeasured on the ground corresponds exactly to theperformance in orbit.The operating temperature of XMM in orbit is−90 ◦ C. This temperature optimizes on one sidethe requirement of ‘warm’ operating conditionsto avoid contamination and to release stress tothe mechanical structures. On the other side, itmatches the need of ‘cold’ temperatures becauseof leakage current reduction and efficient chargetransfer.

FULLY DEPLETED BACKSIDE ILLUMINATED pn-CCDs 17510Counts (keV −1 s −1 )10.10.01edge Si KK K aCa K aTi K aV K aCr K aFe K aNi K aCu K aZn K a Cu K b0.5 1 2Channel energy (keV)5 10Figure 4.1.49 Calibration spectrum with the internal radioactive source including the background with the filter wheel in closedposition. The continuous background below the Mn lines arises mainly from photoelectrons stimulated from the 55 Fe source inthe Al target. The iron Kα line between Mn Kα and Mn Kβ is not resolved. The additional lines are due to X-ray fluorescentbackground from the camera structureUp to now, almost 4 years after launch, noinstrumental surprise has occurred: the energyresolution is equal to the ground measurements,as is the case for the charge transfer efficiency.To date, the electrical stability of the instrumentis perfect. The first light image in (Figure 4.1.50)and the observation of Tycho Brahes supernovaremnant, which includes chemical analysis fromthe X-ray spectra (Figure 4.1.51), qualitativelysummarize the above statements.4.1.12.4 FRAME STORE pn-CCDS FORROSITA AND XEUSFuture missions and other applications requirepn-CCDs with smaller pixels and even fasterreadout. Two potential applications are the German/EuropeanROSITA mission to be installed onthe International Space Station (ISS) in 2007 andESA’s XEUS mission to be launched around 2015.As in conventional CCDs, pn-CCDs can equallybe designed in a frame store format. This optimizesthe photon integration to charge signaltransfer time, but requires more space ona chip because the store area does not serveas an active area but as an analogue storageregion (Figures 4.1.52 and 4.1.53). A crosssectionthrough image and storage area is shownin Figure 4.1.54. In Table 4.1.1 the expected characteristicsof the devices for ROSITA and XEUSare compared to those achieved in XMM.The area to be processed in a quasi defect freemanner increases by the size of the store area.A7.5 × 7.5cm 2 large image area can be realizedmonolithically on a 6 ′′ wafer (Figure 4.1.52). Ifpn-CCDs should be also used for the 14 × 14 cm 2focal plane, there may be a possible extension ofthe focal plane camera on XEUS (Figure 4.1.55).By that technique the whole field of view couldbe covered with a minimum of insensitive gaps in

176 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYFigure 4.1.50 The Large Magellanic Cloud in X-ray colors. First light image of the pn-CCD camera. The field of view of30 arcmin corresponds approximately to our perception of the size of the moon. The image shows the area of 30 Doradus asupernova remnant as an extended source of X-rays. The ‘north-east’ of 30 Dor shows an emission of X-rays up to 5 keV (blue),while the ‘south-west’ rim appears much softer in X-rays (yellow and red). The supernova 1987A is the bright source ‘southwest’ of 30 Doradus. About 40 new X-ray objects have been found in this exposure. The exposure time was about 10 hbetween the buttoned devices. The central part, theinner diameter of 7 cm, would be homogeneouslysensitive.The major change in concept, besides thesmaller pixel size, is the dramatic increase in framerate because of the modified readout philosophy:by doubling the processed area and dividing it inan image and store section, we will get towards therequired readout speed for the large collecting areaof the XEUS mirrors. We expect to get a frame rateof the whole camera of 200 per second.As the pixel size shrinks, the number of readnodes and transfers increases. At the same time,the system will be requiring more readout timeand being more sensitive to radiation damage dueto the higher number of transfers. If spreadingof signal charges over more than one pixel isneeded for the improvement of position resolution(Figures 4.1.56 and 4.1.57), the effective readnoise per event will be higher by a factor √ n(n is the number of pixels involved). The readoutnoise of every pixel involved must be quadraticallyadded to get the total noise for one photon event.To date, the signals of one row (64 pixels)are processed in parallel in 23 µs. The extensionto 128 channels on the CAMEX amplifiers, tomatch the new pixel pitch, was realized in a newfabrication of a CAMEX128 for the low noiseoperation. In addition, the signal processing timemust be shortened by a factor of two to obtain thesame readout time per row. The increased readoutspeed will certainly have an impact on the power

FULLY DEPLETED BACKSIDE ILLUMINATED pn-CCDs 177Figure 4.1.51 Supernova remnant Tycho in the Cassopeia region, discovered in 1572 by Tycho Brahe. The radius of Tycho is12 light-years. The temperature of several million degrees gives rise to X-rays from 0.2 keV to 10 keV. The X-ray spectrumshows an abundance of many elements among those O, Mg, Si, S, Ar, Ca, Fe and Ni. The distribution of the elements is nothomogeneous; the explosion dynamics are currently under studyconsumption which is actually below 1 W for the36 cm 2 array.If 128 channels are read out with 12.8 MHz,10 µs would be required for the parallel readoutof one pixel line. For the parallel transfer fromthe image to the storage area 100 ns are neededfor one transfer. A device of 1000 × 1000 pixelswould be divided (as in the XMM-EPIC case)in two identical halves of the image area, i.e.500 × 1000 pixels each (Figure 4.1.52). For theparallel 500 shifts, 50 µs would be needed for thetransfer from the image to the shielded storagearea. The readout time for the storage area whileintegrating X-rays in the image part, would then be500 × 10 µs = 5 ms. That means, within 5 ms thewhole focal plane would be read out. The out-oftimeprobability for the X-ray events will then be1:100. In this operation mode, 200 image framescan be taken in 1 s with a full frame time resolutionof 5 ms.The above discussion shows the present technologicallimits for applications in space. Of course,for XRF applications smaller (and therefore faster)devices can be made.According to the progress of the developmentfor both detector systems – pn-CCDs and APS – adecision about the final choice for the XEUS widefield imager has to be taken at a later stage.

178 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPY1000 readout nodesFrame store areaf + -Register1000 columnsImage500 rowsf-Register5050Areaf-ResisterFrame store areaf + -Register1000 readout nodesFigure 4.1.52 Example for a pn-CCD operated in a frame store mode. The imaging area may have a pixel size of 50 × 50 µm 2or 75 × 75 µm 2 and a store area of 75 × 50 µm 24.1.12.5 NEW DEVICESRecently, the first prototypes of the pn-CCDsfor the ROSITA mission have been tested withexcellent results. The low energy response wassignificantly improved (Figure 4.1.58). The triggerthreshold was as low as 50 eV, the peak-tobackgroundratio is 50:1 and the FWHM for C KX-rays (277 eV) is below 80 eV. This width is stilllarge compared with the theoretical limit (around40 eV) and reveals some additional improvementsto be done in the near future. At AlKα (1498 eV)the FWHM is also 80 eV.The charge transfer efficiency was improved atleast by a factor of 10 at the critical lower energies(Figure 4.1.59). That enables us to get closer to thelimits given by silicon as a detector material.4.1.12.6 OTHER APPLICATIONSIn recent years many other applications with pn-CCDs have been realized. The fields of applicationare very different as well as the appreciatedadvantages of the pn-CCD. Some examples are:(1) X-ray microscopy. At BESSY II a new generationof X-ray microscope has been installed,equipped with a pn-CCD system. The highefficiency for X-rays below 1 keV and the highradiation hardness were the key properties toswitch from MOS-type CCDs to fully depletedback illuminated CCDs. 52(2) Plasma diagnostics. X-Ray spectroscopy isfrequently used for plasma diagnostics infusion reactors. The temperature can be

FULLY DEPLETED BACKSIDE ILLUMINATED pn-CCDs 17925 mmimage area256 × 256 pixel75 µm × 75 µmX-rayexposure39 mmFast transferof imageframe store area256 × 256 pixel75 µm × 51 µm(shielded against X-rays)Readout ofimageCAMEXCAMEX256 parallel transfer channelsFigure 4.1.53 Smaller (prototype) version of the ROSITA pn-CCD, having a pixel size of 75 × 75 µm 2 and a store area of75 × 51µm 2 and a format of 256 × 256 pixels in the imaging areadetermined quite precisely (the black bodyradiation of the plasma exhibits X-ray energiesup to 10 keV with high flux) and the contaminationof the plasma can be analysed. 53 It isforeseen to install a pn-CCD system at the newfusion reactor in Greifswald, Germany. Thepreferred properties are the high quantum efficiencyat the high energies and the fast readout.(3) Quantum optics. Multi-ionization processeshave been studied with a pn-CCD systemat the MPI for quantum optics. They haveimproved sensitivity by the high efficiency inthe VUV range at energies around 25 eV. Theradiation, stimulated with a femtosecond laserwas recorded in an integration mode, i.e. notin a single photon counting mode. 54(4) Electron emission channelling spectroscopy.The emission channelling spectroscopy techniqueallows the direct determination of thelattice sites of radioactive impurity atomsthat are incorporated into single crystallinesolids. 55 Electrons from a few keV to severalhundreds of keV were recorded with high precisionin energy and position.

180 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYFigure 4.1.54 The frame store pn-CCD as designed for the German ROSITA mission will have a format of 256 × 256 pixelswith a size of 75 × 75 µm 2 in the image area and 256 × 256 pixels with a size of 75 × 51 µm 2Table 4.1.1 Comparison of expected properties of pn-CCDs in XEUS and ROSITA with those reached atXMMProperty XMM ROSITA XEUSStatus Operating Prototyping ResearchType Full frame Frame store Frame store or APSFormat 400 × 384 256 × 256 1024 × 1024Pixel size (µm 2 ) 150 × 150 75 × 75 50 × 50 or 75 × 75Readout noise 5 electrons 3 electrons 1 electronSensitive thickness (µm) 295 450 450Frame rate (frames/s) 50 20 200 (1000)Readout speed (ns/pix) 350 100 50Energy resolution at Mn Kα (5.9 keV) (eV) a 140 130 125Energy resolution at C Kα (eV) 130 80 45Energy range (keV) 0.15–15 0.1–20 0.05–20a The energy resolution (FWHM) refers to incident X-rays of the MnKα line at 5.9 keV and CKα measured at temperaturesaround −100 ◦ C.(5) CAST. The CAST experiment is dedicated tothe search of solar axions. Its main componentsare a large superconducting magnet of 10 T, anX-ray telescope mounted behind the magnetand a pn-CCD camera system to detect theX-ray radiation between 1 keV and 8 keVbehind the telescope caused by the conversionof axions into X-rays through the Primakoveffect.(6) Transition radiation. A novel K-edge imagingmethod has been developed aiming at the efficientuse of transition radiation generated by ahigh energy electron beam for applications inmaterial science, biology and medicine. 55

ACTIVE PIXEL SENSORS FOR X-RAY SPECTROSCOPY 181R 3520sg = 315PHASE A:PHASE B:Rms of precision (µm)10Figure 4.1.55 Possible focal plane layout with a diameter of15 cm, composed by a central detector and four surroundingdetectors with circular shaped pixels. This example shows theuse of pn-CCDs, but can equally be applied to APS detectors125sg = 13Rms of precision (µm)10864200 5 10 15Incident position within pixel (µm)sg = 3sg = 1320 25Figure 4.1.56 Improvement of the position precision as afunction of the Gaussian spreading of the electron charge cloud.1000 electrons have been generated and processed with a noiselevel of 5 electrons (rms). The typical sigma of the Gaussian(‘sg’) electron distribution is 7 µm. The assumed pixel size is50 µm00 1020Incident position within pixel (µm)30 40Figure 4.1.57 The same calculation is made as forFigure 4.1.56 for a pixel size of 75 µm. 1000 electrons havebeen generated and processed with a noise level of 5 electrons(rms). The pixel edge is located at the x-coordinate 0, whilethe centre of the pixel is located at 25 µm (see Figure 4.1.55)and 37.5 µm (this figure)4.1.13 ACTIVE PIXEL SENSORS FORX-RAY SPECTROSCOPYLarge format arrays covering a wide energybandwidth from 1 eV to 25 keV will be used inthe focal plane of X-ray telescopes of the nextgeneration. 56 As the readout speed requirementsincrease drastically with the collecting area, butnoise figures have to be on the lowest possiblelevel, CCD-type detectors do not seem to be ableto fulfil all the experiment needs. Active pixelsensors have the capability to arbitrarily selectareas of interest and to operate at readout noiselevels below 1 electron (rms).One prominent candidate for the use of an APSis XEUS (X-ray Evolving Universe Spectroscopy

182 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYEvents8000700060005000400030002000100000.1 0.2 0.3 0.4Energy (keV)Figure 4.1.58 Carbon spectrum recorded with a frame store pn-CCD. The peak energy is at 277 eV corresponding to 73 electronsgenerated by the incoming low energy X-ray. The measured FWHM is around 80 eV. Due to partial absorption of signal carriers,the measured peak is shifted by 30 eV towards lower energies, if compared to the peak position of the Mn Kα line at 5.9 keV.A peak shift correction was appliedmission). 57 The launch is supposed to be around2015. It represents a potential follow-on missionto the ESA cornerstone XMM currently in orbit.The XEUS mission is considered as part of ESA’sHorizon + 2000 + program within the context of theInternational Space Station (ISS).4.1.13.1 THE WIDE FIELD IMAGERFOR XEUS – AN INTRODUCTIONThe wide field imager (WFI) on XEUS is oneout of three scientific instruments in the focalplane of the X-ray telescope with a field ofview of about 5 arcmin, corresponding to 73 mmon the focal plane detector. The large collectingarea (up to 30 m 2 ) and high angular resolution(2–5 arcsec) of the X-ray optics requires newdetector technologies. 22 The physical quantitiesof interest are imaging (position resolution), andspectroscopy (energy resolution) with a highdetection probability (quantum efficiency) in asingle photon counting mode at a high photon rate(time resolution without pile-up). The first choicefor the WFI is mainly driven by its count ratecapabilities and the flexibility of operation. As thecollecting area of XEUS in phase A is already afactor of 20 larger than XMM and a factor of 100in phase B, it becomes clear, that a new deviceconcept is needed rather than improvements ofexisting schemes. Active pixel sensors will bein the focus of our considerations, being ableto match the relevant physical parameters of theWFI. The concept of the p-channel Depleted FieldEffect Transistor (DEPFET) allows to measureposition, arrival time and energy with a sufficientlyhigh detection efficiency in the range from 0.1to 30 keV. As a fallback solution, fully depletedbackside illuminated frame store pn-CCDs areconsidered (see previous section).4.1.13.2 THE DEVICE AND SYSTEMCONCEPT OF THE DEPFETIn all CCD-type concepts, charges are transferredslowly over large distances, they are intrinsicallysensitive to radiation damage or to metallic contaminationof the base material, because of thepresence of traps in the bulk silicon. In addition,because of the relatively slow charge transfer,X-rays may hit the CCD during the readouttime. This gives rise to events whose positionis erroneously assigned in transfer direction – theso-called out-of-time events.

ACTIVE PIXEL SENSORS FOR X-RAY SPECTROSCOPY 183of the XEUS mirror system and therefore itsastrophysical significance.Perspectives of the DEPFET SystemThe DEPFET detector system belongs to thefamily of APS. That means, that every pixel hasits own amplifier and can be addressed individuallyby external means. This results in a high degree ofoperational freedom and performance advantages.The major advantages of DEPFET type devicesare:Figure 4.1.59 Improvement of charge transfer efficiency fromthe XMM devices to the ROSITA devices. At Al Kα (1.49 keV)the XMM charge losses over 3 cm of transfer were about 15 %,while in the new devices the loss is about 1.5 %The XMM-EPIC pn-CCD system is limitedwith pile-up at count rates in the order of 20 countsper HEW and second. But with the anticipatedcollecting area up to 30m 2 several hundredsof counts per HEW and second are expectedfor comparable observations. That means that afactor of 20 or more in the XEUS phase Aand a factor of about 100 in phase B in framespeed is needed as compared to the pn-CCDcamera on EPIC-XMM, to exploit the capabilities(1) Operation with high spectroscopic resolutionat temperatures as high as −50 ◦ C, keepingthe total readout noise well below 5 electrons(rms) for a single reading of the signal charges.(2) The charge does not need to be transferredparallel to the wafer surface over long distances.That makes the devices very radiationhard, because trapping (radiation induceddefects), the major reason for degrading thecharge transfer efficiency, is avoided.(3) The ratio between photon integration time andread out time can be made as large as 1.000:1for a full frame mode, that means that the socalled out-of-time events are suppressed to avery large extent.(4) As the integration time per event will be inthe order of 1 ms and the read out time perline about 1 µs, more than 1000 cps per HEW(2 arcsec, i.e. 7 × 7 pixel) can be detected witha pile-up below 6 %.(5) No additional frame store area is needed; thedevice is as large as the processed area.(6) Any kind of windowing and sparse readout canbe applied easily, different operation modescan be realized simultaneously.(7) The DEPFET transistor amplifier structureoffers the possibility for a repetitive nondestructivereadout (RNDR). Under those conditionsthe readout noise can be reduced tobelow 1 electron (rms) by a repetitive readingof the physically same signal charge. Thisreadout mode can be applied in selected areas,while the rest of the device is operated in thestandard readout mode.

184 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYThe standard DEPFET and DEPMOS devicesare p-channel devices on n-type material. The useof p-type base material is very interesting for theDEPFET devices. The reasons for that is, that theuse of n-channel JFETs and MOSFETs becomespossible by using holes as the signal charges. Thisoffers an increased transconductance g m of thetransistors by a factor of three, improving the ENCat least by a factor of 1.5.Device Concept and Functional PrincipleOur DEPFET concepts are based on a detector–amplifierstructure, which consists of a FETworking on a depleted high resistivity substrate.The cross-section of such a device is shown inFigure 4.1.60.The device, which was proposed by Kemmerand Lutz in 1986, 6 makes use of the sidewarddepletion principle. 5 Assuming that n-type semiconductormaterial is used, one can deplete adetector chip in such a way, that there remainsa potential minimum for electrons under the channelof a FET 10 being capable of storing the signalcharges for a long time – if needed, up to severalseconds according to the operating temperature.It is straightforward to use such a deviceas detector, where signal charges (electrons) arecollected in the potential minimum, from wherethey can steer the transistor current, acting as a socalled‘internal gate’. The signal charges changethe transistor current by inducing charges insidethe p-type channel of the DEPFET. The result is asimultaneous integration of the first amplifier stageAmplifierp + sourceMO S gatep + drainn + clear− −−Deep n-doping‘Internal gate’Depleted n-Si bulkp + back contactFigure 4.1.60 Cross-section of a linear DEPFET structure with periodic reset mechanism, based on the MOS version of thedetector–amplifier structure. Electrons stored underneath the gate induce holes in the transistor channel, giving rise to anincreased current. Upon request, the charges can be cleared through the n + -clear contact

ACTIVE PIXEL SENSORS FOR X-RAY SPECTROSCOPY 185on the detector chip with a detection fill factorof 1.The potential distribution in the device, calculatedby the 3D POSEIDON 60 code, is shown inFigure 4.1.61. In this figure, the backside, wherethe charge hits the detector is located on thedown-side.The potential maximum of the internal gate(minimum for electrons) is clearly visible and isseparated from the external gate by the p-channel.The potential difference in the pixel area toits direct surroundings is about 1 V, sufficientto collect more than 100 000 electrons in onepixel. The amount of storable electrons can betailored according to the needs of the experiments(Figure 4.1.60).Since the electrons are collected in a potentialmaximum (signal charges as well as leakagecurrent) the device has to be reset from time totime by emptying the corresponding internal gate.One straightforward way of doing it, is applying apositive voltage to an adjacent n + contact, whichacts as a drain for electrons.In a first approach devices were built, whereperiodically (hundreds of µs) all charges areremoved from the potential minimum beneath thetransistor. This is done by applying for a shorttime (hundreds of ns) a positive voltage at thesubstrate contact. The result of a two-dimensionalsimulation shows the continuous rise of the bulkpotential between the region under the transistorand the substrate contact for this particular case(Figure 4.1.62). After the clear procedure, signalelectrons can be collected and stored again inthe electron potential minimum under the transistorchannel. As the signal charges have tobe removed explicitly and as the internal gateis continuously filled up with thermally generatedelectrons, the clear procedure can be appliedupon request or in a repetitive manner. The clearmechanism acts locally where the clear pulseshave been applied. The time required for a completeclear of the internal gate is estimated to bebelow 100 ns.The information about the amount of signalcharges stored can be recorded by measuring therise of the transistor current. This measurementdoes not disturb the stored charges, therefore thereadout process can be repeated several timesand opens the option of a multiple nondestructivereadout.Hence, if a row of DEPFETs is activated(Figure 4.1.63) by the selective application of theexternal gate voltages, the charge content can bemeasured, a clear pulse could be applied andthe charge measurement repeated without havingsignal electrons in the potential minimum. Thatmeans, clearing is done after having read the signalcharge. The difference between both measurementsis the net signal of electrons in the internalgate.Figure 4.1.61 Three-dimensional potential distribution of acircular DEPFET structure. The dark area is the most negativepotential (drain), the red area the most positive potential, wherethe electrons are stored. The clear is the small yellow contacton the right-hand sideSystem PerformanceThe key parameters of the DEPFET systemare listed in Table 4.1.2. Their values havebeen derived from prototype measurements or, if

186 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYFigure 4.1.62 Result of a two-dimensional simulation of the clear procedure. One can see the potential inside the detector chipwhile there is a positive voltage pulse (+15 V) applied to the substrate contact; the simulation was done with the program TOSCAfor a DEPFET with cylindrical symmetry where the source is in the centre of the structure. The reader is looking from the topof the device into the bulk

ACTIVE PIXEL SENSORS FOR X-RAY SPECTROSCOPY 187Amplifier/multiplexerCAMEX MUX ADCpixel75 × 75 µm 2Readout row selection1024 × 1024 pixel(76.8 × 76.8 mm 2 )in 16 sectionsFOV = 5 arcmin727 mmReset row selectiongate ONgate OFFGate SWITCHERclear SWITCHERgateclear ONclear OFFsourceinternalgateclearcommondrainactive rowAmplifier/multiplexerFigure 4.1.63 Layout of the focal plane pixel matrix system, consisting of the detector chip and surrounding read out and controlelectronics. The figure shows the sensitive area and its logical division. The extended chips limits (for electrical and thermalcoupling) are not visibletransferable, from measurements with the XMMpn-CCDs. The main properties are summarized inthe following sections.Energy Resolution and NoiseBeside the statistical fluctuations of the ionizationprocess (Fano fluctuations) the electronic noise isthe dominant limitation of the energy resolution.Therefore, in order to understand the basic noisesources, the physical models of the devices are ofgreat importance.Considering the noise behaviour of the DEPFET,the so called ‘total detector capacitance’ presentin conventional detector–amplifier combinationscan be neglected. Only the capacitance of theinternal gate is relevant. This leads to very lowENC figures for the series noise contribution. Theparallel noise of the structure has its origin inthe volume generation of charges inside the fullydepleted substrate and surface generated currents.As there is a low resistance between source and gate,the gate leakage current normally can be neglected.To examine the noise characteristics, measurementsof the energy resolution were done withthe help of an 55 Fe source. Figure 4.1.64 showsa spectrum with the Mn Kα and the Mn Kβ lineat 5898 eV and 6498 eV.The obtainable energy resolution with a DEPFETdetector is shown in Figure 4.1.45. In the standardfull frame mode with pixel read times of about1 µs the FWHM, including readout noise and Fanofluctuations, is shown.Position ResolutionDue to the diffusion of the signal charges duringtheir drift from the conversion point inside thesilicon into the potential minimum of the pixel,the spatial measurement precision can be improvedsubstantially, for relatively large pixel sizes. Theimprovement is significant, if the signal chargecloud diameter is in the order of the pixel size.Taking into account the thickness of the siliconwafer and the according charge collection times,i.e. collection times for the generated electrons, thecharge cloud, containing 96 % (4 σ ) of all signalcharges will have a diameter of about 30 µm. Thiswould improve the spatial resolution with a pixelsize of 50 µm tolessthan10µm for the eventswhich are all contained in one single pixel and to a

188 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYTable 4.1.2 Expected performance figures of the DEPFETfocal plane detectorIntegration and readoutReadout time per row 2.5 µs(128 channels)Total readout time1.25 msIntegration: readout time 800:1Window mode 150 µs for e.g. 64 × 64pixelsResponse to radiationQE @ 50eV 70%QE @ 100 eV 85 %QE @ 272 eV (C Kα) 90%QE @ 1.740 eV (Si Kα) 100 %QE @ 8050 eV (Cu Kα) 100 %QE @ 10 000 eV 96 %QE @ 20 000 eV 45 %Depletion depth 500 µmRejection efficiency of MIPs 100 %Response to radiationQE @ 50eV 70%QE @ 100 eV 85 %QE @ 272 eV (C Kα) 90%QE @ 1.740 eV (Si Kα) 100 %QE @ 8050 eV (Cu Kα) 100 %QE @ 10 000 eV 96 %QE @ 20 000 eV 45 %Depletion depth 500 µmRejection efficiency of MIPs 100 %SpectroscopyFano noise at 5.9 keV 118 eV FWHMSystem noiseSystem noise with RNDR55 Fe resolution 125 eVCKα resolution50 eVP/V ratio at C Kα 100:1Radiation hardness3–5 electrons (rms)≈1 electrons (rms) forn = 16No change up to (@220K) 1 × 10 10 p with 10 MeV percm 2Focal plane geometriesDevice size 7.5 × 7.5cm 2Device format 1000 × 1000Pixel size 75 × 75 µm 2Position resolution better than 30 µmFill factor of focal plane 1Operating temperature 200–240KQE, quantum efficiency.spatial resolution substantially below that (≤5 µm)for all other events (80 %) (Figure 4.1.56).A theoretical and experimental study on theposition resolution using the charge spreadingtechnique and their impact on energy resolutionmust be considered. However, it seems reasonablethat a pixel size of 75 µm to 100 µm is adequate forthe anticipated angular resolution and focal lengthof XEUS. Tests with the beam trajectory monitorfor the TTF-FEL at DESY confirmed the feasibilityof sub-micron position accuracy by centroiding thecharge cloud of the incident photons 61 at the borderof two adjacent pixels.Figures 4.1.56 and 4.1.57 demonstrate the effectof charge spreading and position reconstructionof the incident photon. The x-axis indicates theposition of the photon hit: at x = 0, the photon hitsthe pixel exactly at the boundary to the neighbouringpixel. Here the position resolution is at its optimum.As the physical situation is symmetrical with respectto the centre of the pixel, the x-axis ends at half thepixel size. On the ordinate we plotted the positionresolution (rms). The parameter ‘sg’ (sigma of theGaussian) scales the lateral signal spread beforearriving in the pixel well. The upper curve indicatesasg= 3 µm and increases to sg = 13 µm atthebottom. For a 500 µm thick detector the typical ‘sg’is between 7 µm and9µm.Quantum Efficiencyand Radiation BackgroundAs the XEUS mission intends to achieve high sensitivityfrom the very low energies (around 50 eV)up to 30 keV the detector entrance window as wellas the sensitive thickness must be optimized. Thepractical thickness of such a detector is limited to500 µm because the Compton background of thespacecraft increases with detector thickness. On thelow energy side the studies on orientedsilicon will continue, in order to improve the spectroscopicresponse down to 50 eV. The limitingquantity for the low energy response is clearly theoptical blocking filters. As a baseline we proposea 500 Å thick monolithically integrated Al filter onthe radiation entrance side.For X-rays in the range of 0.1 keV up to30 keV the response is shown in Figure 4.1.14. Asthe silicon has the same thickness and a similarradiation entrance window, the quantum efficiencyshould not differ.

CONCLUSION 18980006000T = −50 °CCount (adu)4000FWHM = 130 eV2000002000 4000 6000 8000Amplitude (adu)Figure 4.1.64 Manganese spectrum measured with a DEPFET structure at −25 ◦ C. The electronic noise contribution is only 3electrons (rms). It is obtained with a time shaping constant of 6 µS. The device was illuminated from the front side. The energyresolution of the Mn Kα line is ∼130 eV4.1.13.3 THE REPETITIVENONDESTRUCTIVE READOUT (RNDR)In cases where the count rates do not exceed thepile-up limit and/or the area of interest is restrictedto a smaller window, e.g. 2 × 2cm 2 the samesignal charge can be read out several times. Thefield of interest for RNDR in the focal plane canbe chosen relatively free, leaving the rest of thedetector in its conventional readout mode.Because the electrons are confined in theelectric field below the sensing gate of theDEPFET amplifier (floating gate amplifier) and arenot mixed with other charges, the measurementof the amount of signal charges can be repeatedas often as required. The noise, as shown inEquation (4.1.4), can be reduced byENC(n) = ENC 0 / √ n (4.1.14)where n is the number of readings of thesignal charges and ENC 0 the noise of a singlereading.We expect a single read noise of the DEPFETstructure of 4 electrons at −50 ◦ C with a shapingtime of 1 µs. After the single reading, the signalcharge is transferred to the neighbouring DEPMOSor DEPFET cell. The charge is read out again andcompared to the previous reading. Repeating thatprocedure 16 times, spending 16 µs for the readingof two pixels (Figure 4.1.65), we could achievea single electron noise floor, corresponding to anenergy resolution of less than 10 eV (FWHM). Thiswould allow the usable X-ray bandwidth to beexpanded down to 50 eV. Simulations and a designfor a DEPMOS nondestructive readout device wasrecently proposed 62 and is being fabricated.4.1.14 CONCLUSIONSince the invention of the SDD a large variety ofnew detector structures based on the principle ofsideward depletion have been developed. Thosedetectors have left their initial fields of applicationsin high energy physics, astrophysics and synchrotronradiation research. They are now a maturetechnology and open many new industrial applications.Experiments in basic research have driventhe performance parameters towards the optimumfor the specific applications: high quantum efficiency,excellent energy resolution, high radiation

190 SEMICONDUCTOR DETECTORS FOR (IMAGING)X-RAY SPECTROSCOPYSource 1DifferentialamplifierGate 1DrainGate 2Source 2ClearxxxxxxShift of signal charges‘Internal gate’Depleted n-Si bulkBack contactFigure 4.1.65 Two adjacent DEPFET devices are able to transfer the signal charges from one floating gate amplifier to theneighbouring one, reading the same signal charges several times. The read noise is reduced by the square root of n, wheren isthe number of readingstolerance, good position resolution, high speed,large and almost defect-free devices, homogeneousresponse of the full bandwidth of radiation andhigh background rejection efficiency. It will bethe aim of future developments to approach thephysical limits in radiation detection and to addin additional intelligence into the local detectorsystems to face the steadily increasing amount ofdata and power dissipation.ACKNOWLEDGEMENTSWe have profited from many discussions withscientists of the Max-Planck-Institute für Physikand extraterrestrische Physik and of the MPI-Halbleiterlabor and the company pnSensor. In particular,we are indebted to R. Richter, N. Meidinger,R. Hartmann and H. Bräuninger. We are grateful toJ. Trümper for his constant support and numerousdiscussions over the last 15 years. We appreciate theinvolvement of the Universität Bonn (N. Wermes,P. Fischer) in the DEPFET work and the Institutof Astronomie und Astrophysik Tübingen (IAAT)in the pn-CCD work. The frequent discussionswith our friends and colleagues from the Politecnicodi Milano and BNL, New York, were alwaysstimulating. Special thanks to Antonio Longoni,Carlo Fiorini, Marco Sampietro, Emilio Gatti,Andrea Castoldi, Chiara Guazzoni and Pavel Rehak.REFERENCES1. Kemmer, J. Fabrication of low noise silicon radiationdetectors by the planar process. Nucl. Instrum. Methods A169, 499–502 (1980).2. Belau, E. et al. Silicon detectors with 5 µm spatial resolutionfor high energy particles. Nucl. Instrum Methods 217,224–228 (1983).3. Pinotti, E., Bräuninger, H., Findeis, N., Gorke, H., Hauff,D., Holl, P., Kemmer, J., Lechner, P., Lutz, G., Kink, W.,

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4.2 Gas Proportional Scintillation Countersfor X-ray SpectrometryC. A. N. CONDEUniversidade de Coimbra, Coimbra, Portugal4.2.1 INTRODUCTIONX-Ray spectrometry is usually performed with oneof two techniques: energy dispersive and wavelengthdispersive. Energy dispersive techniques useradiation detectors that give a pulse proportional tothe energy dissipated in the detector medium. Mostdetectors used in practical spectrometry applicationsfit into two groups: cooled semiconductordetectors and room temperature gas detectors.While semiconductor detectors generally providesuperior energy resolution, gas detectors present abetter performance for applications requiring roomtemperature operation and/or large areas, or forX-ray spectrometry below ∼2keV. 1Since gas detectors are usually less bulky andcheaper than cooled semiconductor detectors, theyare common in portable X-ray fluorescence analysissystems. Two types of gas detectors can beused: the standard gas proportional (ionization)counter (PC) (Figure 4.2.1) and the gas proportionalscintillation counter (GPSC) (Figure 4.2.2)which was developed later.In both cases, the detector gives a pulse withan amplitude proportional to the number n ofprimary electrons produced by an X-ray photon inthe gas, which is itself approximately proportionalto the energy E of the photon. In addition tothe ionization processes in the gas that lead tothe production of primary electrons, there are alsoexcitation processes that lead to the production oflight, the so-called primary scintillation. However,as the number of primary electrons is quite small(the average value is n ≈ 273 electrons for a5.9 keV photon in Xe) it cannot be properlydistinguished from the noise of the electronicdevices used in the early amplification stages.Thus a sort of amplification is required beforethe electronics can process the detector signals.In PCs, the primary electrons are made to drifttowards a strong electric field region, usuallyin the vicinity of a small diameter (typically25 µm) anode wire (Figure 4.2.1). In this regionelectrons engage in ionizing collisions that lead toan avalanche with an average multiplication gainM of the order of 10 3 to 10 4 .IfM is not toolarge, space charge effects can be neglected, andthe average number of electrons in the end of theavalanche, N a = Mn, is then nearly proportional tothe energy E of the absorbed X-ray photon, hencethe name proportional (ionization) counter givento this device.An alternative solution (Figure 4.2.2), when thefilling gas is a noble gas like Xe, is to drift the primaryelectrons from the absorption or drift region,under a weak electric field (

196 GAS PROPORTIONAL SCINTILLATION COUNTERS FOR X-RAY SPECTROMETRYX-ray photonwith energy E−−−n primary electrons+1 kV25 µmdiameter anode−−−− −− −− − −Electron avalanchewith gain MRAOutputCylindrical cathodeXe, 1 atmFigure 4.2.1 Scheme of a gas proportional (ionization) counter (PC)X-ray photonwith energy EDrift region−−−n primary electronsXe, 1 atmScintillationregion−−VUV scintillationphotonsMetallic gridMetallic grid+1 kV+6 kVVUV photosensorAOutputFigure 4.2.2 Scheme of a gas proportional scintillation counter (GPSC)The intensity of the secondary scintillation istwo or three orders of magnitude stronger thanthat of the primary scintillation. However, sincethe secondary scintillation is produced while theelectrons drift, its rise time is much slower(a few µs) than that for the primary scintillation(a few ns). For a fixed electric field, the numberN ph of secondary scintillation photons produced bya single primary electron is nearly constant and canreach values as large as 500 photons per electron.

THE PHYSICSOFTHEABSORPTION OF X-RAYS IN GASES 197The average total number, N t , of secondaryscintillation photons produced by an X-ray photonis then N t = N ph n, so the photosensor signalamplitude is nearly proportional to E, hence thename of gas proportional scintillation counter [1](GPSC) for this device.The energy resolution of gas counters dependsmostly on the fluctuations of the physical processesinvolved in the detection. For PCs there arefluctuations both in n and M; for GPSCs, sincethe gain is achieved through a scintillation processwith almost no fluctuations, only fluctuations inn need to be considered. Thus a better energyresolution can be achieved for a GPSC than fora PC; typical values for 5.9 keV X-rays are 8 %and 14 %, respectively.The purpose of this subchapter is to delve intothe physics and applications of GPSCs. We shallfirst consider the physics of the absorption ofX-rays in gases, then the transport of electrons andthe production of electroluminescence in GPSCgases, the basic concepts in GPSCs, different typesof GPSCs and the applications of these devices toX-ray spectrometry.4.2.2 THE PHYSICS OF THEABSORPTION OF X-RAYS IN GASES4.2.2.1 ABSORPTION OF X-RAYS IN XeThe probability of absorption of an X-ray photonin a gas depends on the absorption cross-section,which for the heavier gases is nearly equal tothe photoelectric effect cross-section, σ p .Thisisapproximately proportional to Z m /E 3 , where Zis the gas atomic number, m a number between4and5andE the X-ray energy. Therefore, theheavier the noble gas the stronger is the absorption,so pure Xe (Z = 54) or Xe-based mixtures areoften used in gas-filled X-ray detectors. For Xe, thephotoelectric cross-section (Figure 4.2.3) is rather[1] This name was first suggested by J. B. Birks from ManchesterUniversity (UK), where the initial GPSC work took place, to theauthors of the first article. 2 Since there is no charge multiplication ina GPSC, it cannot be considered as a PC that scintillates, so the name‘gas scintillation proportional counter’, that is sometimes found in thescientific literature, is not appropriate.large and varies from about 5 × 10 −17 cm 2 /atom atthe ionization threshold (12.1 eV) to about 3.0 ×10 −20 cm 2 /atom at 10 keV, to which correspond, atroom temperature and 1 atm (20 ◦ C and numberdensity, N = 2.420 × 10 19 atoms/cm 3 ) absorptionlengths, L p = 1/σ p N, ranging from 8.3 µm to∼1.38 cm (right axis). Partial, shell or subshell,cross-sections are plotted as dotted lines. For somesubshells the partial cross-sections are grouped: M 2and M 3 ,M 4 and M 5 ,N 2 and N 3 ,N 4 and N 5 .Also plotted are the coherent (Rayleigh) σ Rand incoherent (Compton) σ C X-ray scatteringcross-sections, which are much lower than thephotoelectric ones. The corresponding absorptionlengths, L R and L C , refer to the right-handside axis.In the following we will refer almost exclusivelyto pure Xe, the most common filling gasfor GPSCs, though in a few cases we will considerXe based mixtures. The binding energies forthe Xe subshells are represented in Figure 4.2.4.Once an X-ray photon is absorbed and aphotoelectron ejected a multitude of processes takeplace, depending on the atomic subshell involved,which lead finally to the production of n primaryelectrons. The residual single charged ion, with avacancy in the photoionized subshell, decays tolower energy states through the emission of X-rays(fluorescence) or electrons (Auger/Coster–Kronigand shake off), increasing then its charge state.Figure 4.2.4 shows the first stages of a typicalcascade: following the photoionization of the Kshell, a K α fluorescence X-ray is emitted. Thevacancy in the L 2 subshell is filled with an electronfrom M 1 and another electron is ejected fromM 5 (Auger effect). Then the M 1 vacancy is filledwith an electron from M 5 and another electron isejected from N 5 (Coster–Kronig effect). The M 5hole is then filled with an electron from N 3 and anelectron is ejected from N 5 (Auger effect), etc. Inthe present example the decaying processes stopwhen the Xe 9+ ion in its ground state is formed.When an energetic electron is ejected it mightalso eject another electron from an outer-shell ina so-called ‘shake-off’ process, which was notconsidered in the previous example.

198 GAS PROPORTIONAL SCINTILLATION COUNTERS FOR X-RAY SPECTROMETRY1.E + 01O 23 O 1 N 45 N 23 N 1 M 45 M 23 M 1 L 3,2,1 K1.E − 03Photon cross-sections s (10 −18 cm 2 )1.E − 011.E − 031.E − 05s R , L Rs p , L p1.E − 011.E + 011.E + 03Absorption length L (cm)1.E − 070.01s C , L C0.1 1X-ray energy (keV)10 1001.E + 05Figure 4.2.3 Photoelectric σ p , Rayleigh σ R and Compton σ C cross-sections for X-rays in Xe. Corresponding absorption lengthsL p ,L R and L C . for Xe at 20 ◦ C and 760 Torr refer to the right-hand side axis. Partial shell and subshell cross-sections areplotted as dotted lines. (Based on Figure 1 of Dias et al. 3 and references therein and in http://www.photcoef.com/212154.htmland http://physics.nist.gov/cgi-bin/Xcom/xcom3 1 )4.2.2.2 NONLINEARITY EFFECTSHighly charged ions like Xe 9+ in the previouselectron cloud. 3–5 can originate false peaks in an otherwise flat X-rayexample, or higher charge, can arise when thedecaying processes are completed. Meanwhile the The study of the variation of n, W and F withejected electrons and fluorescence X-rays proceed the X-ray energy E is of great importance, since itionizing further Xe neutral atoms. The final stage affects the energy calibration and energy resolutionis reached when there are no more electrons or of any gaseous X-ray detector, either of the PC orphotons with sufficient energy (larger than 12.1 eV) GPSC type. It was shown 5 that n varies almostto ionize neutral atoms; as a result n primary linearly with E except near the L and K photoionizationthresholds, where n exhibits discontinuitieselectrons are produced.All these processes can be simulated in full approaching 1 % (Figures 4.2.5 and 4.2.6). Agreementbetween Monte Carlo calculations and exper-detail with Monte Carlo techniques provided allrelevant integral and differential cross-section dataand transition rates are available. 3 This way n canbe calculated for the simulated X-ray absorptionevent. Repeating the calculations a large number oftimes it is possible to calculate with good accuracyits average value, n, the so-called W value (W =imental measurements 5,6 is clearly seen.These effects result from the fact that when photoionizationof a new shell becomes energeticallypossible, this shell is more likely to be photoionizedthan the other (outer) shells and so a new setof decaying channels becomes possible with newE/n), the variance σ n of n, the so called Fano fluorescence X-rays and Auger/Coster–Kronigfactor, F = σ n /n, i.e. the relative variance of nand the size and spatial distribution of the primaryelectron spectra. 5Note that, besides discontinuities, these effects

THE PHYSICSOFTHEABSORPTION OF X-RAYS IN GASES 199Photoelectron K α fluorescenceX-rayL 2 M 1 M 5Auger electronM 1 M 5 N 3Coster–Kronig elctronM 5 N 3 N 5Auger elctronEnergy(eV)Unbound electrons Unbound electrons Unbound electrons Unbound electrons Unbound electrons . . . Unbound electrons0−12.1−13.4−23.4−67.5−69.5−145.5−213.3−676.7−689.4−940.6−1002.1−1148.7IncidentX-ray photon. . .−4782.2−5103.7−5452.8−34564.4. . .Xe + Xe + Xe 2+ Xe 3+ Xe 4+ Xe 9+Figure 4.2.4 Typical decay cascade of a Xe + ion following the photoionization of a K shell in Xe. (Binding energies taken from http://ie.lbl.gov/atom.htm)O 3O 2O 1N 5N 4N 2 , N 3N 1M 5M 4M 3M 2M 1L 3L 2L 1K

200 GAS PROPORTIONAL SCINTILLATION COUNTERS FOR X-RAY SPECTROMETRY248n (primary electrons / X-ray photon)238228218L 3L 2L 1Xe2084.64.8 5.0X-ray energy E xr (keV)5.2 5.4 5.6Figure 4.2.5 Mean number n of primary electrons produced by an X-ray photon near the L subshell binding energies, showingnonlinearity effects (Figure 2 of Dias et al. 5 ). Solid circles are Monte Carlo values; other symbols are derived from experimentalresults. For details see Dias et al. 5energy distribution since X-rays with differentenergies can produce the same n.The calculated W -values for Xe under a varietyof conditions are plotted in Figure 4.2.7 as afunction of X-ray energy. The two lower pointsat 4.7 keV and 5.9 keV are absolute experimentalvalues. 7 Recently 8 the absolute W -value for Xeat 825 Torr and 5.9 keV X-rays was measuredwith improved accuracy (21.61 +0.14−0.10eV) showinga small disagreement with Monte Carlo values(Figure 4.2.7). Since Xe–Ne mixtures are expectedto be important for soft X-ray detection, their W -values have been measured experimentally 9 andcalculated by Monte Carlo techniques; 10 evidencewas found for Penning effects.4.2.2.3 STATISTICAL FLUCTUATIONSFor a given X-ray energy E, the distribution functionof n, f (n), can be calculated by Monte Carlosimulation as shown in Figure 4.2.8 for 6 keV photons.The peak position of its components for theL, M, N and O shells is shifted to the right asthe shell order increases. Thus, its true shape isnot a pure gaussian, as is usually assumed, andthe peak position m, i.e. the most probable numberof primary electrons is not coincident with theaverage number, n. These effects are more pronouncedclose to a shell, if the fluorescence X-rayescapes (as shown in Figure 4.2.9 of Dias et al. 5 ).However, if as usually we approximate f(n) to agaussian, we can define its variance σ n = F n.

THE PHYSICSOFTHEABSORPTION OF X-RAYS IN GASES 2011605Kn (primary electrons / X-ray photon)159515851575∼ 10∼ 207 eV∼ 207 eVXe156534.034.2 34.4X-ray energy E xr (keV)34.6 34.8 35.0Figure 4.2.6 Mean number n of primary electrons produced by an X-ray photon near the K shell binding energy showingnonlinearity effects (Figure 3 of Dias et al. 5 ). Solid symbols are Monte Carlo values; other symbols are derived from experimentalresults. For details see Dias et al. 5The full width at half-maximum, n =2.355 √ σ n can then be calculated, as well asthe Fano factor, F . The experimental energyresolution, R, has then a lower limit given by itsintrinsic value, R int :√FWR int = 2.355EThis expression allows, in principle, the measurementof F from measurements of R, provided Wis known. However, since the experimental energyresolution is for a GPSC (Figure 4.2.2) also dependenton a variety of other factors (noise, nonparallelismof the grids, photosensor imperfections,fluctuations in the number of scintillation photons,etc.) experience can only give an upper limit forF . For X-rays with energies close to the bindingenergies of the shells, the same effects thatproduce discontinuities in n and variations in W(Figure 4.2.7), produce variations in F . 54.2.2.4 TAILING EFFECTS FOR LOWENERGY X-RAYSVery low energy X–rays (below about 1 keV or2 keV) are absorbed very near the detector window(Figures 4.2.1 and 4.2.2) since their absorptionlengths, L (Figure 4.2.3) are very small (about20 µm for 100 eV X-rays and 200 µm for1keV

202 GAS PROPORTIONAL SCINTILLATION COUNTERS FOR X-RAY SPECTROMETRY122.6M 1 L 3 L 2 L 1 K10 −1s phW (eV)22.122.310 −2s ph (10 −18 cm 2 )21.910 −321.61 10E xr (keV)10 −4Figure 4.2.7 W value for X-rays in gaseous Xe as a function of energy (Figure 4 of Dias et al. 5 ). Solid symbols are Monte Carlovalues; other symbols are derived from experimental results or are absolute measurements (⋄,). Continuous line represents theXe photoelectric cross-section. For details see Dias et al. 5X-rays). Thus, some of the electrons in the primaryelectron cloud (its size may be of the orderof tens of µm) can be scattered back to thedetector window, and so be lost. Then, the numberof primary electrons that can contribute to theX-ray detector pulse is smaller than those initiallyproduced, and a tail arises in the function, f(n). 12This tail can be reduced by increasing the intensityof the electric field near the window decreasingthus backscattering, or else by using mixtureslike Xe–Ne with longer absorption lengths. 13 Analternative is to use a driftless detector, 14 whichhas the inconvenience of requiring drift timecompensation.Typical calculated and experimental resultsfor 277 eV X-rays in pure Xe are presented inFigure 4.2.9. Full circles correspond to MonteCarlo calculated events that do not have primaryelectrons lost to the window (A 0 ); open circles correspondto all events (A 1 ). The gray continuousline with no symbols corresponds to an experimentalspectrum obtained with a GPSC.4.2.3 TRANSPORT OF ELECTRONSIN Xe4.2.3.1 DRIFT OF ELECTRONS IN XeThe n primary electrons, once produced at belowthe 12.1 eV ionization threshold, may acquirefurther energy from the electric field in the placethey are located (usually the absorption region inFigure 4.2.2) and at the same time lose energythrough elastic an inelastic collisions. Noble gasesbeing monoatomic have neither rotational norvibrational states, but only electronic states. Thefirst four states of Xe lie at 8.32, 8.44, 9.45and 9.57 eV above the ground state. Therefore forelectrons with energies below 8.32 eV no inelastic(excitation) collisions can take place and so theonly way electrons can lose energy is throughrecoil of a Xe atom in elastic collisions. Classicalmechanics teaches us that if an electron, withenergy E and mass m = 5.4858 × 10 −4 u, collideswith a Xe atom (average mass M = 131.293 u) at

TRANSPORT OF ELECTRONS IN Xe 20325XeE xr = 6 keV(5 × 10 5 events)nmNumber of X-ray events (10 3 )201510LTotal(L + M + N + O)5M0230N240 250 260 270 280 290 300n (primary electrons / X-ray photon)OFigure 4.2.8 Monte Carlo calculated distribution function, f(n), of the number of primary electrons, n, produced by 6 keV X-rayphotons in pure Xe, showing the contributions from the L, M, N, O shells. The shape of the total distribution is not a puregaussian and the position of the peak, m, is not coincident with n. (BasedonDiaset al. 5 and Dias 11 )6XeE xr = 277 eVNumber of X-ray events (10 3 )5432MC, neglecting lossesMC, accounting for lossesGPSCA 1A 01003 6 9 12 15 18n (primary electrons / X-ray photon)Figure 4.2.9 Tailing effects in a very low energy (277 eV) X-ray spectrum in gaseous Xe. The calculated distributions (solidand open circles) and the experimental spectrum (gray continuous line) obtained with a GPSC are represented (Borges et al.(unpublished); based on Borges et al. 15 )

204 GAS PROPORTIONAL SCINTILLATION COUNTERS FOR X-RAY SPECTROMETRYrest, it loses in the recoil, at most, an energy Egiven by:E =4mM(m + M) 2 E = 1.6713 × 10−5 Ewhich is a very small fraction of the incidentenergy. If there is no electric field, an electron withan initial energy of 8.32 eV, losing on the averagehalf of the above E value, requires about 7 ×10 5 elastic collisions before it can reach thermalenergies. However, if the electron is subject toan electric field it may acquire between collisionssufficient energy to compensate for the lossesduring elastic collisions, and so the electrons willdrift along the field lines. For sufficiently strongelectric fields the electron might occasionally reachenergies above the 8.32 eV threshold for excitationan so Xe ∗ species are produced. For even strongerfields ionization can take place.All these processes can be simulated in detailby Monte Carlo techniques 3,4,16 if accurate valuesof the appropriate cross-sections (integral anddifferential) are known. In Figure 4.2.10 we plotthe integral elastic, excitation and ionization crosssections,together with the total electron–Xecollision cross-section for energies ranging from10 −2 to 10 4 eV.Figure 4.2.11 depicts the calculated radial (R)versus axial (Z) position of a single electron startingat the origin with zero energy in Xe at 760 Torrsubject to a 2.5 V cm −1 Torr −1 reduced electricfield along the OZ axis. Each dot correspondsto the electron position after every twentieth collision.As shown, the radial diffusion is already0.3 mm after a drift of 1.0 mm. In Figure 4.2.12we plot the calculated energy of a single electronversus the axial distance, under the previousconditions. Since the energy lost in recoil is verysmall, the energy of the electron is almost proportionalto Z. However, once the electron reaches anenergy above the 8.32 eV threshold it will have agood chance of exciting a Xe atom, and then itsenergy will drop down to a very low value; fromthis low value energy will increase again almostlinearly with the distance until a new excitationtakes place; these processes repeat themselves untilthe electron reaches the end of the region. Thus,1000Electron scattering cross-sections (10 −16 cm 2 )1001010.1s els excsels ions tXe0.01 0.01 0.1 1 10 100 1000 10000Electron energy (eV)Figure 4.2.10 Integral cross-sections for the scattering of electrons in Xe: elastic (σ el ), excitation (σ exc ), ionization (σ ion ) andtotal (σ t ) (based on Figure 2 of Dias et al. 3 )

TRANSPORT OF ELECTRONS IN Xe 205Electron radial distance R (mm)0.40.30.20.1Xe: 760 TorrE/P = 2.5 V cm-1Torr-100 0.2 0.4 0.6 0.8 1Electron axial distance Z (mm)Figure 4.2.11 Calculated axial (Z) and radial (R) position of a typical single electron (every twentieth collision) drifting ingaseous Xe under a reduced electric field intensity of 2.5 V cm −1 Torr −1 . (Calculations by Barata 17 basedonDiaset al. 3,18 ,Dias 4,19 and Santos 16 )1210Xe: 760 TorrE/P = 2.5 Vcm-1 Torr-1Electron energy (eV)864200 0.2 0.4 0.6 0.8Electron axial distance Z (mm)Figure 4.2.12 Calculated energy versus axial distance (every twentieth collision) for a typical single electron drifting in Xe undera reduced electric field intensity of 2.5 V cm −1 Torr −1 . (Calculations by Barata 17 basedonDiaset al., 3,18 Dias 4,19 and Santos 16 )the saw-tooth shape of the plot. In the exampledepicted in this figure, the single electron driftingacross the 1.0 mm distance produced 17 excitationsof Xe atoms.On the other side, if the electric field intensity isvery weak, as in Figure 4.2.13 (0.5 V cm −1 Torr −1 ),the electron will never reach the excitationthreshold.

206 GAS PROPORTIONAL SCINTILLATION COUNTERS FOR X-RAY SPECTROMETRY65Xe: 760 TorrE/P = 0.5 V cm −1 Torr −1Electron energy (eV)432100 0.2 0.4 0.6Electron axial distance Z (mm)0.8 1Figure 4.2.13 Calculated energy versus axial distance (every twentieth collision) for a typical single electron drifting in Xe undera reduced electric field intensity of 0.5 V cm −1 Torr −1 . (Calculations by Barata 17 based on Dias et al., 3,18 Dias 4,19 and Santos 16 )4.2.3.2 THE SECONDARYSCINTILLATION PROCESSES IN XeOnce an excited Xe ∗ species is formed, if thepressure is high enough (above about 50 Torr),there is a good chance 16,20,21 that the followingthree body process takes place:Xe ∗ + 2Xe→ Xe ∗∗2 + Xewhich leads to the formation of the excimer Xe ∗∗2 .If the pressure is not too high the excimer decaysto the repulsive molecular ground state:Xe ∗∗2 → 2Xe+ hν 0with emission of a photon hν 0 in the first VUVradiation continuum.However, if pressure is above a few hundredTorr vibrational relaxation is favoured:followed by the decayXe ∗∗2 + Xe → Xe∗ 2 + 2XeXe ∗ 2→ Xe + Xe + hνForXe these secondary scintillation photons hνare peaked at the VUV wavelength of 170 nm,i.e. within the transmission range of high purityquartz. However, if other rare gases were used thewavelength would be shorter (150 nm for Kr and127 nm for Ar). 21We can assume that for each Xe ∗ species formedby the drifting electrons under the influence of anelectric field, a secondary scintillation photon isemitted. The same Monte Carlo techniques thatwere used to calculate Figures 4.2.11–4.2.13 canbe used to calculate the number of secondaryscintillation photons produced in the scintillationregion. Usually what is calculated or measured 22is the so-called reduced secondary scintillationintensity, Y/p, i.e. the number of secondaryscintillation photons produced per unit of pathlength by a single electron Y , divided by thepressure p. In Figure 4.2.14 we plot calculated 23results (full circles) together with (normalized)experimental values (open symbols) in agreementwith each other. As shown the plot starts at the∼1Vcm −1 Torr −1 threshold and it is a straight lineup to 5 V cm −1 Torr −1 . A numerical expression for

THE GAS PROPORTIONAL SCINTILLATION COUNTER 207Y/p 293 (photons electron −1 cm −1 Torr −1 )E/N (Td)0 3 6 9 12 15 180.753Andresen et al. 1977Conde et al. 1977Favata et al. 1990Fraga et al. 1990Dias 1994, Santos et al. 19940.5020.251Y/N (10 −17 electron −1 cm 2 atom −1 )Xe0.000 1 2 3 4 5E/p 293 (V cm −1 Torr −1 )0Figure 4.2.14 Reduced secondary scintillation intensity (Y/p 293 ) in Xe at 20 ◦ C, as a function of the reduced electric fieldintensity. (Based on Figure 18 of Dias 4 and Figure 4 of Santos et al. 23 .) Solid circles are Monte Carlo results, open symbols areexperimental results (see references in Dias 4 and Santos et al. 23 )Y/p is: 23Y/p 293 (photons electron −1 cm −1 Torr −1 )= 0.1389E/p 293 −0.1325Above about 5 V cm −1 Torr −1 ionization starts andso, the growth is exponential. We must point outthat a single primary electron drifting across ascintillation region with 5000 V applied to it, canproduce more than 500 photons.Since the decay time of the secondary scintillationprocesses is very fast (tens of nanoseconds orshorter) the risetime of the secondary scintillationpulse depends almost exclusively on the drift timeof the primary electrons cloud across the scintillationregion. The drift velocity of electrons in Xe isplotted in Figure 4.2.15. So, we can conclude thatthe secondary scintillation rise time is of the orderof a few microseconds.4.2.4 THE GAS PROPORTIONALSCINTILLATION COUNTER4.2.4.1 BASIC CONCEPTSWe are now in a position to discuss the use ofthe secondary scintillation to measure the numberof primary electrons and so to measure the energyof X-ray photons or other ionizing radiation. Todo so we need to fully absorb the incident radiationin a region of the Xe gas where the reducedelectric field intensity is below the 1 V cm −1 Torr −1threshold for scintillation (Figure 4.2.14) and thendrift all the n primary electrons to another region(the scintillation region) where they produce largeamounts of secondary scintillation, but no (or little)ionization. There, the field intensity should beclose to or below, the 5 or 6 V cm −1 Torr −1 thresholdfor ionization. The secondary scintillation will

208 GAS PROPORTIONAL SCINTILLATION COUNTERS FOR X-RAY SPECTROMETRY10XeDrift velocity (10 5 cm s −1 )10.1Hashimoto et al. 1990Hunter et al. 1988Dutton et al. 1975Bowe et al. 1960Brooks et al. 1982Cumpstey et al. 1980Huang et al. 1978Dias 1994, Santos et al. 19940.010.0010.01 0.1E/N (Td)110 100Figure 4.2.15 Drift velocities of electrons in Xe. (Based on Figure 17 of Dias et al. 3 andFigure10ofSantoset al. 23 ). Solidcircles are Monte Carlo results, open symbols are experimental results (see references in Dias et al. 3 )be detected by a VUV photosensor (usually a photomultipliertube), which produces a pulse lastingas long as there are electrons drifting acrossthe scintillation region (a few microseconds). Thispulse has an amplitude independent of the absorptionposition, i.e. it is proportional to n and soapproximately proportional to E. Such a detector,as stated in the Introduction, is the gas proportionalscintillation counter.An earlier review article for these detectorswas written by Policarpo 24 in 1977; more recentreviews have been produced by Akimov 25 and dosSantos et al. 26Up to the present, GPSC have been implementedmainly in three different geometries:(i) cylindrical geometry counter;(ii) spherical anode geometry counter;(iii) uniform electric field geometry counter.The cylindrical geometry GPSC 2,27 is like astandard proportional (ionization) counter (Figure4.2.1) filled with a noble gas (Xe) and coupledin the end to a photomultiplier, to sensethe secondary scintillation produced. However,since the applied voltage is below the one forstarting avalanche processes it is not a proportionalcounter. The scintillation region is asmall volume of the gas around the anode wherethe reduced electric field intensity lies in the 1to 5 V cm −1 Torr −1 range; the rest is absorptionregion, so almost all the ionizing radiation isabsorbed in this region.In the spherical anode GPSC 28 the voltageapplied to the anode is also close to the thresholdfor starting avalanches, which is well above thescintillation threshold. The scintillation region isalso limited to a small volume close to the anode;the rest, which is the largest part of the detectorvolume, is absorption region.In the uniform electric field GPSC, 29,30 alreadydescribed summarily in the Introduction, there isa high transmission metallic grid delimiting theabsorption region (Figure 4.2.2). This region isusually a few cm thick so that most radiationsare absorbed there. The n primary electrons thereproduced are transferred into the scintillationregion by an electric field, producing then thesecondary scintillation pulse, detected by the

THE GAS PROPORTIONAL SCINTILLATION COUNTER 209photosensor. Since in this geometry the absorptionand scintillation regions are well separated it ispossible to optimize the electric field in each oneand large amounts of secondary scintillation beproduced. This geometry is the most used one.4.2.4.2 THE ENERGY RESOLUTIONOF A GAS PROPORTIONALSCINTILLATION COUNTERThe energy resolution of a GPSC depends mainlyon the fluctuations of n (with variance σ n ),aswellas on the fluctuations in the number of secondaryscintillation photons reaching the photosensor andin the gain A of the photosensor. However, sincethe number of secondary scintillation photonsproduced by a single primary electron is large andwith small fluctuations, the experimental energyresolution for a narrow beam of X-rays 14,31 can besimplified and written as:√FWR = 2.355E+ k Awhere k is a constant and the term k/A representsthe fluctuations associated with the gain A, whichis generally much smaller than FW /E.However, if the beam enters the detectorthrough the full window diameter, there arefluctuations in the number of scintillation photonsreaching the photosensor due to solid angle effects.Indeed for X-rays entering the detector windownear its border, a large number of scintillationphotons will miss the photosensor due to itsfinite size. Thus, these events produce pulses withamplitudes smaller than central events. For a fullopening window, these solid angle effects producepulses with variable amplitudes which deterioratethe energy resolution, limiting the performance oflarge area GPSC.An obvious solution is to use very large areaphotosensors, which has the inconvenience of ahigh cost. Another solution is to concentrate theprimary electrons produced in the drift region intothe scintillation region, 32 a technique which has itsown limitations.4.2.4.3 SOLID ANGLE COMPENSATIONTECHNIQUESTwo other techniques have been recently developedthat allow the construction of GPSCs withwindows approaching in size the diameter of thephotosensor, with little deterioration of the energyresolution. 33–36 Such techniques make use of solidangle compensation.The first one, the curved grid technique, 33,35–37uses a curved grid G 1 followed by a flat grid(G 2 ) (Figure 4.2.16a) delimiting the scintillationregion. Therefore, the electric field there is nolonger uniform: in the centre it is weaker than inthe border of the curvature, which means that theintensity of the secondary scintillation increaseswith the radial distance to the axis. However, thesolid angle through which the photosensor sees thesecondary scintillation photons decreases with theradial distance.With a properly calculated grid curvature 33,35,36it is possible to achieve a radial increasing ofthe scintillation yield, that compensates the radialdecreasing of the solid angle, leading thus to aconstant pulse amplitude whatever the entrancewindow position of an X-ray photon.Both spherical 33,37 and ellipsoidal 38 grids havebeen used. Energy resolutions of 8 % wereobtained for 5.9 keV X-rays and windows 25 mmin diameter, with Xe filled GPSC using standard50 mm diameter photomultiplier tubes. 37The second technique (Figure 4.2.16b), themasked photosensor technique, 34–36 uses a uniformelectric field scintillation region, producedby the parallel grids G 1 and G 2 , and a gradedmask covering the photosensor. This mask absorbsmore secondary scintillation in the centre than inthe border. With proper grading it is possible tocompensate the radial decreasing of solid angleby a radial increasing of the mask transmission.Again, this leads to constant pulse amplitude whateverthe entrance window position of the X-rayphoton. With this technique energy resolutions of10 % were obtained for 5.9 keV X-rays entering thefull 40 mm wide window of a GPSC which uses a50 mm diameter photomultiplier. 34

210 GAS PROPORTIONAL SCINTILLATION COUNTERS FOR X-RAY SPECTROMETRYIndiumgasketKapton40 mm7 6Drift regionG 1G 1G 2Scintilation regionG 2MacorEMID676 QBEpoxy21PhotocathodePMTMacor3450 1 2 3 cmCr film1 2 3 4 cm1 - Quartz wafer with grid G2 and mask compensation2 - G1 feedthrough3 - Chromium film4 - Electrical contacts for G25 - To gas purifier6 - Kapton window, 75 µm thick7 - Stainless steel(a)(b)Figure 4.2.16 Schematic diagram of (a) the curved grid GPSC and (b) the masked-photosensor GPSC (Figure 2 from Condeet al. 33 and Figure 4 from Veloso et al., 34 respectively). Reproduced by permission of The Institute of Electrical and ElectronicsEngineers, Inc.4.2.4.4 PHOTOSENSORS FOR GASPROPORTIONAL SCINTILLATIONCOUNTERSTraditionally, photomultipliers have been the preferredphotosensors for GPSCs. As the secondaryscintillation for Xe lies in the VUV (170 nm) and israther intense (about 10 5 VUV photons per 5.9 keVX-ray) the photomultiplier needs to have a highpurity quartz window (Spectrosil B) and a smallnumber of dynodes 8 like the EMI D676 QB. However,since photomultipliers are expensive, bulkyand fragile, efforts have been made to find otheralternatives. Following the early use of photoionizationchambers with TMAE 39 recent work hasput emphasis on the use of microstrip plate detectorswith CsI and photodiodes.In a compact implementation 40 depicted inFigure 4.2.17, a standard microstrip plate (MSP)XenoninletVa−HV 1 −HV 0WindowinFVaoutG1MSPXenonoutletFigure 4.2.17 A compact GPSC using a CsI covered microstripplate (MSP) as photosensor (Figure 4.2.2 of Veloso et al. 40 ).Reproduced by permission of The Institute of Electrical andElectronics Engineers, Inc.

APPLICATIONS OF GAS PROPORTIONAL SCINTILLATION COUNTERS TO MATERIAL ANALYSIS 211takes the role of the second grid of a GPSC,with the MSP anodes biased positively at a fewhundred volts. With G 1 at a negative – HV 1voltage of a few kV, a scintillation region isproduced between G 1 and the MSP. An appropriatevoltage applied to the window (−HV 0 ) definesan absorption/drift region between G 1 and thewindow. If the MSP is covered with a CsIfilm (Figure 4.2.18) photoelectrons can be releasedfrom the anodes by the VUV scintillation andthen be charge multiplied in the MSP anodes,producing a large amplitude pulse. However, thisimplementation has a drawback: since chargemultiplication takes place in the Xe environment,it is accompanied by light emission that releasesfurther electrons from the CsI covered cathodes,leading to a positive feedback process whichlimits the maximum allowable charge gain. Toavoid this drawback the MSP can be separatedfrom the Xe GPSC scintillation region with athin quartz window and the MSGC filled witha non-scintillating gas like P-10. 31 The achievedenergy resolutions for 5.9 keV X-rays are 12 % 31and 11.4 % 41 for the first implementation (MSPwithin the Xe environment), and 10.5 % for thesecond implementation (MSP in a separate P-10gas environment).Photodiodes, whether of the vacuum type 42 orsolid state (Si) type, 43,44 have also been consideredas alternative photosensors for GPSCs. However,for X-ray detection the Si photodiode noise is toohigh and the performance is rather worse thanthat for a standard photomultiplier based GPSC.The recent development of VUV sensitive largearea avalanche photodiodes (LAAPD), which arephotodiodes with an intrinsic gain resulting froman avalanche process, allowed the development ofhigh performance GPSCs.When the LAAPD is placed in the Xe environment,just in front of the scintillation region, 45an energy resolution of 7.9 % for 5.9 keV X-rayswas obtained. However, LAAPDs have the inconvenienceof having a gain rather sensitive to temperaturefluctuations.4.2.5 APPLICATIONS OF GASPROPORTIONAL SCINTILLATIONCOUNTERS TO MATERIAL ANALYSISThe superior performance of GPSCs over standardPCs makes them suitable for material analysis byX-ray fluorescence techniques, wherever PCs haveRelative Intensity(a)300CrFeNi400 500 600 700Channel numberAbsorption regionG 1d 1ScintillationregionRelative IntensityCrFeNiCslVUVd 2MSGC chargemultiplicationregiond 2 /d 1 = 1/100Figure 4.2.18 Detail of a CsI covered MSP as the photosensorin a GPSC (Figure 2 of Veloso et al. 40 ). Reproduced bypermission of The Institute of Electrical and ElectronicsEngineers, Inc.(b)300400 500 600 700Channel numberFigure 4.2.19 X-ray fluorescence spectra for a stainlesssteel sample excited with a 244 Cm X-ray source, using aphotomultiplier based GPSC and (a) 11 mm and (b) 25 mmdiameter window collimations (Figure 8 of dos Santos et al. 46 ).Reproduced by permission of The Institute of Electrical andElectronics Engineers, Inc.

212 GAS PROPORTIONAL SCINTILLATION COUNTERS FOR X-RAY SPECTROMETRYbeen used: low cost room temperature portableinstruments, large area detectors and very softX-ray detection. Figures 4.2.19 and 4.2.20 depictX-ray fluorescence spectra for stainless steel andcalcopyrite samples excited with a 244 Cm X-raysource 46 using a photomultiplier based GPSC witha curved grid. As shown, the performance does notdeteriorate when the window collimation increasesfrom 11 to 25 mm diameter. The detector canseparate clearly the Cr and the Fe peaks.Figure 4.2.21 shows X-ray fluorescence spectraobtained with a LAAPD based GPSC 47 of nonhomogeneousgeological samples containing Si(Figure 4.2.21a) and anthracite (Figure 4.2.21b)excited with a 55 Fe X-ray source and a calcopyritesample (Figure 4.2.21c) excited with a 109 Cdsource. The good separation power of the GPSCfor low atomic number elements like Si, S, Ca andTi is evident.Relative intensityFe KaFe KbCu KaCu Kb120100806040200(a)500450400350300250200150100500Counts/channelCounts/channel(b)Si0 1 2 3 4 5 6 7 8SEnergy (keV)Ca0 1 2 3 4 5 6 7Energy (keV)Backscatteredsource X-raysTi(a)Relative intensity350 400 450 500 550 600 650 700Channel numberCu KaFe KaFe KbCu Kb350 400 450 500 550 600 650 700(b)Channel numberCounts/channel10009008007006005004003002001000(c)Cu KaFe KaCu Kb0 1 2 3 4 5 6 7 8 9 10 11 12 13Energy (keV)Figure 4.2.20 X-ray fluorescence spectra for a calcopyrite sampleexcited with a 244 Cm X-ray source, using a photomultiplierbased GPSC and (a) 11 mm and (b) 25 mm diameter windowcollimations (Figure 9 of dos Santos et al. 46 ). Reproduced bypermission of The Institute of Electrical and Electronics Engineers,Inc.Figure 4.2.21 X-ray fluorescence spectra obtained with aLAAPD based GPSC for Si (a) and anthracite (b) samplesexcited with a 55 Fe X-ray source, and for a calcopyrite sample(c) excited with a 109 Cd source (Figure 9 of Lopes et al. 47 ).Reproduced by permission of The Institute of Electrical andElectronics Engineers, Inc.

ACKNOWLEDGEMENTS 213Andalusite (AI 2 SiO 5 ) sample excited with a particles ( 144 Cm)Number of X-ray events(a)16001400120010008006004002000O (525 eV)Al (1487 eV)Si (1740 eV)0 100 200 300 400 500Channel numberXe (760 Torr) GPSC600Number of X-ray events500400300200100AlSiKTiMn(b)00 200 400 600 800 1000 1200Channel numberFigure 4.2.22 X-ray fluorescence spectra of an andalusite sample, obtained with a Xe filled GPSC with a very thin polyimidewindow: (a) excitation with a 244 Cm alpha particle source; (b) excitation with 5.9 keV X-rays from a 55 Fe source (Borges(unpublished) and Borges et al. 48 )For very soft X-ray detection and large areas,there are no other detectors (even cooled semiconductordetectors) that can match the performanceof GPSC. In Figure 4.2.22 we present the spectraof an andalusite sample obtained with a GPSCfilled with pure Xe and having a polyimide window(PG-W from Metorex). In Figure 4.2.22(a) thesample was excited with alpha particles from a244 Cm source; in Figure 4.2.22(b) excitation wasproduced by 5.9 keV X-rays from a 55 Fe source.As shown, the oxygen K α peak is clearly separatefrom the carbon peak (this peak arises from impuritiesand the carbon in the polyimide window).The Mn line results from coherent backscatteringof the 5.9 keV X-rays.Detecting low concentration elements is, sometimes,not easy since the corresponding peaksmight be difficult to distinguish from background.However, digital risetime discrimination techniquesapplied to GPSC spectra might improve the peakto-backgroundratio, as already demonstrated. 49 .4.2.6 CONCLUSIONSIt was shown that Xe-filled gas detectors, likestandard proportional counters and gas proportionalscintillation counters, suffer from nonlinearityeffects, approaching 1 %, and that the peakshape is not a pure gaussian. These effects mustbe taken into account when doing spectra fitting.GPSCs offer an energy resolution much better thanthat of PCs, i.e. 8 % for 5.9 keV X-rays and can bebuilt with very large windows (2.5 cm diameter orlarger) and are very useful for very soft X-rays likethe K lines of C and O. New photosensors havealready been developed to replace the photomultiplierallowing more compact GPSCs.

214 GAS PROPORTIONAL SCINTILLATION COUNTERS FOR X-RAY SPECTROMETRYACKNOWLEDGEMENTSThis work was supported by Project CTAE/1920,Fundação para a CiênciaeaTecnologia(FCT),Lisbon, and was done in Grupo de InstrumentaçãoAtómica e Nuclear (GIAN), Centro de Instrumentação(Unidade 217/94), Departamento de Físicaof the University of Coimbra.I thank Teresa H.V.T. Dias for very interestingcomments and for preparing Figures 4.2.3,4.2.5–4.2.10, 4.2.14 and 4.2.15. Thanks are due toFilipa I.G.M. Borges for preparing Figure 4.2.22.I thank Diogo S.A.P. Freitas for preparing Figures4.2.1 and 4.2.2, and for doing the word processingwork. Thanks are also due to João A.S.Barata who did the calculations and preparedFigures 4.2.11–4.2.13 and to Hugo N. da Luz forhelp in preparing Figure 4.2.4.REFERENCES1. Knoll, G. F. Radiation Detection and Measurement, 3rdEdition, John Wiley & Sons, Inc., New York, 2000.2. Conde, C. A. N. and Policarpo, A. J. P. L. A gas proportionalscintillation counter. Nucl. Instrum. 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Res., A357, 406–417 (1995).28. Policarpo, A. J. P. L., Alves, M. A. F., dos Santos,M. C. M. and Carvalho, M. J. T. Improved resolution forlow energies with gas proportional scintillation counters.Nucl. Instrum. Methods, 102, 337–348 (1972).29. Conde, C. A. N., Santos, M. C. M., Fátima M., Ferreira,A. and Sousa, C. A. Argon scintillation counter withuniform electric field. IEEE Trans. Nucl. Sci., 22(1),104–108 (1975).30. Palmer, H. E. and Braby, L. A. Parallel plate gas scintillationproportional counter for improved resolution of lowenergyphotons. Nucl. Instrum. Methods, 116, 587–589(1974).31. Veloso, J. F. C. A. and dos Santos, J. M. F., Conde,C. A. N. Gas proportional scintillation counters with aCsI-covered microstrip plate UV photosensor for highresolutionX-ray spectrometry. Nucl. Instrum. MethodsPhys. Res., A457, 253–261 (2001).32. Manzo, G., Peacock, A., Andersen, R. D. and Taylor,B. G. High pressure gas scintillation spectrometry for X-ray astronomy. Nucl. Instrum. Methods, 174, 301–315(1980).33. Conde, C. A. N., dos Santos, J. M. F. and Bento,A. C.S. S. M. New concepts for the design of large area gasproportional scintillation counters. IEEE Trans. Nucl. Sci.,40(4), 452–454 (1993).34. Veloso, J. F. C. A., dos Santos, J. M. F. and Conde,C. A. N. Large-window gas proportional scintillationcounter with photosensor compensation. IEEE Trans. Nucl.Sci., 42(4), 369–373 (1995).35. Conde, C. A. N., dos Santos, J. M. F. and Bento, A. C.S. S. M. Gas proportional scintillation counter for ionizingradiation with medium and large size radiation windowsand/or detection volumes. US Patent 5,517,030 (14May, 1996) (available in http://www.uspto.gov/patft/index.html).36. Conde, C. A. N., dos Santos, J. M. F. and Bento,A. C. S. S. M. Gas proportional scintillation counter forionizing radiation with medium and large size radiationwindows and/or detection volumes. European PatentEP 0616722 BI (30 December, 1998) (available inhttp://ep.espacenet.com).37. dos Santos, J. M. F., Bento, A. C. S. S. M. and Conde,C. A. N. The performance of the curved grid gas proportionalscintillation counter in X-ray spectrometry. Nucl.Instrum. Methods Phys. Res., A337, 427–430 (1994).38. Silva, R. M. C., dos Santos, J. M. F. and Conde, C. A. N.An ellipsoidal grid gas proportional scintillation counter.Nucl. Instrum. Methods Phys. Res., A422, 305–308 (1999).39. Anderson, D. F. A xenon gas scintillation proportionalcounter coupled to a photoionization detector. Nucl.Instrum. Methods, 178, 125–130 (1980).40. Veloso, J. F. C. A., Lopes, J. A. M., dos Santos, J. M. F.and Conde, C. A. N. A microstrip gas chamber as a VUVphotosensor for a xenon gas proportional scintillationcounter. IEEE Trans. Nucl. Sci., 43(3), 1232–1236 (1996).41. FreitasD.S.A.P., Veloso,J.F.C.A., dos Santos,J. M. F. and Conde, C. A. N. Dependence of the performanceof CsI-covered microstrip plate VUV photosensorson geometry: experimental results. IEEE Trans. Nucl. Sci.49, 1629–1633 (2002).42. Van Standen, J. C., Mutterer, M., Pannicke, J., Schelhaas,K. P., Foh, J. and Theobald, J. P. Vacuum photodiodeas light sensing element for gas scintillation counters.Nucl. Instrum. Methods, 157, 301–304 (1978).43. Campos, A. J. A silicon photodiode based gas proportionalscintillation counter. IEEE Trans. Nucl. Sci., 31(1),133–135 (1984).44. Lopes, J. A. M., dos Santos, J. M. F., Morgado, R. E. andConde, C. A. N. Silicon photodiodes as the VUV photosensorin gas proportional scintillation counters. IEEETrans. Nucl. Sci., 47(3), 928–932 (2000).45. Lopes, J. A. M., dos Santos, J. M. F. and Conde, C. A. N.A large area avalanche photodiode as the VUV photosensorin gas proportional scintillation counters, Nucl. Instrum.Methods Phys. Res., A454, 421–425 (2000).46. dos Santos, J. M. F., Soares, A. J. V. D., Monteiro,C. M. B., Morgado, R. E. and Conde, C. A. N. The applicationof the curved-grid technique to a gas proportionalscintillation counter with a small-diameter photomultipliertube. IEEE Trans. Nucl. Sci., 45(3), 229–233 (1998).47. Lopes, J. A. M., dos Santos, J. M. F., Morgado, R. E. andConde, C. A. N. Silicon a xenon gas proportional scintillationcounter with a UV-sensitive, large-area avalanche photodiode.IEEE Trans. Nucl. Sci., 48(3), 312–319 (2001).48. Borges, F. I. G. M., Santos, F. P., dos Santos, J. M. F.,Dias, T. H. V. T., Rachinhas, P. J. B. M. and Conde,C. A. N. The performance of a gas proportional scintillationcounter for X-ray spectrometry in the 0.1–3 keVrange. IRRMA-V – 5th International Topical Meeting onIndustrial Radiation and Radioisotope Measurement Applicationssubmitted.49. Simões, P. C. P. S., dos Santos, J. M. F., and Conde,C. A. N. Digital risetime discrimination for peak enhancementanalysis. X-Ray Spectrom., 26, 182–188 (1997).

4.3 Superconducting Tunnel JunctionsM. KURAKADORIKEN, Saitama, Japan4.3.1 INTRODUCTIONIn this subchapter, recent references regardingsuperconducting tunnel junction (STJ) detectorsare limited to those related to spectrometric applications.References [1–4] are useful concerningstudies of STJ detectors themselves. Historical andintroductive descriptions also can be found in References5 and 6.The limit of energy resolution due to the statisticalfluctuation N of the number N of initial signalcharges, (N/N)E, is given by 2.355(EεF) 1/2(FWHM), where E is the radiation energy, ε is themean energy required to excite one signal chargeand F is the Fano factor of the detector. Since theenergy gaps (E g = 2) of metal superconductorsare of the order of 1 meV, detectors made of metalsuperconductors potentially provide high resolution.Popular superconductors for STJ detectors areNb (T c ≈ 9K), Ta (T c ≈ 4.5K), V (T c ≈ 5.4K)and Al (T c ≈ 1.2K), whereT c is the superconductingtransition temperature (2 T =0 ≈ 3.5k B T c ).An STJ usually consists of two superconductorlayers and a 1–2 nm thick insulator layer, whichis a tunnel barrier between the superconductorlayers (Figure 4.3.1). Excited electrons or holes,i.e. quasiparticles, can pass through the tunnelbarrier by means of quantum mechanical tunneling(Figure 4.3.2).The dc Josephson current that flows at the biasvoltage V B = 0 is suppressed by applying a magneticfield parallel to the junction plane to stabilizethe bias when an STJ is put to use as a detector.A quasiparticle produces signal current and signalcharge when it passes through the tunnel barrierbefore recombination with other quasiparticles inthe same electrode or escapes from the electrodeto the electric lead. Quasiparticles excited by radiationmust diffuse in the electrode and collide withthe tunnel barrier for many times to tunnel thebarrier, leading to the dependency of the tunnelingprobability on characteristics of the electrodesuch as the thickness, the mean free path in theelectrode and the width of the lead. Consequently,two electrodes produce different magnitudes of signalsthat cause double peaks in the case of X-raydetection when the X-rays can penetrate the upperelectrode. The rise times of signals, i.e. chargeLower lead5 µmTunnel barrierAl-AlO x /AlJunctionUpper leadUpper lead600 nm NbSiO 2Lower leadUpper Nb electrodeLower Nb electrode SiO 2Sapphire substrateFigure 4.3.1 Example of the structure of an STJ detectorX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

218 SUPERCONDUCTING TUNNEL JUNCTIONSElectron-likequasiparticlesDensity of statesof quasiparticlesTypical size:500 µm × 100 µm × 0.8 µm2∆E FBias voltage eV B= E gCooper pairs(a)dcIHole-likequasiparticlesTunneling ofquasiparticles(a)SuperconductorabsorberLowerleadSubstrateSTJJosephsoncurrentCurrentdue to thermalquasiparticlesEnergy gap(b)02∆/eFigure 4.3.2 Energy structure, tunnel effect and current–voltagecharacteristics of an STJ. For low energy X-rays, theinsulator layer covering the STJ is usually removedV BVarnishCopper platePhononsSeries-junctions400 µmSapphiresubstratesignals or current signals, provide good methodsto distinguish the signals produced in an electrodefrom the others.In addition to the single-junction detectors(Figure 4.3.1), there are two other type of STJdetectors as shown in Figure 4.3.3. Type (a) consistsof an absorber superconductor and twoSTJs that are composed of a smaller energy gapsuperconductor and collect quasiparticles excitedin the absorber by means of the quasiparticletrapping effect. In this subchapter, this type ofdetector is referred to as a one-dimensionalimagingSTJ detector. In the case of type (b),i.e. series-junction detectors, radiation is absorbedin a single-crystal substrate and the resultingnon-thermal phonons are detected by many STJsconnected in series on the surface of the substrate.4.3.2 STATISTICAL LIMIT OFENERGY RESOLUTIONFigure 4.3.4 shows the main relaxation processesof the energy deposited from radiation to superconductingSn. 7,8 Radiation excites electrons which(b)RadiationCollimatorFigure 4.3.3 Two kinds of STJ detectors other than single-junctiondetectors: (a) one-dimensional-imaging STJ detector;and (b) series-junction detectorinitiate the cascade of quasiparticle excitation inthe superconductor. The dominant interaction ofquasiparticles with energy E>∼(E D E F ) 1/2 is theelectron–electron interaction, where E D is theDebye energy, i.e. maximum energy of phonons,and E F is the Fermi energy. Such a quasiparticlebreaks Cooper pairs and thus excites otherquasiparticles. The dominant interaction of quasiparticleswith energy E

STATISTICAL LIMIT OF ENERGY RESOLUTION 2191.0∼(E D E F ) 1/2= 300 meVCooper pairbreakingby electronsEnergya 2 (Ω)F(Ω) (relative)0.80.60.40.22∆0.00 2 4 6 8 10 12 14 16 18 20Phonon energy Ω (meV)Phonon emissiona 2 (Ω)F(Ω)E D= 17.2 meVCooper pair breakingby phononsPhonon emission03∆∆Phonon emission2∆= 1.15 meV0Cooper pairsElectronsystemPhononsystemFigure 4.3.4 Cascade excitation processes of quasiparticles and phonons in a superconducting Sn at 0 K. The inset is theα 2 ()F (), whereα 2 () is the effective electron–phonon coupling function and F() is the density of states of phononsFigure 4.3.4 shows α 2 ()F () of Sn. A phononwith energy ≥ 2 breaks a Cooper pair and thusexcites two quasiparticles. A quasiparticle withenergy E ≥ 3 can emit a phonon with energy ≥ 2. Repetition of the phonon emission byquasiparticles and excitation of quasiparticles byphonons increases the number of quasiparticles andphonons, leading to a small ε value.Figure 4.3.5 shows results of numerical simulationsof the cascade excitation processes of quasiparticlesand phonons in a bulk superconductingSn at 0 K. 8 As can be seen in Figure 4.3.5(a), themean energy ε required to excite one quasiparticlebeyond the energy gap is ≈1.7(≈1meV)andthestatistical fluctuation of the number N of excitedquasiparticles defined by F ≡〈(N −〈N〉) 2 〉/〈N〉

∋220 SUPERCONDUCTING TUNNEL JUNCTIONS(meV)Counts(a)100806040200Energy of radiation= 5.75 eV = 10 4 ∆Number of radiations= 3000 = 5932.4Resolution= 78 meVε = 1.68 ∆= 0.969 meVF = 0.1955850 5900 5950 6000 6050N(meV)01.55 101.00.5 0.97500.9700.9657∆1530∆Figure 4.3.5(b) shows the ε value calculatedas a function of the energy of a phonon. 8Non-thermal phonons with energy ≥ 2 canexcite quasiparticles as efficiently as radiations inthe superconducting Sn. ε increases linearly, i.e.ε = /2, for 2 6 is almost constant and equalto that obtained for radiation, i.e. 1.7. It shouldbe noted that thermal phonons with energy

SINGLE-JUNCTION DETECTORS 2212 shown in Figure 4.3.6(b), one electron is transferredfrom the left electrode to the one on theright. The iteration of the processes 1 and 2 doesnot increase the number of excited quasiparticlesbut increases the signal charge. The amplificationof signal charge terminates when the quasiparticleescapes from the junction or recombines with oneof the other quasiparticles in the same electrode.The statistical fluctuation of signal charge associatedwith the tunneling processes deterioratesthe energy resolution R in addition to the initialfluctuation of N, noise and the position dependencyof the signal height. The amplification factor〈n〉 ≡Q/(E/1.7)e and the fluctuation R t associatedwith the multi-tunneling process are given by:〈n〉 =P 1 (1 + P 2 )/(1 − P 1 P 2 )R t = 2.355(EεG) 1/2where G = (1 − P 1 + 3P 2 + P 1 P 2 )/P 1 (1 + P 2 ) 2 ,and P 1 and P 2 are probabilities of processes 1and 2 of Figure 4.3.6(b), respectively. 10 Therefore,R = 2.355[Eε(F + G)] 1/2 .When〈n〉 ≫1, G ≈ 1and thus R ≈ 2.45 × 2.355(EεF ) 1/2 ,whereF =0.2, corresponding to R ≈ 10 eV (7 eV) at 5.9 keVfor Nb-based (Ta-based) STJs. Therefore, multitunnelingis not preferable to attain ultimate energyresolutions but useful to attain ultra-low noise performances.4.3.3 SINGLE-JUNCTIONDETECTORSRecently, STJ detectors realized energy resolutionsabout one order higher compared with semiconductordetectors.An STJ, consisting of (from bottom to top)Nb (240 nm)/Al (200 nm)/AlO x /Al (200 nm)/Nb(150 nm) and having an area of 100 × 100 µm 2 ,showed an energy resolution of 29 eV and noiseof 10.5 eV for 5.9 keV X-rays. 11 The STJ wascooled to 200 mK by an adiabatic demagnetizationrefrigerator (ADR) because 2 of the thick Allayers is considerably smaller than that of Nb.The Al layers acted as traps for quasiparticles.The quasiparticles generated by an X-ray absorbedin a Nb layer are quickly collected to theadjacent Al layer and trapped there, leadingto efficient tunneling, amplified signals, reducedrecombination in the Nb layer and thus decreasedposition dependency of signal heights.As can be seen from Figure 4.3.7, showingcalculated Gaussian spectra correspondingto (a) conventional semiconductor detectors and(b) an STJ detector with a resolution of 29 eVand noise of 10 eV at 5.9 keV, the improvementin resolving power for characteristic X-raysis remarkable.A 100 × 100 µm 2 Al/AlO x /Al STJ, with anabsorption efficiency of about 1 % for 6 keVX-rays, attained the best energy resolution of 12 eVfor 5.9 keV X-rays. 12,13 The STJ detector wascooled to 70 mK and the noise was 7 eV. The AlSTJ was fabricated on a Si substrate coated witha metallic layer, which acted as a buffer layer toreduce the influence of X-ray absorption in thesubstrate on the STJ response. An insulator layer(polyimide) is deposited onto the buffer layer. Thehigh energy resolution is attributed to the bufferlayer underneath the STJ. The rise time of theoutputs of the charge-sensitive preamplifier wasabout 10 µs. The charge signal of the 5.9 keV X-rays corresponded to 61 % of the initially createdquasiparticles (〈n〉 =0.61), suggesting a weakamplification of signal charges owing to the multitunnelingof quasiparticles.A 141 × 141 µm 2 Nb (265 nm)/Al (50 nm)/AlO x /Al (50 nm)/Nb (165 nm) STJ revealed a highstability of the signal heights against temperaturevariation from a temperature (>50 mK) to 500 mKbecause of the enhanced energy gap of the thin Allayers arising from their proximity to the thickerNb layers. 14 The pulse decay time of currentsignals was 4.5 µs. The amplification factor 〈n〉was about 20. The STJ was evaluated by usinglow energy X-rays (70–700 eV) from synchrotronradiation. During the measurements the STJ wascooled by an ADR, and the temperature was notregulated and allowed to drift up to about 500 mK.Most of the low energy X-rays were absorbed bythe upper electrode. The STJ detector showed, forexample, an energy resolution of 5.9 eV and a noiseof 4.5 eV for 277 eV X-rays that correspond to

222 SUPERCONDUCTING TUNNEL JUNCTIONSB:C:N:O = 1:1:1:1Counts0 200 400Energy (eV)600 800CountsB:C:N:O = 1:1:10:1CountsTi (Ka):La (La)= 10:10 200 400Energy (eV)600 800(a) Resolution (@5.9 keV) = 130 eV and noise = 100 eVBoron (B), Carbon (C), Nitrogen (N), Oxygen (O)4400 4500 4600Energy (eV)4700 4800CountsB:C:N:O= 1:1:100:1CountsTi (Ka):La (La)= 100:10 200 400Energy (eV)600 800(b) Resolution (@5.9 keV) = 29 eV and noise = 10 eV4400 4500 4600 4700 4800Energy (eV)Figure 4.3.7 Sample spectra of characteristic X-rays obtainable with detectors with different resolutions: corresponding to (a) asemiconductor, and (b) a Nb/Al/AlO x /Al/Nb STJ detector. The spectra were calculated assuming Gaussian distributions forthe peaksthe K X-rays of carbon at a count rate of severalhundred counts per second (cps) and a resolutionof 13 eV, and a noise of 11.9 eV at 23 kcps. Theenergies of the synchrotron X-rays correspondedto the K X-rays of light elements, i.e. Be, B, C, Nand O, and they produced sharp peaks in the pulseheight spectrum.Katagiri et al. developed a high count rate X-ray detector system with a fast current readout. 15The STJ is a 200 × 200 µm 2 Nb/Al/AlO x /Al/Nbjunction, which has a current rise time of 100 ns,a current decay time of 160 ns and resistance of20 at 0.4 K. The fast current readout system isequipped with a superconducting coil to achievea stable biasing of the STJ. The coil works as aninductive load to signal pulses although it doesnot affect dc biasing by a shunt resistance. Theenergy resolution of bottom layer signals was about230 eV up to 100 kcps, ∼265 eV at 250 kcps, and∼400 eV at 500 kcps for 4 keV X-rays.Verhoeve et al. studied STJs as infrared toultraviolet photon detectors. 16 Optical photons

SERIES-JUNCTION DETECTORS 223with energy of 0.62–6.2 eV were measured by Ta(100 nm)/Al (30 nm)/AlO x /Al (30 nm)/Ta (100 nm)STJs with areas of 10 × 10, 20 × 20, 30 × 30,50 × 50 and 100 × 100 µm 2 . 16 ThebaseelectrodeTa is epitaxial. The STJs were cooled in a 3 Hecryostat with a base temperature of 0.3 K. Therise time of the charge sensitive preamplifier waslonger (2.8–70 µs) and the amplification factor 〈n〉due to the multi-tunneling of quasiparticles waslarger (6–190) for larger STJs. The 20 × 20 µm 2STJ (rise time = 12.5 µsand〈n〉 =30) showed thehighest energy resolution of 0.19 eV and a noise of0.14 eV for 2.5-eV photons.Angloher et al. obtained an energy resolutionof 12 eV and a noise of 4 eV for 5.9 keV MnK α1 X-rays. 17,18 On a 100 × 100 µm 2 Al/AlO x /Aljunction covered by a thin natural Al oxide, asuperconducting Pb absorber (2 Pb > 2 Al ) wasformed (90 µm × 90 µm × 1.3 µm). The junctionwas prepared on a Si 3 N 4 membrane with a thicknessof 0.3 µm (Figure 4.3.8). The detector wasoperated at about 70 mK in a dilution refrigerator.The Pb absorber is coupled to the STJ via phonons.X-rays absorbed by the absorber break Cooperpairs, and the resulting quasiparticles emit phononsin relaxation and recombination processes. Thephonons with energy larger than 2 Al can efficientlyexcite quasiparticles in the Al STJ. Phononsleaving the STJ towards the substrate can bereflected at the backside of the membrane and reenterthe STJ, increasing the signal charge. The risetime of the charge pulses was about 80 µs. Dueto the high absorption efficiency of lead (51.8 %)and weak absorption efficiencies of Al (0.7 %) andSi 3 N 4 (0.5 %) for 5.9 keV X-rays, multiple peaksAl oxidePbAl STJare strongly suppressed and practically only singlepeaks appeared in the pulse height spectrum.The noise measured with pulser signals was 4 eV.The signal charge for 5.9 keV X-rays was 1.82 pC,i.e. 〈n〉 =0.58. With a similar detector, fluorescencelines from Si (K α 1.740 keV) and W (M α1.776 keV) were clearly separated with an energyresolution of 9.7 eV.4.3.4 ONE-DIMENSIONAL-IMAGINGSTJ DETECTORSThe thickness of the absorbers of one-dimensionalimagingSTJ detectors (Figure 4.3.3(a)) is typically500–1000 nm, which is thicker than the typicalthickness of a superconductor electrode of an STJ(200 nm), leading to higher absorption efficienciesthan single-junction detectors. The signal chargecollected by each STJ depends on the incidentposition of radiation in the absorber. This typeof STJ detector, therefore, can have high energyand lateral resolutions, e.g. 60 eV and about 5 µm,respectively, for 5.9 keV X-rays. 19Li et al. obtained an energy resolution of13 eV for 5.9 keV X-rays in an area of 20 µm ×100 µm. 20 The size of the Ta absorber is 200 µm ×100 µm × 0.57 µm. The calculated absorption efficiencyof the absorber is 28 % for 6 keV X-rays.X-rays from a 55 Fe source (Mn K α (5.9 keV) andMn K β (6.5 keV)) were measured at 210 mK.Wilson et al. detected optical and ultravioletphotons with a detector that consists of a Taabsorber of 100 µm × 10 µm × 0.6 µm and two100 µm 2 Al STJs. 21 The detector was cooledto 220 mK in a two stage 3 He cryostat. Anamplification factor 〈n〉 of 23 and an energyresolution of about 1 eV were obtained.Verhoeve detected 4.1-eV photons with a detectorthat consists of a Ta absorber of 400 µm ×50 µm × 0.1 µm and two 50× 50 µm 2 Ta STJswith 60 nm thick Al trapping layers. An energyresolution of 0.4 eV was obtained. 22Si 3 N 4Substrate4.3.5 SERIES-JUNCTION DETECTORSFigure 4.3.8 Schematic drawing of the single-junction detectorof references 17 and 18Series-junction detectors (Figure 4.3.3(b)), wereproposed to increase the effective areas of STJ

224 SUPERCONDUCTING TUNNEL JUNCTIONSdetectors. 5,6 The effective capacitance C eff (≡Q/V S ) can be suppressed by the series-connectionof STJs, where Q is the total signal charge andV S is the resulting signal voltage. C eff = C + nC ′ ,where n is the number of junctions in series, Cis the electric capacitance of the junction, and C ′is the input capacitance of the preamplifier. For agiven total junction area S, C eff takes its minimumvalue 2(Sc 0 C ′ ) 1/2 when n = (Sc 0 /C ′ ) 1/2 , whichis not proportional to S but proportional to S 1/2 ,allowing larger S. The radiation energies are convertedto phonons in a single-crystal substrate, andthe non-thermal high energy phonons are absorbedby the series-junctions on the substrate. Therefore,the thickness of a series-junction detector is givenby the thickness of the substrate. The thickness of asubstrate is usually several hundred µm. Substratescontaining heavy elements, e.g. Ge substrates, arepreferable for detection of high energy X-rays. Calculatedabsorption efficiencies for some materialsare shown in Figure 4.3.9.One of demerits of series-junction detectorsis the position dependence of signal heights.Kamihirata et al. measured incident positions ofα particles (Figure 4.3.10). The thickness of thesapphire (Al 2 O 3 ) substrate was 400 µm. Twodimensionalposition detection was performedwith a detector that is constructed by 4 seriesjunctions.23 Each series-junction consists of 160Nb STJs in series. The diameter of each STJis 110 µm. The layer structure of the STJsAbsorption10.10.011.3 µm Pb400 µm Ge400 µm Al 2 O 30.2 µm Ta0.2 µm Nb1E−30 5000 10000 15000 20000 25000 30000Energy (eV)Figure 4.3.9 Calculated absorption efficiencies for somematerialsis Nb (200 nm)/Al (70 nm)/AlO x /Al (70 nm)/Nb(150 nm). The detector was cooled to about 0.35 Kand was irradiated with α particles (5.486 MeV:85 %; 5.443 MeV: 13 %) from 241 Am through5 holes in a collimator as can be seen inFigure 4.3.10(a). The intensity of the available241 Am source was only about 1000 Bq, and thusthe source was closely attached to the collimator,resulting in a loose collimation of α particles.By making use of the position information,the position dependence of the pulse heights wascorrected, i.e. the initial energy resolution of about10 % was improved to 0.79 %, which correspondsto 47 eV for 6 keV X-rays. 244.3.6 APPLICATIONSNiedermayr et al. studied the interaction of Ar 9+ ,O 7+ , N 6+ , and C 5+ with SiH, Au, and SiO 2targets using a 141 µm × 141 µm Nb (265 nm)/Al(50 nm)/AlO x /Al (50 nm)/Nb (165 nm) STJ. 25 X-ray spectra resulting from the interaction of O 7+with a SiH surface at 10 keV/q were reported.The STJ was cooled by a two-stage ADR, whichhas a base temperature of 60 mK with a holdtime above 20 h (

APPLICATIONS 225Hole in a collimator(0.25 mm in diameter)B0.8 mmADCV DV B + V D1.5 mm(a)3.5 mm(b)V CV A + V C10070080600Counts6040Energy resolution= 10%Counts500400300Energy resolution= 0.79%20200100(c)00 200 400 600 800 1000Pulse height (channel)(d)00 200 400 600 800 1000Pulse height (channel)Figure 4.3.10 Two-dimensional imaging and correction of position dependency of a series-junction detector. (a) Structure andsetup; (b) two-dimensional image; (c) original spectrum; and (d) spectrum after correctionslightly (±5 %) different calibration to align thepeaks. The weak Mn L fluorescence (∼640 eV)was clearly measured even for an acquisition timeof 10 s. The Mn L fluorescence was well separatedfrom the strong O K fluorescence at 525 eV.Frank reviewed time-of-flight mass spectrometry(TOF-MS) with low-temperature detectors. 27Conventional mass spectrometers for biomoleculesuse microchannel plates (MCPs) to measure thearrival times of molecular ions. The sensitivitiesof MCPs decrease for large ion masses above afew tens of kDa because MCPs rely on secondaryelectron emission. On the contrary, low temperaturedetectors can measure low-energy solid-stateexcitation, such as phonons, and are more sensitiveto weakly ionizing, slow-moving particles.In addition to the high sensitivity for large ionmasses, the high energy resolution of low temperaturedetectors is useful for charge discriminationand for studies of ion fragmentation and internalenergies.Sato et al. studied an STJ detector for fast timingmeasurements. 28 The detector was a 20 µm ×20 µm Nb (200 nm)/Al (10 nm)/AlO x /Nb (150 nm)STJ in liquid helium. Instantaneous switching tothe voltage state of an STJ following a decreasein the superconducting critical current (dc Josephsoncurrent) I c induced by a heavy ion beam wasobserved. The output voltage was reset by sweepingthe bias current I b (0.95I c

226 SUPERCONDUCTING TUNNEL JUNCTIONSSTJ detector was about 44 MeV/nucleon. The timewidth of the obtained time spectrum was about1.7 ns, which merely corresponded to the time resolutionof the data acquisition system.4.3.7 COOLING SYSTEMSUsually, three kinds of cooling systems are adoptedto cool low temperature detectors, i.e. Helium 3( 3 He) cryostats, 3 He- 4 He dilution refrigerators, andADRs. Helium 3 cryostats are relatively small andlow cost, for example a cryostat with a diameterof 25 cm and height of 53 cm can maintainabout 0.35 K for 92 h by one shot cooling. 29On the other hand, the attainable temperature isusually higher than 0.3 K. Temperatures lower than0.3 K usually require 3 He- 4 He dilution refrigeratorsor adiabatic demagnetization refrigerators. Theattainable temperatures of the refrigerators areusually lower than 0.1 K. Dilution refrigeratorsare suited for long periods of continuous cooling,for example longer than a month is possible.Less mechanical operations are required for ADRs.Recently, the development of pulse tube cryocoolersthat are of low vibration and can attainabout 4 K has been making it possible to operatethe low temperature detectors without a supply ofliquid helium and liquid nitrogen.Shirron et al. are developing a three-stagecontinuous cooling ADR. The temperature stabilityis 8 µK rms or better over an entire cycle, andthe cooling power is 2.5 µW at 60mK using asuperfluid helium bath (1.2 K) as the heat sink. 30Höhne et al. developed a compact ADR usinga pulse tube cooler for scanning electron microscopes.31Luukanen et al. developed superconductor–insulator–normal metal–insulator–superconductor(SINIS) tunnel junction refrigerators for low temperaturedetectors. They are Peltier type on-chiprefrigerators. 32,33 Electronic cooling from 260 mKto 80 mK with a cooling power of 20 pW at 80 mKwas demonstrated.4.3.8 CONCLUSIONSuperconducting tunnel junctions are showingtheir high possibilities as detectors for X-rayspectrometry: high energy resolution even foroptical photons, high count rate capability, andone- and two-dimensional imaging. They will opennew fields of application for X-ray spectrometry.REFERENCES1. H. Ott and A. Zehnder (Eds), Nucl. Instrum. Methods Phys.Res. A 370, 1 (1996).2. S. Cooper (Ed.), Proceedings of the Seventh InternationalWorkshop on Low Temperature Detectors, Max-Planck-Institute of Physics (1997); urg@mppmu.mpg.de3. P. de Korte (Ed.), Nucl. Instrum. Methods Phys. Res. A444, 1(2000).4. F. S. Porter et al. (Eds),AIP Conf. Proc. 605, 1 (2002).5. M. Kurakado, X-ray Spectrom. 28, 388 (1999).6. M. Kurakado, X-ray Spectrom. 29, 137 (2000).7. M. Kurakado and H. Mazaki, Nucl. Instrum. Methods 185,141 (1981).8. M. Kurakado, Nucl. Instrum. Methods 196, 275 (1982).9. K. E. Gray, Appl. Phys. Lett. 32, 392 (1978).10. D. J. Goldie, P. L. Brink, C. Patel, N. E. Booth and G. L.Salmon, Appl. Phys. Lett. 64, 3169 (1994).11. C. A. Mears, S. E. Labov, M. Frank, M. A. Lindeman,L. J. Hiller, H. Netel and A. T. Barfknecht, Nucl. Instrum.Methods A 370, 53 (1996).12. G. Angloher, B. Beckhoff, M. Bühler, F. v. Feilitzsch,T. Hertrich, P. Hettl, J. Höhne, M. Huber, J. Jochum,R. L. Mößbauer, J. Schnagl, F. Scholze and G. Ulm, Nucl.Instrum. Methods A 444, 214 (2000).13. G. Angloher, M. Huber, J. Jochum., F. von Feilitzsch,R. L. Mößbauer, and G. Sáfrán, J. Low Temp. Phys. 123,165 (2001).14. M. Frank, L. J. Hiller, J. B. le Grand, C. A. Mears, S. E.Labov, M. A. Lindeman, H. Netel, D. Chow and A. T.Barfknecht, Rev. Sci. Instrum. 69, 25 (1998).15. M. Katagiri, T. Nakamura, M. Ohkubo, H. Pressler,H. Takahashi and M. Nakazawa, AIP Conf. Proc. 605, 177(2002).16. P. Verhoeve, N. Rando, A. Peacock, A. Dordrecht,A. Poelart and D. J. Goldie, IEEE Trans. Appl. Supercond.7, 3359 (1997).17. G. Angloher, M. Huber, J. Jochum, A. Rüdig, F. v. Feilitzschand R. L. Mößbauer, AIP Conf. Proc. 605, 23(2002).18. M. Huber, G. Angloher, F. v. Feilitzsch, T. Jagemann,J. Jochum, T. Lachenmaier, J.-C. Lanfranchi, W. Potzel,A. Rüdig, J. Schnagl, M. Stark and H. Wulandari, AIPConf. Proc. 605, 63 (2002).19. H. Kraus, F. v. Feilitzsch, J. Jochum, R. L. Mössbauer,T. Peterreins and F. Pröbst, Phys. Lett. B 231, 195 (1989).20. L. Li, L. Frunzio, C. M. Wilson, K. Segall, D. E. Prober,A. E. Szymkowiak and H. Moseley, AIP Conf. Proc. 605,145 (2002).

REFERENCES 22721. C. M. Wilson, K. Segall, L. Frunzio, L. Li, D. E. Prober,D. Schiminovich, B. Mazin, C. Martin, and R. Vasquez,Nucl. Instrum. Methods A 444, 449 (2000); IEEE Trans.Appl. Supercond. 11, 645 (2001).22. P. Verhoeve, Nucl. Instrum. Methods A 444, 435 (2000).23. S. Kamihirata, M. Kurakado, A. Kagamihata, K. Hirota,H. Hashimoto, R Katano, K. Taniguchi, H. Sato, Y. Takizawa,C. Otani, and H. M. Shimizu, AIP Conf. Proc. 605,149 (2002).24. M. Kurakado, S. Kamihirata, A. Kagamihata, K. Hirota,H. Hashimoto, H. Sato, H. Hotchi, H. M. Shimizu andK. Taniguchi, Nucl. Instrum. Methods A 506, 134 (2003).25. T. Niedermayr, S. Friedrich, M. F. Cunningham, M. Frank,J. P. Briand and S. E. Labov, AIP Conf. Proc. 605, 363(2002).26. S. Friedrich, T. Niedermayr, T. Funk, O. Drury, M. L. vanden Berg, M. F. Cunningham, J. N. Ullom, A. Loshak,S. P. Cramer, M. Frank and S. E. Labov, AIP Conf. Proc.605, 359 (2002).27. M. Frank, Nucl. Instrum. Methods A 444, 375 (2000).28. H. Sato, T. Ikeda, K. Kawai, H. Miyasaka, T. Oku,W. Ootani, C. Otani, H. M. Shimizu, Y. Takizawa,H. Watanabe, K. Morimoto and F. Tokanai, Nucl. Instrum.Methods A 459, 206 (2001).29. M. Kurakado and Y. Ikematsu, Cryogenics 37, 331 (1997).30. P. J. Shirron, E. R. Canavan, M. J. DiPirro, M. Jackson,J. Panek and J. G. Tuttle, AIP Conf. Proc. 605, 379(2002).31. J. Höhne, U. Hess, M. Bühler, F. v. Feilitzsch, J. Jochum,Rv. Hentig, T. Hertrich, C. Hollerith, M. Huber, J. Nicolosi,K. Phelan, D. Redfern, B. Simmnacher, R. Weilandand D. Wernicke, AIP Conf. Proc. 605, 353 (2002).32. A. Luukanen, A. M. Savin, T. I. Suppula, J. P. Pekola,M. Prunnila and J. Ahopelto, AIP Conf. Proc. 605, 375(2002).33. A. Luukanen, M. M. Leivo, J. K. Suoknuuti, A. J. Manninenand J. P. Pekola, J. Low Temp. Phys. 120, 281(2000).

4.4 Cryogenic MicrocalorimetersM. GALEAZZIUniversity of Miami, Coral Gables, FL, USAandE. FIGUEROA-FELICIANONASA/Goddard Space Flight Center, Greenbelt, MD, USA4.4.1 INTRODUCTIONDetectors traditionally used in X-ray spectroscopycan be divided into four groups: solid-state detectors,proportional counters and position-sensitivedetectors coupled to either Bragg crystals orgrazing-incidence diffraction gratings. Solid-statedetectors are the most common because they areeasy to use and inexpensive to operate. Howevertheir energy resolution is limited by the statisticalfluctuations in the number of electron–hole(e-h) pairs that are created. The energy resolutionof such a detector is given by E rms = √ FEwwhere w is the energy necessary to create onee-h pair, F is the Fano factor and E is the energy.In practice the energy resolution of a solid-statedetector is not better than 100–120 eV FWHMat 6 keV. In a proportional counter the energynecessary to create an electron–ion pair is ofthe order of 30 eV, and the energy resolution iseven worse.Grazing incident gratings can provide veryhigh resolution for soft X-rays, on the order of1 eV FWHM, but their low dispersion meansthroughputs are very small at high resolution. Thegrating efficiency also falls off rapidly at higherenergies. The case of Bragg crystals is different.The energy resolution is again very good andthe dispersion and efficiency are higher. However,only one resolution element is reflected, so eachenergy band must be measured independently,one after the other, and the net throughput formeasuring a broad band spectrum is very low.Moreover the energy interval covered by a singlecrystal is limited, in practice, to a factor of twoor so.Almost 20 years ago the idea of detecting theincrease in temperature produced by incident photonsinstead of the ionization of charged pairs wasproposed (Fiorini and Niinikoski, 1984; Moseleyet al., 1984). If all the energy that is depositedis thermalized (converted into thermal phonons),there is no branching of the incident energy andno inherent statistical limitation to the resolution.Moreover the detection of phonons meansthat the choice is no longer restricted to materialswith good electron transport properties, suchas germanium or silicon, but different materials,more desirable for the particular experiment canbe used. Most of the developments on cryogenicmicrocalorimeters have been discussed at the biannualInternational Workshops on Low TemperatureDetectors. We refer the reader to the workshopproceedings as a useful source of information tocomplement this subchapter (De Korte and Peacock,2000; Porter et al., 2002).X-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

230 CRYOGENIC MICROCALORIMETERS4.4.2 MICROCALORIMETERSA schematic view of a cryogenic microcalorimeteris shown in Figure 4.4.1. It is composed of threeparts, an absorber that converts the energy of theincident X-rays into heat, a sensor that detectsthe temperature variations of the absorber anda weak thermal link between the detector anda heat sink. The operating principle is simple.When an X-ray hits the absorber its energy isthermalized, that is, is distributed among thermalphonons and electrons, and the temperature of thedetector first rises and then returns to its originalvalue due to the weak thermal link to the heatsink. The temperature change is proportional tothe energy of the incident X-ray and is detectedby the sensor. The sensor, or thermometer, istypically a resistor whose resistance has a strongdependence on the temperature at the workingpoint, but other, non-resistive, thermometers havealso been investigated.Although the operating principle is simple, theconstruction of a cryogenic microcalorimeter mayprove challenging. The temperature rise of thedetector is inversely proportional to its heat capacity,which must therefore be as small as possiblein order to have a detectable temperature variation.SensorWeak thermal linkHeat sinkX-rayAbsorberFigure 4.4.1 Schematic view of a cryogenic microcalorimeterThis is achieved in two different ways, reducingthe size of the detector and/or reducing its workingtemperature. Typical working temperatures inthe range of tens of mK and volumes of the orderof 10 −3 mm 3 are used for best energy resolution.The temperature variations to be detected may beof the order of µK, so good sensors are also necessaryto detect them. Although these are stringentrequirements, several groups working in the fieldhave obtained impressive results.Requirements for a good microcalorimeter arean absorber with small heat capacity able to convertthe energy of the incident radiation intophonons and/or electrons in thermal equilibriumquickly and with high efficiency, and a sensorwith low heat capacity and high sensitivity to temperaturevariations. We discuss these characteristics,together with the performance of cryogenicmicrocalorimeters in the following.4.4.2.1 THE ABSORBERThe choice of the right absorber is one of the morecritical parts of the design of a microcalorimeter.The main characteristics that must be takeninto account are the quantum efficiency in theenergy range of interest, the collection area ofthe detector, and the efficiency and speed ofthe absorber in thermalizing the incident energy.This must be combined with a sufficiently smallheat capacity for good energy resolution (as wewill see in Section 4.4.3.1, the energy resolutionis proportional to the square root of the heatcapacity). Different materials have been testedand used with relatively good results. Theseinclude metals, semiconductors, superconductorsand insulators.Metals usually have very good thermalizationproperties: the conversion of the incident energyinto thermal phonons and electrons is fast (afew µs or less) and very efficient. The stoppingpower is also generally very good, if a highZ material is chosen. Despite these advantagesthey are often undesirable as absorbers becauseof a large heat capacity at low temperatures dueto the electronic component. Nevertheless, somemetals with a small electronic density of states and

MICROCALORIMETERS 231consequently small electronic heat capacity can beused with very good results. Among these bismuthis certainly the one that is receiving the highestattention and is giving the best results (Lindemanet al., 2002a; Wollman et al., 2000). For smallabsorbers, traditional metals like copper have alsobeen used with very good results (Bergmann Tiestet al., 2002a).Semiconductors and insulators have no electroniccontribution to the heat capacity, which canthen be very small. However, part of the incidentenergy is converted first into e-h pairs that canbe very slow to recombine. It is therefore difficultto have good energy resolution since the thermalizationefficiency is limited and is affected by thestatistical and positional variation in the e-h paircreation and trapping. Some small or zero gapsemiconductors such as HgTe can have very goodperformance due to the negligible energy tied upin charge carrier production (McCammon et al.,2002a; Stahle et al., 2002a).A promising alternative to metals and semiconductorsare superconductors. Their heat capacitycan be small due to the absence of an electroniccontribution at temperatures below ∼0.1 T C ,while the stopping power is very good for high Zmaterials like lead or rhenium. In superconductorsthe incident energy is first converted into quasiparticlesthat then recombine releasing phonons.The details of this process are complicated anddepend strongly on the characteristics of the materialused (Cosulich et al., 1993). Superconductorsas absorbers may sometimes be characterized byincomplete thermalization and very long tails inthe pulses that affect the detector speed and energyresolution. The best results at low energy (below10 keV) have been obtained using tin (Alessandrelloet al., 1999; Silver et al., 2002), but promisingresults have also been obtained using rhenium(Galeazzi, 1998a). Recently, good high-energy(∼50 keV) results have also been obtained usinglead (Bleile et al., 2002).In conclusion cryogenic microcalorimeters canobtain good results using a large variety ofmaterials. The choice of the absorber can thereforebe optimized depending on the requirements ofthe experiment.4.4.2.2 THE SENSORThe main characteristic of a sensor is its responseto temperature variations. This characteristic isdescribed by the sensitivity α, definedas:α = dlogRdlogT = T dR(4.4.1)R dTwhere T and R are the temperature and resistanceof the sensor, respectively. The sensitivity α isdimensionless and describes the fractional resistancevariation versus the temperature variation.Higher α means higher sensitivity to temperaturevariations, corresponding to larger output signals.The most commonly used sensors are resistorsin which the resistance has a strong temperaturedependence at the working point. Figure 4.4.2shows the schematic of a typical circuit used tobias a detector. The detector can be current orvoltage biased, depending on whether the loadresistor R L is bigger or smaller than the sensorresistance R, and the temperature variation is thusread out as a voltage or current variation. We candistinguish two main categories of such sensors inwide use: semiconductor thermistors and transitionedge sensors (TES), the characteristics of whichare reported in Table 4.4.1.Two different kinds of semiconductor thermistorsare used: neutron transmutation doped (NTD)germanium thermistors and ion implanted siliconthermistors. Their resistance versus temperaturebehavior is approximately R = R 0 exp( √ T 0 /T),V biasR LIDetectorFigure 4.4.2 Schematic of the bias circuit for a microcalorimeter.If R ≪ R L , the detector is current biased, if R ≫ R L thedetector is voltage biasedRV

232 CRYOGENIC MICROCALORIMETERSTable 4.4.1 Principal characteristics of commonly used resistive sensorsSensor α Temperature range Resistance Usual bias Read-out electronicsThermistors Negative/small Wide Large Constant current Cold FETTES Positive/ large Narrow Small Constant voltage SQUIDwhere R 0 and T 0 are constant parameters characteristicof the sensor. Their sensitivity is negativeand relatively small, usually around 5–6.They are often biased with an almost constantcurrent and characterized by a very high resistance(tens of M at the working point) where theyare well matched to junction field effect transistors(JFET) operated near 100 K (Gatti and Parodi,2000; McCammon et al., 2002a). To implement thereadout electronics in the fabrication process and tobuild a large number of readout channels in a compactgeometry, the use of single electron transistors(SET) for the readout of semiconductor thermistors(Schoelkopf et al., 1998) and superconductingdevices with transistor-like properties for the readoutof both thermistors and TES (Pepe et al., 2000)are also being investigated.Transition edge sensors are superconductingthin films that are biased so that the temperatureis actually in the phase transition between thesuperconducting and normal state, where α can bevery high. The transition is generally very narrow,so the working temperature for a given TES isfixed. Depending on the application, it is possibleto tune the transition temperature of a TESduring its fabrication using the proximity effectin superconductor–normal metal bilayers (Martiniset al., 2000). For small reductions in the transitiontemperature, implantation of a thin superconductingfilm with ferromagnetic materials hasalso been successfully used (Young et al., 1999).The most commonly used TES are Al-Ag, Mo-Au,Mo-Cu, Ti/Au, and Ir-Au bilayers or W thin films(Hoehne et al., 1996; Cabrera et al., 2000; Wollmanet al., 2000; Hilton et al., 2001; BergmannTiest et al., 2002a; Lindeman et al., 2002a; Tanet al., 2002). Their α is generally very high (a factorof 10 to 100 higher than in thermistors) andpositive, while their resistance is very low. Theyare generally biased at constant voltage and theircurrent is read out using superconducting quantuminterference devices (SQUID) as current transducers(Gallop, 1991).There are also other thermometer types thatcan be classified as nominally non-dissipative ornon-resistive. These include devices whose capacitance,inductance, or magnetization change withtemperature. They can be analyzed the same wayas resistive thermometers by assuming an effectivesensitivity α = (dlogX/dlogT)/Q,whereXis the thermometric parameter and Q −1 is the fractionaldissipation. These thermometers tend to beintrinsically insensitive, but Q −1 can be 10 5 ormore, making them potentially advantageous. Theycan also have a significant amplifier noise contribution,which markedly changes their optimization.Recently particularly interesting results have beenobtained with magnetic thermometers, where themagnetic properties of the sensor are temperaturedependent and can be read out with a dc SQUIDused as magnetic flux transducer (Enss, 2002).We will discuss these detectors in more detail inSection 4.4.4.5.4.4.3 PERFORMANCE4.4.3.1 ENERGY RESOLUTIONIn the standard theory of microcalorimeters (Mather,1982; Mather, 1984; Moseley et al., 1984), four differentnoise contributions can affect the energyresolution: the Johnson noise of the sensor andany excess noise it has, the phonon shot noiseproduced by the random flow of energy carriersthrough the weak thermal link, and the electricalnoise of the read out electronics (Mather, 1982).Current technology allows the construction of readout electronics whose noise is in general negligiblewith respect to the other contributions. As wealready pointed out, for semiconductor thermistors,this is done using low temperature (around 100 K)

PERFORMANCE 233JFET for the first stage of amplification plus roomtemperature electronics for the second stage. ForTES, low temperature dc SQUID are used. In thecase of JFET, the total voltage noise is typically afew nV / √ Hz (Gatti and Parodi, 2000; McCammonet al., 2002a). With SQUID electronics it is possibleto obtain current noise levels of a few pA/ √ Hz usingcommercially available dc SQUID (Gallop, 1991).The Johnson noise is a voltage noise acrossthe detector with voltage spectral density √ 4Rk B Twhere k B is the Boltzmann constant. The phononnoise essentially consists of statistical fluctuationsin the temperature of the detector due to the linkbetween the detector and the heat sink. Thesetemperature fluctuations are then converted into avoltage or current noise by the sensor. Skippinghere the mathematical passages that can be foundin Mather (Mather, 1982), the intrinsic energy resolutionof an ideal cryogenic microcalorimeteroperating in the linear, small signal regime, canbe written as:√kE rms = ξ B T 2 C(4.4.2)αwhere T and C are, respectively, the temperatureand the heat capacity of the detector and ξ isdimensionless and depends on the detector characteristicsand bias power and has an optimizedvalue of 1–2.We would like to discuss some observations onthe result in Equation (4.4.2). First, as intuitivelypointed out before, the energy resolution dependson the heat capacity of the detector. The energyresolution also depends directly on the temperatureof the detector, making the requirement of workingat very low temperature even more important.Moreover, the energy resolution depends on thedetector sensitivity α, which stresses the importanceof working with good sensors. We also wantto point out the fact that the energy resolution doesnot depend on the energy of the incident radiation.This is because the energy resolution is noiselimitedand not statistics-limited, as is the casefor most radiation detectors. We also note that theresolution does not depend on the thermal conductivityG between the detector and the heat sink.This affects the detector speed, as discussed in thenext section.The competition for the best energy resolutionhas been very strong in recent years. Interestinglyenough, different techniques are obtaining verysimilar results. At 6 keV, that is often consideredthe reference energy, recent as-yet unpublished resultsshow an energy resolution of 4.3 eV FWHMusing silicon implanted thermistors and HgTeabsorbers (Stahle, 2002b); 4.7 eV FWHM has alsobeen obtained with a larger detector with similarcharacteristics (Stahle et al., 2002a). With a Ti/AuTES and Cu absorber 3.9 eV FWHM for a 5 minrun and 4.5 eV FWHM for longer runs has beenobtained (Bergmann Tiest et al., 2002a); 4.5 eVFWHM has also been obtained with a Mo/Cu TESthat also acts as the absorber (Irwin et al., 2000),and a resolution below 5 eV FWHM has beenobtained with NTD germanium thermistors and tinabsorbers (Alessandrello et al., 1999; Silver et al.,2002). In Figure 4.4.3 we show the spectrum of theMn Kα line from Bergmann Tiest et al. (2002a).At lower energies, 2 eV FWHM at 1.5 keV hasbeen obtained with an Al/Ag TES (Wollman et al.,2000) and 2.4 eV FWHM at 1.5 keV and 3.7 eVFWHM at 3.3 keV has been obtained with a Mo/AuTES (Lindeman et al., 2002a).4.4.3.2 COUNT RATETo discuss the count rate capabilities of amicrocalorimeter we must first introduce the effectof the detector nonlinearity. So far we implicitlyassumed that whenever an incoming particlewarms the detector the temperature change is sosmall that the characteristics of the detector donot change. That is not true in the case of relativelylarge temperature changes, since the thermometersensitivity, the detector heat capacity, andthe thermal conductivity to the heat sink may betemperature dependent, generating detector nonlinearity.This nonlinearity is usually small and canbe easily taken into account in the analysis of thedata, but it plays an important role in the detectorcount rate. If the count rate is high there willoften be pile-up of pulses on the tails of otherpulses. While this pile-up could be taken care ofin a linear detector, in a microcalorimeter the startingtemperature of the second pulse is higher than

234 CRYOGENIC MICROCALORIMETERS60FWHM = 3.9 eV40Counts2005870 5880 5890 5900 5910 5920Energy (eV)Figure 4.4.3 Spectrum of Mn Kα lines obtained with a Ti/Au TES and Cu absorber. The black line represents the experimentaldata, the gray line the best-fit to the data. (Courtesy of W. Bergmann Tiest, SRON National Institute for Space Research, TheNetherlands; Bergmann Tiest et al., 2002a). Reproduced by permission of the American Institute of Physicsthe equilibrium temperature of the detector. Due tothe different starting temperature, the pulse amplitudecould reasonably be different (usually smaller)than the amplitude of a normal pulse generated bythe same amount of energy, worsening the energyresolution of the detector. To get the best energyresolution, the count rate is therefore limited by thetime necessary for the detector to return to the originaltemperature. The time it takes the temperatureto return to 1/e of the maximum temperature variationduring the pulse is called the time constantof the detector.A microcalorimeter with heat capacity C andthermal conductivity to the heat sink G is characterizedby an intrinsic time constant τ = C/G.This is the characteristic time necessary for themicrocalorimeter to return to the working temperatureafter an X-ray warms it. The temperaturerise, determined by the time necessary for theincident energy to be converted into the thermalsignal, is in general much faster and is a characteristicof the absorber. Since, as we have seen,the energy resolution of a microcalorimeter doesnot depend on the thermal conductivity G, itisin principle possible to build a detector with veryhigh G and consequently very small time constant.In practice, because of technical limitations,and because the classical detector model that wehave used so far does not completely describe amicrocalorimeter (see Section 4.4.3.5) typical timeconstants of cryogenic microcalorimeters are in therange 0.1–10 ms or even longer in the case of verylarge detectors.Instead of increasing the value of G, muchfaster detectors can be obtained using the effectknown as electrothermal feedback. For resistivesensors, when there are no events in the detector,the temperature of the microcalorimeter is higherthan the temperature of the heat sink due to thepower dissipated by the bias signal. This poweris simply equal to I 2 R in the case of constantcurrent bias and to V 2 /R in the case of constantvoltage bias. When an X-ray is absorbed into thedetector the resistance of the sensor changes andtherefore also the bias power changes. This effectcan be quantified by introducing a parameter withthe dimension of a thermal conductivityG ETF = PαTR − R LR + R L(4.4.3)

PERFORMANCE 235that depends on the power P dissipated into thedetector at equilibrium, the detector sensitivityα, the temperature T , and on characteristics ofthe bias circuit (R and R L ). A detector is thencharacterized by an effective time constant τ eff =C/G eff , where G eff = G + G ETF . The value ofG ETF can be either positive or negative, dependingon the sign of the parameter α and on theratio between R and R L , and the effective timeconstant of the detector can be either longer orshorter than the intrinsic time constant τ. FromEquation (4.4.3) we see that if the detector iscurrent biased (R L >R) G ETF is positive whenα is negative and negative when α is positive.The opposite is true if the microcalorimeter isvoltage biased. In the case of voltage biased TES,with very large α, the parameter G ETF is notonly positive, thus reducing the time constant,but, choosing the appropriate working point, itcan be much larger than G (Irwin, 1995). Inthis way it is possible to obtain detectors withtime constant much faster than C/G. Using thisstrong electrothermal feedback effect cryogenicmicrocalorimeters with an effective time constantof 100 µs and count rates of about 500 Hz havealready been built (Wollman et al., 2000).For detectors with lower sensitivity, as semiconductorthermistors, the possibility of using anexternal electrical feedback system that activelyreduces the bias power during an X-ray event hasbeen proposed and tested (Galeazzi, 1998b; Meieret al., 2000). In practical terms this has the sameeffect as using electrothermal feedback. Reductionof more than a factor of 30 in the detector timeconstant (Galeazzi, 1998b) and time constants ofthe order of 100 µs (Silver et al., 2002) have beensuccessfully obtained using this technique.Microcalorimeter arrays are also being developed(Kelley et al., 1999; McCammon et al.,2002a). In particular, arrays of 1000 elementsare under construction (Stahle et al., 2002c), thatwould allow the measurement of net count rates ofthe final detector of about 500 kHz.4.4.3.3 QUANTUM EFFICIENCYThe detection efficiency of microcalorimeters isgenerally very good. The quantum efficiency canbe more than 99 % below 10 keV when usinghigh Z materials. This is due to the fact thatthe thickness of the absorber is not an intrinsiclimit to the detector performance. Nevertheless,even if it is possible to make the detector thickenough to have high stopping power, to keep theheat capacity small, the area of the detector mayhave to be reduced, affecting the collecting area.Another important factor that bears on the effectivequantum efficiency of cryogenic microcalorimetersis that they work at very low temperature. If theX-ray source is at a temperature that is higherthan that of the detector, the detector must ingeneral be shielded to reduce the shot noise dueto the impinging infrared photons and the heatload due to the black body emission of the source.In this case, infrared filters are installed betweenthe detector and the source to reflect the infraredradiation that would warm up the detector and theheat sink. These filters are generally thin organicfilms covered by aluminum. Well-designed filtersystems have transmission efficiency above 95 %for energies above 1 keV, while the efficiency tendsto drop below 200 eV (McCammon et al., 2002a).4.4.3.4 COLLECTING AREATo keep the heat capacity small, the detector collectingarea is complementary to quantum efficiency.The collecting area of an experiment istherefore mainly affected by the requirements onenergy resolution and quantum efficiency and isusually limited to a fraction of a square millimeterper detector. The fabrication of arrays is necessaryto substantially increase the collection areawhile maintaining the best possible energy resolution.Arrays have the other advantage of beingposition sensitive. The main drawback in usingarrays is the need for a readout channel for eachpixel in the array. Currently arrays with up to36 pixels are being used. The best results areobtained by the NASA/Goddard Space Flight Center– University of Wisconsin collaboration withsilicon implanted thermistors (Kelley et al., 1999;McCammon et al., 2002a). The collaboration hasbuilt arrays in 6 × 6and2× 18 geometries for the

236 CRYOGENIC MICROCALORIMETERSX-ray quantum calorimeter (XQC) and X-ray spectrometer(XRS) experiments. The XQC arrays areoptimized to work below 2 keV, while the XRSarrays are designed to have high quantum efficiencyup to 10 keV and a slightly worse energyresolution. The XQC arrays have a collecting areaof 0.36 cm 2 , while the XRS arrays have a collectingarea of 0.12 cm 2 .One-thousand-element arrays are currently underdevelopment and are expected to be realized inthe next few years (Stahle et al., 2002c). Thesearrays are being built mainly to increase the imagingcapabilities of the experiments, but also to increasethe collecting area. Both TES and thermistors arebeing investigated for these larger arrays.4.4.3.5 NON-IDEAL EFFECTSAfter 15 years of experiments, microcalorimetershave reached limits close to those predicted bythe ideal model (Mather, 1982; Moseley et al.,1984). However, the standard non-equilibriumtheory of microcalorimeters fails to completelypredict the performance of real devices dueto additional non-ideal properties that play animportant role at low temperatures. The resistanceof the thermometer becomes dependent on readoutpower as well as temperature, and equilibrationtimes between different parts of the detector can besignificant. Thermodynamic fluctuations betweeninternal parts are then an additional noise source.Excess noise of unknown origin is also limitingthe energy resolution performance in some cases.Absorber and Hot-electron DecouplingSo far we have described a microcalorimeter as amonolithic device. With current devices this is notalways a sufficient approximation. The absorberis often glued to the sensor, or it is connectedto it through a finite thermal conductivity. Thisdecoupling has two main consequences, the firstis to change the response of the thermometerto X-rays. The second is to introduce thermalfluctuations between the absorber and thermometerthat lead to an additional noise source. Both effectstend to worsen the detector performance (Galeazziand McCammon, 2002).The hot electron effect is very similar. Thiseffect is well known in metals at low temperaturesand has recently been studied in semiconductorsin the variable range-hopping regime (Liu et al.,2002). It is due to the interaction between electronsin the thermometer which is much stronger thanthe interaction between electrons and phonons.Consequently the thermometer can be describedas two systems, electrons and phonons, thermallyconnected by a finite thermal conductivity. Theresistance of the thermometer depends directlyon the temperature of the electrons, and the biaspower dissipated into the electron system flowsto the phonon system and then to the heat sink.This increases the temperature of the electronsabove the temperature of the phonons, reducing thethermometer sensitivity to X-rays and worseningthe detector performance.The resulting detector is a very complicatedsystem. For example, the thermal conductivitybetween electrons and phonons depends on thevolume of the thermometer. Bigger thermometershave a lower hot-electron effect, but this increasesthe heat capacity of the detector. Complex modelshave been developed to describe the performanceof a realistic microcalorimeter (Figueroa-Feliciano,2001; Galeazzi and McCammon, 2002). Thesemodels have also been used recently to optimizethe design of new detectors and will be describedin more detail in Section 4.4.4.4.Thermometer Non-ohmic BehaviorIn an ideal resistive thermometer, the resistanceonly depends on the thermometer temperature.We have already seen that this is not completelytrue due to the hot-electron effect. The resistancedepends on the electron temperature, that canbe different from the phonon temperature, whichbecause of this decoupling can lead to a reductionin the detector performance. In addition there areother physical effects that introduce a dependenceof the thermometer resistance on the bias currentor voltage. This is particularly true, for example,in TES (Tan et al., 2002). It is a known property

CURRENT DEVELOPMENTS 237of TES that their transition temperature can bechanged by applying an external magnetic field.Similarly, when a bias current is passed throughthe TES to readout the resistance, it generates amagnetic field around the TES. This field alsochanges the transition temperature of the TES.When an X-ray hits a microcalorimeter the changeof sensor resistance changes the current throughthe sensors which, in turn, changes the transitiontemperature and thus the resistance value. Thisnon-ohmic behavior of the sensor plays against thetemperature dependence of the resistance, reducingthe thermometer sensitivity. A similar effect, buton a much smaller scale has also been seenin semiconductor thermistors due to field effectsin the doped region (Zhang et al., 1998). Thetheoretical models recently developed to predictthe performance of microcalorimeters include thenon-ohmic behavior of the sensor.Excess NoiseWe already pointed out that the energy resolutionof microcalorimeters does not depend on anystatistical effect on the number of pairs or particlesgenerated by X-ray absorption, but it is limited bynoise in the detector.A major problem that historically affected siliconsemiconductor thermistors is 1/f noise (McCammonet al., 2002b). An unbiased thermistor typicallyexhibits the expected noise, but increasingthe bias current often results in an increase in theamount of noise. This excess noise can be modeledas 1/f fluctuations in the resistance, depend onlyon the doping density and the resistivity (or equivalentlythe electron temperature). Spectra taken withlow base temperature and high bias show the samenoise as spectra at higher base temperatures butlower biases, so that the electron temperature wasthe same. The presence of 1/f noise can introducedegradation of up to 50 % in the energy resolution ofthe microcalorimeter. Recently the NASA/GoddardSpace Flight Center, in collaboration with the Universityof Wisconsin has developed a deep implantand diffusion technique for silicon (Galeazzi et al.,2002a) with which they can implant very uniformdevices more than five times thicker than before.The devices produced with this technique do notshowanysignof1/f noise and have demonstratedimproved and impressive energy resolution performance(Stahle et al., 2002a).Excess noise in TES is also the subject of a massiveinvestigation. Single pixel microcalorimeterswith TES have achieved energy resolution of 4.5 eVat 6 keV (Irwin et al., 2000; Bergmann Tiest et al.,2002a). This result is impressive, but is more than afactor of two worse than the predicted performance.The reason for this is the presence of an extra noisesource of unknown origin in the detectors. Very littleis known about this extra noise and currently manydifferent laboratories around the world are trying toeliminate or at least understand it.The current picture is very confusing. Whenthe TES is in the superconducting or normal state,the noise levels agree with those expected. Whenthe TES is in the transition the measured noise isappreciably higher than expected. Measurementsin a number of different laboratories all show thepresence of excess noise, but the characteristicsof the noise appear different (Bergmann Tiestet al., 2002a; Lindeman et al. 2002a; Tan et al.,2002). So far it has been difficult to build acommon, consistent picture between the resultsfrom different groups.4.4.4 CURRENT DEVELOPMENTS4.4.4.1 DETECTORMICROFABRICATIONThe first X-ray microcalorimeters were handmadedevices where an absorber was epoxied to athermometer and the device was suspended by thereadout leads. Apart from being time consuming,this approach also has reproducibility problems: itis hard to cut absorbers to exactly the same sizeeach time, use the same amount of epoxy to attachthe absorber, have exactly the same suspendedlead length, etc. Reproducibility is very importantwhen making microcalorimeter arrays. The moreuniform the energy resolution, time constant, andquantum efficiency are, the easier is the calibrationand data analysis. Ideally one would like to havean array of identical detectors.

238 CRYOGENIC MICROCALORIMETERSLithography provides a way to get very uniformdevices across an entire array. The large amountof knowledge and instruments developed for thecomputer industry can be leveraged for thesevery specialized detectors. Film depositions usingstandard solid-state processing have thicknessvariations across the wafer of less than 5 %, andfeature size variations across a wafer of lessthan a micron. For microcalorimeter arrays, thistechnology produces very uniform arrays, andmost research groups are using lithography insome or all of their process. The University ofWisconsin – NASA/Goddard Space Flight Centercollaboration has made several ∼30 pixel arraysusing photolithography for the thermometer andweak link fabrication, using wafer dicing sawsfor cutting the absorbers and manually attachingthem to the thermometer with epoxy (Kelleyet al., 1999; McCammon et al., 2002a). Impressiveuniformity was achieved, with 5 % spread inquantum efficiency and time constants, and 10 %in energy resolution. In Figure 4.4.4 a photographof a microcalorimeter that is part of the XRSElectrical tracesAbsorber attachment pointsThermistorWeak thermal linksFigure 4.4.4 Photograph of a microcalorimeter built withphotolithography technique, before absorber attachment. Thethermistor is 300 µm × 300 µm is size and 1.5 µm thick andit is suspended using a Deep Reactive Ion Etching (RIE)technique. The absorber attachments are SU8 photoresist tubes(US Patent No. 4882245, 1989; Su8) also fabricated using aphotolithography technique. (Courtesy of Caroline K. Stahle,NASA/Goddard Space Flight Center)detector built using photolithographic techniqueis shown. Full use of lithography promises evenhigher uniformity in detectors currently underdevelopment (Hilton et al., 2001; Beeman et al.,2002; Finkbeiner et al., 2002; Kudo et al., 2002;Stahle et al., 2002c; Ukibe et al., 2002).4.4.4.2 LARGE ARRAYS ANDDETECTOR MULTIPLEXINGFor an imaging instrument, the size of the pixelsused in the instrument’s detector is optimized forthe focal length and the point-spread function(PSF) of the optics. Given a specific pixel size,the number of pixels in the detector determines itsfield of view. For most applications, one desiresthe largest field of view possible.Even if the application does not use imaging,a larger area is usually desirable to increase thenumber of detectable X-rays. As discussed inSection 4.4.3.1, the size of individual pixels isrestricted by the heat capacity of the pixel and itseffect on energy resolution.In both cases, one needs to increase the numberof pixels to increase the detector area. Sincemost microcalorimeters are now fabricated usingsolid-state lithography techniques, fabricating largearrays of microcalorimeters is in principle notmuch more difficult than fabricating a small array.However, reading out these large arrays is aproblem. To reduce noise pickup, the readoutdevices (SQUID, JFET, or SET) need to be in closeproximity to the detector. The wiring and layoutbecomes challenging when designing a systemwith hundreds of channels. These devices alsodissipate power and the wiring adds to the thermalload on the cold stage of the refrigerator, impactingthe performance of the refrigeration system.To work around these issues, several groupsare actively designing multiplexing schemes toread out several (∼10–30) microcalorimeters perelectronic channel. For low-impedance devices,SQUID multiplexers are being developed, forhigh-impedance devices, both SET and JFETmultiplexers are under study. Both time-divisionmultiplexing and frequency-division multiplexingcan be used, and practical implementation

CURRENT DEVELOPMENTS 239X-rayThermal bottlenecksTESTESNitride membrane(Mechanical supportandweak thermal link)Fast thermalization absorbersSolid silicon(heat sink)Figure 4.4.5 Schematic view of a position sensitive microcalorimeter. The heat released by the X-ray is split between the twoTES. The difference in temperature change and time necessary to warm up between the two TES is used to determine the positionand the energy of the incident X-rayissues will likely decide which approach is best.Most groups working toward large (∼1000 pixel)arrays plan to use some form of multiplexing fortheir readout.Benford et al. (2002) have successfully fabricatedand run a time-multiplexed SQUID systemto read out an array of 16 TES bolometers forsubmillimeter observations. Irwin et al. (2002) areworking on the second generation of this technologythat will be compatible with X-ray TESarrays. Kiviranta et al. (2002) and Cunninghamet al. (2002) are developing frequency-divisionSQUID multiplexers for the XEUS and Constellation-XX-ray astronomy missions, respectively. Adifferent approach based on reading out a resistancebridge (with a TES as one of the four resistances)with a frequency-division multiplexer isunder investigation by Miyazaki et al. (2002). Fora more traditional approach, Kraus et al. (2002)have investigated the issues encountered in wiring66 SQUID channels in a low-temperature systemfor the CRESST II dark matter search.4.4.4.3 POSITION SENSITIVEIMAGING DETECTORSSince the number of readout channels is thelimiting factor for going to large numbers ofpixels, position sensitive detectors – where onethermometer reads out several pixels or effectivepixels – becomes attractive.The operating principle of position sensitivemicrocalorimeters is similar to that of positionsensitive proportional counters and semiconductordevices. An imaging calorimeter uses one or morethermometers to analyze the signal produced bya photon absorption event in an absorber. Forthe same energy photons, the signal received bythe thermometers varies in some detectable waydepending on the position in the absorber wherethe event occurred. In other words, the absorberexhibits position dependence. If one can use theinformation in the signal shape to determine theenergy and location of photon absorption one hasan imaging calorimeter. The imaging calorimetercan be a one-dimensional ‘strip’ absorber withone or more thermometers, or a two-dimensional‘plane’ absorber with two or more thermometers.A schematic view of a one-dimensional positionsensitive microcalorimeter with two sensors isshown in Figure 4.4.5.This technique can be used in conjunction withreadout multiplexers, to allow current designs thatwill have 1000 multiplexed readout channels togo to ∼10 000 pixel arrays. Figueroa-Felicianoet al. (2002) are developing an imaging detectorthat has seven 0.250 mm pixels flanked bytwo transition-edge sensors in a one-dimensionalcolumn called a position-sensitive TES (PoST).They have obtained a preliminary result of 32 eVFWHM at 1.5 keV. Trowell et al. (2002) areworking on a similar detector that uses a single

240 CRYOGENIC MICROCALORIMETERSlong absorber, and position determination is carriedout from an analysis of the pulse shape.Another approach by Ohno et al. (2002) uses asingle SQUID channel with a segmented TES thathas different time constants for absorption in thedifferent TES segments.4.4.4.4 MODELING OF NON-IDEALBEHAVIORS AND DETECTOROPTIMIZATIONWe already discussed how microcalorimeter performanceis limited by non-ideal effects that werenot included in the standard theory of bolometersand microcalorimeters developed 20 years agoby Mather (Mather, 1982). These effects havebeen known for a few years now, but onlyvery recently a complete theoretical description ofmicrocalorimeter performance has been derived.The thermometer non-ohmic behavior has beenadded to the standard model to describe the performanceof TES detectors by Lindeman (Lindeman,2000). Two independent models that include allnon-ideal effects of know origin have also beendeveloped. These include the hot-electron effect,the absorber decoupling, the thermometer nonohmicbehavior, and all correlated extra noisesources. One of the two models uses block diagramalgebra to solve the detector equations, obtainingan analytical solution (Galeazzi and McCammon,2002), the other uses matrix notation to numericallysolve the linearized differential equations ofthe microcalorimeter (Figueroa-Feliciano, 2001).The two models are in good agreement witheach other, and predict the behavior of real siliconthermistor devices to high accuracy (Galeazziet al., 2002b).Of particular interest from the experimentalpoint of view is the fact that these models can beused to optimize the design on microcalorimetersfor best performance. Up to now the detectordesign was carried out in a semi-empirical way,based on the standard theory and on experimentaltests. The array for the XRS detector on the Astro-E2 satellite is the first detector whose designwas completely optimized based on the requiredperformance and on the characteristics of thematerial used. The characteristic heat capacityand thermal conductivity of all the detectorcomponents have been measured and the valueshave been used as input to the models to designthe detector geometry for best performance. Sincethe detector was designed to be used in space,mechanical modeling has also been carried outin parallel to ensure the mechanical integrity ofthe microcalorimeter (Stahle et al., 2002a). As wehave shown before, the results are impressive: theenergy resolution for a large detector is 4.7 eVFWHM and it is reproducible over large arrays.This is almost a factor of two better than a previousgeneration of the same detectors optimized in thesemi-empirical way (Stahle, 2002b). The spectrumof the Mn Kα line acquired with such detectors isreported in Figure 4.4.6.4.4.4.5 NON-RESISTIVETHERMOMETERSAs discussed in Section 4.4.2.2, the thermometerused in a microcalorimeter is not limited to avariable resistor. Any quantity that can be measuredand that varies strongly with temperaturecan be used for thermometry. Several devicesshow great promise and some have achievedenergy resolutions comparable with current resistivemicrocalorimeters.A magnetic microcalorimeter (Enss, 2002) usesa paramagnetic material with an applied magneticfield as its thermometer (Figure 4.4.7). The magnetizationof this material is a strong function oftemperature, and can be measured with high resolutionusing a SQUID magnetometer. Due to theneed for fast thermalization in the thermometer,the materials that show most promise are metalsdoped with rare earth ions to provide the paramagneticmoments. The paramagnetic material isthermally connected to an X-ray absorber, andweakly connected to a heat reservoir as in all othermicrocalorimeters. The device is usually placeddirectly on a SQUID to provide the best couplingbetween the SQUID and the paramagnetic material.The best energy resolution of 6 eV at 6 keVhas been obtained by Fleischmann et al. (2003).

CURRENT DEVELOPMENTS 24112010080Fit parametersFWHM: 4.72 ± 0.21 eVAmplitude 96.9 ± 3 countsc 2 : 1.20Counts60402005880 5885 5890 5895 5900 5905 5910Energy (eV)Figure 4.4.6 Spectrum of Mn Kα lines obtained with a Si thermistor and HgTe absorber optimized using the microcalorimeternon-ideal model. The datapoints represent the measured spectrum, the continuous line the best-fit to the data, and the dotted linerepresents the zero-resolution spectrum normalized in amplitude to the best-fit data (Hölzer et al., 1997)ParamagneticsensorPickup loopWeak thermal linkHeat sinkX-rayTo SQUIDFigure 4.4.7 Schematic view of a magnetic microcalorimeter.The X-ray heats the detector, changing the magnetic propertiesof the paramagnetic sensor. The change is read out through thepickup loopOther measurement techniques have also beenproposed. Kinetic inductance and thermoelectricdetectors are further examples of non-resistivethermometers that are under development and willbe discussed in the next section.4.4.4.6 OTHER IDEASMany other developments in microcalorimetry areunderway. Here we outline some of the work thatshows promise for the future.As discussed in Section 4.4.3.5, current TEScalorimeters show excess noise of unknown origin.To understand and/or remove this excess noise,different detector geometries are under study. Oneidea is that the boundary of the superconductingfilm, which due to lithographic processing hassome degree of irregularity, could be the causeof the excess noise. In a circular or so called‘Corbino’ geometry, one bias electrode is at thecenter of a circular film, and current flows radiallyoutward to a ground electrode encompassing thecircumference of the film. This geometry hasno boundary except the electrodes, which aresuperconducting and are not part of the transitionedgesensor itself (Luukanen, 2002). Anotheridea is that when the TES is in its transition,it is actually divided into superconducting andnormal state zones. In a square TES with constantcurrent density along the direction of currentflow, there is no preferred place for these zonesto develop, and they may nucleate in a ratherrandom fashion, possibly shifting in position on the

242 CRYOGENIC MICROCALORIMETERSTES film, creating noise. A non-square geometry(a trapezoid, for example) would have a currentdensity gradient, and the normal zone would tendto form in the highest current density region firstand then propagate monotonically toward the lowdensity region. Trapezoidal TES detectors withdifferent aspect ratios (Lindeman et al., 2002b)and detectors with a ‘zebra’ pattern of normaland superconducting strips (Bergmann Tiest et al.,2002b) are being fabricated and tested.In a resistive calorimeter that has weak thermalcoupling between the electron and the phononsystems, a significant temperature differential canbe established between the electron and phononsystems when the detector is biased. This is theso called ‘hot-electron effect’ that was discussedin Section 4.4.3.5. If the phonon system is thermallyanchored to the heat sink (no weak linkbetween the thermometer and the refrigerator), theelectron–phonon decoupling acts as the weak linkof the calorimeter and the electron temperaturebecomes the thermometer. This mode of operationhas been successfully used for some time for darkmatter and optical photon detectors using tungstenTES (Cabrera et al., 2000; Cabrera et al., 2002).Recently, Moseley and McCammon (2002) proposedsimilar operation of silicon thermistors forsubmillimeter devices. It may be possible to fabricateviable X-ray devices that operate in this hotelectronregime. The benefits of this technique arethe much simpler fabrication (without need for theweak thermal link) and the robustness that comeswith non-suspended devices.To obtain faster devices and better energy resolution,constant temperature microcalorimeters arealso being investigated (Moeckel et al., 2002). Theidea is an extension of the external electronic feedbacksystem that was described in Section 4.4.3.2.If the external feedback is sufficiently fast and withenough gain, it can compensate the power dissipatedin the thermometer by X-rays keeping thethermometer temperature constant. In addition tobeing linear, this system has the potential of beingfaster than conventional detectors. This is especiallytrue in devices that are limited by absorberdecoupling. If properly optimized, they can alsoachieve better energy resolution.The kinetic surface inductance of a superconductoris a function of the number of quasiparticlespresent in the superconductor. Since the numberof quasiparticles depends on the temperature ofthe superconductor, one can use kinetic inductanceas a thermometric parameter. These kineticinductance detectors (KID) can be operated near orwell below the superconducting transition temperatureT C , and can be read out by either a SQUID(Sergeev et al., 2002) or by measuring the resonantfrequency of a circuit of which the KID is aninductive component. This last method may providea simple way to multiplex these detectors(Mazin et al., 2002).Thermometers using the thermoelectric effectare also being investigated (Gulian et al., 2002):a rapid change in temperature in a materialcauses a transient voltage across it that can bemeasured by a SQUID amplifier. They haveproven the concept with gold/iron devices andare now investigating lower temperature systemssuch as lanthanum–cerium hexaborides as possibledetector materials that could achieve resolutionscomparable with thermistor devices.REFERENCESAlessandrello, A., Beeman, J. W., Brofferio, C., Cremonesi,O., Fiorini, E., Giuliani, A., Haller, E. E., Monfardini, A.,Nucciotti, A., Pavan, M., Pessina, G., Previtali, E. and Zanotti,L., High energy resolution bolometers for nuclearphysics and X-ray spectroscopy. Phys. Rev. Lett. 82, 513(1999).Beeman, J., Silver, E., Bandler, S., Schnopper, H., Murray, S.,Madden, N., Landis, D., Haller, E. E. and Barbera, M., Theconstellation-x focal plane microcalorimeter array: An ntdgermaniumsolution. AIP Conf. Proc. 605, 211 (2002).Benford, D. J., Ames, T. A., Chervenak, J. A., Grossman,E.N.,Irwin,K.D.,Khan,S.A.,Maffei,B.,Moseley,S.H.,Pajot, F., Phillips, T. G., Renault, J.-C., Reintsema, C. D.,Rioux, C., Shafer, R. A., Staguhn, J. G., Vastel, C. andVoellmer, G. M., First astronomical use of multiplexed transitionedge bolometers. AIP Conf. Proc. 605, 589 (2002).Bergmann Tiest, W., Hoevers, H. F. C., Mels, W. A., Ridder,M. L., Bruijn, M. P., de Korte, P. A. J. and Huber,M. E., Performance of X-ray microcalorimeters with anenergy resolution below 4.5 eV and 100 µs response time.AIP Conf. Proc. 605, 199 (2002a).Bergmann Tiest, W., Bruijn, M., Krouwer, E., Mels, W., Ridder,M. and Hoevers, H., Microcalorimeter performance:

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4.5 Position Sensitive Semiconductor Strip DetectorsW. D ¸ABROWSKI and P. GRYBOŚAGH University of Science and Technology, Krakow, Poland4.5.1 INTRODUCTIONProgress in technology of semiconductor devicesopens new possibilities for manufacturing semiconductordetectors. From the technological pointof view a semiconductor X-ray detector, being inprinciple a diode, is a relatively simple structure. Avery straightforward way to build a position sensitiveX-ray detector is to manufacture an arrayof independent semiconductor diodes on a commonsubstrate. Such arrays can be made on siliconwith precision much better compared to what isneeded for X-ray detectors. The difficulties areassociated with requirements concerning propertiesof semiconductor materials, which are quite different,compared to typical materials used in theelectronics industry. The two basic requirementswith respect to semiconductor materials used forX-ray detectors are: (a) high density that guaranteesshort absorption lengths; and (b) high resistivitythat allows obtaining sufficiently thick depletionlayers of reverse biased junctions. Although siliconis a relatively poor material for X-ray detection forits low density, semiconductor position sensitivedetectors are based in the majority on silicon.As mentioned, silicon based technologies aresuitable for manufacturing detector arrays withindividual elements of almost any shape, however,each element of an array needs to be read out byan individual electronic channel. This requirementimposes some constraints on the possiblearrangement of such detectors. The most commonlyknown and used types of position sensitivedetectors are:• strip detectors;• pad detectors;• pixel detectors.Within each group one can find large varietyof geometrical configurations. The boundariesbetween the three groups are not sharp anddistinctions between the three types are madeaccording to the schemes of the readout systems.The strip detectors are basically one-dimensional(1-D) position sensitive devices. The readoutelectronics is connected at the ends of strips and itis located outside the sensitive area of the detector.The pad detectors and pixel detectors are both twodimensional(2-D) arrays. The pad detectors areoften considered as 2-D arrays of relatively largeelements, with sizes of the order of millimetres,while the pixel detectors are considered as 2-Darrays of small elements, with sizes of the order ofa few hundreds of microns. A more fundamentaldistinction between these two types of detectorsis established by the scheme of the readoutelectronics. In a pad detector each element isread out by an individual electronic channel. Thereadout electronics is located outside the sensitivearea and the connections between the pads andthe readout electronics are made with metal traces(Weilhammer et al., 1996; Lin et al., 1997). Thus,the electronics for readout of pad detectors has asimilar architecture as the electronics for readout ofstrips. In the pixel detectors the readout electronicscircuit for each sensitive element is located in thedirect vicinity of that element. Depending on howthis is realized we distinguish monolithic pixelX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

248 POSITION SENSITIVE SEMICONDUCTOR STRIP DETECTORSdetectors and hybrid pixel detectors. In monolithicpixel detectors the readout electronics is integratedon the same substrate as the sensor array (Turchettaet al., 2001). Hybrid pixel detectors are built oftwo separate devices; the sensor array is madeas one device while the readout integrated circuitis made as another one and the two devicesare connected together using a technique of flipchip bonding (Breibach et al., 2001; Cihangir andKwan, 2001; Lozano et al., 2001). In either casethe readout electronics overlaps with the sensitivearea of the detector.The technologies used for manufacturing siliconstrip detectors and readout electronics can beconsidered these days as very mature ones. Siliconstrip detectors have been widely used in highenergy particle physics experiments for almost20 years and much development has been donein this area. Special techniques suitable for implementationof standard monolithic planar processeson high resistivity silicon have been developed andare available as industrial standards. It is importantto note that techniques of designing and manufacturingsilicon strip detectors allow building fullcustom devices specific and optimized for givenapplications. Silicon strip detectors of the sametype as used for detection of relativistic chargedparticles can be used for detection of low energyX-rays, up to 20 keV. A great advantage of siliconis its very mature, essentially industrial, technologyand regardless of some drawbacks due to limitedefficiency, silicon strip detectors are most widelyused for low-energy X-rays.Detector structures with position sensitive stripshave been realized successfully in various laboratoriesusing other semiconductor materials: highpurity germanium (HPGe) (Rossi et al., 1997;Rossi et al., 1999; Amman and Lucke, 2000; Vetteret al., 2000) and compound semiconductors,like gallium arsenide (GaAs) (Chen et al., 1996;Smith, 1996), cadmium telluride (CdTe) and cadmiumzinc telluride (CdZnTe) (Eisen et al., 1999;Gostilo et al., 2001; Kalemci and Matteson, 2002),and mercuric iodide (HgI 2 )(Schieberet al., 1998).These materials are more suitable for detection ofharder X-rays, above 20 keV, because of higheratomic numbers. High purity germanium, havinggood spectroscopic properties, could be in principlea perfect material for strip detectors for higherX-ray energies. The complications associated withcooling such detectors, however, means that thereis not much development in that direction. On theother hand, significant progress has been maderecently in the area of so-called room temperaturesemiconductor detectors, which are based mostlyon semi-insulating compounds with high atomicnumbers and high energy band gaps. Poor chargetransport properties of those materials and difficultiesin producing large crystals are still limitingfactors and much effort is focused on technologicalimprovements.The basic concept of a strip detector is very simpleand is based on splitting a continuous electrodefor individual strips, assuming that signalsfrom each strip will be read out by an individualelectronic circuit. Starting from a flat semiconductordetector one can either make one electrode asa multiple strip pattern and obtain a single-sidedstrip detector or divide both electrodes into stripsand obtain a double-sided strip detector. In orderto make such a detector working as a positionsensitive device it is required that the strips arewell separated electrically so that the current signalinduced in a given strip does not flow to theneighbouring strips. The methods of strip separationdepend on the detector structures and will bediscussed in detail later.In order to use position sensitivity of stripdetectors it is required that the signal from eachstrip is recorded and processed independentlyby an individual electronic circuit, like for asingle detector. Thus, strip detectors require multichannelfront-end electronics and the only practicalway is to make such electronics as multi-channelintegrated circuits. Such solutions have becomepossible due to advances in Very Large ScaleIntegration (VLSI) electronics, and in particular,due to advances in techniques of designing,prototyping and manufacturing of ApplicationSpecific Integrated Circuits (ASICs).Generic structures of a single-sided and a double-sidedsemiconductor strip detector are shownin Figure 4.5.1. One can read out every strip, asshown schematically in Figure 4.5.1, or one can

SPATIAL RESOLUTION OF SEMICONDUCTOR STRIP DETECTORS 249Single-sided strip detectorDouble-sided strip detectorFigure 4.5.1 Schematic structure of a single-sided and adouble-sided semiconductor strip detectorread out only every second or every third strip.In such a configuration the signals collected bythe intermediate are coupled to the readout stripsthrough the interstrip capacitance.4.5.2 SPATIAL RESOLUTIONOF SEMICONDUCTOR STRIPDETECTORSThe spatial resolution of a semiconductor stripdetector depends on the intrinsic spatial resolutionof the semiconductor material, strip pitch of thedetector and signal-to-noise ratio of the readoutelectronics. For an ideal position sensitive detectorof X-rays, the measured position is expectedto correspond to the position at the detector surfaceat which the photon entered the detector.There are two effects, which impose some physicallimitations on the spatial resolution of a semiconductordetector, namely, scattering of photons inthe semiconductor material and diffusion of generatedcharge carriers during their transport in thesensitive volume of the detector. These effects areindependent of the segmentation of the detectorelectrodes but the segmentation, i.e. strip pitch ina strip detector, should be designed taking intoaccount these effects. Even if there were no technologicallimitations on precision of electrode patternsone could not obtain spatial resolution betterthan determined by the intrinsic effects of scatteringand diffusion. From a practical point of view itis very important that one understands the intrinsicresolution of the semiconductor material as thisallows one to optimize the design of the detectoraccordingly, taking into account other aspectslike, for example, very important limitations dueto readout electronics.For most of the later considerations it isassumed that the photons enter the detector eitherfrom the top or from the bottom side, perpendicularlyto the surface, as shown schematically inFigure 4.5.2. There are some particular applications,in which the detector is illuminated fromthe edge side, along the strip, and they will be discussedseparately. The measured position of a photonentering the detector at point x entry is given bythe position x meas reconstructed upon the electricalsignals recorded at the readout strips. Dependingon the readout method used the reconstructed positionswill be a set of discrete numbers correspondingto strip positions or some numbers elaboratedin a more sophisticated way using the signal amplitudesmeasured on the strips clustered around theposition of photon entry. Thus, assuming that thedetector surface is illuminated uniformly with photons,as shown in Figure 4.5.2, one can build up adistribution of residuals (x meas − x entry ) for a givenstrip and define the spatial resolution as:√σ x = (x meas − x entry ) 2 (4.5.1)There are two issues, which should be addressedwith respect to such a measure of spatial resolution,namely:• the resolution cannot be measured directlyaccording to Equation (4.5.1) since one cannotmeasure or predefine the real entry position x entryof a photon:

250 POSITION SENSITIVE SEMICONDUCTOR STRIP DETECTORSstrip pitchp+ stripn-typeFigure 4.5.2 Schematic cross-section of a strip detector and definition of the strip pitch• the distribution of residuals (x meas − x entry ) canhave a highly non-Gaussian shape and in suchcases the true rms (root mean square) valueis only partially meaningful for accuracy ofposition measurements.An advantage of such a definition is that it is verygeneric and it allows one to take into account allthe effects which affect the spatial resolution, i.e.scattering of photons in the semiconductor material,diffusion of charge carriers during the collectionprocess, architecture and noise performance ofthe readout electronics. In applications of semiconductorstrip detectors for imaging measurementsthe quality of a system with respect to its spatialresolution is usually described by the ModulationTransfer Function (MTF) (Besch, 1998).4.5.2.1 INTRINSIC SPATIALRESOLUTION OF SEMICONDUCTORDETECTORSLet us first briefly review the basic properties ofsemiconductor materials, which are potential candidatesto be used for position sensitive detectors,namely, Si, Ge, GaAs, CdTe and CdZnTe. Thefundamental parameter, which defines the propertiesof a given semiconductor material as a sensormaterial, is the absorption coefficient as afunction of X-ray energy. The parameter, whichdescribes directly attenuation of a photon beam ina semiconductor material, is the absorption length.Total attenuation of an X-ray beam is determinedby photoabsorption as well as by incoherent andcoherent scattering. The photons scattered eitherin incoherent or in coherent processes are eventuallyabsorbed in the detector within distanceswhich are usually small compared to the dimensionsof the detector. For a non-segmented detectorthe attenuation length defines the efficiency of thedetector of given thickness. In segmented detectors,like strip detectors, one has to consider caseswhen a scattered photon is absorbed in a differentsegment than the one into which the primaryphoton entered.The absorption length for X-rays of givenenergy in a given semiconductor material definesnot only the detector efficiency but also thedistance over which the generated charge carriershave to be transported to the collecting electrodes.For the considered energy range of X-rays thesecondary electrons are stopped within submicrondistances so that one can assume that the chargecarriers are generated in a single point. Duringtransport to the collecting electrodes the carriersdiffuse in all directions. In a non-segmenteddetector the effect of diffusion in the plane parallelto the collecting electrodes has no influence onthe current signal induced in the electrodes. In aposition sensitive detector, like a strip detector, thediffusing cloud of charge carriers can be dividedbetween neighbouring strips. The number of stripsinto which the charge is divided depends on the

SPATIAL RESOLUTION OF SEMICONDUCTOR STRIP DETECTORS 251range of diffusion as well as on the strip pitch. Thiseffect has to be taken into account when designinga strip detector for a given application.The absorption length for the basic materials(Si, GaAs and CdTe) as a function of X-ray energyfrom 1 keV to 100 keV, is shown in Figure 4.5.3.The plots have been generated using the databaseXCOM (Berger et al., 1999). The plots for Ge andCdZnTe are not shown as they mostly overlapwith GaAs and CdTe, respectively, except theregions around the absorption edges. The plotsshown in Figure 4.5.3 are fundamental for usualconsiderations of detector efficiency vs detectorthickness and detector material. In this subchapterwe discuss these plots with respect to the issuesspecific for position sensitive detectors.DiffusionFor each particular detector and particular spectrumof X-rays one can estimate intrinsic spatialresolution due to diffusion by taking into accountthe following aspects:• attenuation profile of the X-ray beam in thesensitive volume of the detector;• distribution of the electric field in the sensitivevolume of the detector;• transport of charge carriers to the collectingelectrodes.Since photons are absorbed at various depthsdistributed according to the absorption law andhave to travel over various distances one has toaverage the effects over some number of photonsinteracting with the detector material. This canbe done either analytically in simple cases or byMonte Carlo (MC) simulation. Several examplesof MC simulation employed for evaluation of theperformance of position sensitive semiconductordetectors, strips or pixels, can be found in recentpublications (D¸abrowski et al., 2000; del RiscoNorrlid et al., 2001; Fowler et al., 2002; Mathiesonet al., 2002). In MC simulation one can combinethe effect of diffusion with the transport of chargecarriers, taking into account accurate distributionof the electric field in particular structures of stripor pixel detectors.For a rough evaluation of the diffusion effectin various semiconductor materials we have usedthe following simplified analytical approach. Letus assume that the detector is well overdepletedso that the electric field is almost constant overthe full thickness of the detector. Examples of siliconstrip detectors show that using high resistivitymaterial, with resistivity of the order of 10 kcm,Absorption length (µm)10 410 310 210 1SiGaAsCdTe10 01 10Energy (keV)100Figure 4.5.3 Absorption length as a function of X-ray energy for Si, GaAs and CdTe

252 POSITION SENSITIVE SEMICONDUCTOR STRIP DETECTORSone can bias the detectors with a voltage by afactor of 3–5 higher than the full depletion voltage(Andricek et al., 2000). The GaAs and CdTedetectors for X-rays are usually made using semiinsulatingmaterials with resistivity of the orderof 1 × 10 5 to 1 × 10 6 cm. Such detectors behavemore like solid-state ionization chambers and onecan assume that the electric field is constant in thetotal sensitive volume. In the strip detector structuresthe electric field distribution around the stripsmay be highly non-uniform. This non-uniformityaffects the trajectories and velocities of charge carriersin the regions around the readout strips. However,these regions are only a small fraction of thetotal sensitive volume of the detector. These detailsare important for construction of the strip detectors,however, they do not affect significantly the rangeof diffusion spread.In addition, we assume that the electric field islower than the value at which the drift velocitysaturates. For most detectors it is possible to fulfilboth conditions, i.e. to bias the detector withvoltage significantly higher than the full depletionvoltage and to keep the electric field below thevelocity saturation point. In numerical calculationboth effects can be easily taken into account butfor analytical evaluation the above approximationssimplify the analysis.Let us assume that photons enter the detectorperpendicularly to its surface from the side of thecollecting electrode. The spread of charge carriersdue to diffusion taking place during transport ofthe carriers to the readout electrode is characterizedhere by the full width at half maximum (FWHM)of the charge carrier distribution arriving at thecollecting electrode when started from a point atthe depth corresponding to the absorption lengthfor X-rays of given energy. The FWHM of thecharge carrier distribution in the plane parallel tothe electrode is then given as:FWMH = 4 √ ln 2t n,p D n,p (4.5.2)where D n,p is the diffusion constant for electronsor holes and t n,p is the drift time of charge carriersover the distance equal to the absorption length.Assuming that the electric field E is constant inthe depletion region one can express the drift timeby a simple formulat n,p = µ n,pE(4.5.3)λwhere λ is the absorption length.Of course, the charge generated by photonsabsorbed at smaller depths diffuse less but asignificant fraction, about 37 % of incident photonswhich are absorbed at the depths larger then theabsorption length, result in wider distributions ofthe collected charge.Taking the absorption length as a functionof energy, as shown in Figure 4.5.3, one canobtain the corresponding values of the FWHM ofcharge distribution due to diffusion. The valuesof the assumed electric field and the parametersof semiconductor materials are summarized inTable 4.5.1.For silicon it has been assumed that the carrierscollected by the readout electrode are holes as themost commonly used silicon strip detectors arebuilt as p + strips in n-type bulk material. For GaAsand CdTe it has been assumed that the collectedcarriers are electrons. It is known that in thesematerials hole trapping is a very basic problem,which affects spectroscopic performance of suchdetectors and special efforts have to be undertakento make those detectors as devices sensing theelectron signal only (He, 2001).The FWHM of distribution of charge collectedon the readout electrode as a function of incidentX-ray energy for the four considered semiconductormaterials is plotted in Figure 4.5.4. One cannotice that the FWHM as a function of X-rayenergy follows roughly the absorption length asTable 4.5.1 Parameters used for calculation of the FWHM ofcharge spread due to diffusionSi GaAs CdTe Ge@77KCollected charge holes electrons electrons holescarriersElectric field (V/cm) 4 × 10 3 2 × 10 3 1 × 10 4 1 × 10 3Mobility of collected 450 8500 1150 42 000carriers(cm 2 V −1 s −1 )Diffusion coefficientof collectedcarriers (cm 2 s −1 )11.6 201 29.8 280

SPATIAL RESOLUTION OF SEMICONDUCTOR STRIP DETECTORS 253Diffusion FWHM (µm)10010SiGaAsCdTeGe@77 K11 10Energy (keV)100Figure 4.5.4 FWHM of charge distribution collected at the readout electrodes for a point charge generated at the depth equal tothe absorption lengtha function of energy. This is not surprising if oneremembers that the drift time is proportional tothe absorption length and the ratio of the diffusioncoefficient and the mobility for a given semiconductormaterial is constant and is given by theEinstein relation as:D n,pµ n,p= kT q(4.5.4)where k is the Boltzmann constant, T is the absolutetemperature and q is the electronic charge.At given temperature a high mobility, like in thecase of GaAs, results in a short charge collectiontime but proportionally higher diffusion coefficientresults in large diffusion spread in a short time.One can expect to gain in terms of reducing therelative effect of diffusion with respect to driftby lowering the temperature. This is shown inFigure 4.5.4 for germanium at a temperature of77 K. The absorption length for Ge is not shownin Figure 4.5.3 since it overlaps almost completelywith the plot for GaAs. In Figure 4.5.4 thediffusion FWHM for Ge at 77 K is systematicallylower than for GaAs, though the reduction is notlarge because the diffusion spread is proportionalonly to the square root of the drift time.The FWHM of charge spread due to diffusion,as shown in Figure 4.5.4, gives a first indicationabout the lower limit of the strip pitch in astrip detector. Using a strip pitch much smallerthan the diffusion FWHM might be in principlean advantage for the spatial resolution as onecould measure the signals collected on severalclustered strips and then evaluate the centre ofgravity of the charge distribution. That way onecould measure the position with a precision muchbetter than the strip pitch. Such methods arecommonly used in particle physics applicationswhere position measurement accuracy better than2 µm rms has been achieved using silicon stripdetectors with 25 µm strip pitch and 50 µm readoutpitch (Colledani et al., 1996). However, one hasto keep in mind that a small strip pitch results individing the total charge generated by a photonbetween too many strips and the signal measuredat each individual strip becomes low. This isa serious limitation for measurements of lowenergy X-rays as the total signals generated inthe semiconductor detectors are small anywayand obtaining a satisfactory signal-to-noise ratiois a non-trivial problem, even before division ofcharge between several strips. For semiconductormaterials other than silicon the processes used

254 POSITION SENSITIVE SEMICONDUCTOR STRIP DETECTORSfor manufacturing strip detectors does not allowreducing easily the strip pitch below 100 µm andin most cases taking diffusion into account doesnot affect the detector design. On the other hand,for silicon there is practically no limitation onprecision of the strip layout and one should takeinto account the results shown in Figure 4.5.4in order to make a reasonable layout of stripsgiven the energy of X-rays to be measured andperformance of the readout electronics.ScatteringIn many cases photon scattering is more importantthan diffusion. The scattered photons are mostlyabsorbed in the detector volume but in positionsdisplaced from their initial trajectories so that thecharge can be collected in strips not necessarilynearest to the point at the surface where the photonhas entered the detector. A complete evaluation ofthe scattering effects for a given detector geometrycan be done only by full MC simulation that takesinto account angular distributions of scattered photons.The two basic scattering mechanisms differwith respect to angular distribution of scatteredphotons. In the case of incoherent (Compton) scatteringmost of the photons are scattered by largeangles from the trajectories of primary photons andsuch scattered photons can produce false positionmeasurements. The angular distribution of photonsscattered in the coherent (Rayleigh) processes has avery dominant peak in the forward direction so thatmost of the scattered photons diverge by very smallangles from the trajectories of primary photons andthey do not affect the position measurements.The contribution of scattering effects to thespatial resolution of a semiconductor detectordepends on the ratio of the cross-sections forincoherent and coherent scattering to the crosssectionfor the photoabsorption. The cross-sectionfor the photoabsorption decreases with increasingenergy E of X-rays as 1/E 3 , while the crosssectionfor Compton scattering shows relativelyflat dependence on the photon energy. Thus, therelative contribution of the incoherent scatteringincreases strongly with increasing energy of X-rays. The cross-section for the coherent scatteringdepends on the photon energy in a similar wayas for the photoabsorption so that the relativecontributions of these two effects remains at thesame level over a wide range of X-ray energy.Scattering/photoabsorption ratio10 010 −110 −2Si_incohSi_totalGaAs_incohGaAs_totalCdTe_incohCdTe_total10 −31 10Energy (keV)100Figure 4.5.5 Ratio of the incoherent scattering coefficient to the photoabsorption coefficient and of the total scattering coefficientto the photoabsorption coefficient

SPATIAL RESOLUTION OF SEMICONDUCTOR STRIP DETECTORS 255The ratio of the incoherent scattering coefficientto the photoabsorption coefficient and the ratio ofthe total scattering coefficient, including the incoherentand the coherent scattering, to the photoabsorptioncoefficient as a function of X-ray energyfor the three considered semiconductor materials(Si, GaAs and CdTe) are shown in Figure 4.5.5.The plots have been generated using the databaseXCOM (Berger et al., 1999). In a first approximationone can consider only the incoherent scatteringfor the coherent scattering due to its angular distributionpredominating in the forward directioncontributes only in a limited way to diverging photonsfrom their primary trajectories. As discussedabove, the relative cross-section of the Comptonscattering increases strongly with increasingenergy of X-rays. The lighter the semiconductormaterial the bigger the relative increase ofthe Compton scattering compared to the photoabsorption.For example, in silicon the ratio of theprobability of incoherent scattering to the probabilityof photoabsorption is 0.1 for X-ray energyof about 25 keV and reaches 1 for X-ray energy ofabout 55 keV.From the plots shown in Figure 4.5.5 one canobtain a rough estimate of how much the scatteringmay degrade the accuracy of position measurements.One should note that the scattered photonsare eventually converted into photoelectrons withindistances from the primary photon trajectories thatare of the order of the corresponding absorptionlengths. In order to evaluate how the scatteringaffects the spatial resolution one needs to takeinto account the angular distribution of scatteredphotons. This can be done employing full MC simulation.Such simulations are helpful at the stageof designing a detection system so that one canadjust properly the strip geometry and parametersof the readout electronics according to the intrinsicspatial resolution of the semiconductor materialused. Several such examples concerning designs ofparticular detection systems can be found in the literature(D¸abrowski et al., 2000; del Risco Norrlidet al., 2001).Most of the work in this area has been donefor silicon as one can easily manufacture siliconposition sensitive detectors with small readoutelectrodes (strips), comparable with the range ofscattered photons. Results of such simulations arepresented elsewhere (D¸abrowski et al., 2000). Thesimulation was performed for a 300 µm thicksilicon detector with a surface dead layer of2 µm for three values of X-ray energy (8 keV,17 keV and 22 keV). For each photon entering thedetector material perpendicularly to the surfacethe spatial distribution of the energy deposited insilicon was calculated using the EGS4 package(Bielajew et al., 1994). Then this distributionwas projected on a line perpendicular to thestrips. In such a way we could estimate theeffect of scattering on the spatial resolution ofa 1-D strip detector. Neglecting for the momentother effects associated with charge transport,diffusion and detector segmentation, the positionat which the energy is deposited corresponds tothe position reconstructed. The distributions ofenergy deposition for photons of 8 keV, 17 keV and22 keV, entering a silicon detector perpendicularlyto its surface, are shown in Figure 4.5.6. The non-Gaussian tails due to Compton scattering extendapproximately up to 150 µm, 800 µm and 1000 µmfor 8 keV, 17 keV and 22 keV, respectively. Thus,although the fractions of incoherently scatteredphotons are small they contribute significantly tothe total rms value of residuals.Assuming that one can measure precisely theposition of the deposited charge x deposition , i.e.neglecting a finite strip pitch, diffusion andnoise of the readout electronics, the intrinsicspatial resolution can be defined according toEquation (4.5.1) as:√σ x = (x deposition − x entry ) 2 (4.5.5)From the results of MC simulation shown inFigure 4.5.6 one obtains the intrinsic spatial resolutionas 4.8 µm, 35.9 µm and 71.1 µm for8keV,17 keV and 22 keV, respectively. These values canbe now compared with the spreads due to diffusion.From the plots shown in Figure 4.5.4 onecan find the FWHM values of charge spread dueto diffusion as 7.3 µm, 21 µm and 32 µm for X-rayenergy of 8 keV, 17 keV and 22 keV, respectively.The corresponding standard deviation values are

256 POSITION SENSITIVE SEMICONDUCTOR STRIP DETECTORS10 010 −18 keVTotal deposited energy (relative units)10 −210 −310 −410 −510 −6−1000 −800 −600 −400 −200 0 200 400 600 800 1000Position X (µm)10 010 −110 −210 −310 −410 −517 keV10 −6−1000 −800 −600 −400 −200 0 200 400 600 800 1000Position X (µm)10 010 −122 keV10 −210 −310 −410 −510 −6−1000 −800 −600 −400 −200 0 200 400 600 800 1000Position X (µm)Figure 4.5.6 Distributions of energy deposition for photons of 8 keV, 17 keV and 22 keV, entering a silicon detectorperpendicularly to its surface. Reported from Nucl. Instrum. Methods Phys. Res., Sect. A 442 (2000) 348, with permission fromElsevier Scienceby a factor of 2.355 lower and one can notice thatonly for the lowest considered energy of 8 keV isthe effect of scattering comparable with the effectof diffusion. For higher X-ray energies the effectof scattering predominates.Up to now we have been assuming that theincident photons enter the sensitive detector volumeperpendicularly to its surface. This is a goodapproximation for many applications since positionsensitive measurements usually require well collimatedX-ray beams. However, the collimation isnever perfect and there is a trade-off between theaperture of a collimator and losses of X-ray intensity.Therefore, considering the intrinsic spatialresolution of a semiconductor detector, in additionto the scattering effects, one has to pay attention

SPATIAL RESOLUTION OF SEMICONDUCTOR STRIP DETECTORS 257Total deposited energy (relative units)−2010 −1 0° 5°10 −210°10 −310 −410 −510 −60 20 40 6010 0 Position X (µm)−2010 −1 0° 5°10°10 −210 −310 −410 −510 −60 20 40 6010 0 Position X (µm)8 keV15°80 10017 keV15°80 10010 0 −2010 −110 −210 −310 −410 −510 −60° 5°10°0 20 40 60Position X (µm)22 keV15°80 100Figure 4.5.7 Distributions of energy deposition for photons of 8 keV, 17 keV and 22 keV, entering a silicon detector at the angleof 0, 5, 10 and 15 ◦ . Reported from Nucl. Instrum. Methods Phys. Res., Sect. A 442 (2000) 348, with permission from ElsevierScienceto the effect of parallax. In a rough approximation,for given incident angle this effect is proportionalto the absorption length as the charge generatedalong the trajectories of primary photons is thenprojected on the detector surface with the readoutelectrodes. In order to illustrate this effect wehave performed MC simulations for the same photonenergy values as considered above and forvarious incident angles (D¸abrowski et al., 2000).Figure 4.5.7 shows the distributions of depositedenergy for the incident angles of 0, 5, 10 and15 ◦ . One can notice that the effect of parallax isfar more significant compared to Compton scattering.In the case of this particular detector thedistributions are limited by the detector thickness,which is only 300 µm. For the photon energy of22 keV the distribution becomes almost flat sincethe detector thickness of 300 µm corresponds tothe initial part of the absorption curve, which isapproximately linear.Following the same procedure as in the caseof 0 ◦ one can estimate the intrinsic spatial resolutionfor the distributions shown in Figure 4.5.7.The results are summarized in Table 4.5.2. It isinteresting to note that for X-ray energy of 22 keVthe spatial resolution does not change very muchwith the incident angle and becomes even betterfor the incident angles different from 0 ◦ , although

258 POSITION SENSITIVE SEMICONDUCTOR STRIP DETECTORSTable 4.5.2 Intrinsic spatial resolution of 300 µmthick silicon detector vs X-ray energy and incidentangle8 keV 17 keV 22 keV0 ◦ 4.8 µm 35.9 µm 77.1 µm5 ◦ 6.9 µm 35.1 µm 64.6 µm10 ◦ 11.0 µm 45.1 µm 70.4 µm15 ◦ 15.6 µm 49.9 µm 67.6 µmthe shapes of charge distributions are very differentdepending on the angle. This effect is due tolimited detector thickness being, in that particularcase, much smaller compared to the absorptionlength of 22 keV photons in silicon. Thus,some fraction of incoherently scattered photonsescape the detector volume before being absorbedand this fraction depends on the incident angleof the primary photons and angular distributionof the scattered photons. Particular combinationsof those two angular distributions result in variationof the intrinsic spatial resolution. For poorlycollimated X-ray beams a thin detector helps toreduce the affect of parallax on the spatial resolution,of course, in expense of losing detectionefficiency.4.5.3 STRUCTURES OF STRIPDETECTORSConcerning the physical and topological structuresthere are significant differences between siliconstrip detectors and strip detectors made of othersemiconductor materials. The use of advancedsilicon technologies allows one to design and manufacturequite advanced and sophisticated structuresof silicon strip detectors. On the otherhand, strip detectors made of other semiconductormaterials, like Ge, GaAs, CdTe, CdZnTe,are relatively simple structures. The same appliesto strip detectors built on lithium-drifted siliconSi(Li). Lithium compensation technique isused for manufacturing thick silicon detectors,however, the technological step of lithium driftis not compatible with other technological stepsemployed in manufacturing advanced structures ofstrip detectors.4.5.3.1 SILICON STRIP DETECTORSMost commonly used silicon strip detectors arebased on reverse biased strongly asymmetricjunctions built on low doped silicon of resistivitybetween 1 kcm and 20 kcm. In majority theseare p + -n junctions built on n-type high resistivitybulk material. Development of high precisionsilicon microstrip detectors of this type has beendriven by applications in high energy particlephysics for measurements of particle tracks. Thoseapplications require thin detectors and thicknessof 300 µm has become almost a standard in thisarea. Silicon strip detectors can be made on thickerwafers using exactly the same technological stepsas for thin detectors and detectors of thicknessup to 2 mm have been manufactured successfully(Ota, 1999; Phlips et al., 2001). In order to makeuse of the full thickness of a detector based onthe p + -n junction one needs to bias the structurewith a sufficiently high voltage, the so-called fulldepletion voltage, to induce the depletion layerover the full physical thickness of silicon, upto the n + ohmic contact on the backside. Thefull depletion voltage increases as the square ofdetector thickness and is given as:V depl = qN dd 2(4.5.6)2ε Siwhere q is the electronic charge, d is the detectorthickness, N d is the donor concentration in n-typebulk and ε Si is the permittivity of silicon.For example, for the above mentioned 2 mmthick detector built on silicon of 20 kcm resistivitythe full depletion voltage is 650 V. The requiredhigh bias voltage for thick detectors becomes ata certain point a limitation since it exceeds thebreakdown voltage of the structure. It is worthnoting that the breakdown voltage of a siliconstrip structure is much lower, by an order of magnitude,compared to the breakdown voltage ofhomogenous silicon bulk because of local highelectric field around the edges of p + strips. Thebreakdown voltage usually decreases with narrowingthe strip width. Significant progress has beenmade recently with respect to increasing breakdownvoltage in silicon strip detectors and structureswith strip pitch of the order of 100 µm with

STRUCTURES OF STRIP DETECTORS 259breakdown voltage up to 500 V are produced routinely(Andricek et al., 2000). This allows not onlyto build thicker detectors but also to use thinnerdetectors with bias voltages much higher than thefull depletion voltage, which helps to reduce thecharge collection time and the charge spread dueto diffusion.Given the fact that there is practically no technologicallimitation on the precision of strip layoutof silicon strip detectors one can easily matchthe strip pitch to the intrinsic spatial resolution sothat the resulting spatial resolution is minimallyaffected by the detector layout. Due to low absorptioncoefficient, silicon devices are suitable forhigh precision position sensitive measurements oflow energy X-rays, up to approximately 20 keV.For this low energy range the noise of readout electronicsand the achievable signal-to-noise ratio arethe limiting factors to be taken into account. Thereadout electronics will be discussed later, however,already at this point it should be mentionedthat the detector geometry, in particular the strippitch that determines the interstrip capacitance,affects the signal-to-noise ratio. Thus, in order tooptimize the layout of a silicon strip detector for agiven experiment one has to take into account allthe discussed issues.It is worth noting that silicon strip detectorsand readout electronics are usually designed as fullcustom devices. Such an approach is affordablemainly because silicon strip detectors and readoutASICs are manufactured using mature industrialprocesses. A designer does not need to interferewith details of technology and, in fact, in mostcases is not allowed to modify the technology.Of course, there are some drawbacks of such anapproach but great advantages are relatively lowcost and fast turn around time for prototyping.Single-sided Silicon Strip DetectorsStarting from a p + -n silicon detector structure onecan make a single-sided strip detector by splittingoff one of the electrodes, either on the junctionside or on the ohmic side, into individual strips.Since the mobility of electrons and holes in silicondiffer only by a factor of 3 the collection timesfor carriers of each type are of the same orderof magnitude. For each type of charge carriersthe lifetime is much longer than the collectiontime so that each electrode senses the motion ofelectrons and holes. The detailed shapes of theinduced current pulse depend on the distribution ofthe electric field in the depletion region but in theend the total charge induced in a given electrodeis equal to the charge of carriers collected bythis electrode. Thus, assuming that the integrationtime in the front-end electronics is longer than thecharge collection time, the total charges of currentsignals induced in the p-side (junction side) andthe n-side (ohmic side) are equal.Regarding a silicon strip detector there is asignificant difference in the strip structure on thejunction side and on the ohmic side. If the stripsare made on the junction side separation of stripsis obtained naturally, without any additional structure,as shown in Figure 4.5.8(a). The neighbouringstrips are separated by two reverse biased p + -njunctions connected back-to-back. One should notethat the surface of silicon between the strips is coveredby silicon dioxide in order to protect the surfaceagainst influence of humidity and impuritiesadsorbed at the surface. The oxide layer grown byoxidation of the silicon crystal is always chargedpositively with holes trapped at the Si–SiO 2 interfaceand holes trapped in the bulk of the oxide.The positive charge in the oxide causes accumulationof electrons at the silicon surface so that theregions between the strips become n + -type. Thisis one of the reasons, for which strip detectors aremade on n-type silicon. For an opposite configuration,i.e. n + strips in p-type low doped silicon,the positive charge in the surface oxide induces aninversion n + layer in p-type silicon underneath theoxide that short-circuit the n + strips.The structure shown in Figure 4.5.8(a) illustratesschematically a DC-coupled detector. Thep + strips are covered with metal strips for two reasons:to reduce the strip resistance and to providecontacts for connection of the readout electronics,which usually is done by wire bonding. In this configurationthe potential of strips is defined by thepotential of the inputs of the readout electronics,usually close to the ground of the system. Positive

260 POSITION SENSITIVE SEMICONDUCTOR STRIP DETECTORSmetalstripp + stripSiO 2n-type(a)metalstripp + stripSiO 2SiO 2metalstripFOXFETn-typep+ stripn-type(b)Figure 4.5.8 Techniques of signal coupling in strip detectors: (a) DC-coupled single-sided strips; (b) AC-coupled single-sidedstrips, cross-sections perpendicular to the strips and along the strip are shown. The FOXFET bias structure is shownhigh voltage bias is then applied to the backsidecontact of the detector. In this configuration theDC leakage current from each strip has to flow tothe input of the preamplifier connected to that strip.Such a configuration is possible, however, one hasto ensure that the front-end electronics is designedin such a way that it can sink that leakage current.In order to cut off the DC leakage current onecan use capacitive coupling between the strips andthe front-end electronics. In silicon detectors thecoupling capacitors can be integrated in the detectorstructures resulting in AC-coupled strip detectors,as shown schematically in Figure 4.5.8(b).The p + strips and the metal strips are separatedby a silicon dioxide layer and these structuresform capacitors extended all along the strips. Inthis configuration each p + strip has to be biasedseparately through an individual resistor. The resistorsare required to be of high enough value sothat they do not contribute to the noise of thefront-end system and they should be integratedin a small area at the ends of the strips. Thereare several technologies for manufacturing suchresistors. The resistor can be made of low dopedpolysilicon layer, a diffusion layer or as channelof a MOSFET (Metal Oxide Semiconductor FieldEffect Transistor) structure built between the stripand the bias line. For our purpose it is importantto note that resistors of values up to a few Mcan be realized using polysilicon and resistors ofhigher values can be realized using the FOXFETtechnique. In many applications to X-ray measurementsthe signal-to-noise ratio is very critical andit is required to reduce all noise sources, includingthe noise due to bias resistors. For such applicationsdetectors with FOXFET bias structure, asshown in Figure 4.5.8(b), are preferable.The readout strips can be made on the ohmicside, but in such a case one needs to implementadditional structure in order to separate n + strips,which otherwise would be short-circuited vian-type bulk material. The interstrip resistancewould be additionally lowered by the accumulationof n + layers formed in the interstrip regionscovered by silicon dioxide.There are two techniques used to separatethe readout strip on the ohmic side, so-called‘p-stops’ and ‘field plates’. The p-stop structure,shown schematically in Figure 4.5.9(a), employsadditional p-type strips laid out between the n +readout strips. This structure can be implementedeither in DC-coupled or AC-coupled detectors.

STRUCTURES OF STRIP DETECTORS 261n + stripmetalstripSiO 2p-stopn-type(a)metalstripn + stripSiO 2inducedp-type arean-type(b)Figure 4.5.9 Strip isolation techniques on the ohmic side of a strip detector: (a) p-stops; (b) field platesThe field plate structure, shown schematically inFigure 4.5.9(b), can be implemented only in ACcoupleddetectors. In this structure the metal stripsare wider than the n + strips in silicon so that theedges of the metal strips are extended over the n-type bulk material. If the metal strips are biasednegatively with respect to n + strips the electricfield induces p-type layers at the surface of then-type bulk, underneath the extended wings of themetal strips. These induced p-type surface layersprovide separation of neighbouring readout strip.The potential of the metal strips has to be adjustedin such a way that inversion layers are induced inthe low doped interstrip regions but not in the highdoped n + strips regions.From this short overview it is clear that the stripstructure on the ohmic side is more complicatedthan the structure on the junction side and as faras single-sided detectors are concerned there isno particular reason to make the strip structureon the ohmic side. A small advantage of n-typereadout can be due to faster signals on the n-sideas these signals are induced mostly by electronsbeing collected faster. However, collection of holesin silicon is fast enough so that in most cases thereis practically no difference between the signalscollected on the n-side and the p-side, except incases when very fast front-end electronics is used.A strip detector can also be made starting fromthe Si(Li) detector structure. The strip structure onthe p + contact side can be realized by patteringmetal strips and plasma etching groves in thearea between the strips in order to separate themelectrically. Given that the thickness of the p +contact is small, about 1 µm, one can obtaina relatively fine pitch, down to 100 µm. Thelithium-diffused contact, on the side opposite tothe p + contact, is rather thick, typically between100 µm and 500 µm. For such a thick lithiumcontact layer the strip structure can be obtainedby sawing deep groves in the contact but the pitchof such a structure can be only in the range ofmillimetres. Recently a technique of making thinlithium contacts, about 30 µm, in Si(Li) detectorshas been reported (Protic et al., 2001a,b). Such acontact can be then divided into strips by plasmaetched grooves. The possibility of producing astrip structure with a pitch of 500 µm has beendemonstrated using this technique.Double-sided Silicon Strip DetectorsOnce the technique of separating the readout stripson the ohmic side is elaborated, the basic conceptof a double-sided strip detector is relatively simple.

262 POSITION SENSITIVE SEMICONDUCTOR STRIP DETECTORSIt is a structure with the strips on each sideof the detector. The relative tilt of the stripon the n-side and on the p-side depends onthe requirements concerning the spatial resolutionfor each coordinate and possible constraint duethe overall assembly of the detectors. Doublesideddetectors are 2-D devices, which are veryattractive for many applications. One has to note,however, a very severe limitation of doublesidedstrip detectors with respect to the intensityof radiation that can be measured with thesedevices. The problem is illustrated schematicallyin Figure 4.5.10.Let us assume that two photons, marked asblack stars in Figure 4.5.10, hit the detector atthe same time. Simultaneity of two events isdetermined by the double pulse time resolutionof the readout system. The two photons willproduce signals in two x-strips and two y-strips.Reconstructing the hit positions by the signalsrecorded at the strips one arrives at four possiblecombinations, of which two correspond to realhits and the other two are fake hits, sometimescalled ‘ghosts’. Such ambiguity introduces a veryserious limitation on radiation intensity, which canbe measured by means of double-sided detectors.Employing a fine strip pitch one can obtain a veryprecise 2-D device for measurements of X-rays,however, this structure only suits applications withrather low radiation intensity.Edge-on Silicon Strip DetectorsAs discussed earlier, there are two basic limitationsassociated with silicon strip detectors,namely low absorption for higher X-ray energiesFigure 4.5.10 Ambiguity of position reconstruction in double-sided silicon strip detectors

STRUCTURES OF STRIP DETECTORS 263and large cross-section for scattering increasingwith increasing energy of X-rays. Both of thesedrawbacks can be overcome to a large extentby employing single-sided silicon strip detectorsin the so-called edge-on configuration. The ideais to illuminate the detector from the edge sothat photons enter the detector along the strips asshown schematically in Figure 4.5.11. The generatedcharge carriers are collected by the strips andthe backplane in the plane perpendicular to thedirection of the incident photon. The active areaof such a detector is small but when combinedwith a mechanical scanning system it can be usedas a large area high count rate 2-D device.In the edge-on configuration the effective thicknessof the detector is defined by the strip lengthand the strips can be made sufficiently long tocover 3 to 5 absorption lengths of X-rays ofgiven energy. One cannot, however, achieve 100 %efficiency in this configuration because of twoeffects: absorption in the dead layer; and scatteringof X-rays.In the edge-on configuration the dead layerappears to be one of the serious problems associatedwith detector construction. In the conventionalconfiguration, with photons entering the detectorfrom the strip side or the backplane side, the thicknessof the dead layer is of the order 1–2 µm andis practically negligible for X-ray energies above4 keV. In the edge-on configuration the strips cannotbe extended to the edge of the detector andthe dead layer is much thicker. After cutting asilicon wafer the edge of the detector is mechanicallydamaged within a distance of a few tensof micrometres, depending on the cutting technique.Due to mechanical damage the edges ofthe detector exhibit low resistivity and the highvoltage applied to the backplane appears on thestrip side of the detector. In order to avoid the surfaceleakage current flowing to the strips one needsto surround the strips with a guard ring structure.For a higher bias voltage one needs a higher distancebetween the strip ends and the edge of thedetector. Usually a multiple guard ring structureis employed in order to make the potential dropbetween the strips and the edge of the detector assmooth as possible. For typical silicon strip detectorsof 300 µm thickness the guard ring structureextends over a distance of about 500 µm from thedetector edge.Another limitation of efficiency in edge-ondetectors is due to scattering effects. The crosssection of such a detector perpendicular to thephoton paths is very small as it is determinedby the thickness of silicon. Thus, the majorityof scattered photons, except those scattered inthe very forward direction, escape the sensitivevolume of the detector. In a first approximation onecan estimate the efficiency from the ratio of thetotal scattering coefficient to the photoabsorptioncoefficient for given X-ray energy, shown inFigure 4.5.4. The ratio reaches 1 for X-ray energyof 50 keV, which means that maximum detectionefficiency can be about 50 % for that energy.Figure 4.5.11 Schematic structure of the edge-on silicon strip detector

264 POSITION SENSITIVE SEMICONDUCTOR STRIP DETECTORSThe edge-on configuration helps, however, toreduce the effect of scattering on the spatialresolution. The scattered photons mostly escape thedetector so that they do not contribute to the spatialresolution. A very small fraction of photons arescattered into the sensitive volumes associated withthe neighbouring strips but in a first approximationthis effect can be neglected. Accurate estimate ofeffect of scattering on the spatial resolution can bedone by full MC simulation for given X-ray energyand given detector geometry, as discussed before.One should note that in the edge-on configurationthe effect of diffusion on the spatial resolutionis decoupled from the absorption length since theabsorption length can be in the range of millimetresand the charge carriers diffuse only while travellingacross the distance equal to the detector thickness.From the illumination side an edge-on detectorlooks like a linear array of pixels, of whichdimensions are defined by the strip pitch in onedirection and by the thickness of silicon in theother direction. One can build a large area 2-Ddetection system by combining such a detectorwith a mechanical scanning slit. In scanningdirection one can improve the spatial resolutionby using a slit which is narrower that the detectorthickness. For example one can use a 100 µmwide scanning slit while the detector is typically300 to 500 µm thick. Using a narrow slit helpsto improve the spatial resolution, however, itrequires more steps in the scanning and increasesmeasurement time. An interesting idea has beenproposed recently to improve the spatial resolutionof silicon edge-on detectors by employing doublesidedstrips and using a timing structure of signalsread out on the p-side and the n-side strips(Cederström et al., 1999). The strips on bothsides of the detector are proposed to be laid outin parallel. The shapes of the signals inducedin the n-side and the p-side strips depend onthe distance from the photon absorption pointto the n-side and the p-side strips, respectively,due to the different mobility of electrons andholes. It has been shown by simulation that thesignificance of the timing information is sufficientto extract additional information about position,however, implementation of this idea requires quiteadvanced and sophisticated readout electronics.It is worth noting that edge-on silicon stripdetectors have been used successfully for imagingsystems using X-rays of 60 keV. A completeclinical apparatus for digital radiology using a 6 cmlong strip in edge-on configuration and a scanningslit system has been built successfully (Hiltet al., 2000). Edge-on detectors combined withmechanical scanning systems are also proposed tobe used as position sensitive detectors for digitalmammography using X-rays in the range of 20 keV(Arfelli, 2000; Mali et al., 2001).4.5.3.2 OTHER STRIP DETECTORSStrip detectors can be, in principle, made on othersemiconductor materials like Ge, GaAs, CdTe andCdZnTe. A significant difference between siliconand other semiconductor materials is due to differenttechnological processes used for manufacturingthe detectors. The position sensitive structures onGe, GaAs, CdTe and CdZnTe are developed atvarious research institutes but none of these developmentshas reached an industrial standard yet. Aconsequence of such a situation is that minimalstrip pitch achievable in strip detectors using thosematerials is rather large compared to what can beobtained in silicon technology. The limitation onthe minimal strip pitch is not only due to precisionof the strip patterns but also due to electricalseparation of the strips. The electrical character ofelectrode contacts in those detectors built on semiinsulatingmaterials is not always well defined.They can be either ohmic or Schottky contacts andelectrical separation of strips relies on very highintrinsic resistivity of the sensor material.High purity Ge is a good sensor material withrespect to many parameters and detection propertiesof this material are well understood. Thesingle-sided and double-sided Ge strip detectorshave been built, however, the smallest strip pitchreported is 2 mm (Protic et al., 2001). This hasbeen achieved by implementing amorphous semiconductortechnology for making the strip contacts.Such contacts exhibit blocking characteristics

READOUT ELECTRONICS 265under either polarity so that they can be used oneach side of a double-sided strip detector. A problem,which appears in such Ge strip detectors,is incomplete charge collection from the regionsbetween the strips. A common technique used toameliorate this effect is to add additional stripsbetween the charge sensing strips. The intermediatestrips are biased at some potential with respectto the charge collecting strips so that they shapethe electric field at the surface in such a way thatthe charge carriers are forced to move to the collectingstrips.The idea to use a timing structure of signalsinduced at the two sides of a double-sided detector,as mentioned earlier for edge-on silicon stripdetectors, has been implemented practically in Gedouble-sided detectors to make 3-D devices. Giventhat Ge detectors can be rather thick devices, of theorder of cm, the collection times of holes and electronsare long and it is relatively easy to measurethe difference in the collection time of electronsand holes, depending on the depth of photon interactionin the detector. The spatial resolution ofabout 0.5 mm in depth has been reported whenusing this technique (Wulf et al., 2001).While the high purity Ge detectors require coolingin order to reduce thermally generated leakagecurrent, materials like CdTe, CdZnTe and GaAsoffer the possibility of building detectors workingat room temperature since the leakage current issuppressed due to a relatively high energy band gap(1.6 eV for CdTe and 1.4 eV for GaAs). A basicproblem of those detectors, from the spectroscopypoint of view, is poor efficiency of holes collectionso that the amount of the collected chargedepends on the depth at which a photon interactswith the sensor material. Therefore, at thepresent stage of technology one can consider onlysingle-sided strip detectors built of these materials.The transport properties of these materialsare being continuously improved. Especially significantprogress has been made with respect toCdTe and CdZnTe resulting in room temperaturedetectors with spectroscopic performance comparablewith this of cooled high purity Ge detectors.The resistivity of these semi-insulating materialsis sufficiently high so that sufficiently high interstripresistance is obtained without implementingadditional separation structures. Employing CdTeand CdZnTe of very high resistivity the interstripresistance in the range of a few G has beenobtained for detectors with strip pitch as low as125 µm (Gostilo et al., 2001).One should mention at this point the coplanarstrip structure used in CdTe detectors, not necessaryfor position measurements. This is one of thetechniques employed to eliminate signals inducedby motion of holes in order to improve the spectroscopicresponse of CdTe detectors. The electrode isdivided into two groups of interleaved strips, eachgroup biased at different potential. The signalsfrom the two strip structures are then subtractedand that way the resulting signal corresponds tothe signal induced only by electron motion in theregion near the readout electrodes. This structurehas been shown to work effectively for improvingenergy resolution of CdTe detectors (He, 2001;Luke et al., 2001). It has been also employed forconstructing a 3-D position sensitive device basedon a single polarity signal (Macri et al., 2001).Because of technological limitations such structuresare usually realized with rather large pitchof about 1 mm.4.5.4 READOUT ELECTRONICSProgress in the development of position sensitivedetectors based on single-sided or double-sidedstrip structures is linked closely with progressin the development of the readout electronics.Advanced VLSI electronics and techniques ofdesigning and prototyping ASICs allow the integrationof a large number of channels in a singlechip. As discussed before, the technology of siliconstrip detectors offers the possibility of designingapplication specific detectors with respect tosize and strip geometry. Such an approach opensnew possibilities for optimizing experimental techniques.However, one has to keep in mind thatcustom-designed strip detectors require customdesignedreadout electronics, which in fact hasbecome a standard in the areas employing siliconstrip detectors. As the progress on other strip

266 POSITION SENSITIVE SEMICONDUCTOR STRIP DETECTORSdetectors built of Ge and CdTe results in smallerpitch, more advanced applications of those detectorsrequire custom-designed integrated readoutelectronics as well.There are two aspects of readout electronics,which should be addressed individually in eachparticular project, namely optimization of thefront-end electronics and the overall readout architecture.Depending on application one may requiregood spatial resolution as well as good energyresolution. For low-energy X-rays the charges generatedin semiconductor detectors are small and thenoise of the readout electronics can be a limitingfactor for energy measurements as well asfor position measurements. Concerning the readoutarchitecture one has to take into accountseveral aspects, like whether energy measurementsare required simultaneously with positionmeasurements, whether 1-D, 2-D or 3-D positionmeasurements are required and the intensity ofradiation. The readout electronics realized as anASIC gives opportunity to optimize the front-endfor each particular type of the detector and for eachparticular application.4.5.4.1 FRONT-END ELECTRONICSConventionally, front-end electronics is understoodas a preamplifier only. Employing ASIC techniqueone can integrate more functions in a readoutintegrated circuit (IC) connected directly to astrip detector. Usually a multi-channel front-endIC, in addition to preamplifiers, comprises alsoshaper circuits. In most advanced solutions frontendICs comprise also circuitry responsible for dataconversion and data storage. Regardless of overallcomplexity of an IC the basic problems associatedwith optimization of the front-end circuit aresimilar to those in conventional circuits.The noise performance of a front-end system isdescribed by the Equivalent Noise Charge (ENC)defined as the charge applied to the input in theform of a short δ-like current pulse, which givesat the output the signal amplitude equal to therms value of noise. For a typical configuration ofthe front-end electronics, comprising an integratorfollowed by a band-pass filter, the ENC is given as√F v vn 2 ENC =C2 t+ F i in τ 2τ p + F vf vnf 2 C2 t (4.5.7)pwhere C t is the total input capacitance includingthe capacitance of the input transistor, detectorcapacitance, feedback capacitance and any straycapacitance of the connection between the detectorstrip and the input of the preamplifier, vn2 is thespectral density of the equivalent input voltagewhite noise, dominated by thermal noise ofthe channel of the input transistor, in2 is thespectral density of the equivalent input currentnoise, dominated by the thermal noise of thefeedback resistor in the preamplifier, thermalnoise of the bias resistor in the detector andthe shot noise of the detector leakage current, vnf2is the spectral density of the equivalent inputvoltage flicker noise, dominated by the flickernoise of the input transistor, τ p is the peakingtime, i.e. the time at which the signal at thefilter output reaches the maximum, and F v , F iand F vf are factors dependent on the filter type.There are three immediate observations resultingfrom Equation (4.5.7), which are important foroptimization of the front-end circuit, namely:• contribution of the voltage white noise tothe ENC is proportional to the total inputcapacitance and inversely proportional to thesquare root of the peaking time;• contribution of the current noise is independentof the input capacitance and it is proportional tothe square root of the peaking time;• contribution of the voltage flicker noise to theENC is proportional to the total input capacitanceand independent of the peaking time.One can optimize the front-end system taking intoaccount various requirements and constraints of agiven application. There are two parameters, thedetector capacitance and the detector leakage current,which are determined by the detector andthey can vary over wide ranges. The total stripcapacitance seen by the input of the preamplifieris the sum of the capacitance of the stripto the backplane and the capacitance of a givenstrip to the neighbouring strips. Both components

READOUT ELECTRONICS 267are proportional to the strip length. For a smallstrip pitch the interstrip capacitance dominates.Given the large variety of possible geometricalarrangements of strip detectors one can have thedetector capacitance in the range from a fractionof pF, for strip lengths of a few millimetres,up to tens of pF for strip lengths of a fewcentimetres. In the first approximation the leakagecurrent per strip is proportional to the depletionvolume corresponding to a given strip and so itis proportional to the strip area. The leakage currentis, in addition, a strong function of temperatureand lowering temperature is a way to reducethe leakage current and the shot noise associatedwith it.Other parameters in Equation (4.5.7) are determinedby the front-end electronics. The first electronicsparameter to be considered is the peakingtime. One can distinguish two categories of applicationswith respect to the peaking time, low countrate and high count rate experiments. In the firstcategory we have experiments with such low rateof X-rays that there is practically zero probabilityof having a pile-up of consecutive pulses regardlessof the duration time of pulses in the shapercircuit. Another class of applications is constitutedby experiments in which the maximum peakingtime is limited by the intensity of X-rays.For low count rate experiments and for givenparameters of the detector and noise parametersof the front-end electronics one can find anoptimum value of the peaking, which yields aminimum value of the ENC. In practice suchan approach leads to reducing all parallel noisesources, including the shot noise of the detectorleakage current, as much as possible and shiftingthe peaking time towards longer values in orderto reduce the contributions from the voltage noisesources. For a system with current noise reduced tozero, Equation (4.5.7) gives infinite peaking timefor minimizing the ENC. In practice there arealways some current noise sources in the detectorand in the front-end electronics but for extremecases one can use peaking time in the range oftens of µs. In many applications, however, peakingtime in the range of a few µs is already consideredas a long one.In high count rate experiments the maximumvalue of the peaking time is a starting point foroptimization of the front-end system. In such applicationsusually one has to make a compromisebetween the count rate performance of the systemand the signal-to-noise ratio. One can take advantageof designing a fully custom detector systemand consider the detector segmentation at the sametime as the concept and parameters of the readoutelectronics. For the required total active area of adetector one can divide it into smaller or largerelements, e.g. shorter or longer strips in the caseof a strip detector. A smaller strip area helps forthe count rate problems in a twofold way: for agiven intensity of X-rays the count rate per stripis smaller, and a smaller strip capacitance helps toreduce the contribution of the voltage noise sourcesto the ENC.Another aspect associated with the count rateperformance concerns construction of the chargesensitivepreamplifier, in particular the scheme ofdischarging the feedback capacitor. A simplifiedblock diagram of a single front-end channelis shown schematically in Figure 4.5.12. Theinput stage is a charge-sensitive amplifier, whichconverts the current signals induced in the stripinto voltage steps. The feedback capacitance ischarged up by these signals and, for DC-coupledstrips, also by the detector leakage current. In orderto avoid the DC level at the preamplifier output toshift off the dynamic range one needs to dischargethe feedback capacitance, either after every pulseor in some solution after a number of pulses.There are two basic techniques used for dischargingthe feedback capacitance, continuous dischargeand switching reset, shown schematically inFigure 4.5.12. Continuous discharging can be realizedeither by a resistor in parallel to the capacitoror by a controlled current source. In either case thedischarging component contributes to the parallelnoise at the preamplifier input. In order to limit thisnoise source one should use a large value resistoror a low discharging current but then the decaytime constant of the preamplifier output signal islong and one still faces limitations on the pulse ratedue to pile-up. Thus, this option can be used eitherin low count rate systems or in systems where short

268 POSITION SENSITIVE SEMICONDUCTOR STRIP DETECTORSReset blockR F+Out′C FV TH−InK VA/D converterOut′′Preamplifier Shaper Data processing blockFigure 4.5.12 Block diagram of single readout channelshaping is employed in the shaper circuit followingthe preamplifier so that the contribution of the parallelnoise to the ENC is limited and one can uselower resistors or higher currents for dischargingthe feedback capacitors.Another way of discharging the feedback capacitoris to employ a switching circuit that periodicallyresets the capacitor. Such a solution iscommonly used in ASICs for readout of siliconstrip detectors in the collider type particle physicsexperiments, in which, if the signals appear, theyappear synchronously in all the channels. The triggersignal for discharging the capacitors is providedby the central clock of the experiment. InX-ray measurements the signals appear randomlyin time and independently in each channel. Afterreceiving a signal from the strip, the circuit hasto generate the trigger signal for discharging thecapacitor. In order to generate such a trigger signalone needs to implement a threshold discriminatorin every channel. Various schemes used for dischargingthe feedback capacitor are discussed indetail elsewhere (De Geronimo et al., 2001).The lowest level of noise optimization concernsthe details of the preamplifier design. The readoutelectronics realized in the form of an ASIC offersthe possibility to optimize the preamplifier circuitfor each particular type of detector and for eachparticular application. A first step in optimizationof the input transistor is to evaluate the level ofnon-reducible current noise, which comes from thedetector and possibly from the feedback resistor.Given the level of the current noise and therequired peaking time one can minimize thevoltage noise by proper choice of dimensions ofthe input transistor and proper bias current. Thisanalysis has to be done separately for preamplifierswith bipolar junction transistors (BJTs) used in theinput stage and for preamplifiers employing fieldeffect transistors (MOSFETs) as input devices. Inprinciple one should consider also the junctionfield effect transistor (JFETs), however, VLSItechnologies including JFET structures are veryspecial and not easily available. On the other hand,the main drawback of MOSFETs due to high 1/fnoise becomes less important as the quality ofCMOS processes improves.There are several basic facts concerning noisein these devices which should be kept in mind,namely:• the voltage noise of a BJT is independent of thetransistor area and is inversely proportional tothe collector bias current;• the current noise in a BJT is generated by thebase current and for given current gain factorβ it increases proportionally to the collectorbias current;• the voltage noise of a MOSFET depends onthe drain bias current I d and the dependencechanges from 1/ √ I d for transistors working instrong inversion to 1/I d for transistors workingin weak inversion;• the voltage noise of a MOSFET dependson transistor channel dimensions as √ (L/W )where L and W are the channel length and thechannel width, respectively;

READOUT ELECTRONICS 269• the input capacitance of a MOSFET is proportionalto the transistor gate area W × L.Due to the presence of parallel noise in the BJTsthey offer advantages compared to MOSFETs onlyin applications where short peaking times arerequired. In Bertuccio et al. (1997), one can finda detailed discussion of various design issues forfront-end circuits based on BJTs. In short, for givendetector capacitance and given peaking time thereis an optimum value of the collector bias currentin the input BJT that gives minimum of noise.In MOSFET based front-end circuits the noiseoptimization requires proper sizing of the inputdevice according to the detector capacitance. Asmentioned above the voltage noise can be reducedby increasing the W/L ratio, however, for a givenminimum value of the channel length L allowed bythe technology this requires increasing the channelwidth W and so the input capacitance of thetransistor. Thus, there is an optimum W/L ratiofor which one obtains minimum of noise.The range of peaking times, in which BJTs offerbetter noise performance compared to MOSFETs,depends on the detector capacitance. For a typicaldetector capacitance in the range 1 pF to 10 pFthe breakpoint is around 100 ns, i.e. for peakingtimes below that value BJTs offer better noiseperformance and for peaking times above thatvalue MOSFET are preferable. Another aspect,which may point to a BJT or a MOSFET, isthe power consumption. Generally, BJTs offerlower voltage noise compared to MOSFETs atthe same bias current and additional advantage inapplications in which the total power dissipation isa limitation. It is worth noting that with decreasingfeature size of modern CMOS processes therange of peaking times, in which MOSFETs offersuperior performance over BJTs, extends towardsshorter values of the peaking time.4.5.4.2 READOUT ARCHITECTURESSemiconductor strip detectors require that eachstrip is equipped with an individual electronicschannel. The ASIC technique allows one to buildmulti-channel front-end systems, as discussedin the previous sections. However, keeping inmind that experimental set-ups may comprisehundreds or thousands of strips, one cannotimagine to build systems with as many completespectroscopic channels working independently.For practical and cost reasons the number ofoutput channels has to be reduced at a certainstage. The multiplexing can be done either inthe front-end ASIC or in an external circuitry.Possible solutions depend on the intensity ofX-rays and on the requirements concerning theenergy resolution. In some solutions one can alsoimplement buffering of data and zero suppressionin the front-end ASICs.From the point of view of system architectureused to read out silicon strip detectors one candistinguish two basic classes of systems: systemsfor position measurements only and systems forsimultaneous position and energy measurements.In various imaging techniques employing monoenergeticX-rays it is sufficient to measure spatialdistributions of X-rays of energies above a giventhreshold, or within a given energy window. Forsuch applications one can use the binary readoutarchitecture. In this scheme each front-end channelis equipped with a threshold discriminator ora window discriminator and delivers only binary(yes/no) signals. If simultaneous measurements ofenergy and position are required one has to preserveinformation on pulse amplitudes. As today, itis not feasible to integrate an individual high resolutionanalogue-to-digital converter (ADC) in eachchannel of the front-end ASIC. The constraints areassociated with the total area of an IC and with thepower consumption. However, if the requirementsconcerning resolution of the ADC are not verydemanding one can implement a simple low resolutionADC in each channel. One of the proposedsolutions is based on the so-called time-overthresholdmethod. Otherwise one has to multiplexsome number of channels into a single ADC whichcan be either integrated in the front-end ASICor can be an external device. The three possiblesystem architectures are shown in Figure 4.5.13.In the binary architecture the informationdelivered by a strip detector is suppressed to a

270 POSITION SENSITIVE SEMICONDUCTOR STRIP DETECTORSV IN1+V TH −V IN2V IN3V INn +V TH−CounterCounterOut1OutnDigital multiplexer n:1Data out(a)DACControlblockV IN1 +V TH−V IN2V IN3V INn +V TH−ToT counterToT counterOut1OutnDigital multiplexer n:1Data out(b)ClockV IN1+V TH−DelayV IN2V IN3V INn+V TH−PeakstretcherPeakstretcherDelayC H1Out1C HnOutnAnalogue multiplexer n:1Data outADC(c)Figure 4.5.13 Three possible schemes of readout of strip detectors: (a) binary architecture; (b) analogue architecture employingtime-over-threshold method; (c) analogue architecture employing multiplexing of analogue signals

READOUT ELECTRONICS 271minimum already in the front-end circuit. This is asignificant advantage in systems comprising hundredsor thousands of channels as one can storethe data in the front-end ASIC for a period of timerequired for performing the measurement. ASICswith binary readout architecture have been developedand used successfully to read out silicon stripdetectors in diffractometry measurements (Comeset al., 1996; Gryboś andD¸abrowski, 2001; Grybośet al., 2002). The RX64 IC (Gryboś et al., 2002)is a complete binary readout ASIC, which comprises64 functionally independent channels, eachbuilt of the front-end circuit, threshold discriminatorand 20-bit counter. The capacity of counters issufficiently large so that one can store all the datafrom one measurement session and then read outthe data into an external data acquisition system. Inthis scheme the intensity of X-rays is limited onlyby possible pile-ups in each individual front-endchannel. Using this IC for readout a strip detectorwith 100 µm strip pitch, a count rate of 100 000random pulses per second and per strip has beenachieved (Gryboś andD¸abrowski, 2001).Although the binary system does not providedirect information on the energy of X-raysthe noise performance and energy resolution areequally important as in the spectrometric systemsbased on analogue readout schemes. One needs agood signal-to-noise ratio in the front-end circuit tobe able to set the discrimination threshold at a levelwhich is sufficiently high to suppress the rate ofnoise counts to a negligible level, and at the sametime, sufficiently low to provide full efficiency forX-rays of given energy. In more complex measurementsone may have X-rays of several energies, orlike in experiments employing X-ray tubes, a continuousspectrum in addition to a distinct energyline. In such applications a window discriminatormay be required instead of a single threshold discriminator.An issue, which is very specific for binaryreadout architectures, and is as important as noiseperformance, is the matching of analogue parameters,like gain, noise and discriminator offset, forall the channels in a multi-channel ASIC. Thisis due to the fact that the only practical way tocontrol the discriminator threshold in such an ICis to apply a common threshold to all channels.Thus, variations of gain and/or discriminator offsetwith respect to the nominal values affect thenoise counts and efficiency in a similar way as thenoise of a given channel.Even with a simple circuit with a single thresholddiscriminator one can extract spectroscopicinformation by scanning the threshold and measuringthat way the integral distribution of pulseamplitudes. An example of such measurementsperformed by means of the ASIC described inGryboś et al. (2002) is shown in Figure 4.5.14.The plot shows complex X-ray spectra derivedfrom integral ones measured simultaneously in 64channels of the readout ASIC. One can noticethat the spread between channels is really smallerthan the noise of each particular channel. Thedifferences of intensity in different channels aredue to a particular distribution of X-ray intensityacross the strips of the detector. Such measurementsare essential for diagnostics of the systemand for optimizing threshold setting for positionmeasurements.In some applications of strip detectors for positionsensitive measurements the requirements concerningenergy resolution are not very demanding.In fact, for detection systems working at roomtemperature usually one cannot achieve the energyresolution like in dedicated high resolution X-rayspectrometers. The requirements for the resolutionof an ADC used for measurements of signalamplitudes are moderate and 6 to 8 bits can besufficient. A simple scheme to extract informationon signal amplitudes is based on the time-overthresholdprinciple (Becker et al., 1996; Manfrediet al., 2000). The idea is illustrated schematicallyin Figure 4.5.13(b). The analogue signal from thefront-end circuit is applied to a simple thresholddiscriminator like in the binary scheme. The durationtime of the discriminator response is measuredin a simple way by counting pulses from a clockgenerator over the period equal to the duration ofthe discriminator response. The width of the discriminatorresponse depends on the relative amplitudewith respect to the threshold and so containssome information about the signal amplitude. Aresponse function of such a system is nonlinear,

272 POSITION SENSITIVE SEMICONDUCTOR STRIP DETECTORS40003500T = 300KU, Lb 117.2 keV3000Counts25002000U, La 113.6keV15001000Fe, Ka 16.4keVU, Lg 120.1keV50000100200 300Threshold (mV)400 500Figure 4.5.14 Spectra of Pu-238 radioactive source and Fe Kα line measured simultaneously in 64 strips of a silicon strip detectorread out by a 64-channel ASIChowever, for a given pulse shape from the shapercircuit, it is well defined.A main advantage of such a scheme is itssimplicity and low power consumption that allowsone to implement it in every channel. One can,however, notice easily basic limitations of thisscheme, like the measurement range being limitedby the discrimination level, low accuracy forsmall signals just above threshold, sensitivity totime jitter of the discriminator, especially for lowamplitudes. The scheme has been implemented inan ASIC used for readout of silicon strip detectorsin a particle physics experiment. Let us note thatin the scheme shown in Figure 4.5.13(b) there isno capability to store data for more than one eventin the front-end ASIC. Thus, one needs either tomultiplex all the channels into one serial output, orelaborate a scheme of sparse readout (Feuerstack-Raible, 2000).A fully analogue readout scheme, employinga true ADC, is shown schematically inFigure 4.5.13(c). In this scheme each channel isequipped with a peak detector and a sample andhold (S&H) circuit. Such schemes are commonlyused in synchronous experiments where an externaltrigger signal, common for all the channels, isavailable. In applications to X-ray measurementsone needs to implement a threshold discriminatorin each channel to generate a trigger signal for theS&H circuit in each channel independently. Theanalogue signals from some number of channelsare then multiplexed into one ADC, which in mostcases is an external device, although one can considerto integrate it in the front-end ASIC. In sucha scheme the intensity of X-rays is limited by themultiplexing rate and the speed of the ADC andnot so much by the shaping in the front-end circuit.There is an obvious trade-off between the intensityof X-rays and the number of channels multiplexedinto one ADC. In experiments with high X-rayintensity one can reduce the number of channelsper ADC and increase the number of ADCs inthe system.Another aspect specific for such an architectureconcerns control of the multiplexer and the ADCoperation. One can either run the multiplexer andthe ADC continuously (Fiorini et al., 2001), allowingfor some probability of pile-ups in the S&H circuits,or trigger the multiplexer and the ADC upona signal occurring in the detector (Overdick et al.,1997). The most commonly used scheme is basedon an OR (logical sum) gate taking inputs from allthe channels. Then each signal occurring in any ofthe channels triggers the readout sequence.One should keep in mind the fact that readoutASICs with architectures as shown in Figure 4.5.13

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Chapter 5Special Configurations5.1 Grazing-incidence X-ray SpectrometryK. SAKURAINational Institute for Materials Science, Ibaraki, JapanRecent advances in grazing-incidence X-ray spectrometry(XRS) cover several important analyticaldirections, such as ultra trace element analysisusing total reflection X-ray fluorescence(TXRF) and surface and interface analysis of layeredmaterials by angular and/or energy resolvedX-ray fluorescence measurements, as well as theircombination with X-ray reflectometry. Anothersignificant recent innovation in grazing-incidenceXRS is micro X-ray fluorescence imaging withoutscans.5.1.1 WHY GRAZING-INCIDENCEX-RAY SPECTROMETRY?For many years, since the discovery by Roentgenin 1895, X-rays have been extensively used asa tool for the nondestructive investigation offairly thick materials. This is because of therather high transmission power of X-rays, whichis usually expressed by penetration depth, i.e.the depth that the incident X-rays attenuate as1/e of the initial intensity. The penetration depthdepends on the kind of materials as well asX-ray energy; for most materials, it is in theorder of µm–cm for 5–50 keV X-rays. If suchtransmission power can be controlled freely, itshould be possible to create a number of novelopportunities for materials analysis using XRS.The use of external total reflection for a flat andsmooth surface, which was first discovered byCompton in 1923, 1 is one of the most promisingways. The critical angle of the total reflectionis usually very small, as listed in Table 5.1.1.The penetration depth becomes extremely shallow,typically 1–100 nm near the critical angle, leadingto the technique even becoming surface sensitive.Since the X-rays impinge almost parallel to thesurface, the technique is generally called grazingincidenceXRS.Table 5.1.1 Critical angles of variousmaterials for 0.155 nm (8.0 keV)X-rays (mrad)Silicon 3.92Glass 3.80Aluminium 4.13Titanium 5.23Chromium 6.54Iron 6.72Nickel 7.01Copper 7.02Silver 7.70Tungsten 9.61Gold 9.70Platinum 10.5X-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

278 GRAZING-INCIDENCE X-RAY SPECTROMETRYAnother possible method for reducing the5.1.2 MODERN TOTAL REFLECTIONof multilayers 15 and/or capillary optics. 16,17 semiconductor companies in Silicon Valley had aX-RAY FLUORESCENCEbackground and improving the detection limit isto use polarized radiation in order to decrease theThe most popular grazing-incidence XRS hasundoubtedly been TXRF spectrometry, ever sincethe first experiment reported by Yoneda and Horiuchiin 1971. 2 In short, such experiments can beconsidered as X-ray fluorescence analysis of particulatesamples, deposited on a flat and smoothsubstrate, with the excitation radiation reachingthe substrate at an angle below the critical angleof total reflection. The advantage of using atotal reflection mirror as a sample support is aremarkable upgrading of the detection power fortrace elements due to the significant reductionof scattering background from the substrate. Thetechnique has been continuously developed, 3,4 andhistorical progresses have been compiled in severalscattered X-rays. When the primary beam has alinear polarization and the detector is placed inthe plane of the polarization vector, the scatteringintensity is proportional to 2 cos 2 φ(r/R) 2 +sin 2 φ(r/R) 4 , while fluorescent X-rays are simplylinear to (r/R) 2 ,wherer and R are the detectorradius and the distance from the beam to the centerof the detector, respectively, and φ is the scatteringangle (the angle between the primary and scatteringbeams). 18 This means when φ approaches90 ◦ , by reducing the solid angle of the detector,the ratio of fluorescent and scattering intensity canbe improved.The advent of the synchrotron radiation (SR)source has had an extremely significant impact ontextbooks, 5,6 and also in the series of pro-the development of the TXRF technique. This X-ceedings of international conferences, 7–13 which ray source has unique properties, such as a highhave been successively held every 2 years since1986. Recently, an interesting account reviewingthe TXRF activities of a leading Austrian researchintensity, a very low angular divergence, energytunability, and a high degree of linear polarization.Following the first experiment performed ingroup over the past 30 years has been published. 14 Japan, 19 a number of TXRF studies have beenIn the early days of TXRF, white X-rays from atube were usually used for excitation, as in the caseof ordinary X-ray fluorescence. Since the criticalangle is a function of the X-ray energy, higherenergyX-rays are most likely to penetrate thesubstrate to generate background. In 1984, Iidaand Gohshi demonstrated that monochromatizingexcitation radiation was effective in reducingunnecessary X-ray photons efficiently, resulting inan upgrading of the detection power for TXRF. 4In their experiment, a Si(111) monochromator wasused for selecting Cu Kα 1 . TXRF experimentsessentially require a very narrow collimated beameven when white X-rays are used, because ofshallow angle irradiation. Their idea was thatintroducing a crystal monochromator, which limitsangular divergence of the beam, does not cause asignificant intensity loss for the required energyX-rays (Cu Kα 1 ). Subsequently, the use of amonochromator for primary photons became themost common, and many kinds of improved opticshave been developed. The recent trend is the usedone using SR at almost all facilities worldwide.One of the most important applications is theultra trace determination of the surface contaminationof semiconductor wafers. In the late 1990s,a detection limit in the order of 10 8 atoms/cm 2 wasachieved for transition metals at Hamburg (HASY-LAB/DESY), Stanford (SSRL) and Tsukuba (PhotonFactory). At that time, such a trace levelwas almost the limit for other promising formsof chemical analysis, such as inductively coupledplasma mass spectrometry (ICP-MS) and atomicabsorption spectroscopy (AAS), and therefore thedetection power of SR-TXRF was a breakthrough.The successful analysis of ultra trace Ni on a Siwafer, for which the detection limit was 13 fg, waspublished in 1997 by an Austrian group. 20So far, synchrotrons have been used mainly byuniversities, and usually most beamlines are sharedfor different experiments. However, for specificindustrial applications, such as wafer analysis, itis extremely important to construct a dedicatedbeamline and experimental station. In Stanford,

MODERN TOTAL REFLECTION X-RAY FLUORESCENCE 279successful pioneering project. 21 They developeda dedicated instrument with an ultra clean environment,and recently reported very competitiveresults. 22 The 3rd-generation SR source 23 is obviouslyattractive for such applications. In ESRF,Grenoble, a new sophisticated beamline and spectrometer(Figure 5.1.1) for wafer analysis by TXRFhas come onstream, 24,25 making it the future worldcenter for this kind of activity. Another directionfor industry is to use a compact synchrotron. 26 Theadvantage would be flexibility in the design of analyticalinstruments and the rather short distancefrom source to sample, leading to high efficiency.When the sensitivity is such that ultra traceelements can be detected, parasitic X-rays caneasily come into the spectrum as a result ofcontamination. Therefore, the use of a clean roomis highly desirable for both sample preparationand measurement. As is often the case withmultipurpose beamlines, it might be difficult tohave a clean hutch. Figure 5.1.2 shows one exampleof a clean TXRF spectrometer used at BL39XU,SPring-8. 27,28 A compact clean booth with an airfilterunit is fitted to the spectrometer. The vacuumchamber is made of resin, and no metallic parts areused around the sample. If such clean equipment isnot used, the sample surface is easily contaminatedby air-particulates from the environment at theexperimental hutch, as shown in Figure 5.1.3. Insome cases, even one particle attached onto the areabeing analysed can distort the experiments.Vacuumenclosure300 mmSi waferWafer positioninghexapode7 elementsSi:Li arrayshnEWaferrotationMain systempositioning hexapodeFigure 5.1.1 TXRF measuring chamber at ID27, ESRF (Grenoble, France). (Reprinted from Comin et al., 24permission from Elsevier Science)Figure 2, with

280 GRAZING-INCIDENCE X-RAY SPECTROMETRYAir-filter unitClean-boothPlasticvacuum chamberSampleSRGoniometerSi(Li)detectorFigure 5.1.2 Clean environment for TXRF experiments at BL39XU, SPring-8 (Harima, Japan)10 5 2 4 6 8 10 12 14Intensity (counts)10 410 310 2SiContamination by air-particulates atOrdinary TXRFthe experimental hatchFeKa NiKaCrMnCl KCaS Ar TiKaKbKbCu NiKbScat.10 110 00TXRF using a cleanboothinside the hatchEnergy (keV)Figure 5.1.3 Influence of parasitic X-rays in TXRF experiments. Spectra of a blank Si wafer measured at BL39XU, SPring-8(Harima, Japan). Clean instruments are crucial to prevent contamination of the sample caused by air-particulates in the environmentat the beamline

MODERN TOTAL REFLECTION X-RAY FLUORESCENCE 2814 axes for scanningX-ray energyYAP:Ce scintillationdetectorCurved crystalJohansson Ge (220)Receiving slitRowland circleR = 120 mm(flexible)SREntrance slitSampleVac. chamber4 axes for alignment andpositioning of the sampleFigure 5.1.4 Schematic view of the Johansson TXRF spectrometer. (Reprinted with permission from Sakurai et al., 29 Figure 1.Copyright (2002) American Chemical Society)One of the biggest challenges overcome veryrecently in terms of instruments is the developmentof an efficient wavelength-dispersive spectrometerfor TXRF applications. 29 The employment of a compactJohansson-type spectrometer (Figure 5.1.4)rather than a conventional Si(Li) detector, as well asthe use of a quasi-monochromatic undulator X-raysource, can completely change the quality of X-ray fluorescence spectra. Typical spectra are shownin Figure 5.1.5. The energy resolution becomes 20times better, which effectively contributes to reducingthe low-energy tail of the scattering backgroundand to separating neighboring X-ray fluorescencepeaks. One can note that even some chemical effectshave become visible in Kβ spectra. Another advantageof this wavelength-dispersive system is itscapability with respect to high-counting-rate measurements,which makes possible the detection ofweak signals from trace materials. The absolute andrelative detection limit for nickel are 0.31 fg and3.1 ppt for a 0.1 µl droplet of pure water, respectively,which is nearly 50 times better than thecurrent best data achieved by conventional energydispersiveTXRF using a Si(Li) detector system.Another significant direction of modern TXRFtechniques is light element analysis. The useof SR is again significant for this application.Figure 5.1.6 shows typical TXRF spectra for Na,Mg and Al on a Si wafer, obtained at BL III-4as well as at BLIII-3, SSRL, Stanford. 30,31 Thedetectors used are HPGe and Si(Li) with an ultrathin (∼200 nm) polymer window, which providesvery low attenuation for the entering X-rays.However, Raman scattering causes backgroundenhancement as indicated in the figure. The detectionlimit was around 0.1 pg, even for Na and Mgas listed in Table 5.1.2. Even B was successfullydetected by using the top layer of carbon of themultilayer as a reflector. The activities are nowmoving to the undulator beamline at BESSY2, inBerlin, leading to further advanced results; detectionlimits for C and N were 0.5 and 0.8 pg,respectively. 32 A further challenge comes withthe introduction of high-resolution detectors, suchas STJ and other cryogenic detectors. Recently,Beckhoff has investigated the technical details forobtaining excellent X-ray spectra in the low energyregion. 33

282 GRAZING-INCIDENCE X-RAY SPECTROMETRYX-raySampleFe, Ni, Co 20ppb0.1 µl5 s/point30 000Substrate25 000Ni Ka 1Intensity (counts)20 00015 00010 0005000Co Ka 1FWHM7.06 eVNi Ka 2Fe Ka Co FWHM1Ka6.62 eV2Fe FWHMKa 5.71 eV2FeKb 1,3 Co Kb 1,3063506400 6450 6900 7000 7100Energy (eV)7400 7500 7600 7700Figure 5.1.5 Wavelength-dispersive TXRF spectra for trace elements (Ni, Co, and Fe, 20 ppb each) in a 0.1 µl drop. (Reprintedwith permission from Sakurai et al., 29 Figure 2. Copyright (2002) American Chemical Society)50004000BL3–4 (100 mA)BI 3–3 (100 mA)Raman peak1.7 keVscatter3000AlSiCts/chn20001000NaMg000.5 1Energy (keV)1.5 2Figure 5.1.6 TXRF spectra of 50 pg Na, Mg and Al as a droplet on a Si wafer. Solid and dashed lines were obtained at BLIII-4using filtered white radiation by a Si filter and at BLIII-3 with a multilayer monochromator, respectively. The spectra werenormalized to 100 mA and 100 s counting time. (Reprinted from Streli et al., 31 Figure 8, with permission from Elsevier Science)

SURFACE AND INTERFACE ANALYSIS OF LAYERED MATERIALS 283Table 5.1.2 Sensitivities (S) and extrapolated detection limits(LLD) for low-Z elements performed at beamlines III-4 and D(θ) = λIII-3, SSRL (Stanford, USA) aBL III-4BL III-3S (cps/ng) LLD (pg) S (cps/ng) LLD (pg)A =Na 591 0.541 4769 0.127Mg 1045 0.277 4740 0.189Al 614 0.815 11989 0.081a Beamline III-4, filtered white radiation by a Si filter; beamline III-3,equipped with a multilayer monochromator. The data are normalized to100 mA beam current.Reproduced with the permission of Streli et al. 31 ,Table2.5.1.3 SURFACE AND INTERFACEANALYSIS OF LAYERED MATERIALSModern grazing-incidence XRS often uses theangular dependence of X-ray fluorescence intensityto explore the depth/height distribution ofthe elements, besides determining the averageconcentration. The angular dependence of X-rayfluorescence intensity from the element, I f (θ) isgiven using the depth profile of the element C(z)and the X-ray intensity distribution in the sampleI(θ,z) as follows:∫whereI f (θ) ∝ I(θ,z)× C(z)dz (5.1.1)This indicates that the unknown C(z) can bebasically calculated back from Equation (5.1.1)using both the experimentally observed I f (θ)and the theoretically given I(θ,z). After somepioneering depth profiling work in the 1980s, 34,35a lot of research has addressed this problem.If the sample is just a uniform substrate, thesituation is rather simple. When primary X-raysimpinge on the surface at grazing incidence,reflection and refraction take place simultaneously.Refracted X-rays propagate as an evanescentwave, 36 and the intensity at depth z (z >0) canbe expressed as follows using a glancing angle θ,X-ray wavelength λ, and real and imaginary partsof the refractive index δ and β:(I(θ,z) = S(θ) × exp −z )(5.1.2)D(θ)4θ 2where S(θ) =(θ + A) 2 + B 24πB√ 2√(θ2− 2δ) 2 + 4β 2 + (θ 2 − 2δ)B = β AFurthermore, during the total reflection, the primaryand reflected X-rays are interfered withabove the surface, and therefore a modulation ofthe X-ray intensity is caused at the same time. TheX-ray intensity at distance z (z

284 GRAZING-INCIDENCE X-RAY SPECTROMETRYwhere(a n = exp −i kf )nd n2b n = exp[−ikf n (z − d j )]f n = √ (θ 2 − 2δ n ) − i(2β n )k = 2π λFigure 5.1.7 shows an example of the calculatedinternal X-ray electric field expressed as a functionof both depth and glancing angle. 44 The sampleassumed is a Cu[100 Å]/Ag[230 Å]/Au[500 Å]/Sithin film, and iron[3 Å], chromium[6 Å] andtitanium[18 Å] are put at the surface and each interface,respectively. Interference oscillation is understoodvisually, and one can see that the intensityat 7 mrad is highest at the surface and exponentiallydecreases. This angle is therefore still inthe evanescent wave region because of the shallowpenetration. However, at 8 mrad, the distributionbegins to change because of the interferenceeffect. The oscillation becomes clear at 9 mradand further changes at 10 mrad. In these ways,the interference effect is expected to cause oscillationof intensity at the surface and interfaces as theIntensity4200Depth (Å)200(a)400510Glancing angle (mrad)15X-Ray intensity42CuAg7 mrad8 mrad9 mrad10 mradAu0(b)0100 200 300Depth (Å)Figure 5.1.7 Calculated internal X-ray intensity distribution in Cu/Ag/Au thin film. (a) Three-dimensional representation.(b) Depth profile for 7, 8, 9 and 10 mrad incidence. (Reprinted from Sakurai and lida, 44 Figures 5 and 6, with permissionfrom Kluwer Academic/Plenum publisher)

SURFACE AND INTERFACE ANALYSIS OF LAYERED MATERIALS 285angle increases. The corresponding experimentaldata are shown in Figure 5.1.8. One can see thatthe integrated fluorescent signal intensity peaksat a different angle with oscillation. Furthermore,when a certain interface is enhanced, the X-rayintensity at the neighboring interface is decreased.When the chromium signal reaches maximum,iron becomes weak, and as the titanium peaks,chromium becomes weak. Grazing-incidence XRSis obviously surface-sensitive at a low angle, butthe technique can be extended further to exploreinterfaces by carefully tuning the glancing angleso as to obtain maximum enhancement.When the thin film is a periodic multilayer, moderngrazing-incidence XRS can analyze the depthposition of trace impurities by using a standingwave generated around the Bragg diffraction condition.The technique has been often used for thedetermination of the atomic position of impuritiesin the crystal as well as of adsorbed molecules onthe surface. 45,46 This method is based on dynamicaldiffraction theory, and therefore the main applicationsare performed for perfect crystals, butexperiments are also possible for multilayers. 47Figure 5.1.9 shows an angular profile of the specularreflection, as well as X-ray fluorescence fromthe trace metal (Fe) for a Ni/C multilayer (2d =9.76 nm), which is a promising optical device forsoft and hard X-rays. A discontinuous change ofFe Kα intensity is apparent at around the Braggpeaks (16.5, 31.9 mrad). As shown in Figure 5.1.10,a comparison with the calculation based on thedynamical diffraction clarifies that the Fe impurityis almost uniformly distributed in the Ni layers, andis not present in the C layers. The result is quiteinteresting when considering the origin of the traceimpurities in the fabrication process. In this way,the X-ray standing wave technique is used for analyzingthe depth position of trace metals within 1periodic unit of the multilayers.Another important trend in modern grazingincidenceXRS is combined analysis of fluorescentX-rays and X-ray reflections. 48 In short, X-rayreflectometry is a θ/2θ scan in a very low angleregion, and not such a difficult experiment, but itcan provide plenty of information on the surfaceand layered structures, i.e., layer thickness, surfaceand interface roughness, density of the near-surfaceCrDRef.ICICX-Ray intensity (a.u.)FeSRMCuAgAuSiTi× 205 10Glancing angle (mrad)15Figure 5.1.8 Experimental angular plot of reflectivity and integrated X-ray fluorescence intensities of iron, chromium and titaniumfrom the surface and interfaces of a Cu/Ag/Au thin film. (Reproduced with permission of Plenum Press, 44 Figure 4)

286 GRAZING-INCIDENCE X-RAY SPECTROMETRYX-Ray intensity (norm.)Ni/C (2d = 97.6 Å)Max. 22063 cts.CrSi ArFeScat.1st(a)2Intensity (counts)468Energy (keV)(b) SpecularscatteringIntensity modulation causedby standing wave10 410 32ndFe Ka10 2B = 16.5 mradB = 31.9 mrad010 20 30 40 50Angle (mrad) q/2q (q i = q s )Figure 5.1.9 X-Ray standing wave for Ni/C multilayer (2d = 9.76 nm). (a) X-Ray fluorescence spectra. (b) Angular profile ofX-ray reflectivity and iron Kα fluorescenceregion, density profiles along the depth, and detailsof the periodic and non-periodic multilayer structures.A very important feature of the X-ray reflectivitytechnique is that it is not very sensitiveto crystal structure, dislocations and defects, soit can be used for probing single crystals, polycrystallinesamples, amorphous materials, and evenliquid samples. This is because the signal dependsonly on the electron density of the studied material.However, this also has a negative aspect,namely the technique cannot distinguish betweeninterface roughness and interface grading (i.e. diffusion,implantation, etc.), which both give almostthe same influence on the X-ray reflectivity curve.Combining the technique with grazing-incidenceXRS could help in the understanding of such problems.Further detailed analysis comes with theextension to the combination with non-specularreflections (diffuse scattering), 49,50 which are weakscattering observed around the strong specularreflection spot, and also grazing-incidence smallangle X-ray scattering (GISAXS). 51,52 In the early1990s, de Boer and his co-workers contributedsuccessive systematic publications on both thedetailed theoretical formulation and experimentalapplications of the angular dependence of X-rayfluorescence as well as specular and non-specularreflections. 53–56 One of their most significantworks is the study on the influence of the interfaceroughness on X-ray fluorescence intensity from

MICRO X-RAY FLUORESCENCE IMAGING 287Si(Li)detectorX-RayDetector4Ni/C interfaceq i q s3(a)24CNiCNiCNi·Si31Iron Ka fluorescence intensityprofile indicating that ironimpurities are included onlyin nickel layers ( ).X-Ray intensity (a.u.)321Ni layerC/Ni interfaceC layer48.8 ÅDepth(b)140Ni 120C100Ni80C60420 18.017.517.016.516.015.515.0AngleReflectivity15.0 15.5 16.0 16.5 17.0 17.5 18.0Glancing angle (mrad)(c)Figure 5.1.10 Calculation of angular dependence of X-ray fluorescence. (a) Basic idea of the X-ray standing wave technique.(b) Three-dimensional map for X-ray electric field intensity in the multilayer. (c) Angular profile for X-ray fluorescence forimpurity iron segregated at: (1) center of the C layer; (2) C/Ni interface; (3) center of the Ni layer; (4) Ni/C interfacelayered materials. 57 The theoretical work employsdistorted-wave Born approximation (DWBA) up tothe second-order, and X-ray fluorescence intensityhas been expressed using morphological parameterssuch as interface rms roughness, lateralcorrelation length, jaggedness parameter, and theperpendicular correlation length. For a Gaussiandistribution of interface heights, the refractiveindexprofile is an error function, with the resultthat the Helmholtz equation cannot be exactlysolved. The breakthrough has come with finding asuitable approximation (see Figure 5.1.11) insteadof trying to introduce a profile that can be solvedexactly (like a tangent hyperbolicus). The properselection of the starting point is significant here,and it was found that the use of graded interfaces(i.e. the roughness is modelled with a packof smooth slices) allows a correct modelling forcalculation of the X-ray fluorescence. The influenceof the second order of DWBA is also animportant problem for cases where the lateral correlationlength is fairly large.5.1.4 MICRO X-RAYFLUORESCENCE IMAGINGRecently, microscopic imaging has been performedby grazing-incidence XRS, which usuallymeasures spatially average information. So far,imaging of X-ray fluorescence has been basedon step-scans with a collimated beam (∼µm,or smaller if 3rd generation SR is available).However, it requires long measuring time, especiallywhen pixel numbers increase to enhance thequality of the image. A novel approach toward

288 GRAZING-INCIDENCE X-RAY SPECTROMETRY[Image not available in this electronic edition.]Figure 5.1.11 Possible errors in the calculation of X-ray electric field intensity distribution along the depth. The differenceis caused when considering the influence of roughness. X-Ray intensity vs depth for Cu Kα radiation with a perpendicularwave vector k = 0.375 nm −1 on a gold sample with a rms roughness of 1.5 nm. Dash-dotted line, no roughness; solid line,calculated using conventional Nevot–Croce factors; long-dashed line, the present approximation; short-dashed line, calculatedfor error–function profile using the slice method. (Reproduced with permission of de Boer, 57 Figure 2)much more rapid X-ray fluorescence imagingcomes with a combination of grazing-incidencegeometry (∼2 ◦ ) using a rather wide beam (∼cm)and parallel optics for detecting X-rays by atwo-dimensional detector. 58,59 A combination ofa charge-coupled device (CCD) camera and collimatorscan be used for micro X-ray fluorescenceimaging of µm scale resolution. Figure 5.1.12shows typical examples of X-ray fluorescenceimaging obtained with a normal bending magnetsynchrotron source (BL-4A, Photon Factory,Tsukuba, Japan). Although the spatial resolutionis only around 20 µm, it should be noted thatimaging with approximately 1M-pixels can be performedin only 1–2 min, or even less. One can seedetailed patterns of the precipitation of metalliccrystals, aggregation to the specific part in the tissue,and segregation at the mineral interfaces. 60Although it is possible to perform the experimentswith a laboratory X-ray source, the use oftunable monochromatic or quasi-monochromaticsynchrotron X-rays is promising with respectto the selective excitation of the elements containedin the specimen. A further advantage wouldbe the availability of more specific imaging,in addition to information on normal chemicalcomposition, like chemical states and local structure,by making use of the X-ray absorption finestructure. 615.1.5 FUTURE OUTLOOKRecent trends in grazing-incidence XRS have beenoverviewed. In spite of the century-long historyof X-rays, this field seems to be still growingrapidly. New X-ray synchrotron sources, suchas X-ray free electron laser (XFEL) based onSASE (Self Amplified Spontaneous Emission), 62and ERL (Energy Recovery Linac), 63 are now inthe design stage, and will commence initial operationno later than 2010. Those sources are like

FUTURE OUTLOOK 289X-Ray image4.8 mm12 mmOptical microscope image(a)X-Ray image4 mm12 mmView areaOptical microscope image(b)Figure 5.1.12 Micro imaging using grazing incidence XRS. (a) Metallic Cr thin film on glass substrate. Incident X-ray energy7.2 keV. Exposure time 50 s. (b) Metallic Ag crystals precipitated from salt solution. Incident X-ray energy 7.3 keV. Exposuretime 10 min

290 GRAZING-INCIDENCE X-RAY SPECTROMETRYa laser in the visible light, and have a furtherhigh peak as well as average brilliance with anextremely short pulse structure. Future grazingincidenceXRS will use the coherence and thepulse structure of the source. The technique willnot remain as a one or two-dimensional probe,at least three-, or maybe four- (including timeaxis)dimensional experiments will become performed.The TXRF technique will be widely usedfor many industrial and environmental applicationsbecause of its extremely high detection power.New chemistry in ppt or in ppq range will beopened up. It will be crucial to perform the experimentswith ultra clean instruments in a dust-freeenvironment. Another important direction of futuregrazing-incidence XRS is more advanced surfaceanalysis, by combining several grazing-incidenceX-ray techniques and other microscopic probes forsurface phenomena. Its capability with respect toexploring buried nanometer-scale structures willno doubt assume a very important role in the futuredevelopment of nanotechnologies.REFERENCES1. A. H. Compton, Philos.Mag. 45 (1923) 1121.2. Y. Yoneda and T. Horiuchi, Rev. Sci. Instrum. 42 (1971)1069.3. P. Wobrauschek and H. Aiginger, Anal. Chem. 47 (1975)852.4. A. Iida and Y. Gohshi, Jpn. J. Appl. Phys. 23 (1984) 1543.5. H. Schwenke and J. Knoth, Total reflection XRF, inHandbook of X-Ray Spectrometry, edited by R.E.vanGrieken and A. A. Markowicz, Marcel Dekker, New York,1993, Chapter 9, p. 464.6. R. Klockenkämper, Total-Reflection X-Ray FluorescenceAnalysis, John Wiley & Sons, New York, 1997.7. Spectrochim. Acta B44 (1989).8. Spectrochim. Acta B46 (1991).9. Spectrochim. Acta B48 (1993).10. Anal. Sci. (Japan) 11 (1995); Adv. X-ray Chem. Anal.(Japan), 26s (1995).11. Spectrochim. Acta B52 (1997).12. Spectrochim. Acta B54 (1999).13. Spectrochim. Acta B56 (2001).14. C. Streli, X-Ray Spectrom. 29 (2000) 203.15. J. Knoth, H. Schneider and H. Schwenke, X-Ray Spectrom.23 (1994) 261.16. M. A. Kumakhov, X-Ray Spectrom. 29 (2000) 343.17. J. X. Ho, E. H. Snell, C. R. Sisk, J. R. Ruble, D. C. Carter,S. M. Owens and W. M. Gibson, Acta Cryst. D54 (1998)200.18. K. Sakurai, A. Iida and Y. Gohshi, Anal. Sci. 4 (1988) 3.19. A. Iida, A. Yoshinaga, K. Sakurai and Y. Gohshi, Anal.Chem. 58 (1986) 394.20. P. Wobrauschek, R. Görgl, P. Kregsamer, C. Streli, S.Pahlke, L. Fabry, M. Haller, A. Knöchel and M. Radtke,Spectrochim. Acta B52 (1997) 901.21. S. Brennan, W. Tompkins, N. Takaura, P. Pianetta, S. S.Laderman, A. Fischercolbrie, J. B. Kortright, M. C. Maddenand D. C. Wherry, Nucl. Instrum. Methods A 347(1994) 417.22. P. Pianetta, K. Baur, A. Singh, S. Brennan, J. Kerner,D. Werho and J. Wang, Thin Solid Films 373 (2000)222.23. D. Mills, 3rd Generation Hard X-Ray Synchrotron RadiationSources: Source Properties, Optics, and ExperimentalTechniques, John Wiley & Sons, Ltd, London2002.24. F. Comin, M. Navizet, P. Mangiagalli and G. Apostolo,Nucl. Instrum. Methods B 150 (1999) 538.25. G. Apostolo, R. Barrett, M. Robichon, M. Navizet andF. Comin, ESRF Highlights (2000) 92.26. http://www.ritsumei.ac.jp/se/d11/index-e.html27. K. Sakurai, S. Uehara and S. Goto, J. Synchrotron Rad. 5(1998) 554.28. K. Sakurai, H. Eba and S. Goto, Jpn. J. Appl. Phys. Suppl38-1 (1999) 332.29. K. Sakurai, H. Eba, K. Inoue and N. Yagi, Anal. Chem. 74(2002) 4532.30. C. Streli, J. Trace Microprobe Tech. 13 (1995) 109.31. C. Streli, P. Wobrauschek, P. Kregsamer, G. Pepponi,P. Pianetta, S. Pahlke and L. Fabry, Spectrochim. Acta B56 (2001) 2085.32. C. Streli, P. Wobrauschek, B. Beckhoff, G. Ulm, L. Fabryand S. Pahlke, X-Ray Spectrom. 30 (2001) 24.33. B. Beckhoff, R. Fliegauf and G. Ulm, Spectrochim. ActaB58 (2003) 615.34. J. M. Bloch, M. Sansone, F. Rondelez, D. G. Peiffer,P.Pincus,M.W.KimandP.M.Eisenberger,Phys. Rev.Lett. 54 (1985) 1039.35. A. Iida, K. Sakurai, A. Yoshinaga and Y. Gohshi, Nucl.Instrum. Methods A 246 (1986) 736.36. R. S. Becker, J. A. Golovchenko and J. R. Patel, Phys.Rev. Lett. 50 (1983) 153.37. M. J. Bedzyk, D. H. Bilderback, G. M. Bonmmarino,M. Caffrey and J. S. Schidkraut, Science 241 (1988)1788.38. M. J. Bedzyk, G. M. Bonmmarino and J. S. Schidkraut,Phys. Rev. Lett. 62 (1989) 1376.39. A. Krol, C. J. Sher and Y. H. Kao, Phys. Rev. B 38 (1988)857940. W. B. Yun and J. M. Bloch, J. Appl. Phys. 68 (1990) 1421.41. A. Iida, Adv. X-Ray Anal. 35 (1992) 795.42. R. Klockenkämper, J. Knoth, A. Prange and H. Schwenke,Anal. Chem. 64 (1992) 1115A.43. L. G. Parratt, Phys. Rev. 95 (1954) 359.44. K. Sakurai and A. Iida, Adv. X-Ray Anal. 39 (1997) 695.

REFERENCES 29145. B. W. Batterman, Phys. Rev. Lett. 22 (1969) 703.46. P. L. Cowan, J. A. Golovchenko and M. F. Robbins,Phys. Rev. Lett. 44 (1980) 1680.47. T. W. Barbee Jr and W. K. Warburton, Mater. Lett. 3(1984) 17.48. K. N. Stoev and K. Sakurai, Spectrochim. Acta B54 (1999)41.49. Y. Yoneda, Phys. Rev. 113 (1963) 2010.50. S. K. Sinha, E. B. Sirota, S. Garoff and H. B. Stanley,Phys. Rev. B 38 (1988) 2297.51. J. R. Levine, J. B. Cohen, Y. W. Chung and P. Georgopoulos,J. Appl. Cryst. 22 (1989) 528.52. A. Naudon and D. Thiaudiere, Surf. Coat. Technol. 79(1996) 103.53. D. K. G. de Boer, Phys. Rev. B 44 (1991) 498.54. D. K. G. de Boer, Phys. Rev. B 49 (1994) 5817.55. D. K. G. de Boer, Phys. Rev. B 51 (1995) 5297.56. D. K. G. de Boer, A. Leenaers and W. van den Hoogenhof,X-Ray Spectrom. 24 (1995) 91.57. D. K. G. de Boer, Phys. Rev. B 53 (1996) 6048.58. K. Sakurai, Spectrochim. Acta B 54 (1999) 1497.59. K. Sakurai and H. Eba, Japanese Patent No. 3049313(2000).60. K. Sakurai and H. Eba, Anal. Chem. 75 (2003) 355.61. M. Mizusawa and K. Sakurai, J. Synchrotron Rad.(submitted).62. B. Sonntag, Nucl. Instrum. Methods A 467–468 (2001)8.63. G. N. Kulipanov, A. N. Skrinsky and N. A. Vinokurov,Nucl. Instrum. Methods A 467–468 (2001) 16.

5.2 Grazing-exit X-ray SpectrometryK. TSUJIOsaka City University, Osaka, Japan5.2.1 INTRODUCTIONGrazing-exit X-ray spectrometry (GE-XRS) is amethod related to total reflection X-ray fluorescence(TXRF) (Figure 5.2.1a). In TXRF, theprimary X-rays irradiate the sample surface atgrazing angles of incidence. In contrast, in GE-XRS (Figure 5.2.1(b)), characteristic X-rays aremeasured at grazing-exit angles, usually less than1 ◦ . Becker et al. 1 demonstrated the equivalenceof grazing incidence and grazing exit X-ray measurementsaccording to microscopic reversibilityand reciprocity, indicating that GE-XRS can beapplied to surface and thin-film analyses withlow background intensity, in a manner similar tograzing-incidence X-ray spectrometry (GI-XRS)and TXRF.Compared to GI-XRS, GE-XRS has uniqueadvantages. In GE-XRS, different types of excitationprobes can be used, not only X-rays butalso electrons and charged particles. In addition,the probes can be used to irradiate the sampleat right angles. This experimental geometryenables a localized analysis depending on thediameter of the probe. This subchapter describesthe principles, methodological characteristics, GE-XRS instrumentation, and recent applications toX-ray fluorescence (XRF), electron probe microanalysis(EPMA), and particle induced X-rayemission (PIXE). At the end of this subchapter,the characteristics of GE-XRS and its futureare discussed.5.2.2 PRINCIPLES OF GRAZING-EXITX-RAY SPECTROMETRY5.2.2.1 REFRACTION OF X-RAYSAccording to the Fresnel relations, the X-raysemitted from inside atoms are refracted on thesurface, as shown in Figure 5.2.2. Since therefractive index of X-rays is slightly less than 1, theX-rays are refracted to the larger refraction angle(θ exit ) than the incident angle (θ in ). The refractedX-rays are obstructed by the edge of the slit,which is placed between the sample and the X-raydetector. Consequently, only the X-rays emittedfrom the surface region are detected through theslit. This refraction effect is important in improvingsurface sensitivity in GE-XRS geometry.Principally, the sample for GE-XRS must beflat in a manner similar to that in TXRF. In TXRF,the entire sample surface must be flat; in GE-XRS,however, the requirement for a flat surface is notas severe. GE-XRS can be applied if the samplehas a flat region of 1 mm or less, although thisrequirement depends, of course, on the diameter ofthe excitation probe. Further influence of surfaceflatness has been reported elsewhere. 25.2.2.2 X-RAY EMISSION INTENSITIESUNDER GRAZING-EXIT CONDITIONSUrbach and de Bokx have proposed a formalismfor the GE-XRS calculations by applying asymptoticsto plane-wave expressions. 3 Here, anotherX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

294 GRAZING-EXIT X-RAY SPECTROMETRYEDSX-rayselectronsprotonsX-raysEDS(a)(b)Figure 5.2.1 Experimental arrangements of GI-XRS (a) and GE-XRS (b)approach using a reciprocity theorem is introduced.The reciprocity theorem in optics is described as ‘apoint source at P 0 will produce at P the same effectas that of a point source of equal intensity placed atP will produce at P 0 ’. 4 It has been confirmed thatthis reciprocity theorem is also applicable in theX-ray region. 1 Thus, the intensity of X-ray fluorescenceunder grazing-exit conditions can be calculatedin the same way as the calculations of theGI-XRS intensities, indicating that we can utilizethe calculation formula for TXRF intensity afterminor modification. Using a multi-layered model,GE-XRS intensities (I exit (θ exit )) are expressed as afunction of exit angle (θ exit ), as follows:I exit (θ exit ) ∝∫ dj0I p (z)|E j (θ exit ,z)| 2 dz (5.2.1)where z is the depth in the jth layer, d j isthe thickness of the jth layer, and E j (θ,z) isthe electric field that is produced at depth zby assuming that the X-rays, which have thesame energy as the detecting X-ray fluorescence,Vacuum(air)q inq exitSlitFigure 5.2.2 Refraction of X-rays on the surfaceDetectorirradiated the sample surface at the grazing angle,which corresponds to the detecting exit-angle. Thecalculation procedure of E j (θ,z) is describedelsewhere. 5 I p (z) is the X-ray intensity emittedfrom depth z, and depends on the type of excitationprobes (X-rays, 6 electrons 7 and charged particles).It is possible to evaluate the informationdepth using Equation (5.2.1). Here, the informationdepth is defined as the depth where the intensityis reduced to be 1/e of the X-ray (fluorescence)intensity in the GI-XRS geometry when applyingthe reciprocity theorem. Figure 5.2.3 shows theinformation depth of Si Kα for the Si wafer as afunction of the exit angle. It is clearly shown thatthe information depth is only a few nm below thecritical angle, which is given approximately by thefollowing equation:θ c (deg) ≈ √ √Zρ2δ ≈ 1.33λ(nm) (5.2.2)AHere, λ is wavelength of X-rays, Z is the atomicnumber, A is the atomic weight, and ρ is thedensity of the sample (g/cm 3 ). This equation isoriginally given for the critical angle for totalreflection. However, the critical angle for GE-XRS can also be evaluated from this equationby applying the wavelength (λ) of the detectingX-ray fluorescence. Figure 5.2.3 suggests thatsurface analysis is possible at grazing-exit anglesless than this critical angle. However, we mustnote that the critical angle in GE-XRS dependson the wavelength of the fluorescence of theobserved X-ray.

GRAZING-EXIT X-RAY FLUORESCENCE (GE-XRF) 295Si KaInformation depth (nm)100100.0 0.51.0 1.5 2.0 2.5Exit angle (deg)Figure 5.2.3 Information depth of Si Kα emitted from a Si wafer as a function of exit angle5.2.2.3 GRAZING-EXIT X-RAYSPECTROMETRY INSTRUMENTATIONCommercially available GE-XRS apparatus isnot common except for the Laboratory Grazing-Emission X-ray Fluorescence Spectrometer. 8 However,it is not difficult to construct GE-XRS apparatus,which consists of an excitation source, sampleholder, slit, and X-ray detector. We can utilize avariety of excitation probes, such as X-rays, electrons,and charged particles. Thus, GE-XRS hasbeen applied to XRF, EPMA (scanning electronmicroscopy–energy-dispersive X-ray SEM-EDX),and PIXE. In any case, an exit slit system is necessaryto restrict X-ray emissions to a specificexit angle, because the X-ray intensity stronglydepends on the exit angle. Since the detected X-rayintensity is weakened due to use of the slit, ahigh-power excitation source is desirable. It is possibleto use both the EDX detector and the WDX(wavelength-dispersive X-ray). In many cases, theEDX is used because of its advantages, such ascompact size and simultaneous detection of manyelements. However, the combination of GE-XRSand the WDX detector is methodologically quitereasonable, 8 and is especially useful for the analysisof low Z elements.In GE-XRS, the control of exit angle is veryimportant, requiring an accuracy of approximately0.01 ◦ . This angle control can easily be performedby using a stepping motor driven stage. Twotypes of experimental arrangement are availableto change the exit angle. In the first setup, thesample stage is tilted to change the exit angle. 9The characteristic X-rays are measured by a fixedX-ray detector. This method is easily applied tocommercially available apparatus, such as EPMAor SEM-EDX. However, if the analyzing positionis not set exactly on the center of rotation (tilt),it moves as the sample is tilted. In the caseof localized analysis (particle analysis), this is asevere problem. 9 In the second setup, the sample isfixed and the X-ray detector is moved to change theexit angle. In this case, the analyzing position andexcitation conditions (incident angles of excitationprobe) are stable even if the exit angle is changed.Therefore, the latter experimental arrangement issuitable for localized analysis.5.2.3 GRAZING-EXIT X-RAYFLUORESCENCE (GE-XRF)Grazing-exit X-ray fluorescence was studied underthe grazing incidence of primary X-rays. 10 It

296 GRAZING-EXIT X-RAY SPECTROMETRYis shown that the method of grazing-incidenceand grazing-exit XRF analysis is quite surfacesensitive.11 In the GE-XRF performed by Nomaet al., synchrotron radiation irradiated thin-film(Cr/Au/Cr/Si wafer) samples at a right angle, andthe X-ray fluorescence was measured at grazingexitangles. 12 As shown in Figure 5.2.4, an oscillationstructure, caused by the interference ofemitted X-rays, was observed in the exit-angledependent curve of the XRF intensity. By fittingthe experimental curve with the theoreticalcurve, the thickness and roughness at the interfaceswere evaluated. They also measured X-raydiffraction under grazing-exit conditions. 13 Sasakiet al. applied a GE-XRF method to the structureanalysis of proteins 14 and organic films 15 usingsynchrotron radiation.[Image not available in this electronic edition.]Figure 5.2.4 Angular dependence of Cr Kα fluorescenceintensity emitted from Cr (20, 50 nm)/Au (100 nm)/Cr (20 nm)layered structure. 12 Reprinted from Noma, T., Iida, A. andSakurai, K. Phys. Rev. B 48 (1993) 17524. Copyright (1993)by the American Physical SocietySampleX-Ray tubeSampletableSlitSlitAnalyzingcrystalDetector withSoller slitcollimatorFigure 5.2.5 Schematic diagram of a GE-XRF instrumentusing a WDX detector. 8 Reproduced by permission of AmericanInstitute of PhysicsX-Ray fluorescence at grazing-exit angles usinga WDX detector is called ‘Grazing Emission XEF(GE-XRF)’, 8,16,17 Figure 5.2.5 is a schematic viewof the GE-XRF setup. X-Rays from an X-raytube directly irradiated the sample in a large area.X-Ray emissions from the sample were collimatedby a double slit system and detected by theWDX detector. This method is especially useful18 – 21for the trace analysis of low-Z elements.The detection limits of Si in several types oforganic matrices (water, beer, urine, etc.) wereat the ppb level. 22 The detection limits of tracemetals (Na–Sr) in mineral water were determinedin an intercomparison survey by several analyticalmethods. 23 As shown in Table 5.2.1, GE-XRFwith the WDX detector covered the weaknessesof TXRF, that is, the determination of low-Z elements.Pérez and Sánchez also developed a GE-XRFsetup using the EDX detector. 24 They carefullycollimated incident and exit X-rays in the samearea. In their setup, a minimum control of an exitangle of 0.03 mrad was achieved.Micro-X-ray analysis is now one of the trendsin X-ray analysis. Grazing-exit X-ray spectrometrywas applied to micro-XRF using a synchrotronX-ray microbeam. 25 Micro-X-ray analysis can beperformed in laboratories by using X-ray capillaryoptics. Two-dimensional scanning of the sampleis used to obtain X-ray elemental mapping. Additionally,depth information is obtained by applyingGE-XRS. Finally, three-dimensional X-ray analysisis performed. 26

GRAZING-EXIT ELECTRON PROBE MICROANALYSIS (GE-EPMA) 297Table 5.2.1 Detection limits for the elements determined in the intercomparison survey by given techniques 23Detection limits (µg/l)Technique Na Mg K Ca Ni Cu Zn SrTitration – – – 700 – – – –Flame photometry – – 500 – – – – –FAAS 3 2–3 3–12 3–22 4–12 1–4 1–10 17GFAAS – – – – 0.1 0.1 – –ICP-AES 0.1 0.3–50 20–500 0.3–30 25 5 5 1ICP-MS – 7 – 20 0.1–3 0.01–3 0.08–1 0.04TXRF – – – – 2 2 2 –TXRF – – 100 50 4 3.5 3.5 4.5GEXRF 40 3 5 20 – – – –FAAS, flame atomic absorption spectrometry; GFAAS, graphite furnace atomic absorption spectrometry; ICP-AES, inductively coupled plasmaatomicemission spectrometry; TXRF, total reflection X-ray fluorescence; GEXRF, grazing emission X-ray fluorescence.5.2.4 GRAZING-EXIT ELECTRONPROBE MICROANALYSIS (GE-EPMA)SEMEDXdetectorHasegawa et al. measured characteristic X-rays atsmall take-off angles during RHEED (reflectionhigh energy electron diffraction) experiments 27and demonstrated that surface sensitivity wasenhanced. Usui et al. applied the same techniqueto the analysis of super-conductive films of YBCOusing SEM. 28 In both cases, the electron beam wasirradiated at glancing incident angles; therefore,localized analysis was difficult and not proposed.ElectronbeamSampleFlexible tubeZ-stage5.2.4.1 GRAZING-EXIT ELECTRONPROBE MICROANALYSIS SETUPIn general, GE-EPMA can be performed usingcommercially available EPMA (or SEM-EDX)apparatus. However, since the exit angle has tobe precisely controlled, some improvements of theequipment are necessary. As described previously,there are two methods to change the exit angle. AnEPMA apparatus has a function of sample inclination.Thus, by using this function, GE-EPMAmeasurement can be performed in the first setupjust after a simple slit is placed between the sampleand the X-ray detector 29 Figure 5.2.6 showsan example of the second type of experimentalsetup. 30 The SEM and the EDX detector were combinedwith a stainless steel flexible tube. The EDXdetector was placed on a stepping motor drivenstage, controlled by a computer. The minimumFigure 5.2.6 Schematic diagram of a GE-EPMA instrument. 30Reproduced by permission of American Institute of Physicsstep of this stage was 0.5 µm. A Ta slit (0.2 mmin the width) was attached on the top of theEDX detector at a distance of about 100 mm fromthe sample. The exit angle for the characteristicX-rays was changed by moving the position of theEDX detector.Awane et al. changed the exit angle by movingthe sample stage up and down, as shown inFigure 5.2.7. 31 Since the EDX detector is usuallyfixed on the vacuum chamber of the SEM (orEPMA), their method would be easy to apply.Although there is still a problem in that thesample position moves when the exit angle ischanged, they have reported interesting results, asdescribed below.The calibration of the exit angle is necessarybefore the GE-EPMA measurements are made. For

298 GRAZING-EXIT X-RAY SPECTROMETRYElectron beamz = 0.0 mm∆z28°Z axisX-Raysq′qExit angleX-Ray detectorSlit48 mm30°Figure 5.2.7 Experimental arrangement of GE-EPMA. 31 Reprintedfrom Aware, T. et al. J. Surf. Anal. 9 (2002) 171.Reproduced by permission of The Surface Analysis Societyof Japanthis purpose, it is useful to measure the angledependence of Si Kα intensity for a Si wafer,which has a flat surface and a well-known density.This angle-dependent curve can be compared withthe theoretical curve calculated by Equation 5.2.1.Finally, we can experimentally determine theexit angle.5.2.4.2 SURFACE ANALYSISBY GE-EPMASurface analysis can be performed by conventionalEPMA using low-energy electrons. The lowerthe electron energy, the smaller the depth ofpenetration of the electrons into the sample.However, the selection of the analytical lines ofthe characteristic X-rays is restricted due to lowenergyelectron excitation. In some cases, this is aserious problem, especially when an EDX detectorhaving a poor energy resolution is used. The useof GE-EPMA enables surface-sensitive analysiswithout reducing the electron beam energy.It is well known that the surface of Fe–Cr metalsis covered with a chemically stable oxide layer,which is primarily composed of Cr oxide. Therefore,the chemical composition of the surface layershould be different from the bulk composition. Theexit angle dependences of Fe Kα and Cr Kα weremeasured and found to be almost constant at exitangles above 10 ◦ . In the exit-angle range from 0 to1.5 ◦ , all characteristic X-ray intensities decreasedas the exit angles were reduced; however, the CrKα intensity decreased more slowly than with FeKα. The ratio of Cr Kα intensity to that of Fe Kαincreased significantly at the grazing angle. 9 Thisindicates that Cr is enriched near the surface. Thisresult agreed well with those obtained by othermethods of surface analysis.Takahashi, in JEOL, observed the surface ofa contaminated semiconductor device, which hadbeen touched with a finger, under grazing-exitconditions. 32 At a conventional exit angle of 40 ◦ ,it was difficult to obtain the X-ray mappingof the contaminating elements (Ca, K, and Cl)due to poor surface sensitivity. However, undergrazing-exit conditions, X-ray mapping was clearlyobtained. The mapping results for K under conventionaland grazing conditions are shown inFigure 5.2.8 with SEM images.Yamanaka et al. studied the growth processof Ga on the Si surface by high-voltage SEM-EDX. 33 They reported a spatial resolution of10–20 nm under grazing-exit conditions. Sincethe X-rays from the substrate are not detectedat grazing angles, it is possible to detect asingle particle as small as 10–20 nm. CharacteristicX-rays are produced within a significantly largerinteraction volume than the impinging beam, asshown in Figure 5.2.9. 34 At conventional detectionangles (typically ∼ 40 ◦ for EPMA), the lateralresolution is determined by the dimensions of theinteraction volume. In the case of GE-EPMA,however, only the X-rays that are emitted near(few nm) the surface are detected. Therefore,the lateral resolution of GE-EPMA is limited bythe cross-section of the most superficial layerof the interaction volume. The lateral interactionvolume (↔ in Figure 5.2.9) was evaluated forseveral metals at different electron acceleratingvoltages by Monte Carlo simulation. 7 The resultsare shown in Table 5.2.2, indicating that thelateral resolution would be improved considerablyunder grazing-exit conditions, especially for low-Zelements.

GRAZING-EXIT ELECTRON PROBE MICROANALYSIS (GE-EPMA) 299Figure 5.2.8 Comparison of X-ray mappings of K Kα taken by conventional EPMA (a, electron beam current: 2 nA) andGE-EPMA (b, 180 nA). 32 SEM images obtained by both methods are also shown. Reproduced by permission of IOP PublishingLimited5.2.4.3 PARTICLE ANALYSISBY GE-EPMAIn the semiconductor device manufacturing process,the detection of contaminants (small particles)on Si wafers is very important, because suchparticles affect the physical properties and functionsof the semiconductor devices. It is not easyto measure the elemental composition of a verysmall particle by conventional EPMA, because theelectron beam easily passes through the particleand produces strong X-rays from the Si substrate,as shown in Figure 5.2.9 Therefore, X-rays fromboth the particle and the substrate are detectedsimultaneously. In many cases, it is difficult to distinguishthe X-rays emitted from the particle fromthose emitted from the substrate.An artificial particle (Fe 2 O 3 ,1µm indiameter)was deposited on a Au layer deposited onthe Si flat substrate. The electron beam irradiateda single Fe 2 O 3 particle. At a large exit-angle of40 ◦ ,AuMα and Si Kα were observed in additionto Fe Kα, as shown in Figure 5.2.10(a). 35 Thisis because the electron beam penetrated into theAu–Si substrate. The same particle was measuredat a grazing-exit angle of about 0 ◦ . As shown in

300 GRAZING-EXIT X-RAY SPECTROMETRYElectronsEDXX-RaysEDXElectron beaminteraction volume(a)(b)Figure 5.2.9 Interaction volume and analyzing region under conventional conditions (a) and grazing-exit conditions (b)Table 5.2.2 Comparison of theoretically estimated interactionvolumes (nm) obtained with conventional vs GE-EPMA (beamdiameter = 50 nm)Electron acceleratingvoltage (kV)5 10 20Si Conv. 311 899 1415GE 68 122 171Cu Conv. 124 294 828GE 84 121 148Au Conv. 85 184 421GE 62 112 190Figure 5.2.10(b), the characteristic X-rays emittedfrom the substrate completely disappeared, makingsingle-particle analysis possible with a lowbackground intensity. Elemental analysis for atmosphericaerosols deposited on a flat substrate, takenunder conventional and grazing-exit conditions,were also reported. 34In addition, interference between the directX-ray beam emitted from the particle and thereflected X-ray beam on the flat substrate can beobserved at grazing-exit angles. 36 This interferenceis useful for the enhancement of the X-rayintensities from the particle. Bekshaev and VanGrieken have theoretically studied the interferencepattern to obtain the information of particlestructure and composition. 37Awane et al. measuredaninclusion(0.3µm indiameter), which appeared on the surface of etchedstainless steel samples 31 They adjusted the exitangle by moving the sample position, as shownin Figure 5.2.7. At the conventional exit angle of30 ◦ , strong X-rays of Fe Kα, CrKα and Ni Kαemitted from the matrix (stainless-steel) weredetected (Figure 5.2.11(a) and 5.2.11(b)), makingit difficult to analyze the inclusion. When theIntensity(a)800060004000Si Ka2000 C Ka Au MaO KaFe Ka00 2 4 6 8Energy (keV)Intensity(b)12008004000C KaO KaFe La1 µmFe 2 O 3AuFe KaSiFe Ka0 2 4 6 8Energy (keV)Figure 5.2.10 X-Ray spectra taken for a single particle of Fe 2 O 3 deposited on a Au (100 nm) layer on a Si substrate at exitangles of 40 ◦ (a) and approximately 0 ◦ (b). 35 Reproduced by permission of Springer-Verlag KG

GRAZING-EXIT ELECTRON PROBE MICROANALYSIS (GE-EPMA) 301(a)Intensity (cps)(c)1500(b)1500OFeFeFe1000Fe1000CrAlCr500 SiMg500Fe NiSiCr FeCa Ti CrNi0100Al SiMn05O50Ca Ti CrMgTi Mn00 5000 10000 (d)00 5000 10000Intensity (cps)Energy (eV)Figure 5.2.11 X-Ray spectra taken under conventional conditions (exit angle of 30 ◦ ) (a, b) and grazing exit conditions (c, d) fora typical single inclusion (a, c) and the matrix (b, d). 31 Reprinted from Awane, T. et al. J. Surf. Anal. 9, (2002) 171. Reproducedby permission of The Surface Analysis Society of Japanelectron beam was irradiated on the matrix ata grazing-exit angle, no X-rays were observedfrom the matrix, as shown in Figure 5.2.11(d),indicating that the X-ray spectrum shown inFigure 5.2.11(c) was obtained for the inclusionat the same grazing angle, although the surfacewas not perfectly flat. In conclusion, GE-EPMAshowed that Fe and Ni were not in the inclusion.5.2.4.4 THIN-FILM ANALYSISBY GE-EPMAA Cr (50 %) – Ti (50 %) ultra-thin film (10 nm)deposited on a Si substrate was measured. 38,39Figure 5.2.12(a) shows the X-ray spectrum takenat an exit angle of 45 ◦ . Due to large continuousX-ray background intensity, it was difficult torecognize the characteristic peaks of Ti Kα andCr Kα. However, these continuous X-rays weresignificantly reduced at a grazing-exit angle of0.75 ◦ , with the result that Ti Kα and Cr Kα wereclearly detected with low background intensity, asshown in Figure 5.2.12(b). Reduction of continuousbackground intensity is important for improvingdetection limits. 40 By applying GE-EPMA, thedetection limits of Ti and Cr were improved byfactors of 4 to 10. 381000Si KaAu Ma100Ti KaAu LaCr KaAu LbIntensity100Ti Ka Au LaCr Ka Au LbIntensityAu Lg1010(a)0 5 10 15 20Energy (keV)(b)0 5 10 15 20Energy (keV)Figure 5.2.12 X-Ray spectra taken for a Cr (50 %) – Ti (50 %) ultra-thin film (about 10 nm) deposited on a Si substrate at anaccelerating voltage of 20 kV at exit angles of 40 ◦ (a) and approximately 0.75 ◦ (b). 38

302 GRAZING-EXIT X-RAY SPECTROMETRY1.5Ag LaNet intensity (cps)1.00.5Au LaAgAu0.0Sample0 10 20 30 40 50Exit angle (mrad)Figure 5.2.13 X-Ray intensities of Ag Lα () andAuLα (○) as a function of the exit angle. A schematic diagram of thesample is shown in the inset. The curves calculated for Ag (40 nm, 8.0 g/cm 3 ) and Au (80 nm, 15.0 g/cm 3 ) are indicated by solidlines. 40 Reproduced by permission of Elsevier ScienceThe determination of the thickness and densityof thin films is also important for their characterization.It is possible to evaluate thickness anddensity of thin films by other analytical X-ray techniques,such as X-ray reflectivity measurement andgrazing-incidence XRF (angle-dependent TXRF).In these methods, the entire surface of the sampleis irradiated by primary X-rays; and the averagethickness and density for the entire surface areobtained. The advantage of GE-EPMA is in localizedthin-film analysis. Figure 5.2.13 shows theangle dependence of Au Lα and Ag Lα for theAu–Ag thin films shown in the inset. 41 The electronbeam was fixed on each film (Au or Ag), andthen dependence on the exit angle was measured.From the curve fitting method, the thicknesses ofthe Au and Ag films were determined to be 80 and40 nm, respectively.5.2.5 GRAZING-EXIT PARTICLEINDUCED X-RAY EMISSION (GE-PIXE)Compared to EPMA, PIXE is considered to besuitable for trace analysis because the continuousbackground intensity is originally low. However,some continuous background intensity is stillobserved, especially in the low-energy region. Byapplying grazing-exit measurement, it is possibleto reduce this continuous background intensity andenhance the surface sensitivity.5.2.5.1 GRAZING-EXIT PARTICLEINDUCED X-RAY EMISSION SETUPFigure 5.2.14 shows an experimental setup of GE-PIXE, which was developed originally for totalreflection PIXE experiments 42 at Amsterdam FreeUniversity in The Netherlands. The proton beam,which was produced in H 2 plasma and acceleratedto an energy level of 2.5 MeV, irradiated thesurface of the sample. The characteristic X-raysProtonsSlitsEDXRotating stageExit slitSampleFigure 5.2.14 Schematic diagram of the top view of theGE-PIXE experimental setup. 42 Reproduced by permission ofElsevier Science

CHARACTERISTICS OF GE-XRS AND ITS FUTURE 303were measured through a slit by an EDX detectorat a detector angle of 45 ◦ with respect to the protonbeam to reduce Bremsstrahlung X-rays. To changethe exit angle, the sample stage was rotated usinga stepping motor with a minimum step of 0.057 ◦in a vacuum chamber.5.2.5.2 SURFACE AND THIN-FILMANALYSIS BY GE-PIXEAu (50 nm) – Cu (500 nm) double layers on glasswere measured by the GE-PIXE setup shown inFigure 5.2.14. 43 At a large exit angle of 45 ◦ ,theCu Kα was the dominant X-ray peak due to therelatively large thickness of the Cu layer. Thesame sample was measured at a grazing-exit angleof about 0.5 ◦ . The background intensity in thelow energy region was considerably reduced. Inaddition, the X-rays emitted from the thin Aulayer were dominantly observed. This indicatesthat surface-sensitive PIXE analysis is possibleunder grazing-exit conditions.Rodríguez-Fernández et al. proposed SPIX (surfacesensitive particle-induced X-ray analysis), 44–46which is essentially the same as GE-PIXE. Theymeasured Cl implanted into a Si wafer by SPIX. 47Cl Kα intensities were plotted as a function of tiltangle, as shown in Figure 5.2.15. By fitting withtheoretical curves, the depth of the implanted Cllayer was determined to be 110 nm with a depthresolution of 8 nm, indicating the potential of SPIXperformance. In this measurement, the sample tiltangle was determined with a precision of ±0.1 ◦without an exit slit. Therefore, they have calculatedthe angle dependent curves after folding inthe extended detector geometry. 485.2.5.3 PARTICLE ANALYSIS BYGE-PIXEThe analysis of atmospheric aerosols is one ofthe most important applications of PIXE. Low-Zelements, such as Ca, K, Na, etc., are significantelements in environmental analysis. However, thecontinuous X-ray background intensity in lowenergyregions is still too high in the conventionalPIXE spectrum, making light element analysisdifficult in some cases. The PIXE spectra, shown inFigure 5.2.16(a), were taken for aerosols collectedon a Si wafer at an exit angle of 4.4 ◦ . 43 Dueto large continuous X-ray background intensity,it was difficult to identify small amounts ofelements in aerosols. The same sample wasmeasured at a grazing-exit angle of 0.4 ◦ . Asshown in Figure 5.2.16(b), the continuous X-raybackground intensity was reduced significantly,and Ca, Ti, and Zn could be detected with the lowbackground intensity.Cl K X-ray yield (µC −1 )2400180012006000z 0 (nm)0255075100125150−44 −42 −40 −38 −36Tilt angle q (deg)Figure 5.2.15 Calculation of Cl Kα X-ray yield produced by1.2 MeV 1 H + ion bombardment as a function of the tilt anglefor Cl layers located at different depths z 0 (nm) in Si. 47Reproduced by permission of Elsevier Science5.2.6 CHARACTERISTICS OF GE-XRSAND ITS FUTUREGrazing-exit X-ray spectrometry has been appliedto conventional X-ray analytical methods, suchas XRF, EPMA and PIXE. In the measurementof X-rays at grazing-exit angles, the detection ofX-rays emitted from deep inside the sample isreduced, leading to the improvement of the degreeof surface sensitivity and the detection limits.Therefore, GE-XRS would provide unique opportunitiesfor surface analysis, thin-film analysis,and particle analysis, using conventional analyticalX-ray methods. Compared with GI-XRS, the mostimportant advantage of GE-XRS is ‘localized surfaceanalysis’. In GE-XRS, the excitation beam can

304 GRAZING-EXIT X-RAY SPECTROMETRY10080(a)Ca KaFe Ka604020Intensity (counts)060(b)Ca Ka40Fe Ka20Ti KaZn Ka00 2 4 6 8 10 12 14 16 18 20Energy (keV)Figure 5.2.16 PIXE spectra measured for aerosols collected on a Si substrate at different exit angles of 4.4 ◦ (a) and 0.4 ◦ (b).The lifetime for EDX measurements was 180 s. 43 Reprinted with permission from Tsuji, K., Spolnik, Z., Wagatsuma, K., VanGrieken, R. and Vis, R.D. Anal. Chem. 71, 5033 (1999). Copyright (1999) American Chemical Societyirradiate the sample at a large angle of 90 ◦ .Therefore,localized analysis is possible, depending onthe diameter of the excitation beam.The X-ray intensity detected by GE-XRS isweak because the X-rays are detected at a smallexit solid angle through the slit. This is one ofthe drawbacks of GE-XRS. To overcome thisdrawback, a multi-X-ray detector system would beuseful. In the present experimental configuration,X-rays are measured only from a small azimuthangle while characteristic X-rays are emitted in alldirections. Thus, the use of a ring-type silicon driftX-ray detector (SDD), 49 shown in Figure 5.2.17,will enable the detection of characteristic X-rayswith high efficiency even at grazing-exit angles,which can be changed by moving either theExcitationprobesRing-typedetectorX–Y–Z sample stageSampleGE-XRSFigure 5.2.17 Ring-type SDD for high efficiency GE-XRSdetector or the sample. In the case of GE-XRF,synchrotron radiation is an ideal X-ray source

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5.3 Portable Equipment for X-ray FluorescenceAnalysisR. CESAREO 1 , A. BRUNETTI 1 , A. CASTELLANO 2 and M. A. ROSALESMEDINA 31 Department of Mathematics and Physics, University of Sassari, Sassari, Italy, 2 Department ofMaterials Science, University of Lecce, Lecce, Italy, and 3 University of ‘las Americas’, Puebla, Mexico5.3.1 INTRODUCTIONEnergy-dispersive X-ray fluorescence (EDXRF)analysis is a nondestructive, multi-elemental andsimple technique, which is based on the irradiationof a sample by a low intensity X-ray beam,and by the detection of secondary X-rays emittedby the sample. 1–3The energy of these secondary X-rays characterisesthe elements present in the sample wherethe intensity is proportional to their concentration.The ‘complex’ of secondary X-rays and primaryscattered radiation is called the ‘X-ray spectrum’.The sample can be in any state (solid, liquid,gaseous or of various size and nature), and itwill absolutely not be altered by the analysis, forthis reason it can be analysed many times. Thesefeatures make EDXRF especially suitable for insitu and on-line analysis.In the past, portable EDXRF equipment wascomposed of radioactive sources and proportionalgas counters. 4 But the high energy resolutionof these detectors limited the range of possibleapplications. Then, in the 1980s, nitrogen-cooleddetectors substituted proportional gas counters.However, the need for liquid N 2 and the intrinsicdelicacy of these detectors limited the use ofsuch equipment.Only in the last few years, has technologicalprogress produced miniature and dedicated X-raytubes, 5–9 thermoelectrically cooled X-ray detectorsof small size and weight, 6,8–14 small size multichannelanalysers 8,15 and dedicated software. 16–19This progress allowed the construction of completelyportable small-sized EDXRF systems thathave similar capabilities as the more elaborate laboratorysystems, and which, by definition, can beused anywhere by one person for in situ analysis,but without the problems connected with nitrogencooling, big size X-ray tubes and high costs.Portable EDXRF equipment is absolutely necessaryin many cases, when objects to be analysedcannot be transported (typically works ofart) or when an area should be directly analysed(soil analysis, lead inspection testing, etc.)or when the mapping of the object would requiretoomanysamples.Typical examples where portable EDXRF systemsare needed are the following:• archaeometry (measurements of frescoes, paintings,alloys in churches, museums, in openair, etc.;• analysis of lead-based paints;• analysis of soil contaminants;• geological surveys;• in vivo analysis of toxic elements (lead, cadmium,platinum, etc.);• quality control in industry (for ex. alloysanalysis);X-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

308 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSIS• quality control of X-ray tubes (maximum energyand spectrum).5.3.2 INSTRUMENTATIONA typical EDXRF system (Figure 5.3.1) is composedof: 1–3• an excitation source (a radioactive source or aX-ray tube);• an X-ray detector with electronics;Radioisotopeor small X-RaytubeSample• a single- or a multichannel analyser;• software for elements identification and quantitativeanalysis.Laboratory EDXRF systems are generally equippedwith high power X-ray tubes, which canbe collimated and used with secondary targets,nitrogen-cooled high resolution Si (Li) or Gedetectors 15,20–22 and multichannel analysers withsophisticated software for quantitative automaticevaluation.Portable EDXRF systems have, of course,different requirements, such as: low weight, smallsize, low counting time and the possibility tobe equipped with batteries. They generally havehigher minimum detection limits and are lessflexible than laboratory systems.5.3.2.1 X-RAY SOURCESPeltier cooleddetectorAmplifierFor portable EDXRF equipment both radioactivesources (emitting α, β, γ , X or bremsstrahlungradiation) or X-ray tubes can be employed. Amongthe commercial PEDXRF equipment, about onehalf use radioisotopes and one half X-ray tubes.Radioisotopes are generally used emitting X-rays(or γ -rays in the X-ray energy region). However,in special cases also α sources are employed foranalysis of low Z elements.X-Ray tubes used for portable EDXRF systemshave a Be window, small size and low power.Radioactive SourcesGeneral requirements for radioactive sources to beemployed in portable EDXRF equipment are:Multichannelanalyzer + softwareFigure 5.3.1 Scheme of portable EDXRF analysis equipmentcomposed of a radioactive source (or small size low-powerX-ray tube), a Peltier- cooled semiconductor detector and aMCA with dedicated software• sufficient long half-time (> ≈ 1 year);• emission of only one or two lines of properenergy and sufficient intensity.Radioactive sources are especially suitable forportable X-ray equipment and are still employed,in spite of the current availability of a variety

INSTRUMENTATION 309of small size X-ray tubes. They have the advantageof having very small sizes (Figure 5.3.2)and of being intrinsically stable but the disadvantageof emitting radiation of fixed energy andlow intensity (orders of magnitude lower thanfor X-ray tubes). Radioactive sources are, therefore,not flexible versus energy and not suitablefor analysis of low amounts of chemicalelements.Xandγ radioactive sources generally employedfor EDXRF analysis are shown in Table 5.3.1. 23–24As observed above, in special cases α radioactivesources are employed or mixed α-X radioactivesources, where the analysis of very low Z elementsis required.X-Ray TubesThe general requirements for a X-ray tube suitablefor portable EDXRF equipment are the following:• low power of a few watts (HV: variable from5 kV to a maximum of 40 kV; current variablefrom 10 µA to a maximum of about 0.5 mA);• air or internal cooling;• small size to allow portability;• anode suitable to analytical problems;• thin Be window;• good shielding and collimation, to guaranteeonly forward irradiation and reduce radiationdose.A great variety of X-ray tubes of various types(maximum voltage, current, anode), size and costis currently available for portable EDXRF analysis,depending on the problem, and more specificallyon the element or elements to be analysed. X-Ray tubes for portable EDXRF equipment areconstructed by many companies 5–9 and some ofthem are shown in Figure 5.3.3.In 2001 a very compact, battery-powered X-raytube, incorporating in the same case a radiation1043 (activedia.)0.2–0.25StainlesssteelMonelmetal5Berylliumwindow1512CopperActivedepositBrazedseal38.022.46.5SpecimenRadioisotope sourceShieldingDetectorSpecimenSourceShieldingDetectorFigure 5.3.2 Radioactive sources for EDXRF analysis (from top left, point disc and annular source) and typical geometries withannular (centre) and central (bottom) source

310 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSISTable 5.3.1 Typical radioisotopes for EDXRF analysisIsotope t 1/2 (years) Energy of emittedradiation (keV)Typical number ofemitted photons/ssteradElements whichcan be analysed55 Fe 2.7 5.9 and 6.5 (Mn K lines) 10 6 –10 7 from Si to Ti238 Pu 86.4 13.5 and 16.8 (U L lines) 5 × 10 6 from Ca to As (K)109 Cd 453 days 22.1 and 25.0 (Ag K lines) 2 × 10 6 from Ca to Mo (K lines) and heavyelements (L lines)241 Am 433 59.5 10 7 from Fe to Gd (K lines) and heavyelements (L lines)57 Co 270 days 122 and 136 2 × 10 6 Heavy elements (K lines)153 Gd 241 days 41.3 and 47.3 (Eu K lines),97.4 and 1035 × 10 6 Heavy elements (K lines)source with HV power and control electronics,was designed and constructed for AMPTEK byPhotoelectron Co. 24 (Figure 5.3.3). It has a bulksilver anode, HV adjustable from 10 to 35 kV andbeam current from 0 to 100 µA. The dimensionsof the external case are 19 × 7 × 3.3cm 3 andit has an overall weight of about 450 g. In2001, Moxtek 9 developed a very compact, batteryoperatedtransmission-anode X-ray tube with thefollowing characteristics: Pd or Ag anode, HVfrom 10 to 30 kV, current from 0 to 0.1 mA,dimensions of 18 × 7 × 3cm 3 and a weight ofabout 450 g. More recently a 40 kV, 0.1 mA,battery-operated X-ray tube was produced byMoxtek (‘Bullet ’). This tube operates at a powerof 4 W with a maximum input of 12 W, andis available in a side-window configuration (Wanode),or with a 2 µm Ag or Pd transmissiontarget. The transmission target X-ray tube has aBe window of 0.25 mm thickness and a volume of30 cm 3 approximately (Figure 5.3.4).Leaving out analysis of trace elements (withconcentration lower than 1 ppm), which requireshigh-current tubes with proper secondary targets,low-power X-ray tubes are generally adequate.They may be selected primarily as a function ofthe atomic number of the element or elements to beanalysed. Table 5.3.2 gives characteristics of X-raytubes useful for EDXRF analysis. It is importantto observe that small portable X-ray tubes arenot available for excitation of K-lines of heavyelements. In this case, the only option currentlygiven, is the use of radioactive sources.A quite different type of X-ray generator, basedon the properties of pyroelectric crystals wasrecently proposed by Brownridge and Roboy 26 anddeveloped by Amptek. 6Also in 2003, carbon nanotube based fieldemission X-ray tubes were developed by AppliedNanotechnologies. 27 The conventional X-ray tubeis based on a metal filament that emits electronswhich are accelerated to bombard the metal target.ANI X-ray tubes utilise carbon nanotube fieldemitters as the electron source.X-Ray OpticsIn some applications, very small areas must beirradiated for EDXRF analysis. This happens whenvery small samples are analysed, such as grainsor microfragments, or when analysis with a veryreduced space resolution is needed.The simplest way to produce an X-ray microbeamis to use a pinhole collimator between theX-ray source and the sample. But, unfortunately,only a small fraction of the original photon flux canpass through the pinhole. This results in low countrates, which limits the sensitivity of the technique.Higher flux densities can be achieved byemploying polycapillary lenses, consisting of severalhundred thousand glass fibres. The channelsare all directed towards one focus point, requiringstraight fibres in the centre of the lens and stronglybent fibres near the surface. The strongly bentfibres are less efficient in transporting X-ray photonsthan the straight ones. This difference in efficiencyincreases with the increase in photon energydue to the energy dependence of the critical anglefor total reflection. Polycapillary optics cause a

INSTRUMENTATION 311350030002500X-Ray spectrumAg target @ 35 kVAg KaCounts20001500100010000 3 6 9 12 15 18 21 24 27 30 33 36 39Energy (keV)Ag KbFigure 5.3.3 Battery-operated ‘Laser’ X-ray tube with Ag anode, which works at 30 kV and 0.1 mA. The case containing thetube and the high voltage supply is also shown (centre), and a typical X-ray spectrum emitted by the tube is illustrated at thebottom of the figure (with permission of Amptek, Inc.)significant change in the shape of the excitationspectrum: high energy photons are filtered out andthe excitation spectrum is distorted towards lowenergies. This effect leads to smaller focal spotsizes in the high energy region.When applied in combination with air-cooled,low-power X-ray tubes, capillary collimators andin particular polycapillary lenses have proven to bevery suited for focusing the X-ray beam in smallareas of 10–100 µm diameter. 28A polycapillary optical element for EDXRFanalysis has a typical length of 40–70 mm, likea cylinder thicker in the middle, with a diameterof 5–10 mm. It is able to focus an X-ray beam

312 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSISTarget material: CaRelative output10080604020Target voltage 9.5 kVCa Kα (3.69 keV)Ca Kβ (4.01 keV)(a)00 1 2 3 4 5 6 7 8 9 10Photon energy [kev](b)Counts/channel2000Mo18001600140012001000800600Mo40020000 2 4 6 8 10 12 14 16 18 20 22 24 26 28Energy [eV]140000Pd120000100000Total counts800006000040000ZnFe NiPd2000000 100 200 300 400 500 600Channel number(c)Figure 5.3.4 Typical X-ray tubes for portable EDXRF equipment. (a) A Ca anode, 8 kV and 0.1 mA from Hamamatsu (8.8 cmlength × 3.7 cm diameter and 35 g weight), and typical X-ray spectrum; (b) Mo anode, 30 kV and 0.2 mA from Oxford (10 cmlength × 3.3 cm diameter and 200 g weight), and typical X-ray spectrum; (c) W anode, battery-operated X-ray tube from Moxtek,40 kV and 0.1 mA (30 cm 3 volume), and typical X-ray spectrum (with permission of Hamamatsu, Oxford and Moxtek)

INSTRUMENTATION 313Table 5.3.2 Characteristics of small-size, portable X-ray tubes and elements which can be analysedElement or elements tobe analysedAnode material Kilovoltage (kV) X-ray emissionAl, Si, P, S, Cl Calcium 5–8 3.7 keV (Ca K lines) plusBremsstrahlungAl, Si, P, S, Cl Silver (L lines) or Pd 5–10 3 keV (Ag L lines) plusBremsstrahlungCl, Ar, K, Ca Titanium 10 4.5 keV (Ti K lines) plusBremsstrahlungFrom Ca to Y (K lines) and fromW to U (L lines)Molybdenum 30 17.5 keV (Mo K lines) plusBremsstrahlungFrom Ca to Mo (K lines) andfrom W to U (L lines)Silver 30 22 keV (Ag K lines) plusBremsstrahlungFrom Ca to Sn (K lines) andfrom W to U (L lines)Tungsten 35 Bremsstrahlung plus 8.3and 9.8 keV (W L lines)From Fe to Ba (K lines) andTungsten 50 Bremsstrahlung plus 8.3from W to U (L lines)Rare earths, from lanthanum tohafnium (L lines)and 9.8 keV (W L lines)Molybdenum 20 17.5 keV plusBremsstrahlungup to energies of about 20 keV. For a portableEDXRF apparatus the polycapillary optical systemshould be rigidly connected to the X-ray tube(Figure 5.3.5).5.3.2.2 X-RAY DETECTORSThe general features for a detector suitable for highquality portable EDXRF equipment should be thefollowing:• sufficient good energy resolution (better than200–250 eV at 5.9 keV);• sufficient good efficiency in the energy intervalto be analysed;• thin Be window;• Peltier cooling, for reducing the size.The typical, high resolution X-ray detector hasbeen for a long time the nitrogen-cooled Si(Li)or HpGe detector, with an energy resolution ofabout 120–150 eV at 5.9 keV 20–22 (Figure 5.3.6).However, the nitrogen cooling makes these detectorsdifficult to be used for portable instruments.Proportional gas counters have typically beenused as substitutes for nitrogen-cooled detectorsin portable EDXRF equipment until about1994–1995, 4,29,30 when thermoelectrically cooledSi-PIN and CdZnTe started to be produced byAMPTEK. 8Currently, equipment based on radioactivesources and proportional gas counters is no longerin use.In the last few years, small size thermoelectricallycooled semiconductor detectors have becomeavailable, such as HgI 2 , 12 Si-PIN, 8 Si drift, 6,10,11CdTe and CdZnTe (CZT). 8,13,14 These detectors arecooled to about −30 ◦ C by means of a Peltier circuit,and are contained in small boxes includinga high quality preamplifier and the Peltier circuit(Figure 5.3.7).The HgI 2 detector was the first to be constructed;it has an energy resolution of about180–200 eV at 5.9 keV (Figure 5.3.6), and an efficiencyof about 100 % in the whole range of X-rays(Figure 5.3.8). It has the disadvantage of producingmany disturbing ‘escape peaks’ when irradiated.The Si-PIN detector is currently the mostemployed in portable EDXRF equipment. A typicalmodel has a Si thickness of 300 µm, exhibitsan energy resolution of 160–200 eV (Figure 5.3.6)and is useful up to about 25–30 keV (Figure 5.3.8),because the efficiency is decreasing at an energylarger than 15 keV, due to the limited thickness.Another model has a thickness of 500 µm, anenergy resolution of about 200–220 eV and can beused up to 50 keV approximately. High energy resolutionsare obtained using high shaping time, in

314 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSISFigure 5.3.5 Typical capillary collimators from Roentgen Optics (Moscow), IfG (Berlin) and X-ray Optical Systems (Albany,NY, USA). (Published with permission)the order of 15–20 µs. Therefore, these detectorsare subject to an energy resolution degradationat a count rate higher than a few thousandsof photons/s.The Si drift detector (SDD) was developed byGatti et al. 10 The bulk detector is produced byKeteK, 31 and the complete detector with electronicsby EIS 6 and by Roentec. 11 It typicallyhas a Si thickness of 300 µm an active area of5–10mm 2 , and an energy resolution of approximately130–150 eV at 5.9 keV (Figure 5.3.6). Theintegration of the first stage of the front-endelectronics enables the operation of the SDD atextremely short shaping times even at low temperatures,making the SDD the optimal solutionfor high count rate applications. Shaping times of0.25 to 2 µs can be used.CdTe and CZT detectors have a typicalthickness of 2 mm, and thus an efficiency ofabout 100 % in the whole X-ray energy range(Figure 5.3.8).The energy resolution of the best CZT detectoris about 250, 500 and 750 eV at 5.9, 59.6and 122 keV, respectively (Figure 5.3.6). A comparisonbetween various thermoelectrically cooleddetectors can be found elsewhere. 32A summary of the useful Peltier-cooled comparedto the nitrogen-cooled detectors is given inTable 5.3.3. It should be observed that the efficiencyin the low-energy region is dependent onthe thickness of the Be window (Figure 5.3.8). Theminimum standard window compatible with theportability and hardiness of the equipment is 8 µmBe, having a transmission of about 80 % at 2 keV.

INSTRUMENTATION 315FWHM (eV)600550500450400350300250HpGeSi(Li)Hgl 2CZTSi-driftSi-PIN200150100500 10 20 30Energy (keV)Figure 5.3.6 Energy resolution (full width at half maximum, FWHM) of 3.5 mm thick HpGe, 3 mm thick Si(Li), 300 µm thickSi-drift, 300 µm thick Si-PIN, 1 mm thick HgI 2 , and 2 mm thick CdZnTeTypical X-ray spectra of a Si-PIN, Si drift, andCdZnTe detector are shown in Figure 5.3.9. Thefollowing considerations can be made, concerningPeltier-cooled semiconductor detectors for portableEDXRF equipment:• the SDD presents the best energy resolutionamong the thermoelectrically cooled detectorsand works also at high count rates, due tothe low shaping time; it is useful up to about25–30keV;• Si-PIN detectors are the most employed in theenergy interval 1–25 keV, in spite of the factthat it works at low count rates;• HgI 2 , CdTe CZT are the best thermoelectricallycooled detectors in the X-ray region of30–120 keV.5.3.2.3 SINGLE- OR MULTICHANNELANALYSERSWhen one or a few elements must be analysed,a single-channel analyser may be employed, witha timer-scaler. The advantage of the small sizeof this solution, which was relevant in the past,is currently replaced by the multichannel analyser(MCA) board coupled to a PC, 6,15,16 or bya pocket MCA coupled to a laptop computer(Figure 5.3.10). 8 All the modern MCA models arenot only able to register and store the X-ray spectra,but are also coupled to dedicated software tocompute chemical elements and relative concentration.5.3.2.4 SOFTWARE FOR THEAUTOMATIC IDENTIFICATION ANDQUANTITATIVE EVALUATION OFELEMENTSThe X-ray spectra recorded by the EDXRF instrumentationmust be analysed in order to extractthe desired information, i.e. the chemical elementcontents.

316 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSIS(a)(b)MERCURY-X(c)(d)Figure 5.3.7 Typical thermoelectrically cooled, small size semiconductor detectors for portable EDXRF analysis. (a) A Si-PINdetector by Amptek, (b) a Si-drift from Roentec (X- Flash 1000), (c) a CZT from eV and (d) a HgI 2 from Constellation Tech.(Published with permission)1001 mm HgI 27.5 µm2 mm CZTEfficiency (%)5012.5 µm3 mm Si3.5 mm Ge25 µm300 µm Si500 µm Si1 10Energy (keV)100Figure 5.3.8 Efficiency of 300 µm thick Si-PIN or SDD, 500 µm Si-PIN, 3 mm thick Si(Li), 3.5 mm thick HpGe, 2 mm thickCZT and 1 mm thick HgI 2 . At low energies the efficiency is determined by the thickness of the Be window (7.5, 12.5 and 25 µmthickness, respectively)

INSTRUMENTATION 317Table 5.3.3 Comparison between the best performances of different commercial X-ray detectorsDetector andperformancesSi(Li) a HpGe b Si-PIN c300 µmSi-PIN d500 µmSi-drift e HgI 2fCZT gEnergy resolution129 115 158 250 129 180 190FWHM at 5.9 keVEnergy resolution at 360 300 – – – 480 50059.6 keVUseful energy range 1–60 1–120 1–25 1–35 1–25 2–120 2–120(keV) hEfficiency (%) at 2 cm 0.002 0.004 0.0014 0.006 0.0006 0.001 0.0018from the sourceShaping time (µs) 6–12 6 20 20 5 12 3Cooling system Liquid N 2 Liquid N 2 Peltier Peltier Peltier Peltier Peltiera Si(Li) with an area of 10 mm 2 and a thickness of 3 mm by VacuTec 21 or ThermoNoran. 22b HpGe with an area of 20 mm 2 and a thickness of 3.5 mm by PGT Sahara. 15c Si-PIN with an area of 7 mm 2 and a thickness of 300 µm by AMPTEK. 8d Si-PIN with an area of 25 mm 2 and a thickness of 500 µm by AMPTEK 8 or Moxtek. 9e Si-drift with an area of 3 mm 2 and a thickness of 300 µm by Roentec Inc. 11 or EIS. 6f HgI 2 with an area of 5 mm 2 and a thickness of 1 mm by Constellation Techn. 12g CZT with an area of 9 mm 2 and a thickness of 2 mm by AMPTEK 8 .h The minimum and maximum detectable energy depends on the thickness of the window (Figure 5.3.8) or of the detector, respectively.Generally an X-ray spectrum is composed of abackground, due essentially to multiple scatteringand noise, and a set of peaks (both fluorescenceand scattered) superimposed to the background.The quantity of interest is the net area under eachphotoelectric peak. To determine it, two possibleapproaches can be used:• a model of the spectrum including the backgroundcontents as well as the peaks part;• extraction of the background on the basis of amodel or a priori hypothesis.The first approach requires a complete knowledgeof the sample, that is generally not available.Thus the second approach is generally used. 16–18,33After extraction and peaks identification, a qualitativedescription of the chemical elements contentscan be given, due to some kind of proportionalityof the peak area to the element content.However, if a quantitative determination ofthe concentrations is required, then peak areamust be further analysed. In fact, the area ofa X-ray fluorescence peak (number of recordedphotons during the analysis time) can be alteredby enhancements and self-absorption phenomenafrom the matrix of the sample or from theenvironment (collimators, detector, air, etc.).The concentration of a given element can beobtained in several ways, and different techniqueshave been developed. The most used in EDXRFis based on the so-called ‘fundamental parameterdetermination’ (FP). It is a set of mathematicalequations of fluorescence emission based on fundamentalphysical parameters and on the instrumentalparameters. The first practical algorithm was proposedby Criss and Birks 34 as a modification of theequations derived by Sherman 35 and Shiraiwa andFujino. 36 A good review article of this and othermethods can be found elsewhere. 18 However, dueto the particular nature of the portable X-ray fluorescencesystems, the FP method cannot be fullyapplied, but requires special procedures for takinginto account the nature of the sample to be analysedor additional information from Compton andRayleigh scattered peaks.A different approach was proposed by Pioreket al., 19 who made use of an identification techniquebased on a χ 2 test of the experimental dataversus reference data. This technique was appliedto commercial alloys and the results are satisfactory.Future improvement of software for EDXRFanalysis with portable equipment will mainlydepend on increasing future computational power.Software which is currently only in top leveldesktop computers and uses sophisticated MonteCarlo codes will be possibly used in normal laptopsand give automatic analysis in a few seconds.

318 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSISPaper analysis from 55 FeCaTiCounts55 FeCaTi5.9 keV6.5 keV0.2 0.9 1.6 2.3 3.1 3.8(a)Energy (keV)4.5 5.2 6.0 6.710 35.55.04.54.03.53.02.52.01.51.00.50.0(b)COFeMg N Si Ca Fe0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 keV6.0005.000Lead fluorescencePb K a175 keV4.000Pb K a272.8 keVCounts(c)3.0002.0001.0000Pb L a10.5 keV Pb L b12.6 keV0Pb L g14.8 keV100 200 300EscapepeaksChannel numberPb K b184.9 keVPb K b287.3 keV400 500 600 700Figure 5.3.9 X-ray spectra from thermoelectrically cooled detectors. (a) Paper analysis with a 55 Fe source and Si-PIN detector; 8(b) low-energy X-ray spectrum collected with a SDD; 11 (c) lead fluorescence with a CdZnTe 8 (with permission of Amptek andRoentec)

INSTRUMENTATION 319EISFigure 5.3.10 Amptek portable EDXRF analysis equipmentwith the pocket MCA. (With permission of Amptek Inc.)Employing codes will also reduce the interactionwith the user to a minimum.In Section 5.3.2.5 some consideration is givento the software used by different manufacturers ofportable EDXRF equipment.5.3.2.5 PORTABLE EDXRFEQUIPMENTIn the last few years there has been an increasingnumber of commercial portable EDXRF equipmentavailable. Some use radioactive sources whileothers use miniature X-ray tubes. The majorityemploy Si-PIN detectors, while several employ Sidrift and HgI 2 . Very few use other detectors, suchas CdTe or CdZnTe (for higher-energy X-rays).Much of this commercial equipment uses multichannelanalysers with dedicated software for theautomatic processing of the data.Table 5.3.4, lists the manufacturers and thecharacteristics of their portable EDXRF equipment.In addition to commercial EDXRF equipment,several research groups have designed and constructedtheir own portable equipment, by assemblingin various combinations X-ray sources,detectors and MCAs.The following is an exhaustive list of commercialEDXRF portable equipment, listed in anarbitrary order:Portable EDXRF analysers were designed andconstructed by EIS, 6 for applications in variousfields (archaeometry, chemistry, industrial). Theyare composed of gas cooled 40–50 kV, 1 mA X-ray tubes with W anode and Be window, of aSDD with about 130–140 eV energy resolutionat 5.9 keV, and of a MCA (Figure 5.3.11). Theequipment is mounted on a tripod. The EISequipment is characterised by the very goodenergy-resolution and reduced thickness of the Bewindow (Figure 5.3.12).No dedicated software is available yet.NITONNITON Co. (Bedford, MA, USA) 37 has developedseveral models of portable EDXRF instruments,such as XL-300, XL-500, XL-700 and XL-800,according to specific applications. The model XL-300 is specifically intended for lead analysis; themodel XL-500 (Prospector) is intended for miningapplications; XL-700 is specifically dedicated tothin film and filters analysis; and the model XL-800 for alloy analysis. All models are composedof a radioactive source and a thermoelectricallycooled detector. The employed radioactive sourcesare: 109 Cd (10 mCi) as standard source, while241 Am, 55 Fe is available upon request.Detectors such as thermoelectrically cooled Si-PIN or CdZnTe are employed.All components are included in a container(size 206 × 75 × 45 mm and weight about 1 kg)(Figure 5.3.13).As the instrument performs multiple measurementsof a sample, the liquid crystal display providesthe following information: the reading number;the serial number of the measurement; theelements that have been detected; and the spectrum.A summary screen is displayed after theinstrument completes a protocol. Measurements foreach detected element are automatically displayedin µg.The mode of operation, ‘paint’, ‘thin’ or‘bulk’ is selected from the main menu displayedon the LCD screen before a test is performed.Measurements for each detected element

320 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSISTable 5.3.4 Characteristics of portable EDXRF equipment and manufacturersManufacturer Radio activesourceX-ray tubeanodekVmaxImaxDetector andenergyresolution (eV)MCA andsoftwareTypicalApplicationWeight of themeasuringheadCost(Euros)EIS – W35 kV1mANITON aXL-800109 Cd– Si-PIN (180 eV)55 Fe241 AmCZTSi-drift (140 eV) MCA Various ≈5 35 000MCA + dedicatedsoftwareAlloys 1 Not availableNITON a XL-300 MCA + dedicatedsoftwareAMPTEK – Mo35 kV0.1 mAThermo MT9000 XRFfield AnalyserThermoNMetallurg. ProLead in paint 1 Not availableSi-PIN (160 eV) MCA Various 3 13 500 b55 Fe– HgI2 MCA + dedicated241 Am109 Cdsoftware55 Fe– HgI2 MCA + dedicated241 Am109 CdsoftwaresVarious, soilsand minerals1.9 Not availableAlloys 1.9 Not availableEDAX a Map-4 c 57 Co – CZT MCA + dedicatedsoftwareEDAX a CT3000 c 109 Cd241 Am– Si-PIN MCA+ dedicatedsoftwaresLead in paint 2.5 Not availableAlloys 2.5 30 000–50 000Roentec ARTAX – W, Mo50 kV1mAXRF Co. 153Gd – CZT MCA + dedicatedsoftwareOxford Instrum.Horizon 600 a ...30 kV– W, Ag, Mo,Warington Inc.LeadStarSi-drift X-flash MCA Works of art High 78 000Peltier-cooleddetectors57 Co – CdTe MCA + dedicatedsoftwareLead in paint Not available ≈10 000Alloys 2 30 000Lead in paint

INSTRUMENTATION 321Figure 5.3.11 EIS portable EDXRF equipment, composed of a small size W anode X-ray tube (40–50 kV, 1 mA) and a highresolution SDD. (With permission of EIS)are automatically displayed and this informationis recorded for later transfer to a PC. Detectionlimits at 99.7 % confidence for a 1 min measurementfor several sample types are reported inTable 5.3.5.The following applications were specificallystudied by NITON:• lead in paint detection;• soil contamination;• site profiling;• confirming containment programmes;• on-site analysis of dust wipe samples;• screening of sludges and liquids;• working exposure monitoring;• air monitoring;• coating and filter analysis.At the end of 2002, Niton Instruments releaseda new generation of portable EDXRF systems:(a) the pistol shaped XL t , an X-ray tube basedanalyser; and (b) the banana shaped XL i , anisotope-based analyser using film 241 . 37AMPTEKAMPTEK Inc., 8 developed over the last few yearsthe Si-PIN detector, which completely changedthe approach of portable EDXRF equipment.Over the years detectors with increasingly betterperformances were constructed and currently Si-PIN detectors with 158 eV at 5.9 keV are available.Also, high resolution CdZnTe detectors wererecently constructed by AMPTEK.AMPTEK researchers applied these detectors toportable EDXRF systems, using various radioactivesources, X-ray tubes and the Pocket AMPTEKmultichannel analyser (Figure 5.3.10).In 2001, a LASER X-ray tube was designedand constructed by AMPTEK, completely batteryequipped. This X-ray tube is contained in a singlecompact enclosure, which includes the X-ray tube,the power supply and the control electronics. TheLASER X box has a weight of 450 g and overalldimensions of 185 × 71 × 33 mm.LASER X has been designed to simplify theEDXRF process by providing a grounded anode,variable current and voltage with operation ease. It

322 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSIS664K531Ar398Cl265132SCaCrFeZn(a)2.22 4.44 6.66 8.88 11.08 13.30 15.521331FeCu1065Zn798532 AlCaMnNiAr265SiCr(b)2.22 4.44 6.66 8.88 11.08 13.30 15.52TiFigure 5.3.12 Typical X-ray spectra obtained with the equipment in Figure 5.3.11. (a) X-ray fluorescence spectrum of the headof a match, containing P, S, Cl, Ar (from the air), K, Ca, Mn, Fe, Zn. (b) X-ray fluorescence spectrum of an Al-alloy, containingAl, Cl, Ar (from the air), K, Ca, Ti, Cr, Mn, Fe, Ni, Cu, Zn

INSTRUMENTATION 323Table 5.3.5 Detection limits (DLs) for the Niton 701 at 99.7 %confidence level for a 1 min measurementElementThin samples(µg/cm 2 )DL (µg) for25 mm diameterfilterL X-raysLead 0.5 4Uranium 0.6

324 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSISFigure 5.3.14 Roentec ArtAX equipment. The X-ray tube and detector, and the XYZ stage with stepper motors, is shown on theleft and the control unit on the right. (With permission of Roentec GmbH)instrument is contained in a case weighing approximately2.5 kg (including the battery) and has a sizeof 25.4 × 20.3 × 10.2 cm (Figure 5.3.15). Dedicatedsoftware is included, based on a specialisedFP method, that carries out automatic calibration,background subtraction, and quantitative evaluationbased on fundamental parameters. Using the‘chemistry’ mode of the ‘Positive Metals Identification’(PMI) software, a quick and accurateresult is obtained. The results of a measurement,the spectrum and the intensity data for each essaycould be easily downloaded into a computer usingRS232C serial cable. With two rechargeable NiCdbatteries, the analyser could be used for 8 h of continuousoperation.Typical alloy analysis includes stainless steel,cobalt alloys, nickel alloys, copper–nickel alloys,bronzes, brasses, aluminium alloys, titanium alloys,molybdenum alloys and lead alloys.As of 2003, EDAX no longer markets andsells radio isotope products. EDAX now constructsand supplies the ‘Alloy Checker’, an X-ray tube based system weighing approximately2.2 kg (Figure 5.3.15). It replaces the CT3000system and the specifications are almostidentical.9000 XRF Field Analyser and Metallurgist Proby Thermo Measure Tech and ThermoNoranThermo Measure Tech 39 constructs a portableEDXRF instrument (9000 XRF Field Analyser,Figure 5.3.16) mainly composed of: (a) radioactiveexcitation sources such as 55 Fe for analysisof S to Cr, 109 Cd, for analysis of Ca toRh (K X-rays) and Ba to U (L lines), and241 Am for analysis of Cu to Tm (K X-rays)and W to U (L lines); (b) thermoelectricallycooled HgI 2 detector; (c) 2000 channels multichannelanalyser with spectrum smoothing, energycalibration and automatic peak identification;(d) dedicated software packages. The 9000 XRFunit includes a probe, with X-ray source anddetector, and the MCA. The probe weighs 1.9 kgand has dimensions of 12.7 × 7.6 × 21.6cm,

INSTRUMENTATION 325(a)(b)(c)"Unlimited" mode assays take as little as 1 toproduce a definitive lead classification with 95%confidence and no substrate correction.A full spectrum analyzer which provides both K and Lshell results simultaneously and can store over 6000assays, including full energy spectra.Detection Limits (mg/kg)AntimonyArsenicBariumCadmiumChromiumMercuryLeadNickelSilverSeleniumThallium145610951071515411Typical Alloy AnalysisStainless SteelHast AlloysTool SteelsCobalt AlloysNickel AlloysCopper−Nickel alloysBrassesBronzesAluminum alloysZirconium alloysTitanium alloysMolybdenum alloysLead alloysFigure 5.3.15 EDAX portable EDXRF models. (a) MAP-4 for lead-based paint analysis; (b) CT2000 for metal analysis;(c) CT3000 for alloy analysis. (With permission of EDAX)and is suitable for either in situ, field or laboratorymeasurements. The 9000 XRF Analysercan be operated from a battery/AC line(Figure 5.3.16). Source selection and acquisitionare automated through stored, user-defined analysisprocedures.Each data acquisition procedure includes selectionof source, acquisition time, computationmethod and display of analysis results. Componentsof the microprocessor based analyserinclude a user interface keypad, LCD display,2000 MCA, data storage memory and RS-232communication port. The system may be poweredby either an internal battery pack or externalAC power with results up to 300 analyses(each with up to 25 elements). The ApplicationGenerator is a PC software package. Its menudrivenoperator interface provides easy access toa complete range of software tools for developingprocedures.The 9000 XRF Field Analyser uses the FPmethod. Three operations are sequentially performed(Figure 5.3.16): (a) measurement of theX-ray lines intensity from a pure element sample;(b) determination of the fluorescent yield ofthe analyte (from tabulated data); (c) determinationof the matrix terms that can alter the originalintensity emitted (enhancement and selfabsorptionphenomena).Several calibration models are also available.Analysis results from each model are comparedwith results from the others to determine the

326 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSISlibrary of over 225 alloys, with the capability forthe user to input 25 custom alloys.Table 5.3.6 shows the minimum detection limitsof the equipment for various elements in alloys.Horizon 600 Alloy Sorter from OxfordFigure 5.3.16 9000 Field Analyser for portable EDXRFanalysis and working operations. (With permission of ThermoMeasureTech)optimum analysis conditions for the application.Typical detection limits for soil analysiswith various radioactive sources are shown inFigure 5.3.17.The Metallurgist Pro equipment uses 55 Fe,109 Cd or 241 Am sources with a HgI 2 thermoelectricallycooled detector (Figure 5.3.18). The equipmentis specifically dedicated to alloy analysis, andis able to analyse up to 21 elements at the sametime. It is preprogrammed with a comprehensivePortable EDXRF equipment was recently constructedby Oxford, 5 called the Horizon 600 AlloySorter. This equipment, shown in Figure 5.3.19,is specifically dedicated to analysis of alloys. It isable to analyse elements from calcium (Z = 20) touranium (Z = 92), and up to 20 elements simultaneously.It is mainly composed of a digital ‘coldcathode’ X-ray tube working up to 30 kV, andequipped with a programmable primary beam filter.The detector is a high resolution, thermoelectricallycooled solid state semiconductor detectorwith the pulses from the pulse amplifier processedin a 1024 MCA. Dedicated software automaticallygives the elements of the analysed alloy with theircorresponding concentration. The equipment isfully battery operated and has a weight of approximately2 kg and a size of 24 × 20 × 12 cm 3 .1000Fe55SoilCd109PPM (mg/kg)10010Cd109Am241All data pertains to a blank (SiO2) soil matrix.Total measurement times were approximately 3 min/source.1 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxFigure 5.3.17 Typical minimum detection limits for soil analysis with the 9000 Field Analyser. (With permission of ThermoMeasureTech)

INSTRUMENTATION 327Table 5.3.6 Minimum detection limits (in %) of the MetallurgistPro for various elements in different alloys, in a measuringtime of 19 sElement Mild steel Stainless Inconel Cu–Zn AluminiumTi 0.015 0.02 0.05 0.03 0.015V 0.008 0.02 0.02 0.01 0.01Cr 0.06 0.3 0.4 0.06 0.07Mn 0.15 0.25 0.2 0.04 0.06Fe 0.5 0.5 0.25 0.07 0.03Co 0.2 0.3 0.2 0.05 0.02Ni 0.15 0.4 0.5 0.08 0.015Cu 0.08 0.2 0.25 0.35 0.015Zn 0.05 0.1 0.25 0.3 0.012Se 0.02 0.02 0.02 0.05 0.003Zr 0.03 0.04 0.04 0.04 0.003Nb 0.005 0.008 0.06 0.008 0.003Mo 0.005 0.015 0.1 0.008 0.003Ag 0.6 0.6 0.9 0.8 0.8Sn 0.15 0.15 0.2 0.2 0.2Ta 0.1 0.15 0.2 0.9 0.025W 0.15 0.2 0.2 0.9 0.025Au 0.1 0.15 0.15 0.4 0.02Pb 0.035 0.04 0.04 0.04 0.005Bi 0.035 0.04 0.04 0.05 0.005As 0.03 0.04 0.04 0.07 0.006Re 0.08 0.1 0.1 0.35 0.015Y 0.01 0.01 0.01 0.01 0.002Figure 5.3.19 The Horizon 600 Alloy Sorter. (Providedcourtesy of Oxford Instruments)composed of a 153 Gd radioactive source, a CdZnTedetector and a MCA (Figure 5.3.20). An annualsource replacement is recommended.Figure 5.3.18 The Metallurgist Pro model. (With permissionof Thermo Noran)ICS-4000 by XRF CorporationXRF Corporation 40 manufactures analytical instrumentationto detect γ - and X-radiation in the field.The ICS-4000 spectrometer is specially designedfor fast, accurate field analysis in a variety ofhealth physics, nuclear medicine and environmentalmonitoring applications. This device incorporatesa sensitive CdZnTe detector with a powerfulMCA.The XRF/Pb model is specifically devoted toEDXRF analysis of lead in painted surfaces, dustand soil. This hand-held equipment is basicallyX-MET 880, 970 and 2000 from MetorexThe X-MET equipment from Metorex 41 is specificallydesigned and constructed for alloy analysisand control of coating processes. The equipmentis mainly composed of a radioactive source ( 55 Fe,109 Cd or 241 Am) of a high-resolution Si-PIN detectorand a 2048 channel MCA for data acquisition.Dedicated software can utilise either fundamentalparameters or empirical methods. Data collection,analysis and management is completelyautomated. The software can store thousands ofanalytical results.The X-MET equipment have a weight of5.8 kg and dimensions of 36 × 29 × 10 cm 3(Figure 5.3.21). The measuring head has a weightof about 2 kg.

328 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSISFigure 5.3.20 The ICS-4000 portable EDXRF analyser for leadanalysis. (With permission of XRF Co.)Typical applications include: phosphate on zinccoated steel, where P is analysed in a range of0.5–2 g/m 2 , in a measuring time of 5 s; chromateon zinc coated steel, where Cr is measured ina range of 0–70 mg/m 2 , in a measuring timeof 120 s; chromium on aluminium, where Cr isanalysed in a concentration range of 0–70 mg/m 2in a measuring time of 120 s; and titanium onaluminium, where Ti is analysed in a range of0–40mg/m 2 , in a measuring time of 120 s.The X-MET 2000 is specifically dedicatedto alloys analysis. The following alloys can betypically analysed: nickel alloys, containing Ti, Cr,Mn, Fe, Co, Ni, Cu, Nb, Mo, W; stainless steels,containing Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Nb, Mo,W; cobalt based alloys, containing Cr, Mn, Fe, Co,Ni, Mo, W; low alloy steels, containing Cr, Mn,Fe, Ni, Cu, Mo; tool steels, with V, Cr, Mn, Fe,Co, Ni, Mo, W; aluminium alloys, with Mn, Fe,Ni, Cu, Zn; copper alloys, with Mn, Fe, Ni, Cu, Zn,Sn, Pb; titanium alloys, containing Ti, V, Fe, Cu,Zr, Nb, Mo, Sn to name a few, there are additionalalloys as well.Lead Star and µ-Lead by WarringtonFigure 5.3.21 The X-MET 880 Alloy Analyser. (With permissionof Metorex International Oy)The X-MET 880 model is a portable tool foranalysis in the field. It is capable of measuring80 elements in the periodic table from atomicnumber 13 (aluminium) through to atomic number92 (uranium). Analyses includes stainless steels,chrome molybdenum steels, tool steels, alloysteels, nickel, cobalt, copper, titanium, aluminium,magnesium, zinc and lead based alloys.The X-MET 970 model is specifically suited forreal-time analysis of thin and ultra-thin coatings.Two models of portable EDXRF instrumentswere developed by Warrington Inc. for leadanalysis of paint. 42 The first one, µ-LEAD, isbased on a 10 mCi 57 Co source, and a scintillationdetector with filtering techniques. Thesecond one, the LeadStar, uses a CdTe detector.Both employ MCAs and dedicated software.Figure 5.3.22 shows the LeadStar instrument.Besides commercial portable EDXRF equipment,various additional equipment has beendesigned, constructed and developed for scientificpurposes by various research groups around theworld. They will be discussed in the next section.5.3.3 APPLICATIONSAs shown above, portable EDXRF equipmentcan be employed in many fields and for manyapplications. In the following, typical applicationsare shown both of commercial equipment and of

APPLICATIONS 329Figure 5.3.22 The LeadStar instrument by Warrington for lead analysis. (With permission of Warrington Inc.)equipment assembled by various research groupsin the following fields:• archaeometry;• environmental analysis;• analysis of lead in paint;• analysis of industrial alloys;• soil analysis;• mineral analysis;• in vivo and human analysis of trace elements;• analysis of soil on Mars (Pathfinder mission).Some selected applications in some of these fieldsare discussed in the following.X-ray tube, working at 5 kV, 0.1 mA (which isnot able to excite Ca), a thin-window Si-PINdetector and an AMPTEK pocket MCA. Thisequipment can also excite lower Z elements,such as Al, Si and P 43–45 (Figure 5.3.23).• For analysis of ancient gold alloys, composedof gold, silver and copper, and bronzes, generallycomposed of copper, tin and lead, theyemployed a W anode 30–35 kV, 0.2 mA X-raytube, a Si-PIN detector and an AMPTEK pocketMCA 46–48 (Figure 5.3.24).• For analysis of pigments in paintings andfrescoes. The same system can be employed,used for analysis of alloys (Figure 5.3.24).5.3.3.1 ARCHAEOMETRYPortable EDXRF equipment is, of course, especiallysuited for analysis of works of art, thatrequire nondestructive and on site analysis.In the last 5 years Cesareo and co-workers 43–49have designed and constructed various portableEDXRF equipment for applications in the field ofarchaeometry:• For analysis of S and Cl in frescoes, theydeveloped equipment composed of a Ca anodeThe most recent and interesting application ofportable equipment used in the study of works ofart was the analysis of the famous frescoes in theChapel of the Scrovegni painted by Giotto in Paduaduring the period 1303–1305. 49Begun in 1303 and consecrated on 25 March1305, the chapel, dedicated to Our Lady ofthe Annunciation, was commissioned by EnricoScrovegni in suffrage for the soul of his father,Reginaldo, accused of usury. It was E. Scrovegniwho commissioned Giotto to execute the frescoesin the interior of the chapel; this cycle of paintings

330 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSISFigure 5.3.23 Portable equipment for the analysis of sulfur in frescoes and monuments. A Ca anode X-ray tube is employed,working at 6 kV and 0.1 mA, a thin window Si-PIN detector, and a SILENA MCAsignals ‘a point of no return in the entire historyof western painting’.In the period of EDXRF analysis, i.e. July2001–January 2002, the frescoes were underrestoration, and the following problems wereexamined:• detection of the presence of S or Cl on thesurface of the frescoes, which is a signal ofpollution, and its removal;• detection of the presence of elements showingprevious restoration areas (signaled, forexample, by the presence of titanium or zinc);• determination of the pigments used by Giotto,with special notice to gold haloes.The variety of X-ray spectra of pigments is shownin Figure 5.3.25.The possible presence of sulfur and chlorinewas determined with two different types ofequipment: one using the Ca anode X-ray tube,described previously, and the second one using aPd anode X-ray tube working at 6–8 kV, to selectivelyexcite Pd L lines, which, having an energyof about 2.8 keV, are suited to the excitation of sulfurand chlorine. The use of the Ca anode X-raytube gives rise to a ‘cleaner’ spectrum with respectto the Pd L X-ray tube, but the counting rates aremuch lower, due to the large output window of thefirst tube (X-ray tubes output irradiate an area ofabout 1 cm 2 ).The fresco pigments were also analysed withthe same Pd X-ray tube working at 10 kV, andwith a W X-ray tube working at 30–35 keV. Thefollowing results were obtained:

APPLICATIONS 331Figure 5.3.24 Portable equipment used for the analysis of alloys (bronzes, brasses, gold) and pigments. A W anode X-ray tubeis employed, working at 35 kV, 0.3 mA and a Si-PIN or Si-drift detector. The equipment is shown during measurements on goldcomposition of the altar of S. Ambrogio, in Milan• Sulfur was detected everywhere, at a concentrationlevel from about 1 % to about 10 %,depending on the exposition and on the undergoingpigment; sulfur content was for examplelower in the case of azurite pigments, higher inthe white and green pigments.• The S content strongly decreased after using acleaning process based on ion-exchange resins(Figure 5.3.26)• Chlorine was detected only once, in an area thatwas possibly recently cleaned.• Titanium was detected in many areas, indicatinga recent restoration; additionally this elementwas then ‘cleaned’.• Gold of the haloes shows a complicated X-rayspectrum, corresponding to a number of layers(Figure 5.3.27).About 40 haloes were analysed, many of them ingood condition (gold haloes), others damaged, andothers completely black.X-ray spectra of a good condition gold halocompared with a black halo are shown inFigure 5.3.27. From left to right peaks are visibledue to the following elements: sulfur K lines at2.3 keV, due to pollution effects; argon K lines, at2.95 keV, due to the air; tin Lα lines, at 3.45 keV;calcium K lines, at 3.7 keV, mainly due to the plaster;iron Kα and Kβ lines, at 6.4 and 7.06 keV;nickel Kα and Kβ lines, at 7.5 and 8.3 keV, dueto background effects; copper Kα and Kβ lines, at8.04 and 8.94 keV; tungsten L lines, at 8.35, 9.8and 11.3 keV, respectively, due to the X-ray tubeanode; gold L lines, at 9.67, 11.5 and 13.4 keV;silver K lines, at 22.1 and 25.2 keV, due to fluorescenceeffects in the detector; lead L lines, at10.5, 12.6 and 14.8 keV; strontium Kα lines, at14.15 keV, due to the plaster; tin Kα and Kβ lines,at 25.2 and 28.7 keV, respectively.There are several cases of partial or totalpeaks overlap: sulfur K with lead M, tin L withcalcium K, gold Lα with tungsten Lβ.

332 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSISFAFACEDBEBDCFigure 5.3.25 A general view of The Last Judgement by Giotto in the Chapel of the Scrovegni, Padua, Italy. There is a varietyof pigments producing a variety of X-ray spectra: A–a red flag; B–a gold halo in good condition; C–a black halo; D–medallionto the left of God; E–white flag; F–green flag

APPLICATIONS 333260024002200200018001600X-Ray spectrum (no treatment)Japanese paperAmmonium carbonate (5 min)CaCounts140012001000800600400200Resins (5 min)Resins (10 min)SResins (15 min)ArKCa01.52.0 2.5 3.0Energy (keV)3.5 4.0 4.5 5.0Figure 5.3.26 X-ray spectra of sulfur in frescoes, obtained with the Hamamatsu Ca anode X-ray tube, and with the Si-PINdetector3000Pb LaCa K2000Sn LAu LaPb LbCounts1500Cu KW LaW LbSn Ka1000Fe Ka9.2Au LbAr KNi K500S KFe KbSrPb LgSn-Kb02 4 6 8 10 12Energy (keV)14 16 24 26 28 30Figure 5.3.27 EDXRF spectra of a golden halo (darker line) and a black halo. The spectra are relatively complicated including:S K lines; Ar K lines; Sn Lα line; Ca K lines; Mn Kα line (in traces); Fe Kα and Kβ lines; Ni Kα line; Cu Kα line; W Lαand Lβ lines; Pb Lα, Lβ and Lγ lines; Sr Kα line and Sn Kα and Kβ lines. The differential attenuation of Pb L lines is clearlyvisible in both X-ray spectra: in the golden halo the Pb Lβ line is more attenuated by the Au leaf than the Lα line; in the blackhalo the Pb Lβ line is less attenuated by the effect of the Sn sheet. The difference in the copper content between the black andgolden halo is also remarkable

334 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSISNot considering X-rays of the elements argon,nickel, tungsten and silver, which are not due tothe interaction of the X-ray beam with the fresco(argon is dependent on the air; nickel on the X-ray tube window, tungsten on the tube anode; andsilver, at least partially, on the Si-PIN detector), theother X lines are related to the fresco pigments.However, they must be assigned to the properfresco layer.In the following, only haloes in good conditionwill be considered. First of all, the ratio of theX-rays of all elements with respect to gold L X-rays was calculated, and the Pb (Lα/Lβ) ratio(Table 5.3.7). If an element belongs to the goldalloy, then its ratio with respect to gold shouldremain approximately constant.From these ratios and from the mean valuesit may be deduced that not one of the elementsbelongs to the gold alloy. Therefore, the goldshould be of high purity.Further, it may be deduced that lead/gold isnot varying too much, and, therefore, lead can beassigned to the ‘second level’. In this hypothesis,the Pb L lines should be attenuated in a differentmanner by the gold leaf. This effect is, in fact,clearly visible in Figure 5.3.27, where the differentialattenuation of Pb Lα andPbLβ lines bygold and in the absence of gold is clearly visible.Calculating this effect for all gold haloes ingood conditions, the mean thickness of the goldlayer may be calculated, which turns out to be1.6 ± 0.5 µm. From this result it may be concludedthat the gold leaf is extremely thin (minimum value1.0, maximum value 2.6 µm) and of relativelyconstant thickness.The attenuation of lead X lines (lead is presentas white lead, i.e. basic carbonate of lead) by thisgold leaf is about a factor of 2. The thicknessof this layer of white lead can be calculatedfrom the Pb/Au counts ratio and from the Authickness as about 5 µm of Pb equivalent thickness,corresponding to a much larger thickness ofthe pigment.The situation concerning the attribution ofcopper to the correct layer is complicated. Lookingat the X-ray spectra, it turns out that X-rays ofCu are clearly more intense when the halo issuperimposed to an azurite background, which isat a deeper layer than lead. Excluding these cases,the ratio Cu/Au will be lower and also moreconstant ≈0.6 ± 0.25. It is therefore reasonablethat Cu X-rays come both from the azurite andfrom the glue between the lead carbonate andgold. This hypothesis seems to be confirmed byFigure 5.3.27. From the ratio Cu/Au ≈ 0.6 it turnsout that the copper equivalent thickness betweenlead and gold is about 1 µm. Larger, by a factorof 2–3, should be the Cu equivalent thicknesscorresponding to azurite.Finally calcium, iron and strontium shouldcome, at least partially, from the plaster. However,in this hypothesis Ca K lines are attenuated bylead carbonate, copper and gold, giving rise toan attenuation factor of about 5 × 10 5 ,whichistoo high to give reasonable Ca counts in the X-ray spectra. These should also come from calciumcarbonate deposit on the surface of the fresco, dueto pollution.In conclusion, the golden haloes in Giotto’sfrescoes are composed of the following layers:• a superficial layer of sulfur, in the form ofcalcium sulfate due to pollution effects overthe centuries;• a layer of pure gold, with a mean thickness of1.6 µm;• a layer of glue containing copper, with anequivalent Cu thickness of about 1 µm;• a layer of white lead, with an equivalent Pbthickness of about 5 µm;• a possible layer of azurite, containing copper;• the plaster containing iron and strontium.Table 5.3.7 Pb(Lα/Lβ) ratio and ratio of the intensity ofelemental X-rays with respect to gold intensityPb(Lα/Lβ) Pb Lα/Au Lβ Fe/Au Cu/Au1.74 ± 0.09 5.6 ± 2.2 4.1 ± 3.0 1.3 ± 1.45.3.3.2 ENVIRONMENTAL ANALYSIS:ANALYSIS OF LEAD IN PAINTSOne of the most serious public health hazards,which particularly affects children, is related to

APPLICATIONS 335lead-based poisoning from the paint found in manyold houses. For example, the estimated numberof apartments in New York City alone that maybe affected by this hazard is greater than 300 000and they are mainly occupied by low-income families.Recent legislation in the US provides specificrequirements for new inspection proceduresin federally funded housing programmes as wellas for the disclosure of information and inspectionsduring the sale and transfer of all private residentialhouses constructed prior to 1978. Inspectioncompanies and state and federal agencies, whichare charged with the responsibility of supervisingcompliance with this legislation, employ EDXRFhand-held instruments for on-site detection of leadconcentration in paint. An abatement plan to eliminatepaint poisoning hazards can be required forconcentrations of lead in paint equal to or exceeding1 mg/cm 2 . This application also demonstratesthe necessity of using K X-rays in the determinationof Pb concentration. The Pb L X-rays canonly serve as supplementary information, due totheir strong attenuation by paint overlays. The highenergy of the Pb K X-rays (75 and 85 keV) imposesalso additional restrictions on the choice of theexcitation source and detector.Excitation radioactive sources can be used, suchas 57 Co and 109 Cd; in this case they are morepractical than X-ray tubes for portable instruments.Further, Peltier-cooled CdZnTe or HgI 2 near roomtemperature are favoured in this application.5.3.3.3 ANALYSIS OF INDUSTRIALALLOYSThe last 20 years are marked by the continuouslyincreasing use of EDXRF analysers for alloyassaying and identification, specifically in thisfield. This trend has been initiated by the adventof inexpensive memory and microprocessor chips.Another factor contributing to the success ofEDXRF in alloy sorting is its ability to make thedecision about alloy grade automatically.Important properties of alloys are the directconsequence of their chemical composition. Up toabout 50 chemical elements are involved to makethousands of alloys known to be in use. However,Table 5.3.8 EDXRF performancein identification of commercialalloysAlloyIdentificationresults (%)Ni–Cu 100Cu 90–100Cr-Mo steels 95–100Ti alloys 95–100Al alloys 90–100only about 10 to 20 elements can be found in anysingle alloy and only about 10 elements need tobe monitored in a sample of an alloy in order topositively identify it.The most obvious approach to alloy identificationwould be to measure the chemical compositionof an alloy, and then compare its composition withtabulated data of elemental concentration rangesfor each alloy. This method of identification isnot very efficient because of the relatively longtime required. Faster and more effective algorithmshave been developed, using a mathematical formalismof the χ 2 distribution, based on comparisonof the net X-ray intensities of selected elementsin the unknown sample, with those of the knownreference samples. 19 Typical identification resultsand performances are shown in Tables 5.3.8 and5.3.9, where Metorex X-MET 2000 equipment wasemployed, which uses a 109 Cd radioactive source.5.3.3.4 ANALYSIS OF SOILS ANDROCKSSoil analysis is a typical subject for commercialEDXRF equipment (Table 5.3.4), but manyresearchers are working in this field also with selfmadeequipment.Field analysis of soils and rocks by portableEDXRF analysis was systematically carried out byPotts et al. 50–54 They employed commercial equipmentwith 55 Fe, 109 Cd and 241 Am sources and aHgI 2 detector for analysing soil and rocks in situ.The authors first developed a correction procedurefor surface irregularity effects. In fact, veryfew samples on which in situ measurements aremade are perfectly flat as calibration samples. Discrepanciesin measurements will then occur. For

336 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSISreal samples, the most common situation is thatthere is an air gap between the sample surfaceand the analyser head. A simple correction procedurewas investigated, based on the intensityof the scatter peaks observed when the sample isexcited with (monoenergetic) radioactive sources.The principle of the procedure is that if the intensityof this scatter peak is affected by surfaceirregularity effects to the same extent as fluorescenceintensity, and if the scatter peak intensityfrom a perfectly flat surface is known, then it ispossible to calculate a corrected fluorescence intensityrepresentative of that that would be observedfor a flat surface in contact with the portableEDXRF analyser. The measurements showed thatthe correction is effective for air gaps of up to 3to 4 mm.Potts et al. 52 further studied the effects of granulometry.Accepting that almost all silicate rocksamples are crystalline, it is clear that for mediumand coarse grained rocks, the volume of samplefrom which the X-ray fluorescence signal originatesmay not have a mineral assemblage that fullyrepresents the average composition of the sample.This effect will cause additional uncertainty in themeasurement due to the finite number of mineralsof each type within the excited volume. A series ofportable EDXRF measurements was made, therefore,of a range of flat polished blocks of rock,having grain sizes that varied from fine to mediumto coarse. Results indicated that a 10 % samplingprecision can generally be achieved for a singledetermination on fine to medium grained rocks.When a coarse grained Shap granite was investigated,the corresponding figure for the number ofseparate determinations that must be averaged toachieve 10 % sampling precision was 21. The conclusionwas that grain size may have a considerableeffect on the precision of analytical results.Argyraki et al. used the same equipment forthe determination of lead in contaminated soil, 53i.e. a medieval lead smelter site at Bowle Hill,Wirksworth, Derbyshire, active over 500 yearsago.Portable EDXRF analysis is particularly suitedfor the analysis of lead, because the detection limitsof portable equipment (typically about 50 ppm)are a factor of 10 times lower than the triggerlevel for this element (500 ppm for domestic parksand allotments) so that sensitive measurementscan be made down to concentrations at which arisk assessment would be necessary to assess theimpact of the lead contamination.The site at Bowle Hill is currently a grass fieldcovering the upper part and top of a scarp slopewhich overlooks a valley. A detailed investigationby Imperial College using Auger sampling andLaboratory ICP-AES was made for comparison.The following observations resulted:• PXRF data gave systematically low resultsbecause of the presence of moisture.• Further discrepancies in the PXRF results aredue to the fact that the analysed sample surfaceis not flat.• Care is required in comparing laboratory measurementson samples removed from the sitewith in situ measurements because of differencesin the nature of the samples, even if determinationsare made at the same location.• It is essential to collect a certain proportion ofsamples in duplicate.Table 5.3.9 Typical performance of the EDXRF analyser in alloy analysis 41Alloy Ti Cr Mn Fe Co Ni Cu Zn NbMo Sn PbLow alloy 0.01 0.02–0.04 0.1 0.2–0.25 0.25–0.50 0.1 0.05–0.25 0.10–0.15 0.006 0.15 0.15steelStainless 0.02 0.2 0.1 0.2 0.1 0.2 0.06 0.2 0.01 0.3 0.05Steels 0.03 0.3 0.2 0.3 0.5 0.5 0.1 0.03 0.3Ni/Co 0.1 0.2–0.5 0.1–0.3 0.12–0.5 0.1–0.5 0.2–0.5 0.05–0.3 0.3 0.04–0.08 0.3 0.15AlloysCu-alloys 0.02 0.1 0.02–0.06 0.02–0.06 0.05 0.05–0.08 0.15–0.4 0.03–0.07 0.01 0.008–0.2 0.2–0.3Al-alloys 0.02 0.05–0.2 0.1 0.04–0.1 0.05 0.04 0.05 0.06 0.003–0.005 0.005–0.2 0.01–0.02Ti-alloys 0.2–0.6 0.1 0.1 0.06 0.05 0.05 0.02 0.02 0.01 0.005 0.01

APPLICATIONS 337• Provided in situ results are corrected formoisture content and for surface irregularityeffects, there is no significant bias betweenin situ portable EDXRF analysis and laboratorymeasurements for lead. However, greatervariation was observed in the portable EDXRFresults, because of the much smaller mass of soilfrom which the analytical signal was derived.Similar measurements were carried out by Pottset al. 54 to evaluate sources of arsenic contaminationat a heritage industrial site.Kump et al. 55 developed a quantification procedurefor in situ EDXRF analysis of soil, basedon the spectrum analysis file from AXIL. 56 Then aMontana soil SRM 2710 was analysed in the laboratoryboth with a Si(Li) and a Si-PIN detector.Typical results are shown in Table 5.3.10.5.3.3.5 ANALYSIS OF TRACEELEMENTS in vivo AND IN HUMANSThe use of X-ray fluorescence for the determinationof heavy metals such as lead, cadmium,platinum, mercury and gold in vivo is nowa fairly widespread technique 1,56–59 In vivo X-ray fluorescence was first used to measure boththe concentration and distribution of iodine inTable 5.3.10 Analysis results and reference data for SRM 2710Montana soil (g/g)ElementReferencedataMeasuredby Si(Li)Measuredby Si-PINAl 0.0644 0.121 0.095Si 0.289 0.31 0.31S 0.0024 0.0049 0.0036K 0.021 0.020 0.020Ca 0.0125 0.0115 0.0121Ti 0.00283 0.0023 0.0023Mn 0.01 0.0105 0.01Fe 0.0338 0.0371 0.0345Ni 0.000014 – 0.00028Cu 0.000295 0.0032 0.0031Zn 0.00695 0.0073 0.0066As 0.00063 0.00095 0.00093Pb 0.0055 0.0045 0.0053Rb 0.00012 0.000114 0.000077Sr 0.00033 0.00030 0.00026Y 0.000023 0.000037 0.000017Zr – 0.00012 0.00009Nb – 0.0000072 –the thyroid. This particular application had theadvantage from the analytical point of view thatthe iodine concentration in the thyroid is comparativelyhigh (≈400 ppm) and the thyroid is arelatively superficial organ. An increasing rangeof applications followed, the first of which waslead in fingerbone and teeth. Bone lead measurementshave subsequently been extended toinclude the tibia and calcaneous, while the otherelements studied include mercury and strontiumin bone, and cadmium, platinum and lead inthe kidney.The use of external radioisotope sources hasbeen very successful for the determination ofmetals in organs with little overlying tissue, suchas lead in the tibia. However, for organs atlarger depths, much higher skin doses and longerirradiation times are required.Concerning lead analysis, the tibia is typicallytested because of the favourable and superficialposition of this bone. Lead concentration inthe tibia ranges between a few ppm to about100 ppm.Two X-ray fluorescence techniques are traditionallyemployed for the in vivo measurement oflead in bone: K X-ray fluorescence (KXRF) andL X-ray fluorescence (LXRF). The KXRF techniquehas been more widely used and validated.It measures lead approximately 37 mm into thebone and therefore, it provides data on the totalamount of lead throughout the bone. The LXRFtechnique, which has been used mainly in paediatricstudies, measures lead only 2 to 3 mm intothe bone.Typical, modern and portable equipment forKXRF analysis uses a radioactive source for KX-ray excitation ( 57 Co, 152 Gd or 109 Cd, usingthe 88 keV emission, but also 99m Tc and 133 Xewere previously employed) and a semiconductordetector that can be a nitrogen-cooled HpGe,or Peltier cooled, high resolution and large areaCdZnTe or HgI 2 .For LXRF analysis portable equipment can beemployed, which uses a low-power Mo anode (orother material) X-ray tube and a large area Si-PIN detector.

338 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSIS5.3.3.6 ANALYSIS OF SOIL ON MARS;THE α-PROTON X-RAYSPECTROMETER (MARS PATHFINDERAPXS)A very interesting application of portable equipmentfor X-ray analysis is the portable apparatustransported on the Martian surface to determinethe chemical composition of Martian soiland rocks 60–62 (Figure 5.3.28). On 4 July, 1997,the portable EDXRF apparatus constructed foranalysing rocks landed on Mars.The principle of the APXS technique isbased on three interactions of α particles froma radioisotope source with matter: (a) simpleRutherford backscattering; (b) production of protonsfrom (α,p) reactions on light elements;and (c) generation of characteristic X-rays uponrecombination of atomic shell vacancies createdby α bombardment. Measurement of the intensitiesand energy distributions of these three componentsyields information on the elemental chemicalcomposition of the sample. In terms of sensitivityand selectivity, data are partly redundant andpartly complementary: α backscattering is superiorfor light elements (C,O), while proton emissionis mainly sensitive to Na, Mg, Al, Si and S,and X-ray emission is more sensitive to heavierelements (from Na to Fe and beyond). Actually,charged particle excitation is preferred to any otherkind of excitation since it produces the best signalto noise ratio due to the absence of any Comptonscattering.The APXS equipment consists of two parts:the measuring head and the electronic box. Themeasuring head contains nine 244 Cm sources in(a)100000SiAlIntensity100001000MgSKCaTiCrMnFe1001001 2 3 4Energy (keV)5 6 7 8(b)Figure 5.3.28 (a) APXS instrument for Martian soil analysis, composed of a 244 Cm α source and a Si-PIN detector; (b) a relatedX-ray spectrum. (With permission of John Wiley & Sons, Ltd.)

REFERENCES 339a ring-type geometry and three detectors for themeasurement of the three components: a telescopeof two Si detectors for the measurement of α-particles and protons and a Si-PIN X-ray detectorwith its preamplifier.One of the most exciting aspects of the MarsPathfinder APXS experiment is the way it willbe deployed to analyse Martian surface soil androck samples. While usually the APXS instrumentis deployed after the landing, and therefore itwill analyse whatever single sample happens tobe under the instrument, the APXS on the MarsPathfinder is mounted on one end of a rover thatwill give it unlimited mobility around the landingsite. The deployment mechanism will place theAPXS vertically for soil analysis and horizontallyagainst a rock.A laboratory unit identical to the flight unitwas used in the laboratory to derive the elementallibrary and to establish the accuracy and thedetection limits of the Mars Pathfinder APXSinstrument (Figure 5.3.28).Figure 5.3.28 also shows X-ray spectra ofthe Allende meteorite obtained in the laboratoryinstrument using 244 Cm α excitation source. Theresolution of the Si-PIN detector is even better thanthe previous version based on HgI 2 detectors: it isgood enough to separate the K lines from almostall elements and for the heavier elements even theK lines. There were other advantages: Si, besidesbeing a much easier material to handle and procurefor space applications produces significantly bettersignal to noise ratio, especially in the 1–10 keVX-ray region.The X-ray spectra provide information on elementsheavier than Na, but matrix effects play animportant role. The approach taken is an interactiveone: in a first step, data from the α and protonspectra are combined and the complex samplespectrum is decomposed into its individual components,using a least square fitting procedurewith a library of standard spectra, and applyingappropriate corrections for matrix effects. In a secondstep the X-ray spectra are analysed, using alibrary of standard spectra and the results fromthe first step for matrix corrections. This stepyields improved data for the ratios of the elements,which are used in a second least squares fit.There are several commercial programs availablefor qualitative and semiquantitative analysis. Afterthe X-ray peaks and their intensities have beenidentified and determined, interelement effects arecorrected with an empirical correction procedureand/or model calculations based on fundamentalparameters.ACKNOWLEDGEMENTSThis work was partially supported by the NationalResearch Council (CNR) Special Project for theConservation of Cultural Heritage.REFERENCES1. Cesareo, R. Photon induced X-ray fluorescence inmedicine, in Nuclear Analytical Techniques in Medicine(Ed. R. Cesareo), Elsevier, Amsterdam, 1988, pp. 1–121.2. Van Grieken, R. and Markowicz, A. (Eds) Handbook on X-ray Spectrometry: Methods and Techniques Marcel DekkerInc., New York, 1992.3. Rhodes, J.R. Design and application of X-ray emissionanalyzers using radioisotope X-ray and gamma ray sources.Am. Soc. Testing Mater. 485, 243–285 (1971).4. Watt, J.S. Radioisotope X-ray analysis, in Handbook on X-ray Spectrometry: Methods and Techniques (Eds. R. VanGrieken and A. Markowicz), Marcel Dekker Inc., NewYork, 1992.5. Oxford Analytical Systems Division, Scotts Valley, CA,USA.6. EIS-XRS, Rome, Italy; eissrlrm@tin.it7. Hamamatsu Photonics, Hamamatsu City, Japan; www.hamamatsu.com8. AMPTEK Inc., Bedford, MA, USA; www.amptek.com9. Moxtek Inc., Oren, UT, USA; www.moxtek.com10. Fiorini, C. and Longoni, A. Application of a new noncryogenic X-ray detector in portable instruments forarchaeometric analysis. Rev. Sci. Instrum. 69, 1523–1527(1998).11. Roentec GmbH, Berlin, Germany; www.roentec.de12. Constallation Techn., Largo, FL, USA; www.contech.com13. eV (a Division of II-VI Inc.), Saxonburg, PA, USA;www.evproducts.com14. Arlt, R., Ivanov, V. and Khusainov, A., Advances in highresolutionCdTe and CdZnTe detectors, in Hard X-ray andGamma-ray Detector Physics, Optics and Applications,SPIE.

340 PORTABLE EQUIPMENT FOR X-RAY FLUORESCENCE ANALYSIS15. PGT Princeton Gamma Tech; www.pgt.com/Nuclear/Xray detectors.html16. Vekemans, B. et al. Comparison of several backgroundcompensation methods useful for evaluation of energydispersiveX-ray fluorescence spectra. Spectrochim. Acta50B, 149–169 (1995).17. Brunetti, A. and Steger T. X-Ray spectra backgroundfitting by projection onto convex sets, Nuclear Instrum.Methods, A441, 504–509 (2000).18. Lachance, G.R. and Claisse, F. Quantitative X-Ray FluorescenceAnalysis, J. Wiley & Sons, Ltd., New York, 1995.19. Piorek, S., Puusaari, V., Piorek, E. and McCann, B. Identificationand quantitative analysis of alloys using X-rayfluorescence analyzer with a Si-PIN detector, in Proceedingsof the European Conference of Energy Dispersive X-Ray Spectrometry, (Eds. J.E. Fernandez and A. Tartari),Editrice Compositori, Bologna, 1999, p. 145.20. Perkin Elmer Instrum., Ortec Products; www.ortec-online.com21. VacuTec Messtechnik GmbH, Dresden, Germany.22. ThermoNORAN X-ray detectors, Middleton, WI, USA;www.thermo.com23. Radiation Sources, The Radiochemical Centre, Amersham.24. Isotope Products Lab., Valencia, CA, USA; www.isotopeproducts.com25. Photoelectron Corporation; www.photoelectron.com26. Brownbridge, J.D. and Roboy, S. Investigations of pyroelectricgeneration of X-rays. J. Appl. Phys. 86, 640–647(1999).27. Yue, G.Z. et al. Generation of continuous and pulseddiagnostic imaging X-ray radiation using a carbonnanotube-basedfield-emission cathode. Appl. Phys. Lett.81, 355–357 (2002).28. Institute for Roentgen Optics, Moscow, Russia; Institutfür Gerätebau GmbH, Berlin, Germany; X-ray OpticalSystems, Inc., Albany, NY, USA.29. LND Inc., Oceanside, NY, USA; www.lndinc.com30. Centronic Ltd., Croydon.31. Ketek GmbH, München, Germany; www.ketek-gmbh.de32. Iwanczyk, J.S., Patt, B.E., Wang, Y.J. and Khusainov, A.Comparison of HgI 2 , CdTe and Si-PIN X-ray detectors.Nucl. Instrum. 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5.4 Synchrotron Radiation for Microscopic X-rayFluorescence AnalysisF. ADAMS, L. VINCZE and B. VEKEMANSUniversity of Antwerp, Antwerp, Belgium5.4.1 INTRODUCTIONX-Ray fluorescence (XRF) spectrometry had animportant impact as one of the first commerciallyavailable instrumental techniques for elementalanalysis (Van Grieken and Markowicz, 2002). Duringmost of this time it suffered from an importantconstraint: the apparent impossibility to limit thebeam size for its use as a microbeam method forthe analysis of small and/or heterogeneous samples.Early attempts to use the method for spotanalysis or profiling heterogeneous samples werebased on the use of pinholes used in conjunctionwith X-ray tubes but the resulting flux throughputwas too low for most practical applications.Direct focusing of X-rays was made quasi impossibleby the opposition between a high absorptioncoefficient and a near unity (and negative) indexof refraction. It was only over the last 20 yearsthat methods of practical use for beam confinementgradually appeared (see Subchapter 2.1) onthe basis of diffraction, refraction or reflection.This evolution led to two new methods in XRFthat are based on the confinement of the interactionvolume of the primary X-ray beam with thematerial being analysed. In total reflection XRF(TXRF), by irradiating a flat sample with a parallelX-ray beam below the angle of total reflection,the in-depth penetration of the primary X-rays isconfined to a few tenths of a nanometer belowthe surface allowing very sensitive surface analysis.Alternatively, the method can be exploitedfor bulk trace analysis of liquids, e.g. aqueoussolutions brought on a clean inert surface. Thismethodology is discussed in detail in Subchapter5.1 of this book. A second confined impingingbeam technique is micro-XRF (µ-XRF) analysiswhich is based on the localised excitation and analysisof a microscopically small area on the surfaceof a larger sample. It provides information on thedistribution of major, minor and trace elementsin heterogeneous materials or can be used forthe analysis of objects of reduced dimensions. µ-XRF is currently exploited with laboratory X-raysources (see Chapter 2) but is considerably morepowerful when applied with X-ray emitted from asynchrotron radiation (SR) source (Janssens et al.,2000). It is the application of this latter methodwith SR that is the topic of this subchapter.Due to their high intensity and directionality SRsources are ideal for the generation of microscopicallyconfined X-ray beams. The high directionalityof the radiation allows the straightforward realisationof monochromatic micron size X-ray beamsfrom the emitted radiation of the storage ring. Inaddition, the polarisation can be used to reduce therelative contribution of scattered radiation reachingthe detector and thus to enhance considerably thesignal-to-background ratio of fluorescence spectra,decreasing significantly detection limits. X-Raygenerated from SR sources are coherent sources(Margaritondo et al., 1998; Lengeler, 2001) butthe exploitation of this characteristic is hamperedby two contrasted length scales: the microscopicX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

344 SYNCHROTRON RADIATION FOR MICROSCOPIC X-RAY FLUORESCENCE ANALYSISX-ray wavelength of the order of nm and the muchlarger cross-section of the beam (spot size) (Pfeifferet al., 2002).SR-based µ-XRF offers a number of advantagescompared to other microprobe techniques: itcombines high spatial resolution with high sensitivity,can be used in atmospheric conditions and isrelatively insensitive to beam damage to the sample.As we will show Later in this subchapter, thesimplicity of the method and the quite good understandingof the physics of the processes involvedmakes it more adaptable for quantitative analysisthan a number of other beam methods of analysis.This subchapter will describe the actual statusof µ-XRF with SR sources with respect tolateral resolution, achievable detection limits andsensitivity for high energy third generation storagerings, particularly the European SynchrotronRadiation Facility (ESRF, Grenoble), previousgeneration sources and other sources of recentconstruction. Storage ring sources and their characteristicsare fully described in Subchapter 2.2.Related methods of analysis based on absorptionedge phenomena such as X-ray absorptionspectroscopy (XAS) and X-ray absorption nearedgespectroscopy (XANES), X-ray microcomputedtomography (MXCT) and microscopic X-raydiffraction (XRD) will also be briefly discussed.We refer to Subchapter 5.3 for details on XAS andits applications.5.4.2 SYNCHROTRON MICROSCOPICX-RAY FLUORESCENCE ANALYSISConceptually, the instrumentation for X-ray microanalysisis extremely simple. It consists of amechanical sample stage with precision computercontrolled microstepping motors for X, Y , Z and(optionally) rotational movement of the samplein the beam path, a semiconductor type detectorfor the measurement of the generated fluorescenceradiation, different visualisation tools for observationand positioning of the sample and, finally, arange of diagnostic and control tools.A particular advantage of SR µ-XRF in comparisonwith the conventional X-tube sources isthe extremely high brilliance that is obtained. Inaddition, in the plane of the storage ring the radiationis linearly polarised with the E-vector paralleland the B-vector normal to the ring plane. Theradiation is highly collimated along a direction tangentialto the movement of the electrons in the ringthus facilitating the delivery of the radiation to apredefined sample area.The high intensity and directionality impliesthat SR is ideally suited for the generation of X-raymicrobeams with very high intensity, exceedingnow considerably 10 10 photons/s/µm 2 . The polarisationof the incident radiation can be used toreduce the relative contribution of scattered radiationreaching the detector, as scattering crosssectionsare dependent on the polarisation whereasthe photoabsorption cross-sections are not. Whenperforming measurements in the plane of theSR source this increases the signal-to-backgroundratios by more than two orders of magnitude,depending on the source characteristics and theparticularities of the XRF set-up (degree of polarisation).Thanks to the high directionality of thebeam, quasi-monochromatic X-ray microbeamscan be generated from the white SR spectrumthrough the use of X-ray monochromators. By tuningthe energy with a monochromator over a givenenergy range, the strong energy dependence ofthe inner shell photoelectric cross-sections can beexploited to either increase specificity of measurementsor, else, to obtain speciation information inthe XAS application mode (see later).A direct exploitation mode with broad bandpolychromatic excitation is also possible. It hasthe advantage that (nearly) all elements in thesample are excited with quite comparable efficiencyproviding a more uniform spectrometerresponse over the range of elements of interest.Since losses in flux due to the monochromatisationprocess do not occur, the elemental efficiencyof polychromatic set-ups is also higher than whenmonochromatic excitation is used, making it moreappropriate for general-purpose materials characterisation.In such circumstances, however, quantificationof the detected X-ray intensities is morecomplicated. Also, the signal-to-noise ratios, andhence, detection limits do not match those obtainedwith monochromatic excitation as is illustrated in

SYNCHROTRON MICROSCOPIC X-RAY FLUORESCENCE ANALYSIS 345Subchapter 6.1 (Figure 6.1.12) for the measurementof rare earth elements. For quantitative analysisthe use of monochromatic radiation is, hence,in general, a preferable approach.Currently, a large number of existing storagerings are employed in µ-XRF experiments. Theycombine the advantages of XRF as an elementalanalytical tool with the unique possibilities of SR.Of special significance are the new third generationstorage rings that are specifically designed toobtain unprecedented intensity, high radiationenergy and brilliance. A number of these are nowroutinely operational, the ESRF, the AdvancedPhoton Source (APS, Argonne, USA) and SPring-8(Harima, Japan) are the most important examples.Compared to earlier second generation rings theseSR facilities are characterised by their high energyof6to8GeV.Significant in these devices also is the systematicuse of insertion devices that are placed in thestraight sections of the storage ring (wigglers andundulators). Wigglers are magnetic structures thatcreate multiple oscillations around the beam pathand hence increase both the energy and the intensityof the radiation. Undulators are designed tocreate smaller and more frequent deflections, givingrise to interference effects and in such conditionsthe coherent radiation is concentrated aroundspecific energies. Other newly built SR sources followthe design characteristics of these sources andnow commonly include the use of insertion devices(Subchapter 2.2).A double crystal monochromator comprising apair of crystals is a standard item in most monochromaticµ-XRF set-ups because the exit direction iskept constant during energy scanning. The energyresolution of the double crystal monochromator isof the order of E/E = 10 −4 or less, and this issufficient for absorption edge applications.In its primary utilisation mode as a tool forelemental analysis by XRF analysis a high photonflux rather than such a high-energy resolution isrequired and an energy resolution of the orderof E/E = 10 −2 is sufficient for the purpose.Synthetic multilayers, made by vacuum depositionof alternate thin layers of two materials with adifferent electron density provide this (‘pink beam’)resolution while, through a wide energy band-pass,yielding a photon flux one to two orders of magnitudehigher than available with a high resolution doublecrystal monochromator.Flux throughput through pinholes is insufficientfor most practical analytical purposes and techniquesfor generating intense X-ray microbeamsare, hence, mostly based on the use of varioustypes of X-ray optics (see Chapter 3). Grazingincidence bent mirrors in various configurationsand geometries using crystals and multilayers,several types of glass mono-capillaries, complexpolycapillary lens systems (Subchapters 3.3and 3.4), diffractive lenses (Fresnel zone plates),Bragg–Fresnel lenses, one- or two-dimensionalwaveguides and refractive lenses (Subchapter 3.4)have been developed and tested for use in micronsize to sub-micron focusing at several synchrotronbeam lines. At present, it is possible to obtain asufficient beam intensity on microscale samplesto allow reliable sub ppm level determinationsof a large number of elements. In particular circumstancesspot sizes of less than 100 nm can beachieved (Bilderback and Hoffman, 1994).In a number of µ-XRF installations capillaryoptics are used as focusing devices (Vincze et al.,2002a,b) because of their inherent constructionalsimplicity. These pseudo-focusing devices providea good lateral resolution and can be usedfor both polychromatic and monochromatic X-ray,but suffer from the short working distance (typically

346 SYNCHROTRON RADIATION FOR MICROSCOPIC X-RAY FLUORESCENCE ANALYSIS60 m 59.5 m 59 m 58 m 56 m 39 m 33 mm-ionSi(Li) chamberAirKapton Be window30 m0X-ray white beamundulatorPhotodiode 2 SamplePhotodiode 1Geometry 2Photodiode 1Geometry 1CRL lensesVacuumMonitorSi(111)monochromatorDiamondwindowFigure 5.4.1 Schematic layout of the ID 18F experimental station. Photodiode 1 is either placed into the sample position if thesample is measured (geometry 1) or in front of the mini-ionisation chamber (geometry 2). Adapted from Somogyi et al. (2003)energy dispersive detection gives rise to complicatedspectra with multiple spectra interferences.Also, the high count rates must be adequately takeninto account, e.g. by using digital pulse processing.To take full profit of the polarisation and, hence,to increase signal-to-noise ratios the X-ray detectorsare positioned in the plane of the storage ringat typically an angle of 90 ◦ to the incident beamdirection. Techniques were developed for fast andreliable nonlinear least squares deconvolution of X-ray spectra that circumvent spectral interferences(Janssens et al., 1996). Multivariate statistical techniquesfor data reduction of image scans are available(Janssens et al., 1996; Janssens et al., 2000).The topic is discussed in detail in Subchapter 6.2.For the measurement of elemental distributionmaps, spectra are taken as the sample is movedover the beam path. Contrarily to the vacuumrequirements of most other microprobe methods,samples are normally observed in air, allowing themeasurement of samples in their natural (e.g. wetstate) conditions. Two-dimensional mapping of therepartition of elements in larger objects than the X-ray beam is possible with relative detection limitsin the ppb region and absolute detection limits formany elements well below the femtogram.All major SR sources are involved with thistype of application with at least one instrumentalset-up. Major SR sources have usually severalpossibilities for µ-XRF and related methods, e.g.in the ESRF there are the following beamlinesthat are at least partly devoted to microanalysisat a number of insertion devices (ID) or bendingmagnets (BM): ID 13 (microfocus beamline formicrodiffraction, microdiffuse scattering includingmicro-small angle scattering); ID 18F (X-rayfluorescence); ID 21 (X-ray microscopy); ID 22(microfluorescence, imaging and diffraction); ID27 (TXRF facility for semiconductor wafer contaminationanalysis); and BM 29 (X-ray absorptionfine structure for EXAFS and XANES).The ID 18F beamline at ESRF is a typical set-upfor XRF and is illustrated in Figure 5.4.1 (Somogyiet al., 2001a,b; Somogyi et al., 2003). Foranother representation of the same instrument seeFigure 6.1.6 in Subchapter 6.1. The design goal ofthis instrument was to make available a dedicatedinstrument for µ-XRF and to improve proceduresof µ-XRF in order to reach 5 % average accuracy ofquantification down to sub-ppm concentration levelsfor elements of Z>13. To do this it is necessaryto insure high reproducibility of the measurementgeometry and instrumental parameters of the set-up,a very good short and long-term stability and precisemonitoring (

MICRO X-RAY FLUORESCENCE ANALYSIS AS AN ACCURATE METHOD OF MICROANALYSIS 347are detected with a Si(Li) detector of 30 mm 2active area, 3.5 mm active thickness placed in 90 ◦geometry to the incoming linearly polarised X-raybeam. Fast scanning XRF measurements (>0.1 slive time/spectrum) are possible.The degree of polarisation is estimated at>99.7 % as could be deduced from the ratio of fluorescencelines with primary and multiple Comptonintensity (see Figure 6.1.11 in Subchapter 6.1).The available relative detection limits (DLs) are25. DLs down toa few ppb are possible for a number of elementson the basis of 1000 s live time measurements andppm DLs can be reached for measurements of afew seconds (Figure 5.4.2). The absolute DLs are25 (Figure 5.4.3). Thefluxinthefocusedbeamis10 9 –10 10 photons/sdepending on the energy of the incoming beam(Vekemans et al., 2003). Figures 5.4.2 and 5.4.3show DLs obtained at ESRF with the instrumentshown in Figure 5.4.1 for reference samples on thebasis of the use of a set of compound refractivelenses (see Subchapter 3.4).The design characteristics of other SR installationscan be found in the literature, e.g. the X-26A beamline of the National Synchrotron LightSource in Brookhaven National Laboratory (Smith,1995), beamline L at HASYLAB (Falkenberget al., 2001) and the 131D beamline ‘GSECARS’at the APS, Argonne (Newville et al., 1999).5.4.3 MICRO X-RAY FLUORESCENCEANALYSIS AS AN ACCURATEMETHOD OF MICROANALYSISMost beam methods for microanalysis (e.g. electronprobe microanalysis, micro-Auger spectroscopy,secondary ion mass spectrometry) cannot beconsidered as accurate analytical methods exceptwhen applied to quite simple samples mainlybecause of matrix effects. The application of beammethods for quantitative analysis should, hence,need to rely on the use of reference materialsfor calibration. Very few are currently available(Adams, 2000).As is explained in Subchapter 6.1, the physicalbasis of the of the X-ray matter interaction isquite well understood and the physical constantsgoverning the interaction and the extent of radiationabsorption can be derived accurately frommeasurements obtained in well-defined conditions.It is thus, in principle, possible to correct fordeviations of linearity between measured intensitiesand elemental concentrations, especially if themeasurement conditions are simplified as much aspossible by using a high intensity monochromaticprimary excitation and employing an energy dispersivedetector for the measurements.Powerful methodologies are now available formodeling by ab initio Monte Carlo (MC) simulationboth the beam optics and the beam–sampleinteraction within the sample and the detector(Vincze et al., 1999a; Vincze et al., 1999b; Vinczeet al., 1999c) (see also Subchapter 6.1). The combineduse of nonlinear least squares deconvolutionof X-ray spectra and the methodology for modelingthe beam optics and beam–sample interactionallow the optimum use of all spectral information,including the use of Rayleigh and multiple Comptonscattering.A number of background effects that were neverfully evaluated in XRF appear in the SR spectra,the most important being electron Bremsstrahlungin sample and detector. Electron Bremsstrahlungis able to generate fluorescence radiation fromlow Z elements and, hence, appears to be a quiteimportant factor in quantitative analysis that wasnever systematically taken into account for quantitativeanalysis. It appeared, for instance, in thesimulation of experimental data that ca. 50 % ofthe fluorescence radiation of bulk Si in a 250 µmthick Si wafer irradiated with 27 keV results indirectlyfrom the 25.16 keV photoelectrons generatedby the beam in the sample, rather than directlythrough impinging X-rays (Vincze et al., unpublishedresults). Also, specific spectral artefactscomplicate the spectra, e.g. resonant Raman scatteringwhich creates peak-like structures in thespectra at excitation energies near the absorptionedge, thus complicating spectral deconvolution(Gel’mukhanov and Agren, 1999).A systematic comparison of experimentallyobtained spectral data with modeling results basedon MC simulations can pinpoint specific artefacts

348 SYNCHROTRON RADIATION FOR MICROSCOPIC X-RAY FLUORESCENCE ANALYSIS1000.000DLs, derived from NIST SRM 1577a, LT = 1000 s100.000: thickness = 1 mm: thickness = 100 µm10.000MDL, ppm1.0000.1000.0107 ppb level0.00115100.0020 25 30 35 40 45Atomic numberDLs, derived from SRM613 (1 mm)10.00MDL, ppm1.000.100.0120 25 30 35 40Atomic numberFigure 5.4.2 Relative detection limits with ID 18F using a 100 component compound reflective lens set at 21 keV at 2 µm × 2 µmin biological material (NIST SRM 1577a, bovine liver) and NIST 613 glass SRM 613 (live time measurement of 1000 s). Adaptedfrom Somogyi et al. (2001)

MICRO X-RAY FLUORESCENCE ANALYSIS AS AN ACCURATE METHOD OF MICROANALYSIS 34910.001.00DL (fg)0.100.0110 15 20 25 30 35Atomic numberFigure 5.4.3 Absolute detection limits with ESRF (ID 13), 21 keV monochromatic radiation at 2 µm × 2 µm (live timemeasurement of 100 s). Adapted from Somogyi et al. (2001)and show ways to correct for them in order tobring eventually the measurement accuracy in linewith the accuracy of the physical constants characterisingthe X-ray sample–interaction processes.Ultimately the quality of results that can be reachedwith this method depends on the accuracy of availablephysical constants, mainly the cross-sectionsfor X-ray interactions in the most favorable circumstances(5 % for K radiation of elements inthe range Z = 20–50, 10–15 % for L radiationbetween Z = 50–80) (Elam et al., 2002).A reasonable goal of all such efforts is to reachan average accuracy of quantification in the rangeof ca. 5 % for elements above atomic number 12determined through the K and L fluorescence radiation.Table 5.4.1 shows a few results obtainedTable 5.4.1 Analysis of SRM 1832 thin glass standardElementCertifiedConcentration(%)MeasuredRelative deviation(%)Ca 12.1 12.6 +4.1V 2.8 2.74 −2.1Mn 2.8 2.88 +2.9Co 0.61 0.63 +3.3Cu 1.50 1.44 −4.0for the standard reference material (SRM) NISTSRM 1832 thin glass (see Figure 6.1.7, Subchapter6.1 for a comparison of the experimental andMC simulated spectra). Deviations of the resultsfrom the certified concentrations are in the 2–4 %range. For more heterogeneous samples such theSRM 1577a (bovine liver) experimental data andcertified results correspond only to within 12 %for some elements such as Fe (Table 5.4.2). Systematicallyrepeated measurements on referencematerials allow the determination of the homogeneitylevel of samples and the determinationTable 5.4.2 Certified and calculated concentrations for theanalysis by iterative MC calculation of NIST SRM 1577 bovineliverElementCertifiedConcentration(ppm)MeaswedRelative deviation(%)Ca (123) 120 −2Mn 10.3 ± 1 10.8 +5Fe 270 ± 20 303 +12Cu 193 ± 10 183 −5Zn 130 ± 10 138 +6Se 1.1 ± 0.1 1.2 +9Rb 18.3 ± 1 18.4 +0.5Sr (0.14) 0.15 +7Mo (3.2) 3.4 +6

350 SYNCHROTRON RADIATION FOR MICROSCOPIC X-RAY FLUORESCENCE ANALYSISof the minimum sample size required to reacha given measurement accuracy. The results showthat at this confidence limit the minimum samplemass to be analysed is of the order of 10 ngfor most elements, which corresponds to a beamsize of 3 × 3 µm 2 . The large deviation betweenthe certified and measured concentration for Fe inSRM 1577a (Table 5.4.2) can be attributed by suchmeasurements to inhomogeneities of the elementaldistribution in the reference material. Indeed theminimum sample mass for obtaining 5 % reproducibilityamounts to 32 µg for this elements,which requires a 400 × 400 µm 2 beam instead ofthe small beam used (Kempenaers et al., 2002).Improvements in quantitative µ-XRF analysisare now taking place in a European Unionproject of the 5th Framework Programme. Theproject ‘Micro-XRF’ investigates the comparabilityof multi-elemental XRF analysis down to subppmconcentration levels with microscopic lateralresolution with the ID18F instrument andwith a µ-XRF instrument built at the ANKASR source (Karlsruhe Research Centre, Germany)(Simon et al., 2003). The two XRF instrumentstogether with selected other ‘microbeam’ analyticaltechniques (X-ray photoelectron spectroscopy,microscopic proton induced X-ray emission andRutherford backscattering, secondary ion massspectrometry) are used for the determination ofthe microscopic heterogeneity of available certifiedreference materials (Kempenaers et al., 2002).Within the project the analytical characteristics ofmicroscopic techniques are compared and feasibilitystudies are undertaken for the production ofreference materials for microanalysis.5.4.4 X-RAY ABSORPTION METHODSIn the applications of XAS (also called X-rayabsorption fine structure spectroscopy, XAFS) theenergy dependence of the inner shell photoelectriccross is exploited to increase specificity of measurementsor to obtain information on the chemicalenvironment (speciation analysis) (see Subchapter5.3). Extended X-ray absorption fine structureanalysis (EXAFS) provides information on thenumber, the atomic number and the distance ofneighboring atoms. The technique is based on irradiationwith a highly monochromatic X-ray beamof tunable energy and scanning over an absorptionedge of an element of interest while recordingeither the absorption of the beam (absorptionXAS), the fluorescence radiation produced(fluorescence XAS) or another shell dependentphenomenon. XANES measures the position ofthe edge and characterisation can be achieved byexploiting specific features of the X-ray absorptionspectrum. Recently, the combination of µ-XRFwith spatially resolved XAS became an importanttool for speciation in environmental and geologicalmaterials and for the study of processes in chemicalspecies transformation. Most µ-XAS applicationsare performed in the XANES fluorescencedetection mode as a ‘fingerprinting’ technique.Recently there were a number of demonstrationson the use of spatially resolved speciationto distinguish valence states of the elements Cr,Mn (Zaw et al., 2002), Fe (Dyar et al., 2002), Zn(Manceau et al., 2000), U and Pu (Cutler et al.,2001; Salbu et al., 2001), etc. in geological, cosmologicaland environmental studies (Hsiao et al.,2002; Pinzani et al., 2002) especially for the determinationof redox state, solution complex formation,and sorption on mineral phases or naturalorganic components, finally the bioavailability ofmetal compounds. Such information is essentialfor risk assessment, management and reduction ofhazards associated with elemental release of contaminants.Bertsch and Hunter (2001) cover theliterature on the subject until 2000.5.4.5 COMPUTERISEDMICROTOMOGRAPHY (CMT)CMT at high spatial resolution with absorption orfluorescence radiation from a spatially confinedSR beam is based on the systematic measurementof the beam as it is impinging on the sample(Simionovici et al., 2000; Rau et al., 2001).For obtaining three-dimensional information X-raytomography exploits one of the weaknesses ofµ-XRF, the penetrative nature of the impingingX-rays. It is now possible to carry out CMT withspatial resolutions as low as about 1 µm 3 andwith more than 10 9 voxels. This provides possibilitiesfor nondestructive observation of the inte-

CONCLUSIONS 351rior of the sample for the study of shape, densityand composition, e.g. in inclusions, interior porestructures, buried phases or other features withinthe sample.For CMT measurements the sample, in additionto being rastered, is also rotated over 180 ◦ throughthe incorporation of a sample rotation stage. Atwo-dimensional elemental distribution map in thehorizontal sample plane can then be obtained usinga reconstruction procedure based on filtered backprojection. A systematic repetition of the processat other planes eventually reconstructs the entirethree-dimensional image. Imaging is possible withthe white spectrum as well as with monochromaticradiation (Larson et al., 2002).The technique is now in full development, withmajor applications being in inorganic matrix composites,transport phenomena in porous media, thestudy of calcified tissues and fatigue cracks inmaterials (Stock, 1999; Maire et al., 2001). Techniquesare being developed to speed up the measurementprocess, combining fast detector systems,high speed data networks and parallel computingsystems to a few minutes (Wang et al.,2001).Major problems are the complexity (and length)of calculations when sample self-absorption istaken into account. In principle it is possibleto combine XAS and CMT with µ-XRF. Thecomplexity of XAS can be diminished by obtainingthe fluorescence or absorption information withtwo closely spaced excitation energies that arecharacteristic for the valence states of different ionsin the sample (Yamamoto et al., 2000).5.4.6 MICRO X-RAY DIFFRACTIONThe measurement of an XRD pattern over a complexsample provides information on the variationof its crystallographic structure. Micro XRDis becoming common on many X-ray microprobes(Rindby et al., 1997; Riekel, 2000). (SeeFigure 6.1.6 in Subchapter 6.1 for its incorporationin the ID 18F beamline.) Micro XRD maps showingthe repartition at every impact point of severalcrystallographic states can be obtained togetherwith the maps of elemental information and canassist considerably in the characterisation of complexsamples.5.4.7 IMAGINGSeveral hard X-rays imaging techniques greatlybenefit from the coherence of the beams deliveredby the modern SR sources. Phase imagingis directly related to the small angular size ofthe source as seen from one point of the sample.Phase radiography and tomography are instrumentallyvery simple. They are often used in the‘edge detection’ regime, where the jumps of densityare clearly observed. Recently a more quantitativeapproach has been developed, which providesa three-dimensional density mapping of thesample (‘holo-tomography’). The combination ofdiffraction topography and phase-contrast imagingconstitutes a powerful tool that can help in monitoringthe areas of a sample to be selected forfurther chemical or structural analysis (Baruchelet al., 2000).The coherence of X-ray radiation does notbring anything directly useful for analysis butthe production of a coherent and divergent X-raybeam allows the observation of small features inobjects both in two and three dimensions. X-Raytomography can provide three-dimensional densityand chemical distributions of such structures withsubmicrometer resolution (Larson et al., 2002).Such techniques are still in development.5.4.8 CONCLUSIONSWithin the field of microanalytical techniquesSR based µ-XRF emerges as an important newmethodology for the characterisation and analysisof diverse materials. The simultaneous applicationof µ-XRF with XAS, CMT and XRDgreatly enhances the capabilities for the study ofmicroscopically heterogeneous materials providingthree-dimensional nondestructive information andspeciation. The gains in brilliance of SR sourcesover the past decade and advances in focusingoptics during the same period provide spatial

352 SYNCHROTRON RADIATION FOR MICROSCOPIC X-RAY FLUORESCENCE ANALYSISresolution at the sub-µm range while maintaininga high sensitivity.Thanks to the full understanding of the interactionprocesses of X-rays with matter (Cesareo,2000), computer techniques, particularly thosebased on MC simulation, are able to predict thespectral response without limitations in approximationsor idealisations of the sample geometry.Hence, they allow methods for calibration and correctionfor radiation absorption, thus opening upthe way to perform reliable quantitatitve analysis.Scanning techniques are wasteful ways and timeconsuming to generate two- and three-dimensionalmaps. The first attempts appeared recently for performingelemental analysis with a full-field XRFmicroscope on the basis of measurements withcharge-coupled device photon counting systems.As demonstrated by Ohigashi et al. (2002), itappeared possible to obtain a spatial resolutionof 10 µm with a field of view of 200 µm andanenergy resolution of 350 eV FWHM.Exhaustive recent reviews of applications ofsynchrotron based µ-XRF and related techniquesare available in the literature (Schulze and Bertsch,1995; Potts et al., 2000; Revenko, 2000; Bertschand Hunter, 2001; Larson et al., 2002).General recent reviews of micro-XRF andrelated methods also provide numerous examplesof the advantages of the methodology (Chevallieret al., 1998; Chevallier et al., 1999; Ellis et al.,1998; Haberkorn and Beck, 2000; Szaloki et al.,2002). A comparison of different excitation modesis given by Gigante and Gonsior (2000).REFERENCESAdams, F. Encyclopedia of Analytical Chemistry (Ed. R.A. Meyers),Chichester, Wiley, 2000, Vol. 15, pp. 13636–13644.Baruchel, J., Cloetens, P., Hartwig, J., Ludwig, W., Mancini,L., Pernot, P. and Schlenker, M. J. Synchrotron Rad. 7,196–201 (2000).Bertsch, P.M. and Hunter, D.B. Chem. Rev. 101, 1809–1842(2001).Bilderback, D.H. and Hoffman, S.A. Science 263, 201–204(1994).Cesareo, R. Riv. Nuovo cim., 23(7), 1–231 (2000).Chevallier, P., Firsov, A., Populos, P. and Legrand, F. J. Phys.8, 407–412 (1998).Chevallier, P., Populos, P. and Firsov, A. X-ray Spectrom. 28,348–351 1999.Cutler, J.N., Jiang, D.T. and Remple, G. Can. J. Anal. Sci.Spectrosc. 46, 130–135 (2001).Dyar, M.D., Lowe, E.W., Guidotti, C.V. and Delaney, J.S. Am.Mineral. 87, 514–522 (2002).Elam, W.T., Ravel, B.D. and Sieber, J.R. Radiat. Phys. Chem.63, 121–128 (2002).Ellis, A.T., Kregsamer, P., Potts, P.J., Streli, C., West, M. andWobrauschek, P. J. Anal. At. Spectrom. 13, 209–232 (1998).Falkenberg, G., Clauss, O., Swiderski, A. and Tschentscher, T.Nucl. Instrum. Methods 467, 737–740 (2001).Gel’mukhanov, F. and Agren, H. Phys. Rev. Lett. 312, 91–140(1999).Gigante, G.E. and Gonsior, B. Fresenius. J. Anal. Chem. 368,644–648 (2000).Haberkorn, R. and Beck, H.P. Mikrochim. Acta 133, 51–58(2000).Hsiao, M.C., Wang, H.P., Wie, Y.L., Chang, J.E. and Jou, C.J.J. Hazard. Mater. 91, 301–307 (2002).Janssens, K., Vekemans, B., Adams, F., Van Espen, P. andMutsaers, P. Nucl. Instrum. Methods B 109/110, 179–185(1996).Janssens, K.H., Adams, F.C. and Rindby, A. (Eds) MicroscopicX-ray Fluorescence Analysis, Wiley, Chichester,2000.Kempenaers, L., Janssens, K., Vincze, L., Vekemans, B., Somogyi,A., Drakopoulos, M., Simionovici, A. and Adams, F.Anal. Chem. 74, 5017–5026 (2002).Larson, B.C., Yang, W., Ice, G.E., Budai, J.D. and Tischler,J.Z. Nature 415, 887–890 (2002).Lengeler, B. Naturwissenschaften 88, 249–260 (2001).Maire, E., Buffiere, J.Y., Salvo, L., Blandin, J.J., Ludwig, W.and Letang, J.M. Adv. Eng. Mater. 3, 539–546 (2001).Manceau, A., Lanson, B., Harge, J.C., Musso, M., Eybert-Berard, L., Hazemann, J.-L., Chateigner, D. and Lanble, G.Am. J. Sci. 300, 289–343 (2000).Margaritondo, G., Tromba, G., Hwu, Y. and Grioni, M. Phys.Low-dimen. Struct. 12, 39–54 (1998).Newville, M., Sutton, S., Rivers, M and Eng, P. J. SynchrotronRadiat. 6, 353–355 (1999).Ohigashi, T., Watanabe, N., Yokosuka, H., Aota, T., Takano,H., Takeuchi, A. and Aoki, S. J. Synchrotron Radiat. 9,128–131 (2002).Pfeiffer, F., David, C., Burghammer, M., Riekel, C. and Salditt,T. Science 297, 230–234 (2002).Pinzani, M.C.C., Somogyi, A., Simionovici, A.S., Ansell, S.,Steenari, B.M. and Lindqvist, O. Environ. Sci. Technol. 36,3165–3169 (2002).Potts, P.J., Ellis, A.T., Holmes, M., Kregsamer, P., Streli, C.,West, M. and Wobrauchek, P. J. Anal. At. Spectrom. 15,1417–1442 (2000).Rau, C., Weitkamp, T., Snigirev, A., Schroer, C.G., Tummler,J. and Lengeler, B. Nucl. Instrum. Methods A 467,929–931 (2001).Revenko, A.G. Indust. Lab. 66, 637–652 (2000).

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5.5 High-energy X-ray FluorescenceI. NAKAITokyo University of Science, Tokyo, Japan5.5.1 INTRODUCTIONTraditionally, the X-ray fluorescence (XRF) analysisof heavy elements is based on their L seriesspectral lines. This is because the K lines ofthese elements are difficult to excite by commerciallyavailable XRF spectrometers. Photoelectricabsorption can only occur if the energy of the photonis equal or greater than the binding energy ofthe electron. The energy of the K absorption edgeof an element increases with the atomic number ofthe element. For example, to measure the K fluorescenceline of uranium, an X-ray photon withenergy of 115.62 keV is necessary to eject an electronfrom the K shell of uranium. In addition, anX-ray detector capable of measuring high-energyX-rays is required.Since the vacancy can be in any of the threesubcells, L1, L2, or L3, the L line XRF spectrum ismore complex than the K line spectrum. A typicalenergy-dispersive X-ray fluorescence (EDXRF)spectrum of a multicomponent material in energyregions of less than 20 keV is, therefore, usuallycrowded with an overlap of the K, L, and Memission lines of the component elements. Incontrast, the XRF spectrum above 20 keV containsonly K lines, and the spectrum becomes simple.Therefore, it is expected that the use of the Klines would be ideal for the analysis of heavyelements of atomic number Z ≧ 45 (=Rh Kα 1 =20.12 keV).This subchapter first presents a brief reviewof work done in this field, and then introducescharacteristic features and analytical performanceof the high-energy XRF technique developedthrough those studies. The potential capabilityof this technique will be demonstrated throughpractical examples in several fields where highenergyXRF is useful and therefore promising.5.5.2 REVIEW OF STUDIES ONHIGH-ENERGY XRF ANALYSIS5.5.2.1 LABORATORY X-RAY SOURCESHarada and Sakurai 1 reported in detail on theadvantages of the use of high-energy X-rays inEDXRF analysis based on their laboratory data.They constructed a sealed X-ray tube (W anode)system with a high-voltage power supply (160 kVand a maximum load of 1.6 kW for normal focusand 0.64 kW for fine focus) for high-energy XRFanalysis. The detection limit of iodine concentrationwas found to be 8 ppm and an absoluteamount of 3 µg, based on the use of a preliminarybeam filter technique (80 kV, 18.5 mA). Thecorresponding values obtained through the use ofwhite excitation (80 keV, 0.6 mA) were 40 ppmand 15 µg. Monochromatic excitation significantlyreduced the background signal compared withwhite X-ray excitation, and is favorable for traceelement analysis. 1Recently, PANalytical began marketing a highenergyEDXRF spectrometer, Epsilon 5 2 (Almelo,The Netherlands). It is equipped with a 600 WX-ray tube with a Gd anode operating in a range ofX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

356 HIGH-ENERGY X-RAY FLUORESCENCE25 kV to 100 kV and a liquid nitrogen-cooled highresolutionsolid state Ge detector. The XRF spectrometerfeatures a three-dimensional (Cartesian)polarizing optical geometry and 15 programmablepolarizing targets. Backgrounds can be an order ofmagnitude lower than traditional two-dimensionaloptics resulting in much lower detection limits,down to sub-ppm levels.5.5.2.2 FIRST- AND SECOND-GENERATION SYNCHROTRONRADIATION SOURCESHeavy element analysis using K line spectra wasfirst studied utilizing either first-generation synchrotronradiation (SR) light sources such asVEPP-4 in Novosibirsk, USSR 3–5 and HASYLABin Hamburg, Germany, 6 or a second-generationlight source at NSLS in Brookhaven. 7 WhiteX-ray excitation or relatively weak monoenergeticbeams with energy of less than 75 keVhave been utilized. Chen et al. 7 reported minimumdetection limits (MDLs) of 6 ppm (La) to26 ppm (Lu) for a counting time of 3600 s whenusing a wiggler beam. Baryshev et al. 3 reported anMDL of 50 ppm for rare earth elements. Janssenset al. 6 reported the use of lead-glass capillaries forthe microfocusing of highly energetic (0–60 keV)synchrotron radiation. With this great improvementin the analytical sensitivity of the focusingoptics, they obtained superb detection limits of1–10 fg/0.8–2 ppm for 100 µm silicate samples forelements from Mn (Z = 25) to Gd (Z = 64) usingtheir K lines with a counting time of 1000 s.5.5.2.3 THIRD-GENERATION SRLIGHT SOURCESThird-generation synchrotron light sources incorporateinsertion devices, wigglers, and undulators.The primary characteristics of third-generationlight sources are their extremely high brilliance andhigh-energy X-rays. The former characteristic isalready well appreciated in relation to the constructionof X-ray microscope or microanalysis systemswith a beam size of less than 1 µm 8–10 and thatof TXRF systems with fg sensitivity. 11–13 However,the utilization of high-energy X-rays fromthird-generation light sources in XRF analyses hadremained a challenge until our first application inthe forensic analysis of arsenic in a murder casein Wakayama city aroused attention in 1998. 14 Weused 116 keV X-rays for the first time as an excitationsource in the XRF analysis of crime-relatedmaterials. A wiggler beam-line at SPring-8 wassuitable for producing high-energy X-rays up to300 keV. This work revealed that high-energy XRFis powerful analytical tool in a variety of scientificfields as well as for forensic analysis. 155.5.3 INSTRUMENTS FORHIGH-ENERGY XRFFigure 5.5.1 compares the detection efficiency ofthe Ge solid state detector (SSD) as a functionof X-ray energy with those of the Si(Li) and Sidrift detectors. As can be seen in Figure 5.5.1,the efficiency of the Si(Li) SSD and that ofthe Si drift detector, which are usually used inan energy-dispersive (ED) spectrometer, decreasedrastically at above 20 keV with an increasein X-ray energy. In contrast, the Ge detectormaintains high efficiency for the energy of theK lines of heavy elements. Therefore, the GeSDD is suitable for high-energy EDXRF analysis.In wavelength-dispersive (WD) XRF, the energyresolution becomes poorer at a lower 2θ angle ofanalyzing crystal, namely at higher X-ray energies.In practical terms, the difference in resolutionbetween the ED and WD spectrometers is thereforeinsignificant for high-energy XRF analysis.Examples of experimental systems for highenergyEDXRF analysis in laboratories and inSR facilities are schematically illustrated in Figure5.5.2(a) and 5.5.2(b). At the National Institutefor Materials Science, the high-energy XRFsystem (Figure 5.5.2a) is composed of a sealedW tube (Comet MXR-160) with a high-voltagegenerator and its controller (Gulmay CP-160 andMP-1). 1 The maximum tube voltage is 160 kV andmaximum loading is 1.6 kW for a normal focus(1.5mm× 1.5mm) and 0.64 kW for a fine focus(0.4mm× 0.4mm). A shielding box is necessary

PERFORMANCE OF HIGH-ENERGY XRF 3571.21.0Ge (5 mm)Relative efficiency0.80.60.4Si(Li) (3 mm)Si-drift (0.3 mm)0.200 5 10 15 20 25 30 35 40 45 50Energy (keV)Figure 5.5.1 Relative efficiency vs energy for Ge SSD, Si(Li) SSD and Si drift detectors 1for conducting experiments. The box is made of4-mm thick lead plate sandwiched between steelplates, and 5-mm thick lead plate is also placed atthe position of direct beam irradiation. The beamsize is limited by the x –y slits (W–Ni alloy, 3 mmthick). The detection system consists of a Ge detector(Canberra, CT, USA, PSR505), a spectroscopyamplifier (Canberra 2021, shaping time 4 s), a multichannelanalyzer (NAIG E-553, 562A, 563A),and a computer (NEC, Tokyo, Japan, PC9801RA).As a laboratory spectrometer, the polarizingoptics adopted in the EDXRF spectrometer,Epsilon 5, demonstrated better performance thanconventional nonpolarizing optics in high-energyXRF analysis. Figure 5.5.3 is a schematic diagramof the optics. The use of targets of differentmaterials enables the optimization of the excitationsource specifically for analyte elements of interest.The primary beam from the Gd anode first irradiatesa polarizing target placed along the first axis.After scattering at 90 ◦ , the X-rays travel along thesecond axis to the sample. The XRF signals aremeasured by the Ge detector placed along the thirdaxis. This Cartesian geometry eliminates the X-raytube spectrum by polarization, thereby reducing thespectral background.The first high-energy XRF experiment utilizingmonochromatic X-rays with energy higher than100 keV was conducted at beam line BL-08 Wof SPring-8 (Figure 5.5.2b). 14,15 MonochromaticX-rays of 116 keV were obtained from a doublybent Si(400) monochromator utilizing the highenergyX-rays from an elliptical multipole wiggleras an excitation source. The energy resolution,E/E, was 1.25 × 10 −3 at 115 keV, and thephoton flux was 10 12 photons/s. 16,17 The EDXRFanalysis system consisted of an XY automaticstage (SIGMA KOOKI, Saitama, Japan), a pureGe SSD (Canberra GUL0055p), a spectroscopyamplifier (Canberra 2021, shaping time 12 µs),and a multichannel analyzer (Seiko EG&G, Tokyo,Japan, MCA7700). The range of the multichannelanalyzer was adjusted to 102.4 keV.5.5.4 PERFORMANCE OFHIGH-ENERGY XRF5.5.4.1 CHARACTERISTICANALYTICAL FEATURESHarada and Sakurai 1 compared the sensitivityof the following three-excitation techniques ofhigh-energy XRF analysis utilizing conventionallaboratory X-ray sources: i.e. white excitation(80 kV, 0.9 mA), primary beam filter (80 kV,0.6 mA, filter 40 mm Al plate), and secondary

358 HIGH-ENERGY X-RAY FLUORESCENCEPersonalcomputerMultichannelanalyzerHighvoltagesourceSpectroscopyamplifierHighvoltagegeneratorSSD (Ge)X-raysControllerW tubeSlit(A)SampleSampleTo detectorX-rays(B)(a)Shield boxSRSampleSlitXY stageSi(400)monochromatorICPulse mortarcontroller(b)GeSSDSpectroscopicMCA PCamplifierFigure 5.5.2 Schematic diagram of the experimental setup for high-energy XRF analyses. (a) Laboratory spectrometer. In theprimary beam filter technique, a filter (A) is interposed between the tube and the sample. In the secondary target technique, thepart enclosed in broken lines is replaced by the system below, where (B) represents the secondary target. 1 (b) SR spectrometerat BL-08 W of SPring-8

PERFORMANCE OF HIGH-ENERGY XRF 359SampleX-raytubeTargetsDetectorFigure 5.5.3 Three-dimensional polarization optics adopted in Epsilon 5Table 5.5.1 Comparison of the results from the three excitationtechniques. The detection limit is given here as three times thestatistical uncertainty of the background 1MethodWhiteexcitationPrimary-beamfilterSecondarytargetConditions of excitationTube voltage (kV) 80 80 150Tube current (mA) 0.6 18.5 10.6 aSignal (counts/300 s) 5367 5403 5444 bBackground (counts/300 s) 17050 786 843 bS/B 0.31 6.9 6.5Irradiation area6 × 7 6× 7 15× 15(mm × mm)Detection limit of iodineConcentration (µg g −1 ) 40 8 8Absolute amount (µg) 15 3 13a Limited by the X-ray generator’s maximum loading.b Compensated by the tube current.target techniques (150 kV, 3 mA, Er target). Thesample was the environmental reference material,sargasso (NIES No. 9), which contains a lowconcentration of iodine (520 µg/g). The results aresummarized in Table 5.5.1. When white excitationwas applied, a high background was caused bythe Compton scattering of incident X-rays. Incontrast, with the primary beam filter technique,an absorbing material of 40 mm thick Al platefiltered out the low-energy part of the primarybeam. This technique reduced the background atthe iodine Kα line, and the signal-to-background(S/B) ratio was improved to 6.9. For measurementsusing the secondary-target technique, a 3 mm thickEr plate was employed as a secondary target.This technique reduced the background around theiodine Kα line, improving the S/B more than 20times that of the conventional method.A combination of secondary target, primarybeam filter, and three-dimensional polarizing opticalgeometry adopted by Epsilon 5 greatly reducedthe scattered X-ray tube spectrum and enhancedthe sensitivity of the high-energy XRF. With theseoptics and a CsI secondary target, the lowerlimit of detection (LLD) of Cd in plastic wasreported to be 0.53 ppm for a measurement timeof 100 s, Gd anode X-ray tube operated at 100 kV,4.6 mA. Here, the LLD was calculated accordingto the equation:LLD = 3 × C/I p × (I b /t b ) 1/2

360 HIGH-ENERGY X-RAY FLUORESCENCEwhere I b is the background count and I p is thesignal (number of counts) produced by the concentrationC (the certified value reported in thereference) of the element with measurement timet b (live time). The sensitivity changes with the voltageof the X-ray tube, as shown in Figure 5.5.4.There are several superior features of synchrotronradiation in high-energy XRF analysis:the SR X-rays are fully polarized small parallelbeams, and brilliant monochromatic high-energyX-rays are obtained from a combination of thewiggler source and monochromator. These featuresprovide the most suitable X-ray source for highenergyXRF. Figure 5.5.5 shows an XRF spectrumof a metamict mineral (a variety of uraniniteUO 2 ) excited by 116 keV SR X-rays, whichshows the Kα peak of uranium. Thus, we haveconfirmed that this system can analyze all heavyelements up to uranium by their K lines. The analyticalperformance of this method was clarifiedby analyzing some standard samples. Figure 5.5.6shows a typical XRF spectrum of a bulk geologicalstandard sample (JG-1: granite, countingtime of 500 s). The certified element concentrationsrange from 54.7 ppm for Zr down to 1.7 ppm for Erand W (Table 5.5.2). As is shown in Figure 5.5.6,tungsten as well as various rare earth elements givethe distinct peaks of the K lines. Here, the valueof MDL was calculated according to the followingequation:MDL = 3 × C/I p × (I b ) 1/2Table 5.5.2 shows the values of MDL calculatedfrom Figure 5.5.6 for Fe, Rb, Sr, Zr, Cs,Table 5.5.2 Minimum detection limit (MDL) values calculatedfrom the XRF spectrum of JG-1 sample in Figure 5.5.6 for ameasurement time of 500 s 15Contents(ppm)I p(counts)I b(counts)MDL(ppm)Fe 2.02 a 1557 366 0.097 aRb 181 577 281 30.8Sr 184 719 258 19.2Zr b 108 395 293.5 54.7Cs 10.2 280 181 4.2Ba 462 7205 354.5 3.8La 23 535 355.5 7.2Ce 46.6 520 86 3.0Nd 20 862 154.5 1.1Sm 5.1 136 45 1.1Gd 3.7 108 42.5 1.1Dy 4.6 110 41 1.3Er 1.7 86 515 1.1Yb 2.7 125 61 1.0Hf 3.5 268 98.5 0.6W 1.7 737 199.5 0.1a wt%.b Calculated by using Kβ line.PlasticLLD (100s)Cd KaI (counts/ch)0.53 ppm0.54 ppm100 kV80 kV00.75 ppm2.53 ppm22.5 23.0Energy (keV)60 kV40 kV23.5 24.0Figure 5.5.4 Cd Kα XRF spectra. Sensitivity (LLD for 100 s) changes with X-ray tube voltage

PERFORMANCE OF HIGH-ENERGY XRF 36112001000Yb KaHf KaU KaIntensity (counts)8006004002000Th La U LaY KaZr KaY KbU LbZr KbU LgCe KaNd KaSm KaDy KaGd KaEr Ka0 20 40 60 80 100X-ray energy (keV)Yb KbHf KbPb KaTh KaPb KbFigure 5.5.5 SRXRF spectrum of a metamict mineral (a variety of uraninite, UO 2 ). The Oddo–Harkins law is clearly observed1500Fe KaBa KaIntensity (counts)1000500Fe KbPbLa,bRb KaSr KaZr KaZr KbBa esc.Ce Ka 1,2La KaCs KaBa Kb Dy Ka 1,2Er Ka 1,2Nd KaCe KbSm KaNd KbGdKaYb Ka 1,2Hf Ka 1,2W Ka 1,20020X-ray energy (keV)40 60Figure 5.5.6 A typical XRF spectrum of geological samples (JG-1, granite rock standard reference sample) excited by 116 keVX-rays and a measurement time of 500 s 15

362 HIGH-ENERGY X-RAY FLUORESCENCE10 mmAIFePenetration depth1 mm100 µmLa10 µm1 µm0 50X-Ray energy (keV)100Figure 5.5.7 Penetration depths of X-rays for Al (Z = 13), Fe(Z = 26) and La (Z = 57) 1Ba, La, Ce, Nd, Sm, Gd, Dy, Er, Yb, Hf,and W together with the certified concentrationof each element. In this sample, the calculatedMDL for W was 0.1 ppm, which is the lowestMDL value in Table 5.5.2. For the higherenergyregion, Compton scattering caused a highbackground, which degrades the signals of lowconcentrationelements. In contrast, the MDLincreased with decreases in energy, which wasdue to the excitation efficiency. Since the energyof the excited X-ray was 116 keV, which isfar from the absorption edge of Fe (ca. 7 keV),there was a much poorer detection limit forFe (0.097 wt%) than for the other heavy elements(Table 5.5.2). The high background regionresulting from the Compton scattering can bechanged by increasing or decreasing the excitationX-ray energy.An advantage of the use of high-energy X-raysin XRF analysis is that they have high transmissionpower. The absorption coefficients of the elementssharply decrease with an increase in the energyof the X-rays. The penetration depths of X-raysfor A1, Fe, and La as a function of X-ray energyare given in Figure 5.5.7. This figure shows thatpenetration depth increases with an increase inX-ray energy. For example, the mass absorptioncoefficients of the JG1 sample were calculatedfor X-rays with energies of 0.011 nm (=113 keV),0.021 nm (=59 keV, which is equal to the energyof the W Kα 1 line), 0.062 nm (=20 keV), and0.148 nm (=8.4 keV, which is equal to that of theWLα 1 line) to be 0.16, 0.28, 3.05, and 37.87,respectively, based on data in the literature. 18These values clearly indicate that the absorptioncoefficient of JG1 sample (3.05) for the 20keV X-rays, typical energy for conventional SR-XRF analysis, is almost 20 times larger thanthat (0.16) for the 113 keV X-rays. The highenergyX-rays, therefore, have a greater penetrationdepth and are favorable for obtaining the bulkchemical composition of a sample. In addition, theabsorption coefficient of the JG1 sample (37.87)for the W Lα 1 line is 135 times larger than that(0.28) for the W Kα 1 line. This suggests thatquantitative analysis using the K lines of the heavy

APPLICATION OF HIGH-ENERGY XRF 36310Normarized net intensity (I Lu /I Gd )10.10.01r 2 = 0.99940.001 0.01 0.1Lu concentration (ng)110Figure 5.5.8 Calibration curves for the determination of Lu. The normalized X-ray intensity of Lu was plotted against theabsolute amount of Lu (ng). The XRF intensity of the internal standard of Gd was used for normalization 15elements requires less absorption correction thanthat using the L lines of those elements.5.5.4.2 DETECTION LIMIT MEASUREDFOR DROPLET SAMPLESThe detection limit of the SR-XRF techniqueis largely affected by the degree of elastic andCompton scattering relative to the XRF signal fromthe analyzed elements. The background countingrate is critical for a bulk sample, and the limitof the counting rate of the detector becomes adominant factor in determining the detection limit.In fact, we must reduce the X-ray intensity byopening the gap of the wiggler to 60 mm in order tomeasure the bulk sample of JG1. However, the gapshould be at its minimum (40 mm) for measuringsuch items as a tiny glass flake of SRM612 ora liquid droplet on Mylar TM film. The detectionlimit in the determination of rare earth elementsby a calibration curve technique using a liquiddroplet sample on a Mylar TM film was evaluated.This method of sample preparation should givealmost the lowest MDL when compared with othermethods except for the use of total reflectiongeometry. Lu was used as the target element, andGd was selected as an internal standard. The netintensities of Lu were normalized by those ofGa and were plotted against the absolute amountof Lu. The calibration curve thus obtained fromthe spectrum with a counting time of 1000 s isshown in Figure 5.5.8. The data show excellentlinearity from a Lu level of 10 ng down to 30 pg.The estimated MDL value at the lowest end is16 pg. These results suggest that a quantitativetrace analysis would be promising for highenergyXRF analysis with proper correction of thematrix effect.5.5.5 APPLICATION OFHIGH-ENERGY XRFFrom the above observations, we found that highenergyXRF analysis enables us to determine allheavy elements with sufficient sensitivity. Theminimum detection limit of the current analysis isat a sub-ppm level. Accordingly, high-energy XRFanalyses will likely become a powerful tool foranalyzing environmental samples, archaeologicalsamples, forensic samples, geochemical samples,and high-tech materials containing heavy elementssuch as rare earth elements. It is expected that theutilization of high-energy X-rays will open newapplication fields for X-ray fluorescence analyses.

364 HIGH-ENERGY X-RAY FLUORESCENCESeveral examples of applications of this techniqueare shown below and the potential advantages ofthis technique are elucidated.5.5.5.1 ANALYSES OF RARE EARTHELEMENTSIn modern industry, rare earth elements are themost important elements used in high-tech devicesemploying lasers, as well as magnetic, fluorescence,and superconducting materials. Therefore,the chemical analysis of rare earth elements isimportant in their industrial use. Thus far, however,XRF analysis of rare earth elements is difficultto accomplish using low-energy X-rays. Developmentof a sensitive, nondestructive method for thetotal analysis of all rare earth elements had beenexpected. Figure 5.5.9 compares the XRF spectraof standard SRM612 glass samples excited by (a)116 keV SR- X-rays and by (b) Pd Kα X-rayswith a tube voltage of 40 kV. The XRF spectra(a) and (b) were obtained from measurementsfor 1000 s and 300 s, respectively. The nominaltrace element concentration of SRM612 glass is50 mg/kg (=50 ppm) foreachofthe61elementsthat have been added to the glass support matrixwith the following composition: 72 % SiO 2 ,12%CaO, 14 % Na 2 O, and 2 % Al 2 O 3 . Figure 5.5.9(a)shows that more than 30 heavy elements are clearlydetectable, and the peak of each rare earth elementis clearly separated in the spectrum. In contrast,the L line peaks of the rare earth elements cannotbe recognized in Figure 5.5.9(b). The problem inthe analysis of rare earth elements excited by conventionalX-ray sources such as Pd Kα X-rays isthat the L lines of the rare earth elements appearfrom 4.650 keV for La Lα to 9.938 keV for LuLβ 2 . The K line spectra of the transition metalsfrom Ti (4.508 keV for Kα) to Cu (8.040 keV forKα) can overlap in the same energy region ofthe spectrum. Practical samples often contain thesetransition elements as major components, and disturbthe analysis of the trace heavy elements by Llines. In fact, this SRM612 sample contains Ti, V,Cr, Mn, Fe, Co, Ni, and Cu. Therefore, it is practicallyimpossible to analyze the rare earth elementsof this sample using the L lines, as can be seen inFigure 5.5.9(b). In addition, without such light elements,possibly 14 rare earth elements (from La toLu except for Pm) and 42 peaks (Lα, Lβ 1 ,andLβ 2lines for each element if we neglect the Lγ line)are present in the XRF spectrum within the smallenergy region of 5.288 keV (=9.938–4.650). Incontrast, in the energy region above 20 keV, thereare no peaks other than the K lines of the heavyelements. Moreover, the energy difference betweenLa Kα 1 (33.4418 keV) and LuKα 1 (52.3889 keV)is ca. 19 keV, which is large enough to distinguisheach rare earth element under the resolutionof a pure Ge SSD, as is demonstrated inFigure 5.5.9(a).Certified values for the rare earth elements havenot been reported for SRM612 glass, but informationvalues (in ppm) are given as follows: Ag(21),Ba(41), La(36), Ce(39), Nd(36), Sm(39), Eu(36),Gd(39), Dy(35), Er(39), and Yb(42). The intensityof the peak of each element in Figure 5.5.9(a)appears to be qualitatively consistent with theseinformation values. This suggests that the presenttechnique is applicable for the nondestructive totaldetermination of rare earth elements as well as forother heavy elements, such as Hf and Ta, at theppm level. 195.5.5.2 ENVIRONMENTALAPPLICATIONSHeavy elements are often environmentally toxic.Recently, many countries have initiated governmentregulations to restrict severely the maximumpermissible concentrations of potentially toxicheavy metals in soils and in sludges used on theland. The heavy elements include Cr, Ni, Cu, Zn,Ag, Cd, Mo, and Pb and their limit values are subppmto a few hundred ppm. Regulation of the concentrationof Cd, Hg, As, and Pb in plastic has alsobecome an important issue in the electric industry.Conventional multi-element analysis techniques,such as ICP-AES (inductively coupled plasmaatomicemission spectroscopy), require decompositionof the samples into solutions, which aretime-consuming treatments. Therefore, the nondestructivefeature of the XRF technique is quite

APPLICATION OF HIGH-ENERGY XRF 3651000Zr KaPb LbTh LbErPb Ka ,1,2Pb LaTh LaU LaSr KaNb KaU Lb, Mo KaTmYbLuRe Ka,Lu KbIntensity (counts)500CaAgCdInSnSbBaCeLaPrNdSmEuGdTbDyHoHfTaWHf KbTa KbW KbReKbBiCsTe5000 00 3 6 9 12 15 18(a)20 40X-Ray energy (keV)60 80Intensity (counts)400300200100Si KaCa KaAg LaCa KbSRM612SiO 2 72%CaO 12%Na 2 O 14%AI 2 O 3 2%Trace 50 ppmelementsMn KaFe KaCo KaNi KaCu KaZn KaGa KaGe KaTl LaPb La & As KaBi LaSe KaAs KbTl LbSr KaPb LbBi LbRb KaYKa & Rb KbZr KaY Kb0(b)Energy (keV)Figure 5.5.9 XRF spectrum of NIST SRM612 glass. Measurement conditions: (a) SR source, 116 keV, GeSSD, measurementtime 1000 s 15 ; (b) excitation source Pd Kα, 40 kV, 1 mA, Si drift detector, measurement time 300 s

366 HIGH-ENERGY X-RAY FLUORESCENCETable 5.5.3 Accuracy and detection limit of the measurement and limit value for heavy metals in soil according to EUDirective 86/278/EECElement Calibration Calibration GSS-1 a GSD-7 a WT-H (sludge) a LLD LLD Limit valuerange (ppm) rms (ppm)100 s 30 min (mg/kg ppm)Certified Measured Certified Measured Certified MeasuredAs 0.23–412 1.39 33.5 34.7 84 84 146 146 1.5 1.5 50Cd 0.03–55 0.63 1.05 0.92 4.30 4.39 55 56 1 0.4 1–3Cr 4.8–1340 17.44 62 58 122 119 1340 1256 4 4 –Cu 4.1–3140 10.53 21 20.9 38.0 36.0 3140 3106 2.5 2.5 50–140Mo 0.09–92 0.93 1.40 1.22 1.40 1.02 78 74 0.7 0.7 4Ni 1.6–1140 5.42 20.4 19.7 53 54 1140 1147 4 4 30–75Pb 4.4–2290 7.57 98 89 350 358 2290 2278 2.5 2.5 50–300Zn 16–6360 10.98 680 679 238 246 6360 6359 2 2 150–300a GSS-1 and GSD-7 are geochemical reference materials (Institute of Geophysical and Geochemical Prospecting, People’s Republic of China. WT-H is sewage sludgereference materials.attractive, and high-energy XRF is expected to providea solution to these problems.Common heavy metal contaminants in soilsand sludges were analyzed with a commerciallyavailable laboratory spectrometer, Epsilon 5. Aseries of soil and rock standards were used forcalibration. The soil samples were analyzed in theform of pressed powder pellets. Approximately12 g of a mixture of sample and wax/styreneadditive was pressed into 36-mm diameter pellets.The measurement time was 200 s (live time). Theaccuracy of the results is presented in Table 5.5.3.Twenty consecutive measurements of a sampledemonstrated relative standard deviations betterthan 4 % at the 24 ppm level (i.e. 25 ± 1 ppm).Typical detection limits for heavy metals in soilare also given in Table 5.5.3. For most elements,the LLDs calculated for 100 s are well within therequirement laid down by the EU soil directive asshown in Table 5.5.3 except for Cd, which requireda counting time of 30 min.5.5.5.3 ARCHAEOLOGICALAPPLICATIONSTrace element components of a material oftenreflect its origin. Heavy elements in particularare useful as fingerprint elements in provenanceanalyses of archaeological samples, as heavyelements are trace elements in nature and exhibitunique geochemical behavior because of their largeionic radii and relatively high valency. To date,neutron activation analysis has often been used foranalyzing heavy elements. However, destructivesample preparation is necessary for this methodbecause the sample becomes radioactive after theanalysis. This precludes the analysis of precioussamples such as those in museums. In contrast, nobeam-induced damage of samples was observedin high-energy XRF analysis, and this techniqueappears to be truly nondestructive, making itsuitable for analyzing archeological samples andworks of art. Here, this technique is applied toreveal the locality of Old Kutani chinaware. 20Kutani chinaware was first produced in the late17th century in Kaga Province, which, today, isIshikawa Prefecture in Japan. In 1710, however,after half a century of continuous production, thekiln was suddenly closed. Pottery from this earlyperiod is known as Old Kutani, and is extremelyprecious. However, it was thought that Old Kutanichina might come from Arita, another worldfamousarea of porcelain production in Japan sincethe 17th century. Therefore, identification of Old-Kutani and Arita is an important problem–almosta mystery–in Japanese art history. The highenergySRXRF analysis of porcelain clay potteryis expected to reveal the origin of the sourcematerials of museum-grade specimens.The reference samples consist of chinawareexcavated from old kilns dated 17th to 19th centuryin the Kutani, Arita, and Fukuyama districts ofJapan. Several original samples of museum-gradedishes have also been nondestructively analyzed(Figure 5.5.10). They were very precious so-calledOld-Kutani and Arita pieces, which were borrowedfrom several collectors and artists. This wasthe first nondestructive analysis of museum-gradesamples of Old Kutani china.

APPLICATION OF HIGH-ENERGY XRF 367SampleX-rayGe-SSDFigure 5.5.10 Photograph showing nondestructive SRXRF analysis of a museum-grade dish (Old Kutani). The measurement wasmade at BL-08 W of SPring-83000BaIntensity (counts)20001000RbSrPbY ZrFeSeLaCsNdCeSmHfGdYbDy ErW00 10 20 30 40 50 60 70Energy (keV)Figure 5.5.11 SRXRF spectrum of a fragment of old Kutani chinaware excavated from an old kiln dated 17th centuryThe analysis confirmed that 116 keV X-ray irradiationcaused practically no damage to the samples.Therefore, this technique is suitable for thenondestructive characterization of precious historicalsamples, as is demonstrated in Figure 5.5.10.An XRF spectrum of the excavated fragment ofOld Kutani ware is shown in Figure 5.5.11. Itshows that tungsten as well as various rare earthelements give distinct fluorescence peaks of Klines and, therefore, the spectrum is rich with information.The XRF peak intensities of these heavyelements were used as the parameters of somestatistical treatments for the provenance analysis.It was found that the Ba/Ce–Nd/Ce plot shown inFigure 5.5.12 is the most useful to estimate theorigin of the chinaware. The result shows thatKutani and Arita chinaware can be clearly distinguishedusing this plot. 20,21 It was found thatthe analytical data of some museum-grade sampleswere located in the region of the Kutanichinaware and that some were from that of theArita chinaware. The data suggest that the formersamples were produced using potter’s clay ofthe Kutani area and that the latter were those of

368 HIGH-ENERGY X-RAY FLUORESCENCE20181614Ba/Ce1210KutaniHimetani86Arita420 0.2 0.4 0.6 0.8 1 1.2Nd/CeFigure 5.5.12 Ba/Ce vs Nd/Ce plot showing three clusters of analytical data. Samples were fragments of chinaware excavatedfrom old kilns of Arita, Kutani, and Himetanithe Arita area. Thus, high-energy XRF has openednew fields of application for nondestructive analysesof historical samples. Detailed results will bepublished elsewhere.5.5.5.4 FORENSIC APPLICATIONSOriginally, we first developed high-energy XRFutilizing 116 keV SR to conduct a scientificinvestigation to aid in the solving of an arsenicmurder that occurred in Wakayama City on 25July 1998. 14,15 Four people were killed and 63people suffered arsenic poisoning after eatingcurry stew served at a summer festival in asmall town in Japan. A trace amount of arsenicwas attached to the crime-related substances. Itwas expected that the use of high-energy X-rays from SPring-8 as an excitation source forXRF would be suitable for distinguishing thedifference in the origin of the trace amountof the arsenic samples, which were producedcommercially. Arsenic compounds often containimpurities of Sb and Bi, whose excitation energiesare 30.5 and 90.6 keV, respectively. Therefore, thehigh-energy X-rays from SPring-8 were requiredas an excitation source for detecting the ppmlevels of Sb and Bi in the trace amounts of thesamples. We had analyzed various arsenic oxidesof different industrial origins for comparison. Thesample was placed on a Mylar TM film on a plasticholder, which was set on the automatic XY stage.The analysis point was irradiated by the laser andmonitored by a video camera.XRF spectra of various arsenic oxides weresuccessfully measured. The examples, which wereproduced in China and Mexico, are given inFigure 5.5.13(a) and 5.5.13(b), respectively. Theformer contains Sn, Sb, and Bi while the lattercontains Sb and Bi. It was found that the traceheavy element compositions are distinct fromeach other, reflecting the different places ofproduction. Our analysis revealed that the arsenicoxide in the curry was the same product as thearsenic powder found in the defendant’s house.These data were presented to the WakayamaDistrict Public Prosecutors Office. This was thefirst successful application of SR in forensicanalysis. The defendant in the case was triedin Wakayama District Court and found guilty.

APPLICATION OF HIGH-ENERGY XRF 369As KαPb Kα 1Sn KαSb KαPb Kα 2Bi KαIntensity (arb. unit)(a)Sb K αSb KβBi Kα(b)0 20 40 60 80 100Energy (keV)Figure 5.5.13 XRF spectra of arsenic trioxide, As 2 O 3 , produced in (a) China and (b) Mexico 14The judge sentenced the defendant to death inDecember 2002. The defendant has appealed theconviction to a higher court.After this experience, we examined severalsamples from the perspective of forensic analysis.Through our studies, the following samples werefound to be suitable for the application of highenergyXRF techniques. Identification of a tinyglass fragment from a hit-and-run car accident andautomobile paint, 22 gunshot residues, 23 cement,etc. Only a tiny sample as small as 100 µm φ isnecessary, and the analysis is truly nondestructive.Through these studies, we have demonstrated thathigh-energy XRF is a powerful tool in the forensicidentification of material evidence based on traceheavy element compositions. This technique hasalready come into routine use by the ForensicScience Laboratory (headed by Dr T. Ninomiya)of the Hyogo Prefecture Police Headquarters tosolve several important criminal cases occurring allover Japan. These cases had been found difficultto solve by conventional analytical techniques.Several practical examples are introduced by T.Ninomiya in this book (Subchapter 7.4).5.5.5.5 GEOLOGICAL ANDGEOCHEMICAL APPLICATIONSIn geochemistry, a chondrite-normalized rare earthelement (REE) pattern is an important indicationof the origin of a sample. The high-energy XRFtechnique enables direct measurement of the REEpattern as stated above. In addition, we can obtaintwo-dimensional information from a small regionof a sample by using X-ray microbeams obtainedby collimators, capillary optics, 6 or Fresnel zoneplate optics. 10,24The cosmic abundance of heavy elements (Z >30) is extremely low and they exhibited uniquegeochemical behavior during the earth’s formationbecause of their large ionic radii and relativelyhigh valence state. Therefore, analysis oftrace heavy elements is an important subject forearth and planetary sciences including geochemistry.Here, the elements of the Pt group play anespecially important role in the evolution of theearth. The potential ability of the high-energy XRFtechnique in the analysis of Pt group elements wasexamined. Measurements were made at BL-08 W,

370 HIGH-ENERGY X-RAY FLUORESCENCE2000FeBiKa BiKbAuKa PbKaPtKa IrKbIntensity1000IrKaOsKa00 20 40 60 80 100X-ray energy (keV)Figure 5.5.14 XRF spectrum of iron meteorite (octahedrite) 25mm543210(a)(b)02 4 6 8mmmm54321mm5432100(c)02 4 6 8mm(d)02 4 6 8mmFigure 5.5.15 (a) Optical microscope image of a garnet sample. XRF imaging of (b) Ce, (c) Gd and (d) Yb measured for thearea indicated by the white square in (a). White to black corresponds to the highest to lowest XRF intensity 26

REFERENCES 371SPring-8 utilizing the same experimental setupas stated above. An example of the XRF spectrumof octahedrite is shown in Figure 5.5.14. 25It is remarkable that trace amounts of Re, Os,and Ir were clearly detected. The advantage ofthe high-energy SRXRF technique is the nondestructive,two-dimensional chemical imaging ofthe trace heavy elements. The distribution of eachREE and other heavy elements in garnet wasanalyzed. 26 The sample showed a zoning of traceREEs, which was formed during the growth of thecrystal. The optical microscope image of the sampleis given in Figure 5.5.15(a). The distributionsof Ce, Gd, and Yb in the garnet are shown inFigure 5.5.15(b), 5.5.15(c) and 5.5.15(d), respectively.These results show that the zoning positionof each element shifts outside the garnet crystalwith an increase in the atomic number. Assumingthat the rare earth elements exist in trivalentions and are 12 coordinated in the garnet crystals,Figure 5.5.15(b), 5.5.15(c) and 5.5.15(d) suggestthat the larger ions (Ce ion, in this case) werepositively incorporated into the garnet crystal atan early stage of growth, while the smaller ions(Yb ion, in this case) are not incorporated into thecrystal until a late stage of growth.The advantages of high-energy XRF over conventionalanalytical techniques used in geologyand geochemistry are summarized as follows. Theidentification of the XRF peaks is more straightforwardand measurement is easy compared with secondaryion mass spectroscopy (SIMS), and enablesus to analyze trace heavy elements with twodimensionalresolution. We can analyze geologicalsamples as large as 100 kg in weight and 1 m inlength. If we used focusing optics such as a Fresnelzone plate, the spatial resolution could reach1 µm or less. This spatial resolution is close oreven better than an electron microprobe, by whichtrace element analysis is difficult.ACKNOWLEDGEMENTSThe author greatly appreciates the help of DrYasuko Terada of SPring-8 for her kind assistancein the high energy XRF experiments at SPring-8, and in the preparation of some of the figuresused in this text. He acknowledges the permissionthat PANalytical has given him to use the diagrams(Figures 5.5.1, 5.5.3 and 5.5.4). The analyticaldata (Table 5.5.3) were supplied by the courtesyof Dr Simon Milner of PANalytical B.V.REFERENCES1. Harada, M. and Sakurai, K. K-line X-ray fluorescenceanalysis of high-Z elements. Spectrochim. Acta B 54,29–39 (1999).2. XRF Globe 1–2, 12–13 (2003).3. Baryshev, V. B., Gil’bert, A. E., Koz’menko, O. A., Kulipanov,G. N. Zolotarev, K. V. Determination of the concentrationsand distributions of rare-earth elements in mineraland rock specimens using the VEPP-4 synchrotronradiation. Nucl. Instrum. Methods Phys. Res., Sect. A 261,272–278 (1987).4. Dar’in, A. V. and Bobrov, V. A. Measurement of rareearth element content in rock standards by XFA methodwith use of synchrotron radiation from the storage ringVEPP-4. Nucl. Instrum. Methods Phys. Res., Sect. A 261,292–294 (1987).5. Khvostova, V. P. and Trunova, V. A. Samples for X-ray fluorescence analysis using synchrotron radiation.Nucl. Instrum. Methods Phys. Res., Sect. A 261, 295–300(1987).6. Janssens, K., Vincze, L., Vekemans, B., Adams, F.,Haller, M. and Knochel, A. Use of lead-glass capillariesfor micro-focusing of highly-energetic (0–60 keV) synchrotronradiation. J. Anal. At. Spectrom. 13, 339–350(1998).7. Chen,J.R., Chao,E.C.T., Back,J.M., Minkin,J.A.,Rivers, M. L., Sutton, S. R., Cygan, G. L., Grossman,J. N. and Reed, M. J. Rare earth element concentrations ingeological and synthetic samples using synchrotron X-rayfluorescence analysis. Nucl. Instrum. Methods Phys. Res.,Sect. B 75 (1–4), 576–581 (1993).8. Snigirev, A., Snigireva, I., Engstroem, P., Lequien, S.,Suvorov, A., Hartman, Ya, Chevallier, P., Idir, M. andLegrand, F. Testing of submicrometer fluorescence microprobebased on Bragg–Fresnel crystal optics at the ESRF.Rev. Sci. Instrum. 66, 1461–1463 (1995).9. Kagoshima, Y., Takai, K., Ibuki, T., Hashida, T., Yokoyama,Y., Yokoyama, K., Takeda, S., Urakawa, M., Miyamoto,N., Tsusaka, Y. and Matsui, J. Formation of X-raymicrobeam using Ta phase zone plate and its applicationto scanning X-ray microscope-III. SPring-8 User Exp. Rep.No. 5, 436 (2000).10. Suzuki, Y., Takeuchi, A., Takano, H., Ohigashi, T. andTakenaka, H. Diffraction-limited microbeam with Fresnelzone plate optics in hard X-ray regions. Jpn. J. Appl. Phys.40, 1508–1510 (2001).11. Wobrauschek, P., Gorgl, R., Kregsamer, P., Streli, C.Pahlke, S. Fabry, L., Haller, M., Knochel, A. and

372 HIGH-ENERGY X-RAY FLUORESCENCERadtke, M. Analysis of Ni on Si-wafer surfaces usingsynchrotron radiation excited total reflection X-ray fluorescenceanalysis. Spectrochim. Acta B52, 901–906(1997).12. Ortega, L., Comin, F., Formoso, V. and Stierle, A. Traceelement analysis on Si wafer surfaces by TXRF at theID32 ESRF undulator beamline. J. Synchrotron Radiat.5(3), 1064–1066 (1998).13. Sakurai, K., Eba, H., Inoue, K. and Yagi, N. Wavelengthdispersivetotal-reflection X-ray fluorescence with anefficient Johansson spectrometer and an undulator X-raysource: detection of 10 −16 g-level trace metals. Anal. Chem.74, 4532–4535 (2002).14. Nakai, I., Terada, Y., Itou, M. and Sakurai, Y. X-rayfluorescence analysis of heavy elements by using Kα X-rayfluorescent lines excited by high energy X-rays. SPring-8User Exp. Rep. (JASRI) No. 3, 88 (1999).15. Nakai, I., Terada, Y., Ito, M. and Sakurai, Y. Use ofhighly energetic (116 keV) synchrotron radiation for X-ray fluorescence analysis of trace rare-earth and heavyelements. J. Synchrotron Rad. 8, 360–362 (2001).16. Hara, M. High energy inelastic scattering (BL08W).SPring-8 Ann. Rep. 1998 53 (1999).17. Sakuari, Y., Hiraoka, N., Ito, M., Ohta, T. and Sakai, N.Performance of a high-resolution Compton scatteringspectrometer for heavy elements at BL08W. SPring-8 UserExp. Rep. No. 3, 80 (1999).18. Sasaki, S. X-ray absorption coefficients of the elements (Lito Bi, U). KEK Rep. 90 16, 1–142 (1990).19. Noma, T., Takada, K., Mukaide, T., Terada, Y., Nakai, I.Application of high-energy X-ray fluorescence analysisfor fluorites. SPring-8 User Exp. Rep. (JASRI) No. 8, 64(2002).20. Nakai, I., Terada, Y., Yamato, S., Yamana, K., Itou, M.and Sakurai, Y. Development and application of highenergy X-ray fluorescence technique for provenance analysisof archaeological samples. SPring-8 User Exp. Rep.(JASRI) No. 4, 69 (1999).21. Nakai, I., Terada, Y., Yamato, S., Yamana, K., Miura, Y.,Itou, M. and Sakurai, Y. Application of high-energy X-ray fluorescence analysis for archaeometric analysis ofold Kutani china wares. SPring-8 User Exp. Rep. (JASRI)No. 5, 128 (2000).22. Ninomiya, T., Nakanishi, T., Muratsu, S., Saitoh, Y., Shimoda,O., Watanabe, S., Nishiwaki, Y., Matsushita, T.,Suzuki, S., Suzuki, Y., Ohta, H., Kasamatsu, M., Nakai, I.and Terada, S. Elemental analysis of a trace of paint chipusing SR-XRF. SPring-8 User Exp. Rep. (JASRI) No. 7,67 (2001).23. Nakai, I., Terada, Y. and Ninomiya, T. Forensic applicationof synchrotron radiation X-ray fluorescence analysis.Proc. 16th Meet. Int. Assoc. Forensic Sci. 29–34 (2002).24. Tamura, S., Yasumoto, M., Kamijo, N., Suzuki, Y.,Awaji, M., Takeuchi, A., Takano, H. and Handa K. Developmentof multilayer Fresnel zone plate for high-energysynchrotron radiation X-rays by DC sputtering deposition.J. Synchrotron Rad. 9, 154–159 (2002).25. Terada, Y., Miura, Y., Nakai, I., Takahashi, Y., Itou, M.and Sakurai, Y. Development and application of newX-ray fluorescence technique for earth and planetarymaterials using high energy X-ray. SPring-8 User Exp.Rep. (JASRI) No. 7, 72 (2001).26. Terada, Y., Nakai, I., Miura, Y., Takahashi, Y., andKato, Y. XRF imaging of the heavy elements in geologicalsamples using high energy X-rays. SPring-8 User Exp.Rep. (JASRI) No. 8, 60 (2002).

5.6 Low-energy Electron Probe Microanalysis andScanning Electron MicroscopyS. KUYPERSVITO (Flemish Institute for Technological Research), Mol, Belgium5.6.1 INTRODUCTIONThe distinction between an electron probe microanalyserand a scanning electron microscope hasalways been clear, at least to the microanalysiscommunity:• An electron probe microanalyser is an analysistool equipped with at least three, preferably five,wavelength-dispersive spectrometers providinghigh spectral resolution. A high beam currentis required and can be provided by a conventionalelectron source. Electron image quality israther poor.• A state-of-the-art scanning electron microscopeis an imaging tool equipped with a field emissiongun providing an electron beam with a veryhigh brightness and is therefore capable ofworking at high magnifications. The preferredattachment for elemental analysis is an energydispersivespectrometer, because the relativelylow current in the electron beam does notallow efficient use of a wavelength-dispersivespectrometer.Low-energy electron probe microanalysis (EPMA)and scanning electron microscopy (SEM) arehighly complementary techniques, essential inmaterials R&D. Wavelength-dispersive spectrometry(WDS) in an electron probe microanalyseris a powerful tool for quantitative near-surfaceanalysis and hitherto unrivalled for quantitativeanalysis of ultra-light-element-based thin films onsubstrates. A scanning electron microscope with afield emitter source allows high resolution imagingat reduced beam energies, where specimen chargingcan be reduced or eliminated. The flexibility,the ease-of-use and the availability of tools forlocal elemental analysis, make low-energy SEM atool equal to none for studying surface morphologyon a nanoscale.Recent developments in instrumentation, suchas high-sensitivity wavelength-dispersive spectrometers,the bolometer and high-current fieldemitter sources, will allow to combine high spectralresolution and high lateral resolution in onescanning electron beam instrument. Only if thiscan be done without compromise, will the distinctionbetween EPMA on the one hand and SEMwith accessories for elemental analysis on the otherhand, disappear completely. Meanwhile, the totalcost of a ‘hybrid’ instrument as compared to twoseparate instruments can be expected to be suchthat many laboratories will allow for some compromisein the near future.In this subchapter, the possibilities and limitationsof low-energy EPMA and of low-energySEM, as performed in two separate instruments,are discussed. The potential of the two techniquesis illustrated with recent examples relatedto the development of ultra-light-element basedcoatings for sliding wear applications, membranesfor ultrafiltration and packaging materialsfor meat.X-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

374 LOW-ENERGY ELECTRON PROBE MICROANALYSIS AND SCANNING ELECTRON MICROSCOPY5.6.2 SOFT X-RAYS IN PRACTICE5.6.2.1 GENERALFor a review on quantitative electron probemicroanalysis touching on all aspects, we referto the textbook by Scott et al. (1995). A goodaccount of the practical use of soft X-rays inmicroanalysis was given by Pouchou (1996). Inthis paper it was pointed out that the presentdefinition of the soft X-ray range as extendingfrom 1 keV down to 100 eV, is largely due to thelimits of spectrometers and absorption correctionmodels in the early days of microanalysis. On theother hand, even with today’s instrumentation andsoftware, accurate analysis in the soft X-ray rangerequires special care and is still a challenge formany applications. Three main reasons can be citedfor using soft X-rays:• Analysis of ultra-light elements (Be, B, C,N, O, F), in which case of course thesoft K lines are the only characteristic linesavailable.• Analysis with increased surface sensitivity byreducing the electron beam energy, in whichcase one should select the L rather than the Klines for medium-Z elements and the M ratherthan the L lines for high-Z elements.• Minimisation of fluorescence effects, because oflow fluorescence contributions in the soft X-raylines.There are a number of (potential) experimentalproblems to be overcome and precautions to betaken when soft X-ray lines in general and ultralightelements in particular are analysed withwavelength-dispersive spectrometers; the more sowhen thin coatings and/or low concentrationsare involved:• Carbon contamination at the point of impactof the electron beam, due to the presence ofhydrocarbons in the vacuum; its influence on theresults can be substantial (Willich and Bethke,1993); the best way to control it seems to be agas-jet combined with a cold finger, in particularfor lengthy measurements (Willich and Bethke,1993; Bastin and Heijligers, 1986).• Insulating specimens can be a serious sourceof problems; coating with carbon is not alwaysthe best choice; good results have e.g. beenobtained with sputtered gold (Pouchou, 1996)and aluminium (see below) films; applying identicalconductive coatings on reference materials(RMs) and unknowns simultaneously is notobvious and not really essential as long as thedifferent conductive coatings applied are takeninto account in the matrix correction.• The choice of RMs should be ideally suchthat the electrical conductivity of RMs andunknowns is comparable; in practice one oftenhas to use what is (commercially) available andmake the best of it.• Dedicated monochromators are required; thenewer synthetic multilayers have advantagesover the conventional lead stearate; the peakcount rates are higher and because of their somewhatpoorer resolution they are less sensitiveto peak shape alterations (Bastin and Heijligers,1990).• Peak shape differences between RMs andunknown can be substantial in the case of boronand carbon peaks and should be taken intoaccount by measuring peak areas rather thanpeak heights; in practice one can use the socalledarea-to-peak factor (APF) concept (Bastinand Heijligers, 1990).• The matrix correction program is of courseessential; software for the analysis of multilayerfilms, based on reliable ϕ(ρz) models, whereϕ represents the ionization and ρz the massdepth in the sample, was made commerciallyavailable some eight to ten years ago (Bastinand Heijligers, 1990; Pouchou and Pichoir,1990; Bastin et al., 1993) and has been furtherrefined since then.• The lack of reliable reference methods for theanalysis of ultra-light elements, especially incoatings, emphasises the unique character andthe importance of EPMA, but at the same timeit prevents the validation of EPMA for thisimportant application.

LOW-ENERGY SEM AND HIGH-RESOLUTION IMAGING 3755.6.2.2 IN PRACTICEOur interest in soft X-rays is primarily for theanalysis of ultra-light-element-based thin coatings.Our microprobe is a Jeol JXA-8621 withthree wavelength-dispersive spectrometers (sixmonochromators) and one energy-dispersive spectrometerwith a Be window. Two monochromatorsare for ultra-light element analysis: a conventionallead stearate crystal (NSTE; 2d = 10.04 nm) anda synthetic W/Si multilayer crystal (LDE; 2d =6 nm). A gas-jet for eliminating carbon contaminationis not available on our instrument. Insteadwe use a combination of a trap at the entranceto the diffusion pump (baffle) and a metal platejust beneath the objective lens, both liquid-nitrogencooled, when analysing ultra-light elements. Withthis system we never detected carbon contaminationwithin the time frame of the measurements.Until recently only ZAF-correction softwarewas available on-line on our system and datahad to be fed manually into separate software forfurther analysis with ϕ(ρz)-based methods. Wecould not take into account peak areas. Matrixcorrection was done with Strata 5.0 (SAMx),which uses the models developed by Pouchou andPichoir (1990).Most of our RMs were commercially availableand were coated by the manufacturer with aprotective carbon coating prior to delivery. Thethicknesses of the protective carbon coatingson the different ultralight-element RMs wereestimated using the Strata program and were foundto be in the range 10–25 nm. The measuredvalues were taken into account in the matrixcorrection program.Ultra-light-element-based coatings for analysiswith EPMA were mostly deposited on siliconwafers. The substrate signals were taken intoaccount for matrix correction. Although the coatingsare insulators, charging was only a problemwhen the coating thickness exceeded theexcitation depth. In such cases reasonable resultswere obtained by depositing an aluminium coatingapproximately 10 nm thick prior to analysis.Results for a series of B–N–Si–:H coatingsobtained by varying different deposition parametersare shown in Table 5.6.1. The thicknessesof the aluminium layers were derived from Strataassuming a density of 2.7 g/cm 3 . The results lookacceptable, perhaps deceivingly so, consideringthe fact that peak shapes were not taken intoaccount, while the boron content does vary overa wide range. The carbon and oxygen contentmight (partly) be due to contamination from thealuminium sputtering process.In Section 5.6.4.1, more experimental detailsare given for EPMA applied to thin coatingsin the boron–nitrogen–carbon (BNC) compositiontriangle.5.6.3 LOW-ENERGY SEM ANDHIGH-RESOLUTION IMAGING5.6.3.1 GENERALLow-energy SEM is defined as SEM at beam energiesbelow 5 keV. An excellent and practical introductionto the subject can be found in the paperTable 5.6.1 Compositions of B–N–Si:H coatings, obtained with EPMA at 8 keV and 100 nA. The coating thicknesses wereobtained independently from EPMA. An aluminium coating was deposited to achieve conductivity in EPMA. Its thickness wasderived from the measured intensity. Reproduced by permission of Springer-Verlag WienSampleB(at%)N(at%)Si(at%)C(at%)O(at%)Total wt%Thickness(nm)ThicknessAl (nm)GLC917 13.9 49.2 33.8 2.1 1.0 97.3 2800 10GLC919 7.6 48.0 40.3 2.8 1.3 97.8 3200 15GLC920 10.8 57.8 27.9 2.3 1.2 97.6 3400 15GLC921 4.7 58.9 32.7 2.5 1.3 99.7 4000 14GLC932 30.8 52.1 9.6 1.5 6.0 101.9 1460 16GLC933 29.0 54.5 10.8 1.4 4.3 102.3 1580 15GLC934 25.1 56.9 14.3 1.1 2.6 100.1 1620 10GLC935 19.4 59.2 17.6 1.9 1.9 97.6 2300 14

376 LOW-ENERGY ELECTRON PROBE MICROANALYSIS AND SCANNING ELECTRON MICROSCOPYby Joy and Joy (1996), while a more theoreticalbackground is provided by Reimer (1993).In principle, low-energy SEM is an excellentapproach to achieving high-resolution imaging(e.g. Goldstein et al., 1992), because theelectron–specimen interaction volume decreasesrapidly with beam energy. The problem is the electronoptics: at low beam energies the source brightnesswill be reduced and one may be left with adegraded probe size or insufficient beam current.This can be overcome by using a high-brightnesssource, i.e. a field-emitter tip, rather than amore conventional tungsten hairpin or LaB 6 filament.A modern field-emission-gun SEM (FEG-SEM) allows imaging at intermediate (10 000 to100 000×) and even high (>100 000×) magnifications,with beam energies well below 5 keV.Advantages of SEM at low beam energies are:• Charging of nonconductive specimens can bereduced or eliminated; this is achieved byworking close to or at the beam energy (‘E2’)where no net charging occurs, i.e. where thenumber of electrons emitted by the specimenequals the number of electrons received; formany materials of technological importance(semiconductors, ceramics, polymers) E2 is inthe range of a few keV; a method to determineE2 experimentally is described by Joy andJoy (1996).• The extent of radiation damage is reduced (notnecessarily the radiation damage as such).• Better topographic contrast is obtained.• Surface sensitivity is increased.• Image resolution in backscattered electron (BSE)mode is improved.• X-ray resolution is improved.Disadvantages are:• Electron-optical performance is reduced.• Overvoltage for X-ray microanalysis is (too)low.5.6.3.2 IN PRACTICEConventional SEM is usually done in the range15–25 keV. This range of electron beam energiesis a bad choice in all respects. Charging ofnonconductive specimens under these conditionscan be severe. In extreme cases of chargingthe electron beam is reflected off the specimenand scans the microscope chamber. The ‘fisheyelens’ view of the specimen chamber of our JSM-6340F, shown in Figure 5.6.1, was obtained inthis way. It reveals the liquid-nitrogen-cooled anticontaminationplate just below the objective lens,the in-lens secondary electron detector (SED), theretracted backscattered electron detector (BSED),the chamber camera and the end cap of theEDS detector. Not visible is the conventionalsecondary electron detector or ‘lower electrondetector’ (LED) below the objective lens.The Jeol JSM-6340F is a digital FEG-SEMwith a cold field emission electron source and asemi-in-lens type objective lens (OL) (Nakagawa,1994; Yamamoto et al., 1996; Yamamoto et al.,1999). The semi-in-lens type OL induces a strongmagnetic field on the sample. The field rolls upalmost all the secondary electrons into the OL,where they are guided towards the in-lens SEDby means of a set of accelerating and retardingelectrodes. This is schematically represented inFigure 5.6.2. An important consequence is that therelative contribution of backscattered electrons tothe LED image is much larger than for an out-oflenstype OL.Images of metal oxide particles and of thesurface of a polymer-based membrane shown inFigure 5.6.3, illustrate the importance of carefullyselecting an appropriate beam energy. Here,the effect on image quality and informationdepth when the beam energy is reduced froma conventional 20 keV to a relatively low 5 keVare dramatic. Figure 5.6.4 demonstrates the highresolutioncapabilities of a modern FEG-SEM atlow beam energies. The images are from aluminiumsurfaces anodised under different conditions.They were obtained in the JSM-6340F at5 keV, working distance (WD) 5–6 mm, originalmagnification 100 000×; approximately 1.5–2 nmof Pt–Pd coat was applied by sputtering. Note thatinstead of trying to achieve dynamic charge balanceconditions at E2, we are working at slightlyhigher beam energies and have applied a very thin

APPLICATIONS 377Figure 5.6.1 ‘Fisheye lens’ view of the specimen chamber of the JSM-6340F seen from the specimen and obtained as a resultof extreme specimen charging. We see the anti-contamination plate (A) just below the objective lens, the in-lens secondaryelectron detector (SED), the retracted backscattered electron detector (BSED), the chamber camera (C) and the end-cap of theEDS detector (EDS). Reproduced by permission of Springer-Verlag, WienPrimary beamRetarding electrode Semi-in-lens type objective lensSecondary electronMagnetic fieldSamplePole piecesSEDAccelerating electrodeFigure 5.6.2 Schematic representation of the semi-in-lenstype objective lens of the JSM-6340F, with accelerating andretarding electrodes and in-lens SED. Courtesy of Jeol Ltd.Reproduced by permission of Springer-Verlag Wienmetallic coating. It is our experience that a sufficientlylow beam energy (very often 5 keV), combinedwith a suitable metallic coating, allows toobtain excellent high-resolution images of nonconductivespecimens. We usually apply 1–2 nm ofPt–Pd (80–20) by sputtering (Cressington 208HR).When applied in this thickness range the Pt–Pdcoating is ‘invisible’ to the JSM-6340F and hencedoes not introduce any observable artefacts. Thisway of working is very often more efficient thanworking under dynamic charge balance conditions,especially for heterogeneous surfaces whereE2 changes with the position of the beam onthe sample.5.6.4 APPLICATIONS5.6.4.1 COMPOSITION OFULTRA-LIGHT-ELEMENT-BASEDCOATINGS – THE BNC TRIANGLEUltra-light-element-based coatings within the BNCcomposition triangle have been studied intensivelyin recent years for a wide range of applications(wear protection, optics, electronics). Crystallinephases such as β-C 3 N 4 , diamond and c-BN seemattractive for wear protection applications becauseof their extreme hardness. When prepared in theamorphous state these materials have the potential

378 LOW-ENERGY ELECTRON PROBE MICROANALYSIS AND SCANNING ELECTRON MICROSCOPY20 kV1 µm 5 kV1 µm20 kV10 µm 5 kV10 µmFigure 5.6.3 Effect of reducing the electron beam energy from 20 keV to 5 keV. Top: Metal oxide grains (ZrO 2 –MgO) imaged withthe lower electron detector (LED). At 20 keV the grain boundaries are vague and all surface detail is lost. Bottom: polymer-basedmembrane imaged with the in-lens SED. At 20 keV the polymer network below the surface is also imaged. Reproduced bypermission of Springer-Verlag, Wiento retain to some extent the excellent propertiesof the crystalline phases. Amorphous coatings canbe deposited at lower temperatures and will inherentlypossess smooth surfaces, which makes themparticularly useful for sliding wear applications.Moreover, amorphous ternary coatings B x N y C zcan be prepared in a wide composition range,allowing material properties to be tailored for specificapplications. We have published results forthin films prepared on the C–N and B–N axes, aswell as for films prepared across the whole BNCtriangle (Dekempeneer et al., 1994, 1995, 1996a,1996b). In each case the correlation betweendeposition parameters and structural, mechanicaland tribological properties was investigated. AllB x N y C z :H coatings were deposited with radio frequencyplasma assisted chemical vapour deposition(RF PACVD), starting from CH 4 –N 2 –B 2 H 6(H 2 diluted) gas mixtures.The B, C, N and impurity-O content of coatingsdeposited on silicon was measured with EPMA,while the H content was measured with elasticrecoil detection analysis (ERDA). Coating thicknesseswere in the range 200 nm – 2.5 µm. Therewere attempts to set up nuclear reaction analysis(NRA) as a reference method for determiningthe B, C, N and O content of some of the coatings.However, reliable NRA results were never

APPLICATIONS 379100 nm100 nmFigure 5.6.4 High resolution images of anodised aluminium surfaces after different anodisation treatments. The insets are100 × 100 nm 2 . The images were obtained at 5 keV with the SED in the JSM-6340F, working distance 5–6 mm, originalmagnification 100 000×; approximately 1.5–2 nm of Pt–Pd coat. Reproduced by permission of Springer-Verlag, Wienobtained. This was very unfortunate because theywould have allowed to employ the coatings analysedwith NRA as additional RMs for EPMA and,most importantly, to assess and validate EPMA forquantitative analysis of B x N y C z :H films.EPMA was carried out in the Jeol JXA-8621.Samples were typically 20 × 20 mm 2 .Theywereglued to the sample holder with carbon tape.Per sample 6–9 points were analysed. Referencematerials were B, C, h-BN, SiO 2 and Si; allcommercially available. The electron beam energywas chosen in the range 5–10 keV; probe currentwas 100 nA. Analysing crystals were NSTE (2d =10.04 nm) for B and C, LDE1 (W/Si; 2d =6 nm) for N and O, PET (2d = 0.8742 nm) forSi. Peak heights were measured. Systematic usewas made of the liquid-nitrogen-cooled baffleand anti-contamination device. A gas-jet wasnot available. There were no indications forcarbon contamination within the time frame of the

380 LOW-ENERGY ELECTRON PROBE MICROANALYSIS AND SCANNING ELECTRON MICROSCOPYTable 5.6.2 Experimental data for C-rich films in the BNC composition triangle, grown with PACVD. Low total weightpercentages for EPMA emphasise the importance of using area-to-peak factors for boron analysis. Reproduced by permission ofSpringer-Verlag WienSample Gas flow (sccm) EPMA results H content Thickness Density(at%) (nm) (g/cmCH 4 B 2 H 6 N 2 C (at%) B (at%) N (at%) O (at%) Total wt%3 )GLC812 9 1 – 97.0 2.8 – 0.2 100.5 32 430 1.49GLC813 8 2 – 93.7 4.7 – 1.6 99.1 32 470 1.38GLC814 7 3 – 90.6 7.5 – 1.9 97.1 31 485 1.43GLC815 6 4 – 89.2 10.2 – 0.6 98.3 32 500 1.31GLC817 5.7 3.2 1.1 80.3 10.4 7.9 1.4 95.2 36 480 1.43GLC818 5.3 2.3 2.4 76.3 7.1 13.2 3.4 94.4 30 380 1.27GLC819 5 1.5 3.5 77.8 4.8 16.4 1.0 93.7 31 380 1.30GLC821 5 – 5 81.8 – 17.4 0.9 100.3 31 175 1.11GLC822 4.5 5.5 – 83.0 16.6 – 0.4 94.8 37 790 1.69GLC823 3 7 – 76.6 22.4 – 1.1 92.5 37 640 1.69measurements. Matrix correction on the data wasdone off-line with Strata 5.0 thin film correctionsoftware, using the XPP model. The measuredSi signal from the substrate and the actualthickness of the protective carbon coatings onthe RMs was taken into account. In Table 5.6.2results are shown for a number of carbon-richB x N y C z :H coatings with thicknesses in the range170–800 nm. Electron beam energy was 8 keV forall analyses. The thicknesses were obtained fromstep height measurements and were fed into Stratato obtain an estimate of the film densities. It isapparent from Table 5.6.2 that the total weightpercentage decreases with increasing B content.Most probably this is due to not taking intoaccount differences in B peak shape between RMsand unknowns. The presence of nitrogen seemsto add to the effect. The results emphasise theimportance of using area-to-peak factors for theanalysis of B. It can be assumed that the reportedresults underestimate the B content of the coatings.5.6.4.2 SURFACE CHARACTERISTICSOF POLYMER BASED MEMBRANESFOR ULTRAFILTRATIONSEM is generally accepted as an indispensable toolfor polymer-membrane research. Its power lies inthe direct visualisation of the membrane pore structure.However, membranes for ultrafiltration (UF)have dense boundary layers with surface pores inthe nanometer range, which is beyond the resolvingpower of conventional SEM, even at high electronbeam energies. Transmission electron microscopy(TEM) has the required resolution, but the samplepreparation (thin foil cross-section or replica) istedious and likely to introduce artefacts. A solutionis offered by FEG-SEM, which combines highresolutionimaging at low beam energies with allthe advantages of conventional SEM. FEG-SEMhas been successfully applied to different typesof commercially available UF membranes (Kimet al., 1990, 1991; Kim and Fane, 1994).In the early 1990s, VITO developed new UFmembranes loaded with inorganic (metal oxide)fillers (Doyen et al., 1990a). The membranes consistof a polymer network (mostly polysulfone)and an inorganic filler (originally zirconium oxide).They possess a dense boundary layer (skin) ontop of a porous support (matrix). Originally thesemembranes were developed for use as separators inelectrochemical systems. Applications in the fieldof ultrafiltration were envisaged when it was discoveredthat the transport properties vary with theinorganic filler content (Doyen et al., 1990b). Thepermeability was found to increase significantlywith increasing metal oxide content. The observedflux behaviour was explained by assuming that themetal oxide particles are present in the skin ofthe membrane where they modify skin morphologyand/or skin thickness. Direct microscopic observationswere required to support this assumption.Feasibility tests with transmission electronmicroscopy (TEM), atomic force microscopy(AFM) and FEG-SEM were set up. The path of

APPLICATIONS 381TEM was soon abandoned: ultramicrotomy did notproduce useful thin sections, mainly because ofthe presence of large (relative to the skin thickness)inorganic grains that were torn out and damagedthe section during cutting. AFM posed noproblems of sample preparation, but the apparentroughness of the membrane surfaces complicatedimage interpretation, it proved extremely difficultto obtain an overview over larger sample areas, andthere was the suspicion of imaging artefacts (poreselongated in one direction). The first FEG-SEMresults (on coated samples) looked very promisingand it was decided to introduce this techniquein UF membrane development and optimisation.Different experiments were set up in which membranecasting parameters were varied and the effecton membrane performance studied. In all theseexperiments low-energy SEM played a key rolein linking membrane performance with membranemorphology (Kuypers et al., 1995; Genné et al.,1996; Aerts et al., 2000).Most of the FEG-SEM work was carriedout in instruments with a cold field emittersource (JSM-6400F, JSM-6320F, JSM-6340F) atelectron beam energies of 5–10 keV and workingdistances of 3–5 mm. Our standard conditions onthese UF membranes with the JSM-6340F are:5 keV, WD 3 mm, in-lens detector, 1.5 nm Pt–Pd,magnification 100 000×. To our experience ametallic coating suited for high magnification workgreatly increases experimental efficiency, withoutintroducing artefacts within the resolution limitsof the instrument. Initially, observations werealso made on uncoated surfaces using electronbeam energies of 1–3 keV. There was little or nocharging, but (minor) beam damage inflicted tothe polymer surface and the moderate performanceof the instrument at the lowest voltages, resultedin insufficient image detail for accurate poremeasurements. After the skin surfaces were coatedwith 1.5–2 nm of Pt or Pt–Pd, the electron beamdid no longer inflict observable damage to thepolymer surface. It has been reported that in certaincases Pt is to be preferred over Cr for highresolution imaging of clean UF membranes (Kimand Fane, 1994).The image in Figure 5.6.5 is representative forthe skin surface of UF membranes with metaloxide filler. In general, surfaces with well-resolvedpores of 3–50 nm are observed. The distributionof pores over the surface is uniform. Apart frompores the image also reveals bright areas ofseveral hundreds of nanometres in diameter, thepositions of which are independent of the pore100 nmFigure 5.6.5 Ultrafiltration membranes. Surface morphology of a polysulfone based membrane containing 85 wt% of inorganicfiller, imaged at 5 keV in the JSM-6340F. The bright regions are due to metal oxide beneath the surface. The inset is100 × 100 nm 2 . Reproduced by permission of Springer-Verlag, Wien

382 LOW-ENERGY ELECTRON PROBE MICROANALYSIS AND SCANNING ELECTRON MICROSCOPYpositions. These areas correspond to conglomeratesof metal oxide particles just below the skin surface.For meaningful quantitative analysis of the porestructure, at least six SE images were taken foreach membrane, at 100 000× magnification, thuscovering an area of about 6 µm 2 . The selectedregions were verified to be representative for themembrane under study by scanning larger regionsof the surface. The images were analysed for poresize, pore distribution, porosity and pore density(pore density is the number of pores per unitsurface area irrespective of their size; porosity isobtained from the ratio of the area of the poresto the corresponding total area). Quantitative dataon how pore density and porosity vary with acasting parameter could easily be derived from thecorresponding images (Kuypers et al., 1995).5.6.4.3 FOULING OF POLYMERMEMBRANES FOR REVERSE OSMOSISFouling (blocking, clogging) of a membrane resultsin a gradual decrease of membrane flux withtime and is obviously undesirable. Fouling canbe caused by: (1) adsorption/deposition of soluteon the surface of the membrane and/or withinthe membrane; (2) gradual, irreversible changesof the polarised layer. Low-energy SEM hasbeen successfully applied for studying foulingmechanisms (cf. Kim et al. (1992) and referencestherein). We were asked to contribute to theanalysis of fouled membranes for reverse osmosis.The flux through these membranes had dropped tounacceptably low values only a few hours afterstart up of an industrial installation. To allowfor SEM investigation of the fouled membrane,a membrane module was cut open and piecesof typically 30 × 30 mm 2 were cut from themembrane at several positions along the surface.The pieces were dried in air at 40 ◦ C. Togetherwith the freshly fouled membrane, pieces of anunused membrane and of a membrane used in apilot installation, both of the same type as thefouled membrane, were prepared for investigation.The pilot membrane had shown a normal fluxdecline over several months of use, typical forgradual fouling. Pieces of all membranes werecut into samples of typically 10 × 10 mm 2 forexamination of the surface; or broken under liquidnitrogen for examination of the cross-section. In allcases they were coated with approximately 2 nmof Pt–Pd. Images (Figure 5.6.6) were obtained inthe JSM-6340F under the following conditions:5 keV, WD 16 mm, in-lens detector for surfaceimaging, lower detector for cross-sections. EDSspectra were obtained at 20 keV over a samplearea of 24 × 18 µm 2 . The pilot membrane revealsa contamination cake with many cracks. Thefouled membrane has irregularly shaped particleson its surface, containing elements strange to themembrane. This contamination is not dense oruniform and cannot explain the drastic drop of themembrane flux. However, when the morphologyof particle-free regions of the fouled membraneis compared with the morphology of the unusedmembrane, it is obvious that a contaminant hasbeen adsorbed on the surface. In EDS the highsulfur signal, typical for the unused membrane, isstrongly suppressed on the fouled membrane, whilethe carbon signal has increased. This stronglysuggests a contamination with an organic fluid suchas oil, which is known to be lethal for membraneperformance. EDS of the pilot membrane revealsthe elements expected from the process. The crosssectionsgive important additional information.The cross-sections of the unused and the pilotmembrane are very similar. The contaminationon the pilot membrane is superficial. Not sofor the fouled membrane, where the morphologyhas changed micrometres deep below the surface,indicating that a contaminant has not only beenadsorbed on the surface, but has penetrated themembrane as well.FEG-SEM/EDS has revealed the nature ofthe fouling and has indicated a possible source(organic fluid). The next challenge is to track downand remove the source of fouling.5.6.4.4 SURFACE CHARACTERISTICSOF CASINGS FOR MEATMeat in general, and sausages in particular, arevery often wrapped in a casing that sticks firmly

APPLICATIONS 3831 µm2 µmsSulfurFS 587cCarbon FS 806sSulfurFS 860cCarbonPhosphorusOxygenpOPtsSulfurCarbonFeIronoPttPdoPtKPdFetaPdK0.0 2.04.0 6.0 8.00.0 2.0 4.0 6.0 8.00.0 2.0 4.0 6.0 8.0Figure 5.6.6 Reverse osmosis (RO) membranes. Comparison between (from top to bottom) surface images, cross-sections andEDS-spectra of (from left to right) an unused membrane, a fouled membrane and a fouled pilot membrane, all of the same type.Reproduced by permission of Springer-Verlag Wiento the meat, protects it and keeps it from goingtaint. The casing can be natural (animal intestines)or synthetic (cellulose-based). The production ofa good casing is not trivial and productionparameters have to be kept within close ranges toassure its quality. One can easily understand thatthe condition of the inner surface of the casing,which will be in contact with the meat, is extremelyimportant. The inner surface is treated to assurea proper degree of adhesion to the meat. If theadhesion is poor, the casing is not effective; if theadhesion is too strong, the meat will stick to the

384 LOW-ENERGY ELECTRON PROBE MICROANALYSIS AND SCANNING ELECTRON MICROSCOPY30 µm 1 µm 30 µmFigure 5.6.7 Casings for meat. Comparison between images of the inner surface at low (left) and high (middle) magnificationand of the cross-sections (right), after four different treatments of the inner surface. The surface images were obtained at 1.5 keV.Reproduced by permission of Springer-Verlag, Wien

REFERENCES 385casing when this is removed prior to consumptionand the consumer will not be happy.On several occasions we were asked to evaluatethe impact of different surface treatments onthe morphology and/or the composition of theinner surfaces by means of FEG-SEM and X-rayphotoelectron spectroscopy (XPS), respectively.An example of a morphological study of the innersurfaces of four casings is shown in Figure 5.6.7.A Pt–Pd coating with a thickness of approximately1.5–2 nm was applied prior to observation inthe SEM. Even then the beam energy had tobe reduced to 1.5 keV to avoid charging. Theworking distance for surface imaging was 3 mm.The in-lens detector of the JSM-6340F was used.The surfaces suffered beam damage resultingin reduced topography when acquiring imagesin slow scan mode. Representative images wereobtained by averaging in fast scan mode. At lowmagnification the surfaces look identical, but athigh magnification the differences are obviousand might explain the different behaviour of theproducts. It would be extremely difficult to obtainthis information in any other way.ACKNOWLEDGEMENTSThe author is indebted to his colleagues ofthe Materials Technology and Process TechnologyGroups of VITO. Special thanks are dueto Mrs Hong Chen and Mr Raymond Kemps ofVITO’s Centre for Materials Advice and Analysis;skilled operators of EPMA and FEG-SEM, respectively.REFERENCESAerts, P., Genné, I., Kuypers, S., Leysen, R., Vankelecom,I.F.J. and Jacobs, P.A. Polysulfone–aerosil composite membranes– Part 2. The influence of the addition of aerosil onthe skin characteristics and membrane properties. J. Membr.Sci., 178, 1–11 (2000).Bastin, G.F., Dijkstra, J.M., Heijligers, H.J.M. and Klepper, D.In-depth profiling with the electron probe microanalyzer.Microbeam Anal., 2, 29–43 (1993).Bastin, G.F. and Heijligers, H.J.M. Quantitative electron probemicroanalysis. X-ray Spectrom., 15, 135–141 (1986).Bastin, G.F. and Heijligers, H.J.M. Quantitative electron probemicroanalysis of ultralight elements (Boron–Oxygen). Scanning,12, 225–236 (1990).Dekempeneer, E.H.A., Meneve, J., Kuypers, S. and Smeets, J.Microstructure and mechanical properties of a-B 1−x N x :Hfilms prepared by r.f. PACVD. Surf. Coat. Technol., 74/75,399–404 (1995).Dekempeneer, E.H.A., Meneve, J., Kuypers, S. and Smeets, J.Tribological properties of r.f. PACVD amorphous B–N–Ccoatings. Thin Solid Films, 281/282, 331–333 (1996a).Dekempeneer, E.H.A., Meneve, J., Smeets, J., Kuypers, S.,Eersels, L. and Jacobs, R. Structural, mechanical and tribologicalproperties of plasma-assisted chemically vapourdeposited hydrogenated C x N 1−x :H films. Surf. Coat. Technol.,68/69, 621–625 (1994).Dekempeneer, E.H.A., Wagner, V., van IJzendoorn, L.J., Meneve,J., Kuypers, S., Smeets, J., Geurts, J. and Caudano, R.Tribological and structural properties of amorphous B–N–Ccoatings. Surf. Coat. Technol., 86/87, 581–585 (1996b).Doyen, W., Leysen, R., Mottar, J. and Waes, G. New compositetubular membranes for ultrafiltration. Desalination, 79,163–179 (1990b).Doyen, W., Proost, R. and Leysen, R., Method for preparing asemi-permeable membrane. European Patent, 0 241 995 B1(1990a).Genné, I., Kuypers, S. and Leysen, R. Effect of the addition ofZrO 2 to polysulfone based UF membranes. J. Membr. Sci.,113, 343–350 (1996).Goldstein, J.I., Newbury, D.E., Echlin, P., Joy, D.C., Romig,A.D., Lyman, C.E., Fiori, C. and Lifshin, E. ScanningElectron Microscopy and X-ray Microanalysis, Chapter 4,Plenum Press, New York, 1992.Joy, D.C. and Joy, C.S. Low voltage scanning electronmicroscopy. Micron, 3–4, 247–263 (1996).Kim, K.J., Dickson, M.R., Fane, A.G. and Fell, C.J.D. Electronmicroscopy in synthetic polymer membrane research. J.Microsc., 162, 403–413 (1991).Kim, K.J. and Fane, A.G. Low voltage scanning electronmicroscopy in membrane research. J. Membr. Sci., 88,103–114 (1994).Kim, K.J., Fane, A.G. and Fell, C.J.D. Quantitative microscopicstudy of surface characteristics of ultrafiltration membranes.J. Membr. Sci., 54, 89–102 (1990).Kim, K.J., Fane, A.G., Fell, C.J.D. and Joy, D.C. Foulingmechanisms of membranes during protein ultrafiltration. J.Membr. Sci., 68, 79–91 (1992).Kuypers, S., Genné, I. and Leysen, R. Surface characteristicsof Zirfon composite ultrafiltration membranes. J. Microsc.,177, 313–319 (1995).Nakagawa, S., Development of JSM-6320F scanning microscope.Jeol News, 31E/1, 36–38 (1994).Pouchou, J.-L. Use of soft X-rays in microanalysis. Mikrochim.Acta (Suppl.), 13, 39–60 (1996).Pouchou, J.-L. and Pichoir, F. Surface film X-ray microanalysis.Scanning, 12, 212–224 (1990).

386 LOW-ENERGY ELECTRON PROBE MICROANALYSIS AND SCANNING ELECTRON MICROSCOPYReimer, L. Image Formation in Low-Voltage Scanning ElectronMicroscopy, TT12, SPIE, Bellingham, 1993.Scott, V.D., Love, G. and Reed, S.J.B. Quantitative Electron-Probe Microanalysis, Ellis Horwood, New York, 1995.Willich, P. and Bethke, R. Electron probe microanalysis of submicroncoatings containing ultralight elements. MicrobeamAnal., 2, 45–52 (1993).Yamamoto, Y., Yamada, A., Kazumori, H., Negishi, T. andSaito, M. Application of semi-in-lens FE-SEM for chargelessobservation. Jeol News, 34E/1, 47–49 (1999).Yamamoto, Y., Yamada, A., Miyokawa, T. and Tamura, N.Development of a high resolution semi-in-lens digital fieldemission scanning electron microscope: JSM-6340F. JeolNews, 32E/1, 39–41 (1996).

5.7 Energy Dispersive X-ray Microanalysisin Scanning and Conventional TransmissionElectron MicroscopyE. VAN CAPPELLENFEI Company, Hillsboro, OR, USA5.7.1 INTRODUCTIONX-Ray microanalysis did not really become acommon technique on transmission electron microscopes(TEMs) until the second half of the 1970s.Designers had to wait until large lithium drifted silicon(Si(Li)) solid-state detectors became availableand it remained to be seen that these liquid nitrogencooled devices would not impair the fundamentalTEM specifications because of their weightand the vibrations caused by the constantly boilingnitrogen. Until the 1990s most laboratories wouldmake a clear distinction between a dedicated highresolutionTEM without analytical capabilities andan analytical TEM with a significantly wider polepiecegap and thus reduced resolution specification.The latter had the capability of accepting an energydispersive X-ray microanalysis system abbreviatedto EDX or EDS (energy dispersive X-ray microanalysisor energy dispersive spectroscopy). Wheneverboth high-resolution TEM imaging and EDXdata were needed, it was up to the scientist to tryto find the same area of a sample on two differentscopes. The 1990s saw this distinction fade andalthough column manufacturers still offer differentpole-pieces with different gaps and resolutionspecifications, the reason no longer is the incompatibilitybetween high-resolution TEM and EDXbut it is just a trade-off between the availablespace between the pole-pieces for other applicationsneeding high tilt or an exotic specimen holderand resolution. Ultra-high-resolution microscopescan now safely be fitted with an EDX system.Besides hardware refinements, the 1970s and1980s were also rich in software developments, notleast in the field of quantitative X-ray microanalysis.It is probably fair to say that by the end of the1980s EDX had matured into a relatively easy-tousetechnique, compatible with most commerciallyavailable TEMs. Single point analysis, line scansand X-ray maps were by then relatively straightforwardto obtain. If one criticism is to be voiced,it is the fact that commercially available softwarepackages are clearly derived from their counterpartsdeveloped for scanning electron microscopyanalysing bulk samples instead of thin specimens.Apart from the sometimes-erroneous terminology,many non-expert users have been misled by thequantitative analysis outputs that industry wide aregiven with an incredible precision of two digitsafter the decimal point of atomic or weight percentages.Systematic errors and ill-defined correctionschemes for absorption and fluorescence have ledto erroneous results.The 1990s have not really addressed this issuebut at the same time a clear shift from quantitativeanalysis back to qualitative analysis was noticeablealbeit in a totally different ballgame than in theearly days. Field emission gun (FEG) technologyX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

388 ENERGY DISPERSIVE X-RAY MICROANALYSIS IN STEM AND TEMcapable of producing much smaller electron probeshad been around since the 1970s but had neverseen widespread use on TEMs because of theircomplexity and ultra-high vacuum requirements.In the course of the last decade, however, the thermallyassisted Schottky FEG with less stringentvacuum needs and a constant beam current becamethe norm on high-end TEMs. One of the benefits isthat these microscopes can produce much smallerprobes and as a consequence the bulk of EDXresearch shifted back from quantitative to qualitativeanalysis but this time on a much smaller scale:the nanometer or even smaller. When objects orfeatures become so small, a two-dimensional grainboundary for instance, detection limits and/or concentrationgradients became the ultimate pursuit.The technique’s spatial resolution improved dramatically,so much that the term ‘microanalysis’,probably too well established by now, should bereplaced by ‘nanoanalysis’.The 1970s brought along a new technique onTEMs: EELS or electron energy loss spectroscopy.EELS measures the characteristic energy-loss ofthe primary electron due to the ionization ofa target atom. In that respect, EELS and EDXlook at the same ionization events, the differencebeing that EELS measures the primary eventwhile EDX looks at a secondary product of theionization, the emitted X-ray. The first generationof spectrometers was the so-called serial EELS(SEELS) because the energy-loss range is acquiredsequentially. SEELS only enjoyed a moderatesuccess because it was time consuming and theinterpretation of the spectra was all but trivial.In the mid 1980s the PEELS or parallel electronenergy loss spectrometer was introduced with a1024 diode array capable of acquiring a wholeenergy interval at once. It became fashionable toadd a PEELS to a TEM column and soon thedecline of EDX on TEMs was predicted because ofEELS’s significantly better energy resolution andfar greater collection efficiency. This predictionnever came true and actually EDX on TEMshas never been stronger than right now. Thissubchapter about EDX on TEMs is not only meantto be a tribute to the technique, but also tries toexplain this revival.5.7.2 BRIEF HISTORICAL OVERVIEWOF HARDWARE DEVELOPMENTSFor a complete review on this matter we referto the textbooks edited by Williams and Carter(1996a,b) and Joy et al. (1986).The first attempts to fit a WDX (wavelengthdispersive X-ray microanalysis) on a TEM dateback to the early 1960s. Only by the end ofthe decade was a real 100 kV TEM successfullyequipped with two twin WDX spectrometers. Aspecially designed mini-lens allowed EMMA-4to have almost comparable TEM performanceto other contemporary 100 kV TEMs. Despiteobvious advantages to be able to combine TEMimaging and diffraction with chemical analysis, thecumbersome WDX systems had only encountereda very moderate success because of their slowness.Also, the bulky set-up of a WDX system wasnot compatible with the new emerging field ofhigh-resolution TEM (HR-TEM) imaging. Phasecontrast lattice imaging rapidly became the mostcompelling reason to purchase a TEM. This isprobably the reason why WDX equipped TEMsdid not enjoy the same success as their electronprobeand SEM (scanning electron microscope)counterparts.When the Si(Li) solid-state detector combinedwith a multichannel analyser became availableX-ray microanalysis really tookoff on TEMs.Because a whole energy range can be acquiredsimultaneously the new technique was called EDX(energy dispersive X-ray microanalysis) or EDS(energy dispersive spectroscopy). Not withstandingthe fact that EDX systems have energy resolutionsabout ten times worse than WDX spectrometersand as such are not well suited for light elementdetection, EDX systems did far better because oftheir smaller dimensions and larger solid-angles.Because of bad light element performance causedby peak overlap and because of inherent fragility,windowless detectors never really broke through.Instead, diamond windows with a detection downto sodium and later the so-called ultra-thin windowswith a theoretical detection down to boronbecame the industry standard. Beam diameters onTEMs in these days were of the order of several

SIGNALS GENERATED IN A THIN TEM SPECIMEN 389hundreds of nanometers and analysis of submicronareas showed a tremendous potential and wasrightfully called ‘microanalysis’.The 1970s saw the development of the cold fieldemission gun (CFEG) with a source brightness ofat least a thousand times that of the best thermionicsource, lanthanum hexaboride (LaB 6 ). This highbrightness, a consequence of the small size of theemitter, translates into improved beam coherenceand much smaller electron probes. This technologyenabled the development of the scanning transmissionelectron microscope (STEM) in which asmall intense electron probe is scanned on a thin,TEM-like sample. Instead of detecting the secondaryor backscattered electrons as in a scanningelectron microscope (SEM), the STEM detectorsare beneath the specimen, where different typesof ‘transmitted’ electrons can be used for imaging.Just as a TEM, a STEM can yield bright field(BF) and dark field (DF) images. Although differentin nature and thus yielding slightly differentinformation, STEM imaging initially was not thedecisive argument in favor of the new instrument,especially because STEM images require longerexposure times and are much noisier than theirTEM counterparts. The major reason to developSTEM was indeed its natural compatibility withEDX. The smaller probe sizes allowed EDX analysisof much smaller features and beam controlenables line scans and X-ray maps to be generatedjust like in a SEM but with a phenomenally betterresolution because of the absence of the pearshapedinteraction volume present in bulk samples.It is fair to say that it is exactly these EDX andEELS analytical capabilities that drove the developmentof the so-called dedicated STEM.Over time two tendencies emerged, resolutionwiseSTEM imaging caught up with TEM imagingand TEMs were fitted with scanning coils and laterwith field emission guns (FEGs) which enabledTEMs to operate in STEM mode. Althoughoriginally the STEM mode was not intended as areal competitor for the dedicated STEM, but just toboost the EDX capabilities of the TEM, the scopechanged when the only manufacturer of dedicatedSTEMs went out of business. Simultaneously italso became clear that there are some advantagesof doing STEM on a TEM column because of thepost-specimen lenses. One can look at a highlymagnified image of the probe and although thecorrelation with the probe shape at the samplelevel is not perfect because of the sphericalaberration of the lower pole-piece, it is a goodapproximation and allows to roughly focus andstigmate the STEM image before even switchingto STEM mode. They also allow changing thevirtual distance between the sample and the STEMdetectors so that with one fixed size annulardetector different minimum collection angles canbe selected yielding different types of dark fieldimages (see below). Figure 5.7.1 shows a 2002model of a 200 kV STEM/TEM capable of thehighest TEM and STEM resolution and equippedwith all the analytical techniques, an EDX detectorand an electron energy filter for PEELS and energyfiltered TEM (EFTEM).5.7.3 SIGNALS GENERATEDIN A THIN TEM SPECIMENThis section is not intended to review the electronbeam– thin sample interactions in detail, theintention is to discuss without the use of formulaethe different signals that are generated within athin sample and that are used in a (S)TEM. Thiswill help us understand the importance of EDX intransmission electron microscopy. For a completedescription, please refer to the literature (Joy et al.,1986; Egerton, 1996; Williams et al., 1996a,b).A high-energy incident electron can go througha thin foil without interacting with it or it canhave a phonon interaction with a sub-eV energyloss too small to be measured. Such electrons arelocated on the optical axis and are obviously notvery interesting from a chemical standpoint, asthey carry no (measurable) information. From animaging point of view this on-axis signal is calledthe BF signal since a hole (vacuum) shows upbright. Both TEM and STEM modes yield aboutthe same information.Electrons can also undergo different types ofelastic scattering: Bragg diffraction and Rutherfordscattering. The Bragg diffracted electrons are

390 ENERGY DISPERSIVE X-RAY MICROANALYSIS IN STEM AND TEMFigure 5.7.1 Modern STEM/TEM capable of combining the highest STEM and TEM resolution. It is equipped with EDX andan energy filter for PEELS and EFTEM. (Courtesy of FEI Company)those that are diffracted by the regular array oflattice planes in a crystalline structure and thereforecarry crystallographic information. A crystalwill generate discrete diffracted beams whereasan amorphous material will produce diffuse rings.Imaging with Bragg diffracted electrons is calledDF imaging as vacuum will show up dark. Inthe TEM mode one or several Bragg diffractedbeams can be selected with the objective aperture,whereas in STEM mode, an annular solid-statedetector averages over all Bragg diffracted electrons.This is called annular dark field (ADF) imagingand is equivalent to conical dark field imagingin TEM. Further away from the optical axis,where the intense Bragg diffracted electron signalfades, the Rutherford scattered electrons, thosethat have been scattered by the sample’s nuclei,can be recorded. Figure 5.7.2 schematizes the locationof Bragg diffracted and Rutherford scatteredelectrons around the optical axis. Rutherford scatteredelectrons carry atomic mass or Z-contrast,just as the backscattered electrons in the SEM(also Rutherford scattering) and since they alsoare recorded with an annular detector, but with ae −Specimen5 mrad25 mradFigure 5.7.2 Transmitted electrons can be found in three zones:the optical axis and just around hosts the electrons thathave not interacted with the sample and the inelasticallyscattered electrons; an annular region between 5 and 25 mrad(at 200 kV) where the Bragg diffracted electrons are located;the outer region only contains Rutherford scattered electrons,which carry Z information

SIGNALS GENERATED IN A THIN TEM SPECIMEN 391larger minimum acceptance angle, it is referred toas high angle annular dark field (HAADF) imaging.Figure 5.7.3(a) is an example of a HAADFimage and shows that this mode is particularlysuited for analytical microscopy because the Z-contrast image greatly helps to determine whereto acquire point spectra. In the case of elementalmaps it is also useful to correlate the Z-contrastimage with the EDX or PEELS elemental maps oreven with line profiles.Far more interesting chemically, are the inelasticallyscattered electrons as most lose a characteristicamount of energy when ionizing the targetatoms. Ionized atoms will relax by isotropic emissionof either an Auger electron or an X-ray photon.In general Auger emission is more likelyexcept for K shell ionization of elements withan atomic mass exceeding 30. The problem withAuger electrons is that because of their high matterinteraction cross-section only those emitted within1(a)TiOTiSi30000100CountsTiCounts200005010000NOTi01.02.0 3.0 4.0Energy (keV)5.00450500Energy (keV)550(b)(c)Figure 5.7.3 (a) HAADF STEM (Z-contrast) image of a semiconductor device. At the location marked with a cross, an EDX(b) and an EELS (c) spectrum were acquired. Notice the huge difference in signal intensities and background shapes. (Courtesyof Y.C. Wang, FEI Company)

392 ENERGY DISPERSIVE X-RAY MICROANALYSIS IN STEM AND TEMafewångstroms from the surface will escape unalteredwhich makes it a surface analysis methodonly. Auger spectroscopy also requires ultra-highvacuum to avoid interaction of the Auger electronswith the residual molecules. As a consequenceAuger electrons are not used in a TEM.However in a TEM (or STEM) there are twoways of looking at the inelastic scattering processes,one is to measure the actual energy lossof the primary electron (PEELS) and the otheris to measure the energy of the emitted X-ray(EDX). Figure 5.7.3(b) and 5.7.3(c) show a comparisonbetween an EDX and a PEELS spectrumfrom the same sample.Because of the relatively small energy lossesthat can be measured (maximum 2000 eV lossabove which the signal is too small), and the highinitial accelerating voltage (at least 200 kV), conservationof energy and momentum dictates smallscattering angles, a few milliradians maximum. Soinelastically scattered electrons are located close tothe optical axis and are superimposed on the BFsignal (Figure 5.7.2).5.7.4 ELECTRON ENERGY LOSSSPECTROSCOPY VERSUS ENERGYDISPERSIVE X-RAY MICROANALYSISThis section, while mentioning the similarities, willprimarily focus on the dissimilarities of EDX andEELS. It is mostly the differences that explainthe modern trend to combine both techniqueson one instrument and being able to performboth simultaneously on a sample has proven tobe invaluable.When looking for chemical information, EDXand EELS both analyse the same physical phenomenon:the ionization process of the targetatoms. In the case of EELS the energy of primaryelectron that has lost energy because of the ionizationof an atom is measured whereas in the case ofEDX a secondary product, an emitted X-ray photonbecause of the relaxation process, is detected.Because both techniques basically look at the sameevents, one could argue that one spectroscopictechnique should fulfill all the needs. The maindifference between them lies in detection efficiencyand energy resolution.The previous paragraph alluded to the fact thatinelastic scattering angles are very small becauseof energy and momentum conservation and asa consequence most of the inelastic signal canbe detected in an on-axis spectrometer. It is notuncommon to detect 90 to 95 % of the corelossevents. In this respect the EDX case isentirely different. The EDX spectrum is builtupof characteristic X-ray photons related to the deexcitationof the target atoms and Bremsstrahlungor white radiation that results from primaryelectrons slowingdown in the Coulomb fields inthe sample. Bremsstrahlung obeys scattering lawsand is found in a forward peaked thorus aroundthe optical axis. Emission of characteristic X-rayphotons however happens isotropically since it is asecondary process that has forgotten its past. Thereis no preferential direction and the optical axis nolonger has a special status. Modern EDX set-upshave 30 mm 2 Si(Li) detectors which at a practicaldistance translates into an effective detection solidangle of about 0.1 sterrad. A whole sphere, spans4π(= 12.6 sterrad), so only about 0.8 % of thegenerated events can possibly be detected. Manyattempts, such as bigger or multiple detectors, havebeen made to maximize the collection angle, butbecause X-rays are nearly impossible to focus andbecause of the limited available space betweenthe pole pieces, the difference with EELS willremain huge. Furthermore, characteristic X-rayemission competes with Auger electron emissionfor the de-excitation process of atoms. In fact,unless these are K-shell ionizations of heavy atoms(Z >30), Auger emission is far more likely. Forlight elements (Z

ELECTRON ENERGY LOSS SPECTROSCOPY VERSUS ENERGY DISPERSIVE X-RAY MICROANALYSIS 393no plans to develop these systems for transmissionmicroscopes. The EELS spectrum has a resolutionmainly determined by the energy distribution ofthe source, which depends on the type of sourcebut also on the beam intensity. When electronsare squeezed into a condenser crossover theytend to repel each other, which increases theenergy spread. This is the so-called Boersh effect.All in all the following energy resolutions canrealistically be achieved: 1.2 eV for a LaB 6 source,0.7 eV for a thermally assisted field emission gunand 0.5 eV for a CFEG. FEI Company has recentlylaunched a ‘monochromator’ which further reducesthe energy resolution below 0.1 eV. This meansthat EELS has an energy resolution that is two tothree orders of magnitude better than EDX.It is precisely because of the far superiordetection efficiency and energy resolution of EELSthat about 20 years ago it was predicted that EELSspectroscopy would replace EDX on transmissionmicroscopes. We will now highlight the reasonswhy this has not happened.One of the biggest problems EELS faces ismultiple scattering. As soon as multiple scatteringevents start to occur, the information in the EELspectrum starts to scramble and the signal tobackground ratio deteriorates rapidly. This meansthat in practice the samples need to be significantlythinner than one mean free path of the electrons inthe specimen (1λ). Lambda is primarily a functionof the sample and the accelerating voltage of themicroscope. To a certain extent the spectrometeracceptance angle also has an influence, but forpractical purposes we will assume λ to be about100 nm at 200 kV. This means that the TEMsample has to be less than, say, 50 nm in orderto do EELS, which is not always practical.The signal to background ratio in general isthe other major EELS problem and is obviousfrom the comparison between Figure 5.7.3(b) andFigure 5.7.3(c) showing and EDX and EELS spectrumof the same specimen. Because of the farsuperior detection geometry, the EEL spectrumclearly has a much better signal to noise ratio butits signal to background ratio cannot compete withthe EDX spectrum because of the large exponentiallydecaying background. Whatever algorithm isused to do quantitative analysis and whether it isEELS or EDX, the first step needs to be the backgroundsubtraction to extract the sample specificsignal. In the EELS case this is a major causefor uncertainties whereas in the EDX case, evena bad job will still yield a realistic result. Theway background subtraction is done in EELS is byextrapolating pre-edge background under the edgeand in that respect, the high energy resolution ofan EEL spectrum does not help as edge overlap oreven edge proximity will make any extrapolationimpossible. Just as in EDX, EELS quantification isdone by a k-factor ratio technique (see next paragraph).However in the case of EELS the k-factorsare not only functions of the chemical species,but also of the specific chemical binding and theacquisition parameters such as convergence angleand acceptance angle (Egerton, 1996). As a consequenceexperimental k-factors are very difficult toobtain and are only practical in a limited number ofcases. The problems of background subtraction andexperimental k-factor determination make it practicallyimpossible to obtain accurate quantitativeEELS results in a timely manner. This makes EDXthe technique of choice for quantitative analysis.Because of the higher energy resolution and thelarge dynamic signal range because of the stronglydecaying background, EEL spectra usually onlycover a limited energy range, which complicatesqualitative analysis of truly unknown samples.It is therefore probably fair to say that EDXis also used for determining which elements arepresent. Fast, qualitative analysis and relativelyeasy quantitative analysis are the main reasonswhy EDX has not and will not disappear ontransmission microscopes, as the output of an EDXanalysis will often be the starting point of a moredetailed EELS study.Because of its superior detection geometry andtherefore better signal to noise ratio, EELS is muchbetter for detecting minor constituents or eventrace elements. For elements exhibiting a steepedge, a so-called white edge, detection limits canbe as low as the 10 to 100 ppm range, whereasEDX is limited to 1000 ppm. The lateral analyticalresolution is defined by the primary excitationvolume defined by the size of the electron probe

394 ENERGY DISPERSIVE X-RAY MICROANALYSIS IN STEM AND TEMand subsequent beam broadening in the sample.As such the best practical resolution is determinedby the smallest probe yielding sufficient currentto generate a decent EELS or EDX spectrum in areasonable amount of time. Because of its betterdetection geometry, EELS can be done with thesmallest available probes whereas EDX cannot.Practically speaking this translates into 0.2 nmEELS resolution and 0.4 nm EDX on most modernfield emission microscopes.Another consequence of its better than 1 eVenergy resolution, is that the EELS applications gofar beyond just identifying and maybe quantifyingthe chemical species present in the sample. Werefer to the book by Egerton (1996) for adetailed review of all EELS applications, butin a nutshell we will just mention some majorEELS applications so as to better understandthe need to have both techniques EDX andEELS available on the same instrument. The‘energy loss near edge structure’ (ELNES) isa fingerprint of the chemical binding and bandstructure. In other words, just by looking at theedge fine structure enables to distinguish betweendifferent compounds. As an example, the Si Ledge signature can distinguish pure Si from SiO 2or Si 3 N 4 and the C K edge is different foramorphous carbon, graphite and diamond. The socalledchemical shift allows the valence state ofan element to be determined by simply measuringthe energy shift of a core-loss edge. Last butnot least, the ratio of the total spectrum intensityover the zero-loss peak (electrons that have notinteracted with the sample) is related to the samplethickness divided by λ, the mean free path ofthe electrons. Provided λ can be calculated orexperimentally measured on a sample with knownthickness, the logarithm of the whole spectrumintensity divided by the zero-loss peak yields aquick value for sample thickness as a functionof λ, a bonus for many other applications suchas a conventional absorption correction for aquantitative EDX analysis.The combination of EDX and EELS offersone of the most powerful analytical tools and arecent trend has been the acquisition of so-called‘spectrum images’. A spectrum image is a STEMimage with behind each pixel a full-size spectrum.This can be an EDX spectrum or an EEL spectrumor better both can be acquired simultaneously(Figure 5.7.4). A spectrum image is a data cube(or two) with the third axis being energy. Theadvantage of spectrum imaging is that the wholeexperiment is canned and can be archived. Furtherdata mining, such as determining the compositionof a particle or extracting a line profile across agrain boundary can be done even after the samplehas been destroyed. A spectrum image can ofYYEEy ix i x jy ix i x jy jy jXX(a)(b)Figure 5.7.4 The principle of spectrum imaging: a full EELS (a) and EDX (b) spectrum associated with each pixel of the STEMimage. Data mining is done off-line after the acquisition is completed

QUANTITATIVE ANALYSIS IN EDX 3951(a)1150010001N-EDXTi-EDXSi--EDXO-EDX2.5 × 10 52.0 × 10 51N-EELSTi-EELSO-EELSCountsCounts1.5 × 10 55001.0 × 10 55.0 × 10 4 00(b)0100200Position (nm)300(c)0100200Position (nm)300Figure 5.7.5 (a) HAADF STEM (Z-contrast) image of a semiconductor device. Along the vertical line a one-dimensionalspectrum image with 100 points and 300 nm long was acquired. A posteriori the EDX (b) and EELS (c) line profiles wereextracted. The cursor (1) is located in a titanium silicide layer also shown on the profiles. (Courtesy of Y.C. Wang, FEI Company)course be one-dimensional. Figure 5.7.5 shows anexample of a one-dimensional spectrum image.The line profiles were extracted off-line.5.7.5 QUANTITATIVE ANALYSISIN EDXAs explained in the previous paragraph, the singlemost important reason why EDX has not disappearedfrom the TEM scene, as predicted 20 yearsago, is its capability of doing quantitative analysis.Therefore a review of the different quantitativetechniques seems pivotal and special attentionwill be given to the recently developed correctionschemes which all have in common the desire toeliminate the problem of unknown parameters.Basic quantitative EDX still relies on theCliff–Lorimer ratio equation relating the intensitiesof the characteristic X-rays above background(denoted I A , I B , etc.) to the compositions (denotedC A , C B ,etc.):( )C A IA= k AB (5.7.1)C B I Bwhere k AB is the Cliff–Lorimer k-factor. Thereare two fundamental limitations associated with

396 ENERGY DISPERSIVE X-RAY MICROANALYSIS IN STEM AND TEMEquation (5.7.1). First the k-factors are not universaland vary from instrument to instrument andsecond the Cliff–Lorimer equation assumes thatthere is no significant X-ray absorption in thinTEM-compatible samples. Often this assumptionis not realistic especially when both low- and highenergypeaks are used, as the low-energy line willbe more absorbed. Methods to overcome both theselimitations have been developed over the years,but all are based on the Cliff–Lorimer equationthat remains the basis for quantification more than25 years after its initial publication by Cliff andLorimer (1975).5.7.5.1 ABSORPTION ANDFLUORESCENCECharacteristic X-rays are generated isotropicallyin the thin TEM sample. Only those emitted inthe small solid angle seen by the EDX detectorare eligible for detection provided they are notabsorbed in the sample on their way out. Ifall characteristic X-rays would be absorbed withthe same probability, quantification would not beaffected, as the intensities are ratioed. Howeverabsorption is a function of the energy and lowenergy peaks will be more strongly absorbed thanhigh energy ones. A quantitative analysis withoutany kind of absorption correction will thereforepenalize light elements. The magnitude of the errorwill depend on the specimen thickness and densityas well as the take-off angle, which is the anglebetween the sample surface and the detector axis.When X-ray absorption is no longer negligible, thecomposition is no longer simply proportional to theintensity and Equation (5.7.1) becomes:( ) [ ]C A IA (µ/ρ)Asp= k AB ×C B I B (µ/ρ) B sp{ }1 − exp[−(µ/ρ)Bsp ρt cosec θ]×1 − exp[−(µ/ρ) A sp ρt cosec θ](5.7.2)where (µ/ρ) A sp and (µ/ρ)B sp are the mass absorptioncoefficients of the characteristic X-ray lines Aand B, ρ and t are, respectively, the density andthickness of the specimen at the beam positionand θ is the X-ray take-off angle. Straightforwardcorrection of absorption requires ρ, t and θ, whichis also uncertain unless the sample is perfectly flatand horizontal at zero tilt.Primary X-radiation, generated by the electronbeam, will partially be absorbed in the sample andthis in turn generates secondary or fluorescenceemission. Although this phenomenon can also alterthe peak ratio of two elements, it is negligiblein TEM-like samples except for ‘bulky’ samplesand even then only when the energy of a strongcharacteristic peak is just above the ionizationthreshold of another element. For most of theperiodic table, this happens when two elementshave an atomic number difference of two. Thistranslates into an exceptionally large fluorescenceyield. It has been demonstrated by simulations(Van Cappellen et al., 1990) that fluorescencestrongly depends on the shape of the sample andnot so much by the orientation of the specimenin the electron beam. It should also be realizedthat the secondary excitation volume is orders ofmagnitude larger than the primary one. It goeswithout saying that a fluorescence correction of apoint analysis is almost impossible as it is virtuallyimpossible to determine the shape of a samplein the millimeter range, which is the size of thesecondary excitation volume.5.7.5.2 THE PARAMETERLESSCORRECTION METHODThe parameterless correction method, first presentedat the ICXOM 10 conference in 1983 (VanCappellen et al., 1984) and extensively reviewedin 1990 (Van Cappellen, 1990) was also independentlycalled the extrapolation method in1986 (Horita et al., 1986). The parameterless correctionmethod got its name because it performsabsorption and fluorescence corrections withoutrequiring external parameters such as sample thicknessand density; absorption coefficients and fluorescenceyield coefficients. The price to be paid isthat not one but several spectra are needed for oneanalysis. The spectra are taken at different sites on

QUANTITATIVE ANALYSIS IN EDX 397the specimen with different thickness. The samplehas to be homogeneous in the analysed area.A characteristic line in an EDX spectrum can beconsidered as being composed of primary and secondarycharacteristic radiation, both attenuated dueto absorption in the specimen. Both componentscan be expressed as polynomials in T , the massthicknessof the foil. The intensity of a characteristicline tends monotonically to zero for vanishingspecimen thickness. Consequently the polynomialin T will have no constant term. Hence the ratioof two net intensities such as in the Cliff–LorimerEquation (5.7.1) is a polynomial with a constantterm. This term times the proper k-factor yieldsthe mass concentration ratio of the elements underconsideration. From the different spectra taken atdifferent thickness, uncorrected concentrations arecalculated with Equation (5.7.1). These are plottedversus the foil thickness and a least square fitextrapolates the concentrations at zero thickness.Zero thickness-extrapolated concentrations arefree from absorption effects as absorption isa two-dimensional phenomenon confined to theoptical axis – detector axis plane. For any arbitraryspecimen geometry the absorption path towards thedetector tends to zero when the sample thicknessvanishes. The same conclusion does not applyfor fluorescence because here the phenomenonis truly three-dimensional. One can imagine thatonly one electron hits the tip of a wedge-shapedspecimen (where thickness is zero) and that onlyone primary X-ray photon is generated. Thisphoton could travel into the wedge and producea secondary photon that eventually ends-up beingdetected. In this hypothetical case no primaryradiation is measured whereas one secondaryphoton is captured. The fact that fluorescence is notcompletely extrapolated away was confirmed viasimulations (Van Cappellen et al., 1990), howeverit was also shown with a worst case scenario thatthe absolute systematic error on the extrapolatedconcentrations was below 0.25 wt%, which issmaller or at least comparable to the overallstatistical error.In order to be ‘parameterless’, the samplethickness or mass-thickness used as the parameterfor the extrapolation, needs to be replaced by aninternal thickness measure. This substitute mustmonotonically tend to zero for vanishing specimenthickness so as to ensure the same extrapolationvalues as with the true thickness. A valid candidatefor this internal measure is characteristic radiation.A net peak or better the sum of net peaks forincreased statistics are suitable.The parameterless correction or extrapolationmethod corrects for absorption and fluorescence,irrespective of the shape of the specimen. Besidesthis unquestionable advantage and also in contrastwith more conventional approaches, the procedurealso provides the final results with an accuracyfigure. This statistical error which typically liesbetween 0.2 and 1.0 at wt%, easily allows todistinguish between good and bad experiments.A bad k-factor will introduce a systematic error,however accurate k-factors can be measured withaccuracy estimates with the parameterless correctionmethod.5.7.5.3 THE ZETA-FACTOR METHODA variant of this approach is the recent ζ -factormethod which allows k-factor determinations withoutprior knowledge of the mass-thickness of thesample (Watanabe et al., 1996). For a TEM-likesample, it is safe to assume that the ionizationcross-sections do not change with depth. Most incidentelectrons will not undergo inelastic scatteringand the average energy of the incident beam canbe considered constant. Consequently the intensityof a characteristic peak is proportional tothe local mass-thickness ρt. Inversely the massthicknesscan be expressed as a function of thegenerated intensity:( ) Iρt = ζ(5.7.3)Cwhere ζ is the proportionality factor connectingthe characteristic intensity I and C is theweight fraction. The zeta-factor (ζ ) is independentof the sample composition as the characteristicintensity is normalized by the weightfraction. Equation (5.7.3), or the proportionalitybetween mass-thickness and intensity, is valid

398 ENERGY DISPERSIVE X-RAY MICROANALYSIS IN STEM AND TEMon condition that absorption in the sample isnegligible.Assuming that a characteristic line of elementB is not significantly absorbed, Equation (5.7.3)becomes:( ) (IB ) mρt = ζ B (5.7.4)Cwhere (I B ) m is the measured intensity of elementB. Substituting (5.7.4) into (5.7.2) eliminates ρt( ) [ ]C A IA (µ/ρ)Asp= k AB ×C B I B (µ/ρ) B sp{ }1 − exp[−(µ/ρ)Bsp (cosec θ)ζ B (I B ) m /C B ]×1 − exp[−(µ/ρ) A sp (cosec θ)ζ B(I B ) m /C B ](5.7.5)Equation (5.7.5) no longer requires the knowledgeof the local mass-thickness. The determination ofthe zeta-factor is done simultaneously with thek-factor on a standard sample with known composition.For a known sample Equation (5.7.5)only contains two unknowns: k AB and ζ B .Theseare extracted using the parameterless correctionmethod. With the k- and zeta-factors determined,quantification through Equation (5.7.5) and theboundary condition that the sum of all concentrationsshould be one becomes straightforward.When using the zeta-factor technique, it isparamount to use the same beam current as forthe k- and zeta-factor determination. It should alsobe realized that an iterative procedure is requiredsince Equation (5.7.5) contains mass absorptioncoefficients, which are composition dependent.The main advantage of the zeta-factor approachis that once the k- and zeta-factors for the differentelements are determined through a parameterlessor extrapolation method, only one spectrum isneeded for a quantitative analysis. Moreover massthicknessand thus thickness if density is knowncan also be retrieved through Equation (5.7.3).This approach is extremely well suited to determinequantitative line scans and even X-ray maps.The same approach had already been usedto analyse second-phase precipitates in copper/zinc/aluminumshape memory alloys (VanCappellen et al., 1987). Because of the highlyabsorbed Al K line, some kind of absorption correctionis needed, but because the precipitates arepreferentially etched during sample preparation, itis virtually impossible to apply a conventional correction.An analysis of the surrounding matrix withthe parameterless correction method allows determiningthe exact k-factors and provided the beamcurrent is stable, it is also possible to calibrate themass-thickness as function of the net intensities inthe same way as the zeta-factor approach.5.7.5.4 QUANTITATIVE CHEMICALMAPPINGBecause of the amount of data and the tediousnessof a conventional absorption correction, real quantitativemaps only showed up recently. Williamset al. (1998) presented a few years ago real quantitativemaps using the zeta-factor approach. Themaps show interfacial segregation with a spatialresolution of better than 5 nm. Williams is keento point out that while line scans are very useful,they are very selective and operator-biasedbecause of the choice that has to made of whereto acquire the line-scan. Quantitative X-ray mapshave been a standard procedure on bulk sampleboth in the SEM and the electron probe microanalyser(EPMA) for many years now. BecauseX-ray generation in bulk samples is significantlymore important than in thin specimens and samplethickness is not an issue, quantitative maps can beacquired in a timely manner and absorption andfluorescence corrections can be applied on the flyor off-line depending on the computing power. Themain problem with X-ray maps on bulk samples isthe poor spatial resolution which depending on theinitial beam energy is of the order of 0.5 to 1.0 µm.For most materials science problems, such as interfacialsegregation, this is by far insufficient.X-Ray spatial resolution when using thin TEMlikesamples is mainly determined by the electronprobe size and some beam broadening occurring inthe foil. The primary excitation volume is ordersof magnitude smaller than in the bulk case. Animmediate consequence is that the X-ray count rateis dramatically reduced which means that probeintensity and X-ray collection angle have to be

QUANTITATIVE ANALYSIS IN EDX 399maximized in order to achieve realistic acquisitiontimes. A FEG is key to high resolution X-raymapping. A FEG is capable of producing a probecurrent of 1 nA with a probe size of 1 nm (FWHM).A way to maximize the detection solid angle is touse two EDX detectors, but even with everythingoptimized, the trade-off will always be spatialresolution against acquisition time. Besides testingthe operator’s patience, long acquisition times canalso be detrimental to the sample because of beamdamage. Also drift can become an issue and thisruins the spatial resolution if no measures are takento compensate for this. A way to compensate fordrift is to acquire intermediate images at fixedintervals to measure the drift through a crosscorrelationprocedure and to use this informationto move the beam accordingly. More sophisticatedsystems assume the drift to be linear in betweenmeasurements and have the beam follow the driftbetween two images.When generating a quantitative map, the firststep is to subtract the background under thecharacteristic peaks in each pixel. This yieldsthe net intensities, which can be converted intoweight concentrations by the k-factor. Dependingon the elements and the sample’s thickness,the zeta-factor approach must be used to correctfor absorption. Williams et al. (1998) carriedout a full zeta-factor analysis to generate theexample shown in Figure 5.7.6. It is an investigationof the boundary segregation of Cu in anAl–4 wt% Cu alloy. The alloy had been agedto cause segregation to the grain boundaries. Ahigh magnification analysis was performed froman edge-on grain boundary with the followingparameters: 2 M magnification, 64 × 64 pixels anda dwell time of 200 ms per pixel. The probesize was estimated to be below 1 nm, the currentwas 0.5 nA and the pixel size was 0.625 nm.The ADF image (Figure 5.7.6a) was acquired witha small camera length to increase the minimumacceptance angle to reduce diffraction contrastand increase Z-contrast (atomic number contrast).The bright diagonal line in Figure 5.7.6(a) revealsa layer of higher atomic number. A quantitativeCu map (Figure 5.7.6b) was generated fromthe background subtracted Cu K and Al K linesthat are nothing else but the net intensity maps,using a k-factor measured from stoichiometric θ-phase (Al 2 Cu) particles, which were distributedthroughout the material. The quantitative Cu map(Figure 5.7.6b) confirms that Cu has segregated tothe boundary, but the extra information is that righton the boundary the Cu concentration is about10 wt% compared to the average matrix concentrationof 3wt%. Granted, the image is noisy, butstatistical meaningful data may be extracted byaveraging over many pixels. The matrix compositionwas determined to be 2.6 ± 0.1 wt% bysampling 1600 pixels. This is close to the equilibriumsolubility of 2.75 wt% Cu in Al at 475 ◦ C, theused homogenizing temperature.Line profiles can be extracted from the imageas shown in Figure 5.7.6(c). To obtain a statisticalmeaningful profile, the profile was integrated(a)wt% Cu(c)1086420ADF04 8Distance (nm)Figure 5.7.6 (a) High magnification HAADF image showingthe increase in average atomic number at a grain boundary.(b) Quantitative Cu map from the same boundary. The grayscale goes from 0 to 18 wt%. (c) Compositional profileextracted from (b). (Reprinted from Mikrochim. Acta [Suppl.],15, Williams, D., Watanabe, M. and Carpenter, D., Thin filmanalysis and chemical mapping in the analytical electronmicroscope, 49–57, Copyright (1998), with permission fromSpringer-Verlag)(b)12

400 ENERGY DISPERSIVE X-RAY MICROANALYSIS IN STEM AND TEMparallel to the boundary over 30 pixels, givingit an effective width of about 20 nm. The lineprofile reveals the degree of local boundaryCu enrichment, and shows a spatial resolutionof composition variation of about 4 nm. Thisis expected to improve with thinner specimens,although thinner samples would generate lessX-rays exacerbating the signal problem. The errorbars on the profile are based on counting statisticsand represent the 95 % confidence limits.Williams et al. (1998) also performed a lowermagnification analysis to visualize more than oneboundary at the time. X-Ray maps of Cu Kand Al K were gathered at 240 kV and 256 ×256 pixels with a dwell time of 40 ms, for atotal frame time of about 1 h. The BF image(Figure 5.7.7a) shows diffraction contrast, fromwhich it can be seen that most of the boundariesare not oriented in the ideal configuration parallelto the beam. Figure 5.7.7(b) is the correspondingquantitative Cu concentration map, calculatedusing an experimentally determined k-factor fromnearby θ-phase particles.5.7.5.5 QUANTITATIVE ANALYSISOF IONIC COMPOUNDSAnother absorption correction based on a ‘known’property of the sample was presented in 1994 (Van(a)BF80 nm80(b)wt% Cu80 nmFigure 5.7.7 (a) Bright field image of several grains.(b) Quantitative Cu map at a lower magnification thanFigure 5.7.6, showing the Cu distribution in several grainboundaries. The lower intensity from the Cu-rich boundaries isdue to the fact that the boundaries are generally not parallel tothe electron beam. (Reprinted from Mikrochim. Acta [Suppl.],15, Williams, D., Watanabe, M. and Carpenter, D., Thin filmanalysis and chemical mapping in the analytical electronmicroscope, 49–57, Copyright (1998), with permission fromSpringer-Verlag)Cappellen and Doukhan, 1994). Just like theparameterless correction method and the zetafactormethod it does not require specimenthickness, X-ray take-off angle and specimendensity. Modern ultra-thin window X-ray detectorsare capable to detect light elements such asnitrogen (N K: 392 eV) and oxygen (O K:532 eV) but even in the thinnest possible samplesan absorption correction will be necessary.Absorption does not only occur in the sample itselfbut also in surface layers such as contamination oron purpose evaporated carbon or metal conductivelayers. Also the ultra-thin detector window cannotbe neglected in the case of nitrogen or oxygen. Thecorrection procedure described in Van Cappellenand Doukhan (1994) was originally developed forionic compounds (oxides, ceramics, minerals, etc.)and is based on the principle of electroneutralityor, in other words, the sum of all anions andcations times their respective valence states mustcancel out.The ionic compound method uses the conventionalabsorption correction software available onall commercially available systems and based onEquation (5.7.2). The exponentials of the absorptioncorrection factor A of Equation (5.7.2) can beexpanded in specimen thickness and up to the firstorder in t equals:A ≈ 1 + 1/2[(µ/ρ) A sp − (µ/ρ)B sp ]cosecθ × ρt(5.7.6)Whenever the difference between the massabsorptioncoefficients is small the absorption correctionwill be close to unity, which is the sameas saying that when both characteristic peaks areabsorbed the same way, no correction is needed.However with light elements such as O andN[(µ/ρ) A sp − (µ/ρ)B sp ] is always significant andeven for a very thin sample the amplitude ofthe correction will be substantial. A new parametercalled the ‘mean mass-absorption length’ isdefined as:τ = 1/2cosecθ × ρt (5.7.7)When considering a perfect plane parallel sample,τ corresponds to the mass-distance throughwhich an X-ray photon generated in the middle

QUANTITATIVE ANALYSIS IN EDX 401of the foil has to propagate in the sample beforeescaping in the direction of the detector. Asmentioned before, the X-ray generation probabilityis uniform throughout the thin film and thusτ also represents the average mass-distancethe X-ray photons have to travel in the sampleon route to the detector. For all other samplegeometries τ has no straightforward meaning,but still represents the mass-absorption length thatwhen used in a conventional absorption correctionyields the correct concentrations. Equation (5.7.2)reduces to:( )C A IA= k AB ×{1 + [(µ/ρ) A spC B I − (µ/ρ)B sp ]τ}B(5.7.8)In appearance, Equation (5.7.8) is a linear equationin τ, but since the mass-absorption coefficients(µ/ρ) A sp and (µ/ρ) B sp are concentration dependent,the relation is quadratic. Mass-absorptioncoefficients in a particular compound are linearcombinations of the values in pure element targetsand the coefficients are the weight fractionsof the different elements. Therefore in practice,concentrations are obtained through an iterativeprocedure.The ionic compound method does not attemptto ‘measure’ τ, but instead uses random numbers.Only one value for τ will yield a compositionthat will be electroneutral. Three arbitrarilychosen values for τ are used to process the spectrumto be quantified. One spectrum yields threesets of concentrations. This unequivocally definesa parabola per analysed element showing how theconcentrations of these elements change as functionof the mean mass-absorption length τ. Eachcurve is then multiplied by the valence state ofthe element it represents. The sum of all cationcurves yields a parabola showing how positivecharge varies with τ and a similar curve for thenegative charge is obtained by adding the anions.These two ‘positive’ and ‘negative’ curves intersectin one point, the only value of τ for whichthe condition of electroneutrality can be met. Thereal value of τ now being available, the correctcomposition of the sample can be calculatedby simply reprocessing the spectrum a fourth timewith the exact value for τ.706050At %4030O at %Zr at %Al at %10 Y at %20100−200 −150 −100 −50 0 50 100 150 200Distance (nm)Figure 5.7.8 Diffusion profiles of O, Zr, Al and Y across an Al 2 O 3 /Y-TPZ interface. The Y profile is multiplied by a factor 10.(Reprinted from Ultramicroscopy, 53, Van Cappellen, E. and Doukhan, J. C., Quantitative transmission X-ray microanalysis ofionic compounds, 343–349, Copyright (1994), with permission from Elsevier Science)

402 ENERGY DISPERSIVE X-RAY MICROANALYSIS IN STEM AND TEM5.7.5.6 REAL WORLD APPLICATIONSTwo problems using the ionic compound correctionmethod to obtain truly quantitative data arereviewed to demonstrate the power of quantitativeEDX in transmission microscopy (Van Cappellenand Doukhan 1994). The first example is theaccurate quantification of diffusion profiles in finegrainedceramic composites. The analysed materialis an Al 2 O 3 reinforced (20 vol%), yttria-stabilized(3 mol% Y 2 O 3 ), tetragonal zirconia polycrystallinecomposite (Al 2 O 3 /Y-TZP). The purpose is toinvestigate mutual diffusion of Al and Zr inneighboring grains after superplastic deformation.Figure 5.7.8 shows that Al does not penetratein ZrO 2 grains whereas Zr slightly diffuses intothe Al 2 O 3 crystals. Noteworthy is that on bothsides and away from the interface the correct Oconcentrations are obtained (60 and 66.7 at%).Oxygen, the only common element on both sides,is used, as the ratio element in the Cliff–Lorimerratio technique, confirming that contrary to somebeliefs, strongly absorbed elements can be usedas the ratio element. The k-factors are measuredexperimentally on well-characterized standardsusing the parameterless correction method. Therelative errors on k AlO and k ZrO are approximately2 %, whereas for k YO , the error is believed as highas 5 %, which is not a problem as Y is only a minorconstituent.The second example is the study of a complexgarnet [(Mg, Ca, Fe) 3 Al 2 Si 3 O 12 ]/ortho-pyroxene[(Mg, Fe) 2 Si 2 O 6 ] interface. The concentration profilesobtained with the ionic compound correctionscheme (Figure 5.7.9) are consistent with therules of crystal chemistry and show that the interfacecontains a certain amount of silica especiallyon the ortho-pyroxene (OPX) side of the interface,a conclusion that would have been difficultto draw otherwise. In this sample, not only theinterface is altered, but also the garnet phase iscontaminated with monoxide layers. This can beconcluded from the following facts: first the measuredSi concentration is well under 15 at%, secondthere is a systematic excess of 2+ valenceelements, and third the O/Si ratio far exceedsfour. At 5 µm from the interface, the O/Si ratioequals 4.41 whereas on clean garnet samples themeasured ratio consistently is within 1 % of thetheoretical value. It is not possible from the X-rayspectra to determine which monoxide is present,but the concentration at 5 µm from the interfaceis consistent with: 89 at% of (Mg, Ca, Fe,Mn) 3.0 (Al,Cr) 1.9 Si 3.0 O 12.1 plus 11 at% of (Mg, Ca,Fe, Mn)O. Noteworthy in this sample is that theOPX phase is pure. Also at 5 µm from the interface,the measured OPX composition is (minorelements are omitted): (Mg 1.48 Fe 0.48 Al 0.10 ) [Si1 .85Al 0.10 ]O 5.96 . The sum of the so-called M 1 andM 2 sites, the elements between the round bracketsequals 2.06 instead of 2.0 and the tetragonalsite elements between the square brackets add upto 1.95 instead of 2.0. Even more impressive arethe O index of 5.96 and the O/Si ratio of 3.05,which theoretically should be 6 and 3. The k-factors for this study are also measured experimentallywith the parameterless correction method.All cations have k XSi s with relative accuracies ofbetter than 3 % and k OSi , which was measured ondifferent compounds, has a statistical accuracy ofbetter than 1 %. With an estimated take-off angleof 34 ◦ and the known densities of garnet andortho-pyroxene (3.95 and 3.4 g/cm 3 , respectively)it is also possible to calculate the thickness profile(Figure 5.7.10).5.7.6 CONCLUSIONMore than ever EDX on (S)TEMs is an extremelypowerful technique in materials science that surelydid not vanish in favor of EELS as predicted20 years ago. The main reasons are its relativeease-of-use and the possibility of truly quantifyingthe data. The examples discussed in the previousparagraph are not the most trivial ones, but theyclearly show that with some care, quantificationcan be accurate and precise. As a matter offact, all modern analytical (scanning) transmissionmicroscopes are equipped with at least an EDXsystem whereas not all of them have electronenergy loss spectrometers.

CONCLUSION 403(At %)(At %)6563615957552220181614−5 −4 −3 −2 −1 0(m)O at %1 2 3 4 5Si at %(a)(At %)1216141210864210−5 −4 −3 −2 −1 0(m)−5 −4 −3 −2 −1 0(m)1 2 3 4 5Mg at %Fe at %1 2 3 4 5(At %)(b)86420−5 −4 −3 −2 −1 0(m)Al at %Ca at %1 2 3 4 5Figure 5.7.9 Diffusion profiles across a garnet (a)/ortho-pyroxene (OPX, b) interface, extending from −5 to+5 µm. The oxygenand silicon curves clearly show that the OPX side of the interface is contaminated over a range of about 1 mm, with silica (SiO 2 ).(Reprinted from Ultramicroscopy, 53, Van Cappellen, E. and Doukhan, J. C., Quantitative transmission X-ray microanalysis ofionic compounds, 343–349, Copyright (1994), with permission from Elsevier Science)

404 ENERGY DISPERSIVE X-RAY MICROANALYSIS IN STEM AND TEM5000−500−5000−4000 −3000 −2000 −1000 0 1000 2000 3000 4000 5000Figure 5.7.10 Calculated thickness profile perpendicular to the garnet/OPX interface. The vertical and horizontal scales areidentical and are in nm. (Reprinted from Ultramicroscopy, 53, Van Cappellen, E. and Doukhan, J. C., Quantitative transmissionX-ray microanalysis of ionic compounds, 343–349, Copyright (1994), with permission from Elsevier Science)REFERENCESCliff, G. and Lorimer, W. The quantitative analysis of thinspecimens. J. Microsc., 103, 203–207 (1975).Egerton, R. F. Electron Energy-loss Spectroscopy in the ElectronMicroscope, 2nd Edition, Plenum Press, New York,1996.Horita, Z., Sano, T. and Nemoto, M. Determination of theabsorption-free kANi factors for quantitative microanalysisof nickel base alloys. J. Electron Microsc., 35, 324–334(1986).Joy, D. C., Romig, Jr, A. D. and Goldstein, J. I. Principles ofAnalytical Electron Microscopy, Plenum Press, New York,1986.Van Cappellen, E., Van Dyck, D., Van Landuyt, J. andAdams, F. A parameterless method to correct for X-rayabsorption and fluorescence in thin film microanalysis. J.Phys. (Suppl. C2), 45, 411–414 (1984).Van Cappellen, E., Van Landuyt, J. and Adams, F. X-raymicroanalysis of second-phase precipitates in copper/zinc/aluminium shape memory alloys based on the parameterlesscorrection method. Anal. Chim. Acta, 195, 257–263 (1987).Van Cappellen, E. The parameterless correction method inX-ray microanalysis. Microsc. Microanal. Microstruct., 1,1–22 (1990).Van Cappellen, E., Deblieck, R. and Van Dyck, D. On thesecondary X-ray emission induced by electron irradiation inthin samples. Microsc. Microanal. Microstruct., 1, 127–140(1990).Van Cappellen, E. and Doukhan, J. C. Quantitative transmissionX-ray microanalysis of ionic compounds. Ultramicroscopy,53, 343–349 (1994).Watanabe, M., Horita, Z. and Nemoto, M. Absorption correctionand thickness determination using ζ factor in quantitativeX-ray microanalysis. Ultramicroscopy, 65, 187–198 (1996).Williams, D. B. and Carter, C. B. Transmission ElectronMicroscopy, Volume 1: Basics, Plenum Press, New York,1996a.Williams, D. B. and Carter, C. B. Transmission ElectronMicroscopy, Volume 4: Spectrometry, Plenum Press, NewYork, 1996b.Williams, D., Watanabe, M. and Carpenter, D. Thin film analysisand chemical mapping in the analytical electron microscope.Mikrochim. Acta (Suppl.), 15, 49–57 (1998).

5.8 X-Ray Absorption TechniquesJ. KAWAIKyoto University, Kyoto, Japan5.8.1 INTRODUCTIONX-Rays are absorbed by matter and the intensity isattenuated. The degree of absorption (absorbance)depends on the wavelength of the X-rays as wellas the thickness, density, atomic number, andthe local structure of the absorber. Figure 5.8.1 1shows typical X-ray fluorescence spectra measuredby an energy dispersive X-ray fluorescence(EDXRF) spectrometer, a Shimadzu EDX-700desktop spectrometer, 2 which has Zr, Al, Ti, Ni,and polymer filter to absorb part of the primaryX-rays. The X-ray tube is a Rh anode tube. Thesample is a 1000 ppm cadmium standard solutionfor atomic absorption spectrometry, which is ina sample cell with a Mylar film window. Withouta Zr filter, the Cd Kα peak (23.2 keV) cannotbe observed because the Rh Kβ peak (23.1 eV)overlaps. The Cd Kα peak becomes observablewith the use of the Zr filter. The Zr K absorptionedge is at 18.0 keV, which corresponds tothe sharp edge at 18 keV in the spectrum inFigure 5.8.1. The Zr filter effectively absorbs theRh Kα and Kβ X-rays, which are not used toexcite the Cd X-ray fluorescence, but the highenergy continuum X-rays go through the filter toexcite the Cd. This kind of automatic spectrometerhas now a quantitative analysis computer programincluding the effect of X-ray absorber filter withan automatic change of the filter. The computercode also includes the effect of 6 µm thicknessMylar window X-ray absorption and air absorptionof the X-ray path in the spectrometer. Wecan successfully obtain the Cd concentration of thesample solution. The filter technique is also widelyused in PIXE (particle induced X-ray emission),radioisotope X-ray analysis, 3 and X-ray absorptionspectroscopy using the X-ray fluorescenceyield method.The interaction between X-rays and matter isclassified into absorption, elastic scattering, andinelastic scattering. The basic physical formula ofX-ray absorption are described elsewhere. 4–6 Thephysical constants, such as X-ray absorption coefficientsor equivalently the imaginary part of theatomic scattering factor are listed elsewhere. 4–9The relation among the imaginary part of theatomic scattering factor, the imaginary part of therefractive index, the linear absorption coefficient,and the mass absorption coefficient, are conciselydescribed in the literature. 4,6,7 The measurementand interpretation of the X-ray absorption coefficientsas the change of the X-ray energy arecalled the X-ray absorption spectrometry or spectroscopy.Since most of the materials analysistechniques using the X-ray absorption phenomenahave already been described in the Encyclopediaof Analytical Chemistry 4 the present subchapter isdevoted to the concise summary and addenda tothe Encyclopedia.X-Ray absorption spectroscopy is referred toas XANES (X-ray absorption near edge structure)and EXAFS (extended X-ray absorption finestructure) (Figure 5.8.2). 10 XANES refers to thefine structure about 50 eV around the edge. EXAFSis used for the oscillating fine structure from 50 to1000 eV above the absorption edge. The Fouriertransform of this EXAFS oscillation yields aX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

406 X-RAY ABSORPTION TECHNIQUESRh KaCRh KaCd KaCd KbIntensityWith Zr filterRh KbCRh KbWithout filter0 10 20 30 40X-ray fluorescence energy (keV)Figure 5.8.1 X-Ray fluorescence spectra of cadmium 1000 ppm solution with and without Zr filter. Taken from Furuya et al. 1Reproduced by permission of Adv. X-ray Chem. Anal. JapanXANESEXAFSCu foil Cu K-edgeAbsorption (arb. units)i oUndulatorgap tuning8.85Photon energy (keV)9.91Figure 5.8.2 K-edge EXAFS spectra of Cu foil measured using an undulator beamline. Taken from Oyanagi et al. 10 IncidentX-ray intensity (i 0 ) is also shown, which has saw-teeth like structure due to the undulator gap change. The EXAFS spectrum(heavy solid line) after being normalized with respect to the incident X-ray intensity has a smooth oscillation but no discontinuity.Reproduced by permission of Electrotechnical Laboratoryradial distribution function of the X-ray absorbingatom. The XANES spectra represent the electronicstructure of the conduction band. XAFS (X-rayabsorption fine structure) is the generic namefor XANES and EXAFS. XAS (X-ray absorptionspectroscopy) is less used than XAFS, but has asimilar meaning.5.8.2 BASICS FOR XAFSXAFS has a long history since de Broglie and asummary is given by Lytle. 11 The 10th InternationalConference on XAFS was held in Chicagoin 1998, 12 the 11th at Ako, Japan in 2000, 13 andthe 12th at Malmö, Sweden in 2003 (near to

EXTREME CONDITIONS 407Figure 5.8.3 Web page of XAFS publication database. Reproduced from http://ixs.csrri.iit.edu/the Swedish synchrotron radiation facility MAXlab). 14 Other earlier international conferences andtheir proceedings are listed elsewhere. 4 We canobtain information on the activity of the XAFSSociety as well as analysis programs and otherscientific issues through The International XAFSSociety web page. 15 The XAFS PublicationsDatabase is freely accessible (Figure 5.8.3). Thefundamental review of X-ray spectrometry is publishedin even years in a journal, 16 and X-rayabsorption spectroscopy is included.XAFS is classified into two different spectroscopies,XANES and EXAFS, as described above.EXAFS is a structural analysis method, and thusit has similarities to X-ray diffraction data analysis,such as the requirement for standardizationmethods. The multiple scattering method is themajor method of EXAFS analysis. 17,18 XANES,which is also called NEXAFS (near edge X-rayabsorption fine structure), is analysed by molecularorbital or band structure calculations, andis similar to the soft X-ray emission/fluorescenceline shape analysis. 19–24 The basic measurementmethod is common to these two spectroscopies,EXAFS and XANES. The monochromatized incidentX-ray intensity (I 0 ) is measured, and theX-ray intensity transmitted through a specimen (I)is measured. The value − log(I/I 0 ) is plotted versusthe incident X-ray photon energy.5.8.3 EXTREME CONDITIONSThe measurement of XAFS is now a routine experimentfor local structure or electronic structurecharacterizations. Therefore techniques to measurethe XAFS spectra under extreme conditions, suchas high pressure and/or high temperature, havebeen developed.With a combination of an atomic absorptionspectrometer and XAFS spectrometer, Nakaiet al. 25 measured a 2000 ◦ C flame nebulized fromCu(NO 3 ) 2 solution at various heights of the flame.The spectra showed that the chemical state of Cuwas different with the change of the position inthe flame (Figure 5.8.4); It went from divalent toatomic like, according to the height in the flame.High temperature solid phase (3000 K), 26 hightemperature liquid phase (3000 K), 27 and bothhigh temperature (1650 ◦ C) and high pressure(2000 bar) supercritical fluids 28 have been measured.The effect of temperature was interpretedthrough the Debye–Waller factor 29 andanharmonic vibration. 30,31 Isotope effect, though

408 X-RAY ABSORPTION TECHNIQUESabsorption peak as shown in Figure 5.8.5, whichwas an effect due to the molecular vibration. 32I f /I o08.92(a)(b)(c)(d)(e)8.979.02Energy (keV)9.07Figure 5.8.4 Cu K XANES spectra of Cu(NO 3 ) 2 solution inflame at various heights from an atomic absorption burner head.Taken from Nakai et al. 25 (a) Flame at 6 mm height; (b) 3 mm;(c) 1.8 mm; (d) Cu metal foil; (e) Cu(NO 3 ) 2 solution itself.Reproduced by permission of Elsevierthis was not measured under an extreme condition,was observable for the line broadening of the5.8.4 COMBINATION WITHSCANNING TUNNELINGMICROSCOPESWhen the X-rays are absorbed, secondary quantawill be created by the energetic X-ray photons.Probing these secondary quanta using a scanningtunneling microscope (STM) or scanningcapacitance microscope, 33–38 high spatial resolutionmicroscopes will be realized in the near future,though the present spatial resolution is only 1 mmor less. Figure 5.8.6 shows a schematic diagram ofthe experimental set-up for STM-XAFS. 35 Capacitancemeasurements can be performed both withscanning and without scanning mode as shown inFigure 5.8.7. 38 We can change the bias potentialin these tunneling or capacitance probe methods.Though the details of the physical processes havenot yet been clarified, the change of bias potentialwill change the probing site on the surface or positionin the valence band, and we will obtain novel4(a)432v (n 1 ) = 0 1(b)n 22 3 4H 2 OIntensity (arb. units)3214a 12b 23pa 1 /3pb 14pa 1 /4pb 1Intensity (arb. units)105432v (n 1 ) = 0 1(c)n 22 3 4 5 6D 2 O10534 536 538 540Photon energy (eV)0535.5 536.0 536.5 537.0Photon energy (eV)Figure 5.8.5 Oxygen K edge XAFS spectra of water. Reproduced from Hiraya et al. 32 (a) Total ion yield O 1s absorptionspectrum of H 2 O; (b) 2b 2 peak of H 2 O; (c) 2b 2 peak of D 2 O. Vibration fine structures are different due to the isotope effect

COMBINATION WITH OPTICAL LUMINESCENCE 409X-raysSTMIonchamberMicroscopeSemiconductorMetal electrodeX-rayComputerScaleri-VV/FSampleV/FSTM controllerFigure 5.8.6 Experimental set-up of a scanning tunnelingmicroscope under synchrotron radiation. Taken from Tsujiet al. 35 Reproduced by permission of John Wiley & Sons, Ltdinformation on the electronic and local structureswith an atomic scale using these techniques.5.8.5 COMBINATION WITH OPTICALLUMINESCENCEWhen X-rays are absorbed, visible light is emittedfrom the sample. This is called the X-rayexcited optical luminescence (XEOL). Its intensitydepends on the absorbance, but does notdirectly depend on it, because of very complicatedCapacitancemeterFigure 5.8.7 Experimental set-up for the capacitance XAFSmeasurement. Taken from Ishii 38relaxation processes. 4 Its wavelength depends onthe analyte. Figure 5.8.8 shows a decay spectrumof Y 3 Al 5 O 12 :Ce measured with single bunchsynchrotron radiation as an input, 39 which wasregarded as a delta function in the time domain.When a narrow time window is selected in thedecay line shape, for recording the XAFS spectra,some optical relaxation process correspondingto the time delay can be probed, because someoptical processes are delayed depending on its transitionprobability, or in other words, lifetime of anexcited state. When a narrow wavelength windowis selected in the optical luminescence spectra, achemical species can be probed. By selecting thesetime and wavelength windows at the same time,a novel characterization method will be realized.Porous materials, 40 nanoparticles 41 and optically10 4XEOL intensity (counts)10 310 210 110 0 0 200 400Time (ns)600 800Figure 5.8.8 Decay curve of Y 3 Al 5 O 12 :Ce optical emission measured with 8 keV X-ray irradiation using single bunch operationmode at the Photon Factory. Taken from Hayakawa et al. 39 Reproduced by permission of John Wiley & Sons, Ltd

410 X-RAY ABSORPTION TECHNIQUESactive materials 42 are suitable targets for the XEOLmethod. The line shape measured by the luminescenceyield is usually broader than those of thetotal electron yield XAFS spectra. 43 The XEOL-XAFS can easily be performed using a conventionalgrating optical spectrometer (either by a stepscan type or a position sensitive detector type) atthe synchrotron radiation beam line. The detectionlimit is low compared with the transmissionmethod. Though the thickness or concentration of afilm specimen should be adjusted to yield a strongXAFS modulation in the conventional X-ray transmissionmeasurement, the XEOL is measurableeven for bulk samples.5.8.6 COMBINATION WITH X-RAYFLUORESCENCEWhen the stronger incident X-rays are absorbed,the stronger X-ray fluorescence is emitted. Thereforethe X-ray fluorescence intensity is a measureof absorbance. This type of measurement is calledthe X-ray fluorescence yield (XFY) method. TheXFY method has been used with an X-ray detectorsuch as a photodiode or a proportional counterwithout wavelength selection. The X-ray detectoris placed close to the sample and the total X-rayfluorescence intensity is measured. Jaklevic et al. 44pointed out in 1977 that the XFY method was quitesensitive down to 10 19 atoms/cm 2 concentrations.This value has become several orders of magnitudelower after 25 years.De Groot pointed out that, by the use of a wavelengthdispersive X-ray fluorescence spectrometer,spin-state selective XAFS spectra could beobtained. 24 The Kβ’ XFYandKβ 1,3 XFY spectraof early transition metal compounds yield theminority and the majority spin state XAFS spectraseparately.Muramatsu et al. 45 measured XFY-XAFS spectraby two parts of an X-ray fluorescencespectrum using a grating spectrometer (Figure5.8.9). Figure 5.8.10 shows the XANES spectra ofSample90°Fluorescent X-Rays andscattered X-RaysBeam monitorEMonochromatizedundulator radiationEntrance slitSphericalgratingHigh-energy maskLow-energy maskHigh-energy windowLow-energy windowPosition sensitive detectorFigure 5.8.9 Experimental set-up of Lα and Lβ selective X-ray fluorescence yield method at BL-8.0 at ALS. Taken fromMuramatsu et al. 45 To put a blind mask on a part of the position sensitive detector makes it possible to measure the XAFSspectra of a certain X-ray fluorescence line yield method. This is also electrically possible, because the output of a positionsensitive counter is usually pulse height signal dependent on the position

PHOTOCONDUCTIVE AND ELECTROCHEMICAL MEASUREMENTS 411X-ray intensity (arb. units)830 850(a)X-ray intensity (arb. units)(b)(A)(B)(C)La(A) - (B)NiO(A) wide window(B) low-energywindow(C) high-energywindowLb870PFY absorptionTEY absorptionL II 2p 3/2L II 2p 1/2890840 850 860 870 880(c)Photon energy (eV)Figure 5.8.10 (a) Nickel L X-ray fluorescence spectrum. (b) Labsorption spectra of (A) Lα,β X-ray fluorescence yield,(B) Lα yield and (C) Lβ yield XAFS spectra. (c) Total electronyield spectrum. From Muramatsu. 46 . Reproduced by permissionof Adv. X-ray Chem. Anal. Japantotal XFY, Ni Lα and Lβ partial X-ray fluorescenceyields, the difference of these two, and thetotal electron yield (TEY). 46 X-Ray fluorescencespectra show chemical shift due to the differencein effective charges. Therefore the XAFS spectrayielded by the chemical-shifted X-ray fluorescencepeaks can be obtained. Izumi et al. 47 measuredsite-selective XANES spectra utilizing the chemicalshift of Cu Kα 1 between Cu on ZnO andCu metal in a catalyst. The signal from a positionsensitive X-ray detector in an X-ray fluorescencespectrometer has a relation; electric voltageto the position. Therefore we can obtain the partialX-ray fluorescence yield XAFS spectra by the useof discrimination of electric pulses using an electriccircuit, without using a mechanical mask onthe position sensitive detector, which was used byMuramatsu et al. 45The resonant Raman scattering peak is observablewhen the incident X-ray energy is just belowthe absorption edge. The remarkable feature ofthe X-ray Raman peak is that the line width isnarrower than the X-ray fluorescence, though thetransition from the Raman peak to the X-ray fluorescenceis continuous. Utilizing this phenomenon,XAFS spectra free from lifetime broadening can beobtained. 48–505.8.7 PHOTOCONDUCTIVE ANDELECTROCHEMICALMEASUREMENTSThe electrical conductance of a solid changeswith the change of the wavelength of the incidentX-rays. This is because the valence electrons areexcited into the conduction band and thus the densityof conduction electrons changes, or, an atom,whose core electron is photoionized, behaves asan impurity in the metal. The response of conductanceis thus sometimes positive and sometimesnegative. 51 Compared with solid samples,liquids are suitable to measure the conductivitywith the change of the incident X-ray wavelength.Sham and Holroyd 52 used a liquid cell with electrodes,and measured the change of the conductivityof (CH 3 ) 4 Sn in trimethylpentane near the Sn K

412 X-RAY ABSORPTION TECHNIQUESedge. The behavior of conductivity was positivefor low concentration (0.07 M) but negative forhigh concentration (0.10 M). This behavior alsodepends on the structure of the sample liquid cell.Though the interpretation is very complicated, wecan get information on the liquid or solution usingXAFS spectra.Many kinds of electrochemical cell or in situcell for EXAFS measurements were proposedand are summarized by Sharpe et al. 53 Yamaguchiet al. 54 used an in situ electrochemical celldesigned by Heineman’s group 55 to measure unstablechemical species synthesized during a redoxreaction and thus very difficult to stabilize themwithout applying the electric potential. They measuredXAFS spectra of a Mn IV /Mn III system atseveral points in a cyclic voltammogram.Nakai et al. 56,57 measured the XAFS spectra of alithium battery electrode during charge–dischargeprocesses using an in situ cell as shown inFigure 5.8.11. 56 They observed the chemical shiftof the strongest absorption peak (the so-calledwhite line) during the charge–discharge process,emergence of pre-edge structure, which means thechange of coordination structure, and the change ofatomic distances from the Fourier transform of theEXAFS data.The stainless steel corrosion process was analysedusing an electrochemical cell by the measurementof EXAFS. 585.8.8 TOTAL REFLECTION XAFSHeald et al. 59 proposed measuring a buried CuAl 2layer in an Al(100 nm)/CuAl 2 (5 nm)/Cu(100 nm)multilayer using the glancing angle incident XAFS.Adjusting the glancing angle, the signal from aburied layer could be maximized due to the interferenceeffect between the incident and reflectedX-rays. Recently, Shirai et al. 60 and Kawai et al. 61developed the total reflection XAFS method. Mosttotal reflection papers have been cited in Kawaiet al. 62Figure 5.8.12 63 shows the schematic probingand information depth of total reflection XAFS.The TEY method is more surface sensitive than theX-ray fluorescence yield method. Figure 5.8.13 64shows the use of polarization of the incidentX-rays for the determination of the orientation ofadsorbates on a substrate. Sample holders 65,66 andan X-ray detector 67 suitable for the measurementof polarized total reflection XAFS were developed.Polarization total reflection XAFS has been usedto study structure transformation of a Pt cluster onKapton ® filmAl foilStainless bodyX-rayI 0IIon chamberdetectorStainlessdiskCathodematerialReservoirO-ringAnodematerialStainlessdiskIon chamberdetectorElectrolyte: 1 M LiBF 4 in a 50/50 mixture of Pc and ECFigure 5.8.11 Schematic illustration of an in situ electrochemical cell for transmission XAFS measurements. Taken from Nakaiet al. 56 Reproduced by permission of Elsevier

TOTAL REFLECTION XAFS 413q >> δ cPhotons ReflectedFluorescenceX-raysphotonsPhotoelectronsX-raypenetrationdepth111-2-121-2Electronescape depthX-rayescape depth(a)q ≤δ cqFluorescenceX-raysElectronescape depth(b)X-raypenetrationdepthX-rayescape depthFigure 5.8.12 Schematic representation of normal (a) and surface sensitive (b) X-ray fluorescence excitation. Taken from Oyanagiet al. 63 The critical angle of X-ray total reflection is denoted by δ c . Total reflection geometry can reduce the probing depthby several orders of magnitude, achieving a surface-sensitive excitation. Reproduced by permission of International Union ofCrystallographyan Al 2 O 3 substrate 68 and molybdenum oxide on asingle crystal. 69The X-rays emitted from a bending magnet of asynchrotron light source is polarized in such a waythat the electric vector is parallel to the horizontalplane. Thus the electric dipole moment in thisplane in a sample can be easily excited and thusthe X-rays are strongly absorbed when a column ofatoms is present in this direction. Figure 5.8.14 70shows π and σ orbital components in Cu KXANES spectra of an oxide superconductor singlecrystal by adjusting a crystal axis to the electricvector of the incident X-rays. This experimentwas not a total reflection, but similar to thetotal reflection method in such a way that bothmethods used the polarization of X-rays. When L 3edge spectra are measured with polarized X-rays,the orientation of the empty d band can bedetermined, 71 because the 2p–3d electric dipoletransition is dominant over the 2p–4s transition.The polarization dependent XANES spectra ofthe L 2,3 edge of a TiO 2 single crystal are alsoobservable. 72Different thermal treatment of a Nb/Al interfacewas studied by the total reflection EXAFS. 73Total electron yield XANES under a total reflectioncondition was measured for Cr thin films onFe. 74 The small change of the incident glancingangle makes it possible to change the probingdepth. This will be a powerful tool to characterizethe depth-selective analysis of multilayersamples.

414 X-RAY ABSORPTION TECHNIQUESSR RingPolarized X-rayScintillation counterSlitFluorescenceIon chamberSampleSPIon chamberqqqqM M MM M MMMMMMM(a)(b)Figure 5.8.13 Schematic diagram of polarized total reflection X-ray fluorescence XAFS, with the molecular adsorbates onthe surface. Reproduced by permission of ElsevierThe total reflection X-ray method is suitablefor the characterization of liquid surfaces, e.g. ametal stearate Langmuir monolayer on a metalion aqueous solution. 75 Figure 5.8.15 shows aschematic illustration of the experimental set-up. 76Usually the conversion electron yield method usingHe gas, a schematic illustration of which is shownin Figure 5.8.16, is used to measure the spectra. 77Applications of XANES spectroscopy to solutionshave been summarized by Sakane. 78X-Ray reflectivity is an alternative method tomeasure the XAFS spectra. When the absorption isstronger, the reflectivity becomes weaker, and viceversa. Therefore the X-ray reflectivity intensityis a replica of the XAFS spectra. 79,80 An anodicsilver oxide film treated in situ electrochemicallyis measured by the reflectivity method. 81The total reflection experimental set-up alsoreduces the self-absorption effect, 82,83 as shown inFigure 5.8.17. 83 The self-absorption effect heavilysmears the XAFS spectra when the X-ray fluorescenceyield method is used.5.8.9 ELECTRON AND OTHERSECONDARY YIELD METHODSAND THEIR SURFACE SENSITIVITYWhen X-rays are impinging on a surface andabsorbed, then photoelectrons, consequently Augerelectrons or X-ray fluorescence, and secondaryelectrons are emitted. These electrons are generatedboth in deep places where the incident X-raysreach, as well as in the shallow surface region.Therefore the detection of these electrons, or alternativelythe measurement of the sample electriccurrent (this method is called the TEY method),was thought to be bulk sensitive. Recently it has

STRONG FIELD EFFECTS 415Absorbance (arb. units)3dA0(B)B4pπP4pπC4pσD4pσQE10 20 30 40Energy (eV)(a)(b)(c)(d)50 60Figure 5.8.14 Polarized Cu K edge XANES spectra of a singlecrystal of Sr 2 CuO 3 . Taken from Kosugi et al. 70 (a) The electricvector is parallel with the single crystal axis b; (b) parallel witha; (c) powder; and (d) Cu 2 O powderhowever been clarified that the electrons emittedfrom the sample surface, or the sample electriccurrent, are both surface sensitive. This evidencehas been independently found by severalresearchers. 61,84–86 The mechanism and differenceof the TEY (sample electric current), secondaryelectrons, and Auger electrons are described inKawai 4 and a detailed analysis is reported in Erbilet al. 87 The signal to background ratio of thetotal reflection X-ray TEY method was estimatedby Zheng and Gohshi. 88 The conversion electronyield method, under atmospheric conditions 89,90was compared with the TEY method, using thetotal reflection X-ray method in order to changethe probing depth. 91 The surface sensitivity of theTEY method, where the majority of the detectedelectrons are so-called secondary electrons (kineticenergy is less than 50 eV), is approximately 2 nm,which is comparable with the photoelectron inelasticmean free path. The ion yield method is nolonger a difficult technique because a channeltronelectron multiplier can be used. 92Energy dispersive incident X-rays (describedlater in Figure 5.8.33) on the surface are used asthe excitation source. In this experiment, the emittedAuger electrons are detected by a position sensitiveelectron detector after the energy selectionby a hemispherical electron energy analyzer, asshown in Figure 5.8.18. 93 An Auger electron yieldXANES spectrum can be obtained with one shot.A surface sensitive XANES spectrum can be thusquickly measured. These electron yield methodsare not suitable for measuring insulators. However,as shown in Figure 5.8.19, 94 with the use ofan electron flood gun as well as an Ar ion gun,and also with an electron yield detector equippedwith an electron energy filter to avoid the effect oflow energy electrons from the flood gun, the electronyield XAFS spectra become observable forinsulators. 95The coincidence spectra are observable by theuse of e.g. Auger electron yield and XFY. Thiskind of coincidence method is useful to clarifythe electron transition process in a single atom.We can still obtain chemical information on boththe surface and bulk separately for environmentalsamples such as aerosol or flyash, where theelectron yield (surface sensitive) and XFY (bulksensitive) are measured in one scan. 45.8.10 STRONG FIELD EFFECTSXAFS are measured for a sample with theapplication of a strong field, such as laser light or amagnetic field. With a combination of an externalfield, we can obtain a new chemical informationon the sample.

416 X-RAY ABSORPTION TECHNIQUES(f)Solution(g)145 V145 V145 V(g)(d)(c)(b)(e)(e)(a)He gasCooling water25 cmHe gasFigure 5.8.15 Schematic diagram of total reflection TEY XAFS experiment. Taken from Tanida. 76 (a) Synchrotron storage ring,(b) monochromator, (c) mirror to remove the higher order harmonic X-rays, (d) ion chamber to monitor the incident X-rayintensity, (e) a polyethylene window, (f) a wire electrode for measuring electrons from sample solution, (f) to amplifier from acollector electrode, and (g) a fringe electrode. Reproduced by permission of H. TanidaHe gasElectrodeABias voltageHe gasIncidentbeamHee −He +X-rayWindowSample water bathSample cellSampleDetectorFigure 5.8.16 Mechanism of conversion electron yield methodusing helium gas. Taken from Harada et al. 77 Reproduced bypermission of Japan Society for Analytical ChemistryFigure 5.8.20 shows a schematic illustration ofthe transition in the pump-probe XAFS method. 96Using strong laser irradiation, most of the valenceelectrons are excited and X-ray absorption spectraof the optically activated state can be measured.The EXAFS measurement of a glassy sampleduring laser irradiation has been reported. 97 TheEXAFS data of a glassy sample show that thestructure is changed temporarily or permanentlyby the laser irradiation.We can obtain a magnetic property of asample by the measurement of XAFS spectra in astrong magnetic field as shown in Figure 5.8.21. 98The X-rays from an undulator in a synchrotron(a)(b)SampleIncidentbeamDetectorFigure 5.8.17 Sketch of the geometry among incident beam,fluorescent beam, and detector at (a) normal incidence and(b) grazing incidence. Taken from Pfalzar et al. 83

STRONG FIELD EFFECTS 417Dispersed X-raysSES-2002Auger electronsXAFSspectrumSampleCCD camerayxElectron kinetic energy2D-detectorX : position (photon energy)Y : electron kinetic energyPhoton energyFigure 5.8.18 Schematic diagram for the energy dispersive NEXAFS. Taken from Amemiya et al. 93 The horizontal position atthe sample surface corresponds to the photon energy. Reproduced by permission of Japan Society of Applied PhysicsElectron yielddetectorhnMetallic meshRefocusing mirrorSampleAAElectronflood gunElectronanalyzerArgon ion gunAFigure 5.8.19 Schematic drawing of the experimental set-up for an insulator of which charge is neutralized by a flood gun. Takenfrom Tanaka et al. 94 Reproduced by permission of Japan Society for Analytical Chemistryradiation facility can be polarized in such a waythat the electric vector of the incident X-raysare circulated clockwise or counter-clockwise withrespect to the magnetic field applied to the sample.This is also achieved by a phase retarder, such as aλ/4 wavelength slab. The absorption coefficient isslightly different for these two polarizations of theincident X-rays. The transmitted X-ray intensityas well as the X-ray fluorescence intensity showthe X-ray magnetic circular dichroism (XMCD).Figure 5.8.21 shows an experimental set-up. Eitherthe helicity or magnetic pole is to be changed,and the resulting difference in X-ray absorbanceis measured. This is a Faraday effect in the X-rayregion. One of the most important fundamentalsof the interpretation of the change in absorptionspectra due to the magnetic field is a sum ruleproved by Thole et al.; 99 general expressions aregiven by van der Laan 100 and Ankudinov et al.; 101how to use the sum rule is given in Tobin et al. 102Recently a monoatomic wire was characterizedusing XMCD. 103Yokoyama et al. 104 studied carbon monoxideadsorbed on nickel and cobalt thin layers using

418 X-RAY ABSORPTION TECHNIQUESPumpCBVBOpticalexcitationX-ray excitationLattice distortionRelaxationRearrangementProbeL3L2L1IncidentX-Ray beamRadiative decayhwKaKaReflectedbeamKFigure 5.8.20 Principle of pump and probe XAFS. Taken from Oyanagi et al. 96 An electron in a valence band (VB) is excitedinto a conduction band (CB) by laser light pumping, and the XAFS spectra of such a system are measured using the XFY method.Reproduced by permission of International Union of CrystallographyX-Ray45°Ion chamberSampleIon chamberMagnetic fieldsFigure 5.8.21 Schematic diagram of an experimental layoutfor the measurement of magnetic circular dichroism X-rayabsorption fine structure. Taken from Nakamura et al. 98XMCD and clarified the interaction between themagnetization film and CO unoccupied orbital π ∗ ,which had orbital magnetic moments.The XMCD experiment will be useful, whencombined with the grazing incident technique, forthe characterization of thin multilayer films madeby changing the parameters (temperature, pressure,concentration, etc.) in a processing method.X-Ray beam fromundulator sourceMonochromatorFZP/CRLSamplezPinhole yxLarge areadetector(a)OpticalmicroscopeEnergydispersivedetectorHigh resolutiondetector(b)45 m 0.2 mFigure 5.8.22 Experimental set-up for (a) µ-X-ray absorption, µ-X-ray diffraction and µ-X-ray fluorescence and (b) µ-tomography.Taken from Salbu et al. 105 Reproduced by permission of Elsevier

EELS, ELNES AND EXELFS 4195.8.11 MICROSCOPYMicroscopy and imaging of various samplesusing the X-ray absorption techniques aresummarized in Figure 5.8.22; 105 the techniquesused are the microbeam scanning technique (thesample is moved in the real experiment) andtomography technique. Transmission-type microimagingwithout an X-ray optical lens has beenwidely used. Microscopes using a soft X-raylens (Figure 5.8.23 106 ) have also been extensivelyused. 107,108 The scanning microbeam method is109 – 112usually combined with µ-X-ray diffractionor X-ray fluorescence 113,114 beamlines in asynchrotron radiation facility.The principle of X-ray microtomography isshown in Figure 5.8.22(b), which also utilizesthe X-ray absorption effect. The X-ray absorptionspectra can be obtained by a synchrotron microtomographyset-up. 115 Figure 5.8.24 105 shows µ-Xrayabsorption spectroscopic tomography of a Ufuel particle collected from Chernobyl soils. Theimage of a cross-section of the fine particle canbe numerically reconstructed. Oxidation states ofthe particle can be determined from the chemicalshift of the XANES spectra. The spatial resolutionof laboratory microtomography is not better thansynchrotron radiation microtomography, but it isnow less than 0.1 µm. 116 Figure 5.8.25 shows theinner structure of a lithium electric battery measuredby laboratory microtomography developedby Hirakimoto. 117 Desktop microtomography hasalso been developed. 118XANES microscopes have been used to studygeological and environmental samples, 119 – 122 bioand organic materials which show phase separation,123 – 125 and adsorbates which are studiedusing X-ray linear dichroism microscopy. 126 Themicrobeam analysis method has the potential tobe used as a screening method in combinatorialchemistry using an integrated microchemicalchip. 1275.8.12 EELS, ELNES AND EXELFSElectron energy loss spectroscopy (EELS) is atechnique used in transmission electron microscopy(TEM), where electrons transmit through athin film and energy absorbed by the thin filmduring transmission is measured by an electronenergy analyser. EELS is classified into energy lossnear edge structure (ELNES) and extended energyloss fine structure (EXELFS). This classification issimilar to XANES and EXAFS. When the electronenergy is measured in the forward direction, thee −e − SDisplaySample stagee −Zone platexMonochromatorX-RaysyUndulator SEnergyanalyzerNSNNScanScontrollerNFigure 5.8.23 Schematic representation of the µ-NEXAFS and XPS beamline. Taken from Ade et al. 106permission of ElsevierReproduced by

420 X-RAY ABSORPTION TECHNIQUES10 µmFigure 5.8.24 Tomographic reconstruction and computerised slicing of the three-dimensional image demonstrating aninhomogeneous distribution of U within a Chernobyl particle measured using the beamline shown in Figure 5.8.22. Takenfrom Salbu et al. 105 . Reproduced by permission of Elsevierselection rule of an electron transition in an atomis similar to that of an optical (X-ray) transition, i.e.the electric dipole selection rule. Thus the resultingEELS spectra can be interpreted in the sameway as the X-ray absorption spectra. 128 – 130 Thepresence of the extended fine structure in EELSspectra was found by Leapman et al. 131 and theycoined the term ‘EXELFS’. EELS measurementsare suitable for low energy loss, such as lightelements (B, C, N, and O) and soft X-raylines (L edge of Si and transition metals 132 – 134 ).This is because an overlap of the spectra isavoidable among different elements for low energylosses. EELS has the potential to detect a singleatom spectrum of even a biological structure, 135because the resolution of a transmission electronmicroscope becomes as high as an atomic levelspatial resolution.5.8.13 EXEFSVery weak fine structures are always found atthe low energy side of strong characteristic X-rayfluorescence or X-ray emission lines. The intensityis usually less than 1 % of the Kα main line.These fine structures are called the ‘radiativeAuger satellites’. Kawai et al. 136,137 pointed outthat the overall line shape of the radiative Augersatellites is similar to that of XAFS spectra and theFourier transform of the radiative Auger satellitesyields a radial distribution function. 136 They coined‘EXEFS’ for the use of the radiative Augersatellites to measure XAFS spectra. 137 The EXEFSmethod is now occasionally used with an EPMA(electron probe microanalyser) 138 – 140 for chemicalstate mapping or imaging, and microarea chemicalstate analysis. Figure 5.8.26 shows the mapping

EXEFS 421Figure 5.8.25 An inner structure of a lithium electric battery measured by a microtomography developed by Hirakimoto. 117Reproduced by permission of Shimadzu Corp.BayeriteGibbsiteAlAl(OH) 3a-Al 2 O 3 g-Al 2 O 32 mmFigure 5.8.26 Chemical state imaging of aluminum standard chemicals using the EXEFS method. Taken from Watanabe et al. 140Reproduced by permission of International Union of Crystallography

422 X-RAY ABSORPTION TECHNIQUESFigure 5.8.27 EXEFS background subtraction window of EXEFA analysis computer software. Taken from Taguchi. 141 Thespectrum shown is a real α-Al 2 O 3 radiative Auger satellite spectrum. The resulting k-χ spectrum shows an oscillating finestructure. Reproduced by permission of Adv. X-ray Chem. Anal. Japanof aluminum oxides, α- and γ -Al 2 O 3 , bayeriteand gibbsite. 140 These aluminum oxides containsimilar elements, thus the discriminations amongthese different phases are not achieved only by theelemental mapping using the characteristic X-raylines. However, with the use of EXEFS we canobtain an image due to the difference in phase.Recently a wavelength dispersive X-ray fluorescencespectrometer was equipped with anEXEFS analysis computer program as shown inFigure 5.8.27. 141 Basic studies on the radiativeAuger spectra compared with the Auger electronspectra 142 have become active after the emergenceof the EXEFS method. The reason why the EXEFSspectra coincide with the XAFS spectra was at thefirst stage not clear, but an exact theory has beenproposed using a T-matrix expansion; 143 the phaseshift is slightly different from the true EXAFSanalysis. EXEFS in X-ray fluorescence spectrometryis used to investigate environmental samplesbecause such samples are sometimes very difficultto insert into an ultrahigh vacuum chamber at thesynchrotron radiation facility. 1445.8.14 DAFSDiffraction anomalous fine structure (DAFS) is analternative method to measure the XAFS spectraproposed by Stragier et al. 145 The imaginary partof the X-ray scattering factor is closely related tothe X-ray absorption coefficient, and thus the measurementof the X-ray diffraction peak by changingthe X-ray energy reveals an EXAFS-like oscillation.This method has diffraction peak selectivity,which means that the site or phase selectiveinformation is obtainable. The measurement of TiK XAFS spectra in BaTiO 3 is always interferedwith by the overlap of the close Ba L 3 edge, butthis interference is avoidable by using the DAFSmethod. 1465.8.15 THEORY ANDINTERPRETATION OF XAFS SPECTRAThough the contribution from many electron excitationsin XAFS spectra was suggested more than20 years ago, 147 this effect was not seriously considereduntil recently. These multiple-excitationphenomena were studied by Ito et al. 148 for Br −in organic solvents and by Magnuson et al. 149 fornickel metal. These more-than-one electron excitationsignals are a source of spurious noise in theanalysis of XAFS spectra 150 .‘Atomic XAFS’ has been said to exist inXAFS spectra. It is another origin of a step-likestructure in EXAFS spectra. Usually EXAFS

STANDARDIZATION 423oscillation is due to the condensed matter effect;the outgoing photoelectron wave interferes withthe backscattered waves by its neighboring atoms.Therefore, the EXAFS signal is not observablefor an isolated single atom. However, the shapeof the potential of a single atom itself has theeffect to backscatter the electron wave and somekind of interference pattern with longer periodthan the EXAFS oscillation is observable. Thestructures observed in an isolated single atomEXAFS are interpreted both from the view pointof double-electron excitation and from atomicXAFS; the existence of ‘atomic XAFS’ is stillcontroversial. 151,152The relativistic effect is also an important factorfor the analysis of XAFS spectra. One of the longstandingtheoretical problems was that the absenceof a sharp absorption line (i.e. white line) in theL 2 XANES of Pt metal, though L 3 has a sharpabsorption line. This problem has been solved bythe inclusion of the relativistic effect. 153All kinds of computer calculation programs ofXAFS spectra are accessible through the InternationalXAFS Society (http://ixs.csrri.iit.edu/). Oneof the most widely used programs is the FEFFseries. 154 The newest version is FEFF8. FEFF isa computer program for ab initio multiple scatteringcalculations of EXAFS and XANES spectrafor a cluster molecule. The FEFF8 code includesrelativistic Dirac–Fock atomic calculation, selfenergies,a fully relativistic cross-section, polarizationdependence, and many other features.Another class of computation code is themolecular orbital (MO) method expressed by alinear combination of atomic orbitals (LCAOs).The discrete variational Xα (DV-Xα) method ismost convenient in the LCAO-MO method, whilethe multiple scattering Xα (MS-Xα) method is thebasis of the FEFF and other multiple scatteringmethods. The DV-Xα method can calculate thecore-hole relaxation state easily. This is the reasonwhy the DV-Xα method is extensively used.The LCAO-MO method including the DV-Xαmethod is only applicable to XANES (below50 eV above the absorption edge) spectra, thoughthe multiple scattering methods are applicableto both XANES and EXAFS spectra. Jiang andEllis 155 calculated the XANES spectra of variousCo compounds using the DV-Xα method. Themolecule SF 6 has been a reference material formore than 30 years 156,157 in experiments as well asa check for a computer code. 158,159 The measuredspectra are satisfactorily reproduced by the DV-Xα calculation for the SF 6 molecule. XANESspectra of transition metal complexes, 160,161 siliconoxides 129 and oxyanions 162 are well interpreted byusing the DV-Xα method.The core-hole effect is an important factor tointerpret mixed valence compounds. According tothe calculation of Suzuki et al., 163 the number of3d electrons in the late transition metal compoundsincreases by one electron after the creation ofa core hole. Contrary to this, that of the earlytransition metal compounds does not change beforeand after the creation of the core hole, as is shownin Figure 5.8.28. Therefore the interpretation of thevalency or oxidation number of transition metalcompounds is very controversial, especially for Cocompounds. 164‘White line’ is the name given to the strongestsharp lines in XANES spectra, because these linesdevelop white when the X-ray spectra are recordedon photographic film. The intensity ratio of thewhite lines is closely related to the occupancyof valence orbitals, as shown in Figure 5.8.29. 165The white lines in oxygen K absorption spectraof transition metal oxides (Figure 5.8.30 166 ) arealso interpreted in a similar way, though thecharge-transfer effect 163 and other effects 167 shouldbe included.The pre-edge structure is a good index ofthe chemical environment of the X-ray absorbingatom. It is strong for tetragonally coordinatedtransition metals, but weak for octahedrally coordinatedtransition metals. The pre-edge structureis sometimes assigned to the 1s–3d electricquadrupole transition, but the relation to168 –Kβ 170 5 should be studied more extensively.5.8.16 STANDARDIZATIONThe standardization of EXFAS spectra and theirnumerical processings are important in the practical

424 X-RAY ABSORPTION TECHNIQUESNumber of unpaired 3d electrons in the core-hole state543210Ti–Cr compoundsMn compoundsFe–Cu compoundsMnO2V 2 O 3 BaCoO 2 FeO 4TiONa 5 CoO 4K 3 CoO 4Na 4 CoO 4Sr 2 CrO 4VO 2Ti 2 O 3NiO Charge-transfer typeBa 3 (MnO 4 ) 2Mn 2 O 3FeMott–Hubbard type2 O 3MnO 2FeOCr 2 O SrFeO 33VONa 5 FeO 4CrO 2K 2 MnO 4LaNiO 3CaNa 5 NiO 4OHCrO 4K 2 FeO 4CuOCo 2 O 3 SrCoO 20 1 2 3 4 5Number of unpaired 3d electrons in the ground stateFigure 5.8.28 Plot of the calculated number of unpaired 3d electrons in the ground state and the 1s −1 hole state. Taken fromSuzuki et al. 163 The compounds whose spin states are zero both in the ground state and in the core hole state are omitted. Theeffect of 1s −1 and 2p −1 are approximately the same. Reproduced by permission of ElsevierNiCuIntensityFeCoCrVTiEnergy loss (1 div = 50 eV)Figure 5.8.29 L 2,3 edge spectra of 3d transition metals. Taken from Pearson et al. 165

STANDARDIZATION 425Sc 2 O 3TiO 2MnO 2Normalized intensityTi 2 O 3VO 2V 2 O 3Normalized intensityFe 2 O 3Fe 3 O 4NiOCr 2 O 3CuO(a)530 540 550Energy (eV)(b)530 540 550Energy (eV)Figure 5.8.30 Oxygen 1s X-ray absorption spectra of transition metal oxides, taken from de Groot et al. 166 The shaded area isassigned to the oxygen p character in the transition metal 3d banduse of EXAFS spectroscopy. This is similar toX-ray diffraction data standardization. The EXAFSspectra measured at many synchrotron beamlinesand measured by laboratory spectrometers shouldbe compared with each other. The white lineintensity is related to the coherence of the incidentX-rays. 171 The problem of the standardizationof EXAFS spectra has been discussed withcomparison of calculation codes 172 and standardspectra. 173 The International XAFS Society hasa committee for the standardization of EXAFSmeasurements and data analysis. The committeereport can be read at http://ixs.csrri.iit.edu/. Thereport includes: (1) user controlled parameters atbeamlines; (2) data collection methods such astransmission, fluorescence, or electron yield methods;(3) detectors used; (4) data analysis programs;(5) error assessment; (6) standardized error reportingprocedure; (7) sample preparation; (8) dataprocessing; and (9) modeling.Many methods have been devised for the analysisof XAFS data. Taguchi and White 174 proposedthe use of a crystal structure database to simplifythe modeling problem in EXAFS analysis. A rapidcalculation method using parallel computation hasbeen proposed. 175 The second derivative of theXANES spectra reveals a doublet structure whenthe raw spectra themselves look similar. 176Cross-correlation analysis of binary mixtures(Co 3 O 4 and CoAl 2 O 4 ) of EXAFS spectra isused to obtain a quantitative analysis of eachcomponent. 177 The EXAFS analysis of Co 3 O 4 andCoAl 2 O 4 has no problem, but XANES analysisshould include the charge-transfer effect and spinflip phenomena due to the creation of a corehole. 163,164 Many kinds of empirical parameters areproposed to classify the complicated Cu and CoXANES spectra. 178,179Diffraction peaks sometimes contaminate theEXAFS spectra as is shown in Figure 5.8.31. 180

426 X-RAY ABSORPTION TECHNIQUESIntensity (arb .units)(a)(b)(c)(d)6.0 6.5Photon energy (keV)7.0Figure 5.8.31 (a–c) Cr K edge raw X-ray fluorescence yieldXAFS spectra of ruby. Taken from Emura and Maeda. 180Diffraction peaks interfere with the analysis of spectra. (d) Adiffraction-free spectrum numerically synthesized from spectra(a) and (b). Reproduced by permission of American Instituteof PhysicsUsing a numerical method, a diffraction-freeEXAFS spectrum (Figure 5.8.31d) is available.two ion chambers. To scan the incident X-rayenergy, the double-crystal monochromator is stepscanned.A mirror effectively excludes the higherorder X-ray reflection. The step-scanning methodneeds time to scan, and thus energy-dispersivegeometry is developed to measure the XAFS spectraby one shot as shown in Figure 5.8.33. 182Laboratory EXAFS spectrometers are commerciallyavailable 183,184 as shown in Figure 5.8.34,which looks like an X-ray diffractometer. The laboratoryEXAFS machines use rotating anode highpower X-ray tubes such as reported by Sakurai 185and recently a parabolic cylinder mirror has beenused. 186 The commercially available spectrometersare usually modified versions of spectrometersdeveloped in academic institutions. 187 – 189 Thespecimen in these laboratory XAFS spectrometersis moved with a change in the incident X-rayenergy but the X-ray tube is fixed. Therefore, complicatedexperiments using a cryogenic cooler orhigh temperature furnace are very difficult to perform.To overcome these difficulties, a new spectrometerwhere the sample is fixed and the X-raytube moves has been developed. 190A soft X-ray synchrotron beamline for XAFSmeasurements looks like an electron spectrometer,such as an ESCA (electron spectroscopy forchemical analysis) instrument. This is because thesoft X-ray beamline (less than 1 keV) requires awindowless system due to the strong absorptioncoefficients of any type of X-ray windows. Thereforethe sample chamber is directly connectedto the synchrotron main ring without a window.Consequently the samples allowed into the samplechamber are very limited because of the ultrahigh vacuum system. However, recently using athin film such as BN, liquid samples have beenmeasurable 191 at ALS (Advanced Light Source).5.8.17 INSTRUMENTATIONAND SPECTROMETERA typical synchrotron beamline for XAFS measurement(Figure 5.8.32) can be found in a beamlinemanual, 181 where a sample is inserted between5.8.18 SUMMARYX-ray absorption techniques are used in commerciallyavailable film thickness process monitors,which are used in plating, printed circuit and magneticdisk processes. Though these process monitorsare not spectrometers, because only thin film

SUMMARY 427Figure 5.8.32 Ritsumeikan University SR center; 1 m diameter synchrotron radiation facility. Several beamlines are for XAFSspectroscopy. Taken from http://www.ritsumei.ac.jp/se/d11/index-e.htmlPolychromator(curved crystal)qld(a)WE 0Position-sensitivedetector (PSD)fMaskFocusR∆x 0pFrom synchrotronradiation sourcedqCurvedcrystalfFocusp(b)WPSDRSource (bending magnet)CurvedcrystalpR mf Focus R(c)WPSDF 2 F1DispersingmirrorSource (undulator)Figure 5.8.33 Focusing geometry of energy-dispersive set-up (a) and arrangements of optical elements for a bending magnet (b)and an undulator (c). Taken from Oyanagi et al. 182 Dispersed X-rays with different energies are focused at a sample position. Theundulator band width is optimized to match a typical EXAFS scan range, 1 keV. Reproduced by permission of ElectrotechnicalLaboratory

428 X-RAY ABSORPTION TECHNIQUESFigure 5.8.34 A typical in-laboratory EXAFS spectrometer. Taken from the RIGAKU catalogue 183filters are used to select the X-ray wavelengths,they are used in a variety of industries.On the other hand, X-ray absorption spectrometersare used in both laboratories andsynchrotron facilities for basic science, such assurface science, 192,193 cluster chemistry 194 andelectron correlation in transition metal oxides. 167Other applications are in electrodes, 195,196 biologicalsamples, 197 catalysts, 198 especially in situ reactionconditions, 199,200 industrial materials, such asflat panel displays, 201 geological samples 202 andenvironmental analysis. 203 – 205 An unknown chemical,called ‘manganese blue’, has been characterizedby Mn L XANES and concluded to be amixture of Mn 4+ :Mn 6+ = 1:1, which was believedto be Mn 5+ before the XANES analysis. 206A simple method for fabricating uniform andlarge area X-ray absorption filters from powdermaterials has been published. 207The X-ray absorption techniques described inthe present section are summarized using threekey words, namely probe, signal and field. Theprobes used at present are X-rays and electrons;the X-rays are sometimes polarized and sometimestotally reflected. The detected signals aretransmitted X-rays, X-ray fluorescence, electrons,electric currents, and many other measurable signalssuch as ions, reflectivity, and energy selectedX-rays or electrons. The number of fields arebecoming remarkably greater, such as high temperature,high pressure, low temperature, in situchemical reaction, strong magnetic field, applyingan electric potential, short measurement time, andplasma state, using the timescale selection such ascoincidence or delay. New opportunities are proposedfrom time to time. 208 After the absorption ofX-rays, the de-excitation processes we consider areusually X-ray fluorescence and Auger, but nuclearexcitation by electron transition (NEET) has beenactively studied recently. 209 – 211 The NEET is, inother words, a nuclear Auger process. The nuclearenergy level is excited by the inner shell electrontransition. Recently, it was found that theγ -radiation rate was accelerated by the absorptionof X-rays above the absorption edge. This kindof X-ray absorption can be applied to shorten thelifetime of radioisotopes.One of the shortcomings of X-ray absorptionspectroscopy was that absorption spectra of all theelements were not measurable using one beamline.

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Chapter 6New Computerisation Methods6.1 Monte Carlo Simulation for X-ray FluorescenceSpectroscopyL. VINCZE, K. JANSSENS, B. VEKEMANS and F. ADAMSUniversity of Antwerp, Antwerp, Belgium6.1.1 INTRODUCTIONWith the tremendous development of computertechnology – virtually beyond recognition – in thepast few decades, computer simulation has becomea standard tool in solving particle transport problems,approaching in importance the traditionalexperimental and theoretical scientific methods.Computer simulation traces back its origin to thework of Neumann, Ulam and Metropolis in thelate 1940s, when they applied a mathematical techniquethey called ‘Monte Carlo analysis’ to solvecertain nuclear shielding problems which wereeither too expensive to solve experimentally or toocomplicated for analytical treatment (Metropolis,1985). The feasibility of applying analytical techniques,such as the Boltzmann transport equation,for solving photon (or other particle) transportproblems becomes very limited when concerningthe description of real systems in which thetransport phenomena occur. These realistic situations,possibly involving complicated geometrieswith complex boundaries, complex source distributionsor different kinds of particles, most oftencannot be represented with a mathematical modelthat can be treated by analytical techniques. In thisrespect, Monte Carlo (MC) simulation has becomean attractive solution for complicated particletransportproblems.A summary of the most important MC codes forphoton-transport problems with a detailed comparisonof the employed photon scattering models hasbeen given by Fernández (Fernández et al., 1993;Fernández, 1997). Important general purpose MCcodes capable of treating electromagnetic radiationtransport problems are EGS4 (Nelson et al.,1985; Bielajew et al., 1994), MCNP (Briesmeister,1993), ITS (Halbleib, 1992) and GEANT4 (Apostolakis,1999). Especially the low-energy extensionsof EGS4 to its photoelectric and Compton/Rayleighscattering and electron-treatment model make itan appropriate choice for simulating X-ray fluorescence(XRF) experiments (Namito et al., 1998;Hirayama et al., 2000; Namito and Hirayama,1999, 2000). Similarly to dedicated MC models,developed to simulate XRF spectroscopy experiments(Vincze et al., 1995; Vincze, 1995; Ao et al.,1997a; Evans et al., 1998), these extensions includeK and L fluorescence from multielement samples,Compton and Rayleigh scattering of linearly polarizedphotons from bound (atomic) electrons as wellas Doppler broadening in Compton scattering.X-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

436 MONTE CARLO SIMULATION FOR X-RAY FLUORESCENCE SPECTROSCOPYA MC simulation of the complete responseof an energy dispersive (ED) XRF spectrometeris interesting from various points of view. Withrespect to quantification, even simple MC models,which only take the major fluorescent lines ofeach element into account and dispense withsimulation of scattering phenomena altogether,are useful. For example, quantification can beachieved by establishing the X-ray intensitiescorresponding to a number of standard samples viaMC simulation. The composition of the simulatedstandard can be chosen to be close to that ofthe unknown samples so that simple calibrationrelations can be employed. A more complete MCsimulation of an EDXRF spectrometer also coversscattering of the primary radiation and includessecond and higher order effects such as theenhancement of fluorescent lines by higher energyfluorescent or scattered radiation. As phenomenathat contribute to the background of EDXRFspectra can be accounted for (e.g. low energymultiple scattering tails of the scatter peaks inthe case of monochromatic excitation and thescattering of the primary spectrum in the case ofpolychromatic excitation), it is possible to ‘predict’the complete spectral response of an EDXRFspectrometer (Vincze et al., 1999a, 1999b).A significant advantage of the MC simulationbased quantification scheme compared to othermethods, such as fundamental parameter (FP)algorithms, is that the simulated spectrum canbe compared directly to the experimental datain its entirety, taking into account not only thefluorescence line intensities, but also the scatteredbackground of the XRF spectra. This is coupledwith the fact that MC simulations are not limitedto first or second order approximations and toideal geometries.In the past, MC models have been applied inan iterative manner to quantification of XRF datacorresponding to homogeneous or simple heterogeneoussamples in much the same way as otherquantification algorithms based on the fundamentalparameter approach. Relative deviations in therange of 2–15 % have been achieved by the MCquantification scheme, depending on the analysedelement and sample type (Vincze, 1995). Errorsare mostly due to the uncertainties in the physicalconstants (cross-sections, fluorescence yields, transitionprobabilities, etc.) applied in the simulations.Important applications of MC simulations includethe optimization/characterization of in vivoXRF analysis systems in the field of medicalscience. Al-Ghorabie reported on the use of EGS4to aid the design of a 90 ◦ geometry polarizedXRF system for the measurement of cadmiumconcentration in deep body organs such as thekidney (Al-Ghorabie, 1999) and compared theperformance of EGS4 and MCNP for modelingin vivo XRF systems (Al-Ghorabie et al., 2001).Hugtenburg et al. have described the use ofEGS4 to model the measurement of cisplatinuptake with in vivo X-ray fluorescence (Hugtenburget al., 1998) while Lewis et al. used the samecode to aid the design of a polarized source forin vivo XRF analysis (Lewis et al., 1998). The useof a dedicated XRF code CEARXRF for in vivoXRF was demonstrated by Lee et al. who studiedthe possibility of combining K and L XRF methodsfor in vivo bone lead measurements (Lee et al.,2001). The same code was used for the optimizationof in vivo XRF analysis methods for bonelead for a 109 Cd source based K and for an X-ray tube based L XRF spectroscopy system (Aoet al., 1997b). O’Meara et al. used MC simulationmodels to improve the in vivo XRF measurementof renal mercury and uranium in bone (O’Mearaet al., 1998, 2000).While a number of models exist for solvingphoton-transport problems for both unpolarizedand (linearly) polarized incident beams,their direct usability is often limited when dealingwith the case of conventional (X-ray tubebased) or synchrotron radiation XRF on multielementsamples due to the lack of a sufficientlydetailed combination of photoelectric/fluorescenceand scattering models for low X-ray energies. Thecomputer model discussed in this subchapter isoptimized specifically for calculating the results ofsynchrotron radiation induced X-ray fluorescence(SRXRF) experiments not only for homogeneousbut also for heterogeneous samples. Figure 6.1.1shows the generic experimental arrangement thatcan be simulated.

GENERAL FRAMEWORK OF THE MC SIMULATION FOR XRF SPECTROSCOPY 437e −SROPTICSSampleIntensity, counts/counsel10 510 410 310 210 110 0TiAr K10 6 0 5 10 15Fe Zn Pb Pb ScatterpeaksEnergy, keVX-ray beam with known size,divergence, degree of polarization andenergy distributionFluorescenceand scatteringSolid-statedetectorFigure 6.1.1 Generic experimental set-up for synchrotron radiation induced X-ray fluorescence studies for which the MC codeby Vincze et al. (Vincze et al., 1995) is optimizedDetailed description of this code and validationfor X-ray tube excited XRF setups isgiven in Vincze (1995), the case of monochromaticsynchrotron excitation with primary photonenergies below 20 keV (linearly polarizedbeam) is described in Vincze et al. (1995) andthe case of high energy, linearly polarized primarybeams (60–100 keV energy range) is discussed inVincze (1999a,b).In what follows, we will briefly describe thegeneral framework of MC models which arecapable of predicting the spectral response ofEDXRF spectrometers using either conventional orsynchrotron radiation sources. Next, applicationsof MC simulation are presented in the field ofquantitative XRF analysis, calculation of multiplescattering contribution to XRF spectra as wellas the simulation of XRF tomography experiments.6.1.2 GENERAL FRAMEWORK OFTHE MC SIMULATION FOR XRFSPECTROSCOPYA MC code which models photon–matter interactions,simulates the fate of individual photons,from the point where they enter the volume ofinterest with a certain direction and energy tothe stage where they are either absorbed by asample atom or emerge from the sample and areoptionally detected. For a typical XRF experiment,the simulation code must consider the three mostimportant interaction types in the X-ray energyrange of 1–100 keV, i.e. (i) photoelectric absorptionfollowed by XRF or Auger electron emission,(ii) Rayleigh and (iii) Compton scattering.The simulation of these interactions allows thecomplete spectral response of materials subjectedto X-ray excitation in the above energy range tobe built up.A simulated photon can be represented by fiveparameters: its energy (E), propagation vector k,degree of linear polarization p, the plane of polarizationwith respect to a given reference planeand its initial weight factor W . The latter correspondsto e.g. the intensity of the photon beamat the particular energy E in case of a polychromaticincident beam. As the photon undergoesa given interaction, some or all of these photonparameters change and these changes are simulatedon the basis of the appropriate probabilitydensity functions (pdfs) derived from basic atomicdata (cross-sections, fluorescence yields, emissionrates) characterizing the photon–matter interactionprocesses. During the simulation, the photon is raytracedwithin the volume of interest, that is, withinthe solid angle accepted by the detector.

438 MONTE CARLO SIMULATION FOR X-RAY FLUORESCENCE SPECTROSCOPYyr i − 1xz(Θ i , Φ i )(Θ i + 1 , Φ i + 1 )f iS i + 1q ir iS ie i e i + 1r i + 1PFigure 6.1.2 The elemental step of the simulation of the photon trajectory. S i is the distance between two subsequent interactionsoccurring at r i−1 and r i respectively. At r i an interaction with polar angle θ i and azimuth angle φ i occurs, after which the angles i+1 and i+1 characterize the direction of propagation in the laboratory system and ε i+1 denotes the electric field vector of thephoton after the ith interactionThe trajectory of each photon is modeled asconsisting of a number of straight steps. The basiccalculation step is illustrated in Figure 6.1.2.6.1.2.1 SELECTION OF STEP LENGTHA basic element of a simulation is the selectionof distance between the subsequent interactionsby generating the so-called step-length values in away that the produced (pseudo) random sequencesatisfies the well-known exponential attenuationlaw in a statistical sense. Suppose, we have a volumeof interest including a heterogeneous sampleand its surrounding medium, in which the differentphases are separated by distances s j in the directionof propagation of the photon (Figure 6.1.3).These s j distances are calculated by the geometrymodule of the simulation after each interaction forthe given sample topology (Vincze et al., 1999c).The phases of the simulated volume of interest arecharacterized by their linear absorption coefficients{µ j } n j=1at the particular photon energy E.yPhase n + 1, m n + 1 (environment gas)S 1S 2S maxS n − 1 SnPhase n, m nPhase n − 1, m n − 1r 0k 0Phase 1, m 1Phase 2, m 2SamplexFigure 6.1.3 Illustration of the pathlength calculations in two dimensions. The steplength S between the subsequent interactionsat a given photon energy is determined by the pathlength values s i within the different sample phases

GENERAL FRAMEWORK OF THE MC SIMULATION FOR XRF SPECTROSCOPY 439Once the path length values {s j } n j=1withinthe various phases are known, the (pseudo) randomstep length S i , defining the location of thenext interaction, is calculated as follows. First, thelargest index m is found, for which the inequalityholds:m∑µ j s j < − ln(1 − RP abs ) withj=1⎛P abs = 1 − exp ⎝−n∑j=1µ j s j⎞⎠ (6.1.1a)As a second step, S i is calculated according to:m∑(S i = 1 − µ )js j − 1 ln(1 − RP abs )µj=1 m+1 µ m+1(6.1.1b)where R is a uniform random number. It is clearfrom the equation above, that for an infinitelythick homogeneous material (P abs = 1) in whichµ j = µ = constant, Equation (6.1.1b) reduces tothe well-known choice of step-length:S i =− 1 ln(1 − R) ≡−λ ln R (6.1.2)µwhere the λ term is the absorption length of thephoton at energy E i at the beginning of this step.Note that Equation (6.1.1b) does not allow thephoton to escape from the volume of interest evenin case of low-absorption material, which is animportant improvement in terms of the efficiencyof the model. After applying this basic variancereduction technique, preventing the loss of photonsfrom the volume of interest, the weight fraction ofthe photon must be updated with the probabilitythat the photon remains (i.e. absorbed) within thevolume of interest:W = W × P abs (6.1.3)The initial step (i = 0) starts from where thephoton enters the volume of interest (i.e. the solidangle seen by the detector), along the originaldirection of propagation of the photon.In the laboratory coordinate system XYZ, thedirection of propagation is described by two angles( i , i ). At the end of each step, coordinates ⃗r i =(x i ,y i ,z i ), an interaction with a particular type ofsample atom (with atomic number Z) occurs.6.1.2.2 SELECTION OF ATOM TYPEOnce the location of the simulated interactionis determined from Equation (6.1.1a) and (6.1.1b),the next step is to choose the atom type forthe subsequent interaction. In case N differentatomic species constitute the sample material inthis location, each present with a weight fractionof w i and mass absorption coefficient µ ∗ ianinteraction with an atom of species 1 ≤ k ≤ N(atomic number Z k ) is chosen by means of arandom number R so that:∑k−1k∑µ ∗ iw i m i ≤ R< w i m i with m i =N∑i=1i=1w j µ ∗ j6.1.2.3 SELECTION OFINTERACTION TYPEj=1(6.1.4)For photons with energy in the range 1 to100 keV, three interaction types are important:the photoelectric effect, Rayleigh (elastic) andatomic Compton (inelastic) scattering. These interactionscan take place respectively with probabilityτ Z (E i )/µ Z (E i ), σ R,Z (E i )/µ Z (E i ) and σ C,Z (E i )/µ Z (E i ) where µ Z = τ Z + σ R,Z + σ C,Z .Accordingly, the interaction type for atomicnumber Z is chosen as follows:⎧0 ≤ R< τ ZPhotoelectric effectµ ZIf⎪⎨⎪⎩τ Zµ Z≤ R< τ Z + σ R,Zµ ZRayleigh scatteringτ Z + σ R,Zµ Z≤ R

440 MONTE CARLO SIMULATION FOR X-RAY FLUORESCENCE SPECTROSCOPYas the Evaluated Photon Data Library, ’97 Version(EPDL97) by Cullen, Hubbell and Kissel (Cullenet al., 1997).Depending on the type of interaction, theenergy and/or the direction of propagation of thephoton is changed. The change in direction in thelocal coordinate system attached to the photon isdescribed by a polar angle θ i and azimuth angleφ i , as shown in Figure 6.1.2.The orientation in the laboratory system( i+1 , i+1 ) of the next segment (if any) ofthe photon trajectory (from r i to r i+1 ) can thenbe calculated and the coordinates of the nextinteraction point established:x i+1 = x i + S i sin i+1 cos i+1y i+1 = y i + S i sin i+1 sin i+1 (6.1.6)z i+1 = z i + S i cos i+1When the photon is not absorbed at r i+1 (Figure6.1.2) and this location is still inside the volumeof interest, a specific interaction is simulated(see below the simulation of various interactiontypes) after which the next segment of the trajectoryis calculated. In case the photon has escapedfrom the sample and has a direction within thedetector solid angle Det , the content of the appropriatechannel (corresponding to the final photonenergy) is incremented in the equivalent of a multichannelanalyser (MCA) memory. In this way,the energy distribution of the photons just beforethey enter the detector crystal is obtained.6.1.2.4 SIMULATION OFPHOTOELECTRIC EFFECTThis type of interaction causes the original photonto be absorbed. Depending on the relative magnitudeof the shell-specific contributions to µ Z (E i ),in a particular shell s (K, L I , L II , L III ,...) a vacancyis created with the ejection of a photoelectron. Incase of an L shell excitation, the finite probabilityof non-radiative transitions of electrons between Lsub-shells (L i , L j ) is accounted for by the so-calledCoster–Kronig transition probabilities f i,j .A choice between fluorescence or Auger electronemission is made on the basis of the fluorescenceyield ω Z,s of the shell in question. Valuesfor ω Z,s and f i,j are taken from Krause (Krause,1979). In the case of Auger electron production,the trajectory is terminated; for simplicity, it isassumed that the X-ray production due to Augerand photoelectrons is negligible compared to thatby direct fluorescence. Alternatively, in the trajectorycalculation, the photon path can be simplycontinued along a random direction (θ i ,φ i ).The probability of a fluorescent line l originatingfrom a shell s of atom Z can be written as:P Z−sl = ω Z,S × τ Z,sµ Z× p Z−sl (6.1.7)Accordingly, by means of a uniform randomnumber R, a particular line l of a specific shells of atom Z can be chosen which satisfies thecondition:S∑s=0 l=0l∑P Z−sl

GENERAL FRAMEWORK OF THE MC SIMULATION FOR XRF SPECTROSCOPY 441xΓzk 1qe 1 dqafk 0e 0Figure 6.1.4 The coordinate system attached to the photon usedto describe the scattering phenomena. The photon is travelingalong the Z-axis before the interaction (propagation vector k 0 )and its net electric field vector ε 0 is parallel with the X-axis.After the scattering, characterized by the scattering angle θ andazimuth angle φ (indices dropped for clarity), the propagationand net electric field vectors of the photon change to k 0 andε 0 , respectively. From Vincze et al. (1999b), reproduced bypermission of Elsevier Science LtdTable 6.1.1 Simulated fluorescent lines in the MC modelimplemented by Vincze (1995)Shell Transition Siegbahn notationK K-L 3 , K-L 2 K α1 , K α2K-M 3 , K-N 2,3 , K-M 2 K β1 , K β2 , K β3L 1 L 1 -M 2 ,...,L 1 -M 5 L β4 ,...,L β9L 1 -N 2 ,...,L 1 -N 5 L γ 2 ,...,L γ 11L 2 L 2 -M 1 , L 2 -M 4 L η , L β1L 2 -N 1 , L 2 -N 4 L γ 5 , L γ 1L 2 -O 1 , L 2 -O 4 L γ 8 , L γ 6L 3 L 3 -M 1 , L 3 -M 4 , L 3 -M 5 L α3 , L α2 , L α1L 3 -N 1 , L 3 -N 4 , L 3 -N 5 L β6 , L β1,5 , L β2L 3 -O 1 , L 3 -O 4,5L β7 , L β56.1.2.5 SIMULATION OF SCATTERINGINTERACTIONSIn the case where a scattering interaction (Comptonor Rayleigh scattering) is selected by Equation(6.1.5), the change in direction of the photonis sampled on the basis of the appropriate differentialscattering cross-sections dσ/d, which characterizethe angular distribution of the scattered photons.A detailed description of the treatment of thescattering of linearly polarized X-rays is given byseveral authors (Namito, 1993; Vincze, 1995; Mattyet al., 1996; Vincze et al., 1999b). The treatment ofgeneral beam polarization state, including ellipticallypolarized X-ray beams, is given by Fernández(Fernández, 1995a,b, 1996, 1997, 1998a, 1998b,1999, 2000; Fernández et al., 1998).In the following paragraphs, the approachadopted by Vincze et al. (Vincze et al., 1999b)for a linearly polarized photon beam is described,which can be easily implemented in MC calculations.The local coordinate system is chosen insuch a way that the photon beam (having an initialpropagation vector k 0 ) travels along the Z-axisprior to the interaction and its (net) electric fieldvector ε 0 is parallel with the X-axis (Figure 6.1.4).After the scattering event, the new direction ofphoton propagation in the attached coordinate systemis characterized by the (unit) propagation vectork 1 and the (net) electric field vector ε 1 .In case of linearly polarized radiation having adegree of polarization p with respect to the referenceplane XZ (Figure 6.1.4), the expressions forthe Rayleigh (dσ R /d) and Compton (dσ C /d)differential scattering cross-sections are, respectively,given by:dσ Rd (θ,φ,E)= dσ Td (θ, φ)F 2 (x, Z)= r2 e2 [2 − sin2 θ(1 − p+ 2p cos 2 φ)]F 2 (x, Z)(6.1.10)dσ Cd (θ, φ, E) = dσ KN(θ, φ, E)S(x, Z)d( )= r2 e E 2 [ E+ E 02 E 0 E 0 E − sin2 θ]× (1 − p + 2p cos 2 φ) S(x,Z)(6.1.11)where dσ T /d denotes the Thomson and dσ KN /dthe Klein–Nishina differential scattering crosssections(Hanson, 1986). F(x,Z) and S(x,Z) arethe atomic form factor and the incoherent scatteringfunction, respectively (Hubbell et al., 1975),for an element with atomic number Z, x(Å −1 ) =sin(θ/2)E (keV)/12.39 is the momentum transferof the photon and r e is the classical electron radius.

442 MONTE CARLO SIMULATION FOR X-RAY FLUORESCENCE SPECTROSCOPYThe probability that a photon is scatteredwithin a finite solid angle characterized by theangles (θ,θ + dθ; φ,φ + dφ) is calculated by thefollowing equation:f(θ,φ,E)dθ dφ = 1 dσ(θ,φ,E)sin θ dθ dφσ(E) d(6.1.12)where f(θ,φ,E) is the probability density functionof this process at energy E. The integrationof Equation (6.1.12) over φ in the interval [0, 2π]gives the probability that the scattered photon isfound in a spherical section Ɣ characterized by(θ, θ + dθ) (Figure 6.1.4):f(θ,E)dθ = 1 (∫ 2π)dσσ(E) 0 d (θ,φ,E)dφ sin θ dθ= 2π ( ) dσσ(E) d(θ, E) sin θ dθ.U(6.1.13)As a result of the integration over φ, the polarizationdependence drops out (Equation 6.1.5), whichmeans that the probability of scattering into theregion characterized by (θ, θ + dθ) is independentfrom the degree of linear polarization p. As a consequenceof this, the scattering angle θ can besampled on the basis of the differential scatteringcross-sections for unpolarized radiation.By defining the cumulative distribution functionF(θ) for the scattering angle at a fixed photonenergy E as:F(θ,E) = R =∫ θ0f(t,E)dt (6.1.14)the scattering angle can be numerically sampledby θ = F −1 (R, E), whereR is a uniformly distributedrandom number in the interval [0,1]. (SeeVincze 1995) for the details of the selection ofθ for both Rayleigh and Compton scattering forthe unpolarized case. In practice, the F −1 (R, E)inverse cumulative distribution function is precalculatedfor a well-defined energy-random numbergrid for all elements in the atomic numberrange of 1 ≤ Z ≤ 92. An example of suchpre-calculated ‘scattering surface’ is shown forRayleigh scattering on Fe in Figure 6.1.5. The200150q(R, E)100500020Energy (keV)4060Random number800.0 0.2 0.4 0.6 0.8 1.0Figure 6.1.5 Pre-calculated scattering (polar) angle θ(R,E) surface in the energy range of 0 to 80 keV for coherent scatteringby an Fe atom

GENERAL FRAMEWORK OF THE MC SIMULATION FOR XRF SPECTROSCOPY 443scattering angle θ can be chosen by means of asimple bilinear interpolation scheme for a particular(R, E) combination.Once the scattering angle θ is generated fromthe appropriate cumulative distribution functionsfor unpolarized radiation, the azimuth angle φ,which has a non-uniform distribution in the linearlypolarized case, can be calculated as follows.At a given scattering angle θ, the probability P ′that the azimuth angle falls within the interval(φ, φ + dφ) is given by:P ′ (φ, φ + dφ)= 1 A − sin 2 θ(1 − p + 2p cos 2 θ)2π A − sin 2 dφθ(6.1.15)where A = 2 for Rayleigh and A = E/E 0 + E 0 /Efor Compton scattering. It can easily be seenthat the special case of p = 0 (unpolarized beam)yields a uniform distribution which is independentof φ:P ′ (φ, φ + dφ) = 1 dφ. (6.1.16)2πThe term A for Compton scattering can be derivedfrom the well-known expression for the Comptonenergy. The energy E ′ after a Compton scatteringevent of a photon with energy E 0 (withoutconsidering Doppler broadening) is determined bythe scattering angle θ as:[E ′ = E 0 1 + E ] −10m e c (1 − cos θ) (6.1.17)2where m e is the rest mass of the electron and c isthe speed of light.Using Equation (6.1.15), the cumulative distributionfunction for the azimuth angle at a fixedscattering angle θ can be written as:F(φ) = R = 12π[φ −]p sin2 θA − sin 2 θ sin(2φ)(6.1.18)The azimuth angle for a particular random numberR can then be selected by the numerical solutionof φ = F −1 (R).The modeling of a scattering event at agiven photon energy E 0 can be summarized asfollows. First, the scattering angle θ is sampledon the basis of the angular distribution f(θ,E)described by Equation (6.1.13). The correspondinginverse cumulative distribution function (shownin Figure 6.1.5 for Fe as an example) can bepre-calculated for both Compton and Rayleighscattering events for each element present in thesample in order to accelerate the simulation byreducing on-line calculations.After the scattering angle is selected, the correspondingenergy of the scattered photon E 1is determined as follows. For Rayleigh (elastic)scattering during which the energy of the scatteredphoton is preserved E 1 = E 0 is chosen; forCompton scattering Equation (6.1.17) is used todetermine the energy of the inelastically scatteredphoton.In the case of Compton scattering, so far noDoppler has been included in the calculations. Thiseffect is caused by the non-zero momentum of thescattering atomic electrons. In order to take thiseffect into account, the energy E 1 after Comptonscattering is chosen according to:(E0E 1 = E 0 − 2p zE ′ m e c sin θ ) −1(6.1.19)2where E 0 is the photon’s incident energy, E ′ isthe energy calculated by Equation (6.1.17) withoutDoppler broadening and E 1 is the final energyof the scattered photon after considering theDoppler effect.The second term in the above equation refers tothe influence of the momentum p z of the scatteringelectron on the energy-transfer during the Comptonscattering, which can be calculated according to:p z = q m ee 22ε 0 h(6.1.20)where q is the reduced momentum of the scatteringelectron, ε 0 the vacuum permittivity, e the electroncharge and h Planck’s constant. Biggs et al. (Biggset al., 1975) provide numerical values for theprobability density function f Z (q) for every atomicnumber Z. Whenever necessary, a suitable q value

444 MONTE CARLO SIMULATION FOR X-RAY FLUORESCENCE SPECTROSCOPYis chosen based on the distribution f Z (q) by meansof a uniform random number. (See Vincze (1995)for a detailed description of the method.)Once the polar (scattering) angle θ and azimuthangle φ which define the new direction of propagationof the photon, are determined, the degree ofpolarization corresponding to this direction can beobtained as:√[p 0 cos 2φ(cos 2 θ + 1) − sin 2 θ] 2+4p0 2p(θ, φ) =sin2 2φcos 2 θA − sin 2 θ(1 + p 0 cos 2φ)(6.1.21)where p 0 is the degree of linear polarizationbefore scattering.The net electric field vector corresponding tothe new direction, defined by (θ, φ) in the localcoordinate system is given by:⎛1 − sin12 ⎞θ cos 2 φε 1 = √ ⎝ − sin 2 θ sin φ cos φ ⎠1 − sin 2 θ cos 2 φ − sin θ cos θ cos φ(6.1.22)Using Equations (6.1.10)–(6.1.22) we obtain allthe necessary parameters which describe the photonafter a particular scattering event: θ and φ,defining the direction of propagation after theevent, the energy E 1 as well as the degree oflinear polarization p and polarization plane ofthe photon.6.1.2.6 VARIANCE REDUCTIONThe general concept of variance reduction may befound in various standard works. A detailed discussionon the theoretical background of variancereduction techniques in particle transport problemshas been given recently by Milgram (2001). Inorder to escape a formidable or even impracticalamount of simulation work, it is profitable to reformulatethe original problem in such a way that thestatistical uncertainty in the answers is reduced.Fishman (1996) describes variance reduction in thefollowing terms: ‘von Neumann, Ulam and othersrecognized that one could modify the standardMonte Carlo method in a way that produced asolution to the original problem with specifiederror bound at considerably less cost, in terms ofcomputing time, than directly generating the randomtour that corresponded to the original problem’,and then goes on to equate the concept withthe term ‘efficiency-improving technique’, or variancereduction.In case of our present XRF MC model, theoptimized code essentially follows the basic randomwalk of photons within the simulated sample,including the simulation of higher-order phenomena.However, at each interaction point r i , theprobability of every possible pathway for that photonto travel from r i to a point on the detectorsurface (assuming no other interactions along theway) is calculated. This point is selected randomlyon the detector surface. Each pathway is defined toconsist of (i) an interaction process during whichthe direction of propagation (and energy) of thephoton is altered so that it travels towards thedetector and (ii) the path the photon must travel tofinally reach the detector. Scatter-type interactionssimply involve a scattering interaction with a sampleatom; fluorescent-type of conversion consistsof a photo-ionization followed by the emission ofa fluorescent photon in the appropriate direction.In general, the probability P c,Z of a pathwayresulting in detection which involves an interactionwith a sample atom of type Z and a conversion oftype c can be written as:P c,Z = P (conv)c,Z× P (dir)c,Z× P (esc)c,Z(6.1.23)where P (conv)c,Zdenotes the probability for the particularconversion (interaction) process to occur,P (dir)c,Zthe probability of the photon to change itsdirection over the appropriate angles (θ i ,φ i ) withinthe detector solid angle and P (esc)c,Zthe probabilityto escape from the sample when it is traveling inthis direction.During the simulation of a photon history, priorto simulating the next interaction on the trajectory,the probabilities of all possible pathways (andthe corresponding energies) leading to detectionare calculated, as explained above. These pathwayswith probability P c,Z can be thought of as ‘fractionalphotons’ with a final weight fraction equalto W × P c,Z which travel towards the detector.

SIMULATION VERSUS EXPERIMENT 445The arrival of each fractional photon is recordedby adding the weight P c,Z to the content of theappropriate channel of the MCA memory. Onlythen, the next step of the current photon’s trajectoryis calculated.6.1.2.7 DETECTOR RESPONSEFUNCTIONIn order to compare the simulation results withexperimental data, the simulated distributions needto be convoluted with a so-called detector responsefunction. The model proposed by He et al. (1990)was used for this purpose, with values of the empiricalparameters appropriate for the detector thatwas employed. Next to Gaussian peak broadening,the detector response function considers spectralartifacts such as escape peaks, short- and longtermexponential tails of the Gaussian peaks andflat continuum from zero to the full peak energy.An additional artifact being considered is the lowenergyCompton escape contribution, which isclearly visible in case of detected X-rays in the60–100 keV energy range.6.1.3 SIMULATION VERSUSEXPERIMENTA very important step in the development ofany MC simulation is its validation, which canbe done either by comparison of results fromvarious simulation codes (e.g. Al-Ghorabie et al.,2001) or comparing simulated data directly toexperimental results (Fajardo et al., 1998; Vinczeet al., 1999b). The latter validation method isdiscussed in this section.A recently established experimental set-up,called ID18F, at the European Synchrotron RadiationFacility (ESRF) for microscopic XRF isshown in Figure 6.1.6 (Somogyi et al., 2001). Atthis instrument the above-discussed MC simulationcoupled with a sophisticated spectral deconvolutionsoftware provides a no-compromise, generalsolution for the XRF quantification problem (Vekemanset al., 1995, 2002).Two examples of simulated and experimentalXRF spectra measured at this beamline are shownin Figure 6.1.7 for a NIST SRM1832 thin glasscalibration standard and for a NIST SRM1577bBovine Liver biological reference material. Thespectral distributions correspond to monochromaticexcitation by a 21 keV microbeam of 3 ×14 µm 2 . Relative deviations between simulatedand experimental fluorescent line intensities of2–4 % for the glass standard and 1–12 % for themore heterogeneous biological standard have beenachieved (Vekemans et al., 2002), which illustratesthe high potential of the method as an XRF quantificationtool.DiffractionCCD cameram-beamstopSamplem-monitorFocusing devicesFresnel zone plate90°Compound refractivelensAlignmentCCD cameraVideomicroscopeDouble bent multilayermirrorSi(Li) detectorFigure 6.1.6 Schematic illustration of the micro XRF end-station ID18F at the ESRF. Reproduced by permission of John Wiley& Sons from Somogyi et al., 2001

446 MONTE CARLO SIMULATION FOR X-RAY FLUORESCENCE SPECTROSCOPY10 610 5CaVWMnCuIntensity (counts)10 410 310 2SiPArCoBrWRbSrSrMoMo Comp.Rayl.10 00(a)5 10Energy (keV)15 20 2510 610 5Intensity (counts)10 410 310 2 (esc)S ClPKFeMnCa(esc)Cu ZnRbZn BrHgRbPb SePbSrMoComp.Rayl.10 1(b)10 1 010 05 10Energy (keV)15 20 25Figure 6.1.7 Experimental (dots) and simulated (solid lines) XRF spectra of (a) NIST SRM1832 thin glass calibration and(b) NIST SRM 1577b Bovine Liver standard, corresponding to 21 keV excitation at the ESRF ID18F end-station

SIMULATION VERSUS EXPERIMENT 447For higher incident energies, typical simulatedspectral distributions for Al (4 mm thickness) andCu (10 mm thickness) samples, irradiated witha high-energy monochromatic beam of linearlypolarized X-rays, are shown in Figure 6.1.8. Thesespectral distributions were collected at the highenergyscattering beamline BW5 of HASYLAB(Hamburg, Germany) (Schneider, 1995). Here theenergy distribution of the scattered synchrotronbeam is compared with the simulated equivalent inthe case of the two sample matrices. The energyof the incident beam is 80 keV and the degreeof linear polarization is estimated to be 90–91 %(Vincze, 1999b). The figure also shows the individuallycalculated contributions of the various scatteringorders, i.e. the spectral components whichare generated by single, double and higher ordermultiple scattering. The calculation was done up tothe 6th scattering order for Al and the 4th for Cu,above which the contribution of multiple scatteringis negligible to the total scattered distribution.By summing up these scattering orders oneobtains the full spectral response of the irradiatedsample which can be compared directlywith experimental data. The residual values (Figure6.1.9) derived from the simulated and experimentaldata show deviations which are in generalbelow the statistical uncertainties of the experimentalspectrum in the multiple Compton scatterregion of 45–65 keV. In Figure 6.1.9, the statisticaluncertainties are indicated as dashed curves,corresponding to 3σ confidence limits. In thesefigures, σ is the relative standard deviation perchannel content.In the region of the primary/multiple Comptonscattering the agreement between simulationand experiment is considered to be satisfactory inview of the uncertainties of the individual physicalconstants involved in the calculations, the uncertaintiesof the degree of polarization of the primarybeam and that of the angles involved in the excitation/detectiongeometry.In Figure 6.1.8(b), next to the contribution ofRayleigh and Compton scattering, the Cu K linescan also be observed at 8.05 and 8.90 keV. Theratio of these fluorescent lines to the scatterpeaks is correctly calculated by the simulationcode indicating that the assumed degree of linearpolarization (p = 0.91) is a good estimate in thecase of the primary beam available at beamlineBW5 of HASYLAB. It is interesting to note thatthe elevated spectral background in the energyregion of 5–20 keV around the Cu Kα and CuKβ fluorescent lines is also correctly modeled bythe simulation code. This background contributionis mostly attributed to the effect of high energyphotons escaping from the detector after Comptonscattering within the Ge crystal, depositing partof their energy during the inelastic scatteringprocess. As estimated from simulation studies bythe current MC code, the magnitude of suchCompton escape for a high-purity Ge (HPGe)detector is about 2–3 % at incident X-ray energiesof 80 keV.6.1.3.1 VARIATION OF THEDETECTION GEOMETRYFigure 6.1.10 illustrates the change in the spectraldistribution of the scattered radiation as theangle of detection (and therefore also the scatteringangle) is varied. The experimental and simulatedscattered distributions correspond to scatteringangles of 112 ◦ ,90 ◦ and 62 ◦ , obtained froma 2 mm thick polypropylene disk irradiated by an80 keV incident beam. In the case of the simulateddistributions, the higher order scatter contributionsare also shown up to the 6th interactionorder. Note, that in the case of the simulation anarbitrary number of subsequent interactions canbe modeled, however, beyond the 5–6th orderthe final result does not change in a significantway. Next to the evident change in energy of theprimary Compton peak (65.8, 69.2 and 73.9 keVcorresponding to scattering angles of 112 ◦ , 90 ◦and 62 ◦ , respectively), the structure of the multiplyscattered Compton continuum also clearlychanges with the scattering angle. These changesare correctly taken into account by the simulation.Especially the first- and second-order scatter distributionsare influenced by the observation anglewhile this dependence gradually diminishes for thehigher orders. This is understandable, as the multiplyscattered radiation field becomes more andmore isotropic.

448 MONTE CARLO SIMULATION FOR X-RAY FLUORESCENCE SPECTROSCOPY10 5Intensity (counts/channel)10 4 2010 3: Experiment: Full simulation: First order: 2ndCompton: 3rd: 4th: 5th Multiple Compton: 6thRayleigh10 2(a)10 104060 80 100Energy (keV)10 5 Cu: Experiment: Simulation: 1st: 2ndIntensity (counts/channel)10 4 2010 310 2: 3rd: 4thMultiple ComptonComptonRayleigh10 110 00(b)40Energy (keV)60 80Figure 6.1.8 Comparison of experimental (dots) and simulated (solid curves) scattered distributions from (a) an Al disk with athickness of 4 mm and a diameter of 25 mm and (b) a Cu disk with a thickness of 10 mm. The experiment was done using an 80keV incident beam with a degree of linear polarization of about 0.91. Next to the full simulations, the various scattering ordersare also shown up to the 6th order. Reproduced by permission of Elsevier Science Ltd from Vincze et al. (1999b)

SIMULATION VERSUS EXPERIMENT 44910050Relative deviation (%)0+3s−3s−50(a)−1004010050 60Energy (keV)70 80 9050Relative deviation (%)0+3s−3s−50(b)−1004050 60Energy (keV)70 80 90Figure 6.1.9 Relative deviations between the simulated and experimental distributions shown in Figure 6.1.8 for (a) Al and(b) Cu. Here, σ = 1/ √ N denotes the relative deviation corresponding to the statistical uncertainty of the measured channelcontent N. Reproduced by permission of Elsevier Science Ltd from Vincze et al. (1999b)

450 MONTE CARLO SIMULATION FOR X-RAY FLUORESCENCE SPECTROSCOPYRayleigh10 610 1 2040 60: ExperimentCompton: Full simulation10 5: 1st order: 2nd: 3rd: 4th Multiple Compton10 4: 5th: 6th10 3Sb BaSn10 2(a)Energy (keV)Intensity (counts/channel)80 10045°qq = 112°: Experiment: Full simulationCompton10 4: 1st order: 2nd: 3rd Multiple Compton10 3: 4th: 5thRayleigh: 6th10 210 110 0 2040 6080 100(b)Energy (keV)Intensity (counts/channel)Intensity (counts/channel)10 510 51040 602080 100: Experiment: Full simulationCompton10 4: 1st order: 2nd: 3rd10 3: 4th Multiple Compton Rayleigh: 5th: 6th10 210 1(c)Energy (keV)45°qq = 90°45°q = 62°qFigure 6.1.10 Scattered distributions from a 2 mm thick polypropylene disk measured using various detector positions. Theposition of the detector determines the scattering angle θ to be (a) 112 ◦ , (b) 90 ◦ and (c) 62 ◦ . The experimental data are indicatedby the dots and the simulations are shown by the solid line. Next to the full simulations, the various multiple scattering ordersare shown. Reproduced by permission of Elsevier Science Ltd from Vincze et al. (1999b)

SIMULATION VERSUS EXPERIMENT 4516.1.3.2 ESTIMATION OF DEGREEOF LINEAR POLARIZATIONBy means of the simulation model, it is possibleto estimate the degree of linear polarization of theprimary beam from the ratio of known fluorescentline intensities to the primary and multiple Comptonintensity. The fluorescence to Compton scatterratio for given and fixed experimental conditions(fixed incident beam divergence, detector solidangle) and sample is determined by the degree oflinear polarization of the incoming beam, and thisratio is very sensitive to even slight changes of punder 90 ◦ scattering in the plane of polarization.Figure 6.1.11 shows simulated XRF spectra,calculated for different linear polarization valuesfor a 420 µm thick polypropylene standard havingknown trace-element composition (Ca, Fe, Zn).In the simulations, instrumental conditions of theID18F beam line of the ESRF were assumed. Theexperimentally obtained spectral distribution at thisinstrument is also indicated on this graph (dots),corresponding to an excitation energy of 21.1 keV.From the comparison of spectra normalized tothe Zn Kα line, it is clear that the low intensity ofthe Compton scatter peak obtained experimentallyrequires a degree of linear polarization which ishigher than 99 %. The effective degree of linearpolarization of the primary beam available atID18F of the ESRF is estimated to be about 99.7 %by this simple method, which is expected foran instrument installed at a high-brilliance thirdgeneration SR source.A major source of uncertainty of this simplemethod, next to uncertainties in the physical constantsused in the simulation, is the possible errorof the concentration of the employed reference line(Zn Kα in this case) in the test sample. Next to fluorescence/Comptonratio, the multiple-to-primaryCompton ratio can also be used for the estimationof the degree of linear polarization for energeticmonochromatic synchrotron beams (Vincze et al.,1999b). Recently, They et al. have described apolarimeter for synchrotron photon beams basedon the measurement of the angular distribution ofCompton intensities (They et al., 2001).6.1.3.3 PREDICTION OF XRFDETECTION LIMITS FOR RARE EARTHELEMENTSAs an application of the simulation code, theimprovement of detection limits (DLs) is calculatedfor K-line based XRF analysis of rare earth10 510 4FeZnSingle + multiple comptonRayleighP = 95%Intensity (counts)10 310 2BrSrP = 99%P = 100%10 110 0 510 15Energy (keV)20 25Figure 6.1.11 Calculated spectral distributions corresponding to the spectral response of a polypropylene standard of 420 µmthickness for various degree of linear polarization of the incident beam. The experimentally recorded XRF spectrum, measuredat the ID18F end-station of the ESRF is shown by the dotted curve. The latter corresponds to a degree of linear polarization ofp>99.5%

452 MONTE CARLO SIMULATION FOR X-RAY FLUORESCENCE SPECTROSCOPY: Experiment10 4: SimulationComptonIntensity (counts/channel)10 5 4510 310 210 110 0CsBa Ce Nd Sm Gd Dy Ho Er Tm Yb Lu Hf TaTbWPrLaEuMonochromatic excitation (E 0 = 80 keV)White beam excitation(a)10 −1 304050Energy (keV)60 70100.0: Experiment (E 0 = 80 keV): Simulation (E 0 = 80 keV): Simulation (white beam)10.0DL (ppm)1.0(b)0.1505560Atomic number65 70Figure 6.1.12 (a) Experimental (dots) and simulated (solid lines) spectral distributions corresponding to monochromatic (80 keV)and white beam excitation measured from a 3 mm thick NIST SRM 612 glass standard indicating the energy region of REE Kfluorescence lines. The simulated and experimental spectra corresponding to the white excitation are scaled down by a factorof 100 for visual clarity (b) Detection limits corresponding to mono (80 keV) and polychromatic (bending magnet, white beam)excitation modes as calculated by the simulation code. The experimentally determined DLs corresponding to the monochromaticprimary beam are also shown. Reproduced by permission of Elsevier Science Ltd from Vincze et al. (1999b)

MODELING OF XRF ON HETEROGENEOUS SAMPLES: SIMULATION OF XRF TOMOGRAPHY 453elements (REEs) when an 80 keV monochromaticexcitation is employed instead of white incidentradiation, such as available at the SRXRFspectrometer installed at Beamline L, HASYLAB(Lechtenberg, 1996). The calculation of DL valuesrequires the reliable estimation of both fluorescenceline intensities of interest and the backgroundlevel which, at the high X-ray energiesin question, are determined mainly by singleand multiple Compton scattering. In the case ofmonochromatic excitation tuned above the absorptionedges of the examined elements, the fluorescencelines of interest are separated in energyfrom the primary Compton and Rayleigh scatterpeaks. Even though at the incident energy of80 keV the multiple Compton scattering region(35–65 keV) overlaps with the characteristic linesof REE, there is still a significant improvementin terms of peak-to-background ratios when comparedto the white beam excitation. In the caseof the latter, the fluorescence lines are superimposedon the scattered primary and multipleCompton/Rayleigh continuum without anyenergy separation.In the following calculations, the estimation ofDL values for the elements in the atomic numberrange of 47–68 is based on simulated spectrafrom the glass calibration standard NIST SRM612 (3 mm thickness) corresponding to the aboveexcitation modes. In Figure 6.1.12(a) simulatedand experimental SRXRF spectra of this standardare compared for an 80 keV incident beam and forwhite beam excitation.For the simulation of the monochromatic casethe parameters of beamline BW5 and for the polychromaticsituation the parameters of the bendingmagnet source of Beamline L of HASYLABwere used. For clarity, the spectrum correspondingto this source was scaled down by a factorof 100. In Figure 6.1.12(b), experimentally determinedand calculated DL values for both modesof excitation are compared. All simulated spectraused in these calculations were normalized toan integrated intensity of 1.10 × 10 6 which wasrecorded experimentally at Beamline BW5 using alive time of 1000 s, corresponding to a count rate of1100 s −1 . In both simulated cases (i.e. mono- andpolychromatic excitation) a degree of polarizationof 91 % was assumed.Overall, a very good agreement is foundbetween experiment and theory. As shown inFigure 6.1.12(b), the DLs in case of the monochromaticexcitation are in the range of 0.5 to 1 ppm forthe elements Nd (Z = 60) to Er (Z = 68). TheseDLs are nearly an order of magnitude lower thanthose obtained for the polychromatic incident beamassuming the same counting conditions in whichcase the DLs are situated in the 2–10 ppm range.It is clear from Figure 6.1.12 that the simulationmodel discussed in this work can reliably beused for estimating the analytical characteristicsof SRXRF spectrometers operating in the incidentenergy range of 60–100 keV.6.1.4 MODELING OF XRF ONHETEROGENEOUS SAMPLES:SIMULATION OF XRF TOMOGRAPHYMany applications of microscopic XRF aim tostudy the heterogeneity of the analysed materials,i.e. two- or three-dimensional distributionof chemical elements, such as heavy metals indifferent environmental, geological and biologicalsamples. Owing to its high sensitivity andnon-destructive nature, synchrotron radiation basedmicro XRF computed tomography (XFCT) is oneof the emerging methods of providing potentiallythree-dimensional, quantitative information on theelemental distribution in the probed sample volumewith trace-level DLs (Bohic et al., 2001;Simionovici et al., 2001; Vincze et al., 1999c,2002a). The technique can be easily performed ona regular scanning micro XRF set-up with the additionof a sample rotation stage to the usual xyzlinear stages (Janssens, 1998).By performing repeated line scans at a fixedsample-height under a large number of observationangles (i.e. taking different views of thesample) around a given sample axis and recordingthe emerging fluorescent and scattered signals,the conventional X-ray fluorescent mappingis replaced by a XFCT experiment. In this wayone obtains a special representation of the elementalintensity distributions across the investigated

454 MONTE CARLO SIMULATION FOR X-RAY FLUORESCENCE SPECTROSCOPYcross-section of the sample, called elemental sinograms.The usual two-dimensional elemental distributionin the investigated horizontal sample plane(i.e. the tomographic plane perpendicular to thevertical rotation axis) is obtained by a mathematicalreconstruction procedure called filtered backprojectionalgorithm (Russ, 1995).In Figure 6.1.13 an example of the type ofheterogeneous sample which can be simulated isshown. The horizontal cross-section of the sampleis divided into several phases having boundariesof arbitrary polygonal and circular shape. Thesample composition does not change in the verticaldirection. This invariance along the vertical axisimplies that the simulated object is only quasithree-dimensional and so the simulated trajectoriesare dependent only on the horizontal and not on thevertical coordinates.Figure 6.1.14 shows XRF microtomographyresults taken from a phantom sample of threeattached glass capillaries filled with 1 % solutionsof Mn, Ni and As (Figure 6.1.14a), which were usedto verify and validate the simulation code for heterogeneoussample types. The experimental datawere collected at HASYLAB, Beam line L. Therecorded sinograms (Figure 6.1.14b) correspond to100 translation steps of 6 µm and 180 rotation stepsof 2 ◦ , with a live time of 10 s per point.The reconstruction of the displayed tomographicdata sets was done by a filtered backprojectionalgorithm, without using self-absorptioncorrections. This results in a clearly poorerxzPolygonboundaryX-Raysourcex’SRz’EllipticalboundaryFigure 6.1.13 An example of the modeled heterogeneoussample, containing heterogeneities of polygonal and/or circularboundariesqy’y(a)180 × 2°10 µmbeamMnNiAsDetectorCa Mn Ni As SrSinogramsReconstructionCa Mn Ni As Sr100 × 6 µm(b)Figure 6.1.14 (a) Phantom sample of three attached glasscapillaries filled with 1 % solutions of Mn, Ni and As,which were used to verify and validate the simulation codefor XRF microtomography on heterogeneous sample types.The experimental data were collected at HASYLAB, Beamline L. The recorded sinograms and reconstructed images(b) correspond to 100 translation steps of 6 µm and 180rotation steps of 2 ◦ , with a live time of 10 s per point.Reproduced by permission of SPIE from Vincze et al. (2002a)reconstructed image for Ca Kα (E Kα = 3.69 keV)when compared to the reconstruction of e.g. Sr Kα(E Kα = 14.16 keV) even though Ca and Sr havethe same spatial distributions (glass walls). Lowenergylines suffer from sample self-absorption,which can be accounted for by appropriate reconstructionalgorithms. Several methods exist to correctfor the attenuation of both primary and fluorescentX-rays within the sample matrix (Schroer,2001; Simionovici et al., 2001), however, the useof these algorithms is beyond the scope of thepresent subchapter.Figure 6.1.15 shows a comparison of experimentaland simulated sinograms and reconstructedimages for Ca and Sr (both of which are presentin the glass capillary walls), indicating that the

QUANTITATIVE TRACE-ELEMENT ANALYSIS OF INDIVIDUAL FLY ASH PARTICLES 455Experiment Simulation ReconstructionSrSr100 × 6 µmCaCa180 × 2°Figure 6.1.15 Comparison of experimental and simulated sinograms as well as reconstructed images for Ca and Srsimulation code can describe adequately the sampletopology represented by the particular phantomsample shown in Figure 6.1.14(a). The fact thatboth sinograms and reconstructed images can bereproduced from the simulated data set indicatesthat the numerical model for the heterogeneoussystem approximates well the topology of the samplein question.6.1.5 QUANTITATIVETRACE-ELEMENT ANALYSIS OFINDIVIDUAL FLY ASH PARTICLESIn this section we focus on micro XRF spectroscopycoupled with MC simulation as a usefulanalytical tool for determining the sample compositiondown to trace concentration levels. Themethod is appreciated for its high sensitivity, nondestructivenessand because of its simple relationto the fundamental physics of atom – radiationinteraction.Several papers have appeared on the applicabilityof microscopic XRF for the analysis of particulatematter without aiming to determine traceelement concentrations quantitatively (Török et al.,1994; Rindby et al., 1997). Lankosz and Pellaapplied recently the fundamental parameter (FP)method for quantitative XRF analysis of individualparticles having irregular shapes, but only for majorand minor elements (Lankosz and Pella, 1997).The theoretically derived calculations were verifiedby analysis of standard glass particles with knownstoichiometry and an agreement within 3–10 % wasfound between calculated and nominal concentrations.The measurements were performed using anX-ray microbeam with 177 µm diameter.Generalized iterative procedures based on FPfor quantitative XRF analysis were published(Szalóki et al., 1999). In general, the estimation ofthe matrix attenuation for the iterative calculationis based on the average atomic number of thesample matrix. The procedure offers a wideranging extension for quantitative standardlessXRF analysis of complex samples, especiallyfor environmental and biological materials. Incontrast to these methods, our approach uses theMC technique.The quantification method presented belowis based on MC simulations for dealing withthe energy and spatial distribution of the X-raymicrobeam, the interaction between the excitingphotons and the sample elements taking intoaccount the geometry effects caused by the sizeand topology of the particles. The applicability ofthe method is demonstrated on fly ash particlesbecause they are common atmospheric particleshaving relatively elevated concentrations of sometoxic elements (Vincze et al., 2002b).6.1.5.1 THE QUANTIFICATIONALGORITHMThe concentration values are calculated by an iterativeMC simulation method taking into account not

456 MONTE CARLO SIMULATION FOR X-RAY FLUORESCENCE SPECTROSCOPY1000Intensity (counts/channel)10010ClSArKK + CaMnTi CrFeNiCuZnScatt.(a)10 5 10 15Energy (keV)10000Intensity (counts/channel)100010010KArSi SCaFeTiV CrZnAsScatt.(b)10 5 10 15Energy (keV)Figure 6.1.16 Measured (dots) and simulated (solid lines) XRF spectra obtained by the X-ray tube based set-up for typical wood(a) and coal (b) fly-ash particles. Reprinted with permission from Vincze et al. (2002b). Copyright 2002 American ChemicalSocietyonly self-absorption within a spherical particle, butalso more subtle higher-order effects, such as interelementenhancement, or fluorescence induced byin-sample scattering. In order to get the initialconcentration values, necessary to start the iteration,self absorption was neglected as a first step.The initial concentration of element i, C i,0 withdetectable X-ray line was calculated as:⎛I i,meas /S iC i,0 = ∑ nj=m+1 I × ⎝1 −j,meas/S jm∑j=1C j⎞⎠(6.1.24)where n is the total number of elements in the sample,and the first m elements constitute the darkmatrix (which can be derived from stoichiometryor known from other, bulk measurements), I i,measthe experimental intensity and S i the experimentallydetermined sensitivity factor for element i.As a second step, the above detailed MC simulationcode is used to iteratively refine the initial concentrationvalues. The iterative procedure to refinethe concentration of each element is given by:C (k+1)i= C (k)i·I i,calc · ∑nI i,measj=1 C(k) j·Ij,measI j,calc(6.1.25)

QUANTITATIVE TRACE-ELEMENT ANALYSIS OF INDIVIDUAL FLY ASH PARTICLES 45710 610 5Intensity (counts)10 410 310 2Fe NiMnZnKCaPbCl ZnPbTiBr RbSrYZrMo Ag Cd Sn BaSb Sn10 1SeNb10 00 10 20 30 40(a)Energy (keV)10 610 5CaFeIntensity (counts)10 410 310 2SKMnTiCrNi As+PbSrZn Rb ZrSe YNbBa10 1Cu10 00 10 20 30 40(b)Energy (keV)Figure 6.1.17 Experimental (dots) and simulated (solid lines) SRXRF spectra of the individual wood (a) and coal (b) fly-ashparticles. Reprinted with permission from Vincze et al. (2002b). Copyright 2002 American Chemical Societywhere C (k)iis the calculated concentration of elementi after k iteration steps.The procedure is terminated, if either of thefollowing conditions are met:|C (k+1)ii=1− C (k)i|

458 MONTE CARLO SIMULATION FOR X-RAY FLUORESCENCE SPECTROSCOPYof 100 individual coal and wood fly ash particles,originating from Hungarian power plants, isdetermined by the above-described iterative MCquantification method.In Figure 6.1.16 measured and simulated XRFspectra (corresponding to the final iteration stepof the MC calculation) of a typical coal andwood fly ash particle are shown, measured by amono-capillary based laboratory micro-XRF setup.This instrument is installed at the Universityof Antwerp (UIA) making use of a high-powerrotating anode Mo X-ray tube (Janssens et al.,1996). The agreement between the measured andsimulated spectra is satisfactory for both typesof fly-ash particles, both with respect to thefluorescence line and scatter peak intensities.The trace element content of the fly-ash particleswas determined from the micro-SRXRF measurementsat HASYLAB Beam line L.In Figure 6.1.17 two examples of simulated(result of the final iteration) and measured spectracorresponding to the two types of particleare shown. Using the elemental composition ofthe (low-Z) fly ash matrix, determined from thetube-excited measurements, the trace element contentof each individual fly-ash particle could bedetermined and the results are summarized inTable 6.1.2.In Table 6.1.3, the average minor and majorelemental concentrations and the variation in theparticles of the wood and coal fly ash particlesdetermined on the basis of 40 wood and 60 coal flyash particles are shown. The same major elementscould be detected in both types of fly ash and theseelements are visible in most of the particles. Themajor element concentration ratios are differentin the two cases: in the case of wood fly ash ahigher concentration of S and Cl can be detected(originating from the organic component of thewood) while in case of the coal fly ash the amountof elements characteristic to the mineral such as Si,Ca, Fe is larger. In the case of coal fly ash a highernumber of potentially hazardous trace elements,e.g. Cu, As, Pb, are detected. The variation of theelemental concentrations is large for both typesof particles showing the highly inhomogeneousnature of the ash material.Table 6.1.2 Major and minor element concentrationsof a typical wood and coal fly ash particlewith corresponding experimental and simulatedspectra shown in Figure 6.1.5(a). The calculatedconcentrations were obtained by assumingρ = 0.5g/cm 3 density and 50 % carbon residualmatrix for the wood fly ash and by assumingρ = 2.6g/cm 3 and ρ = 1.0g/cm 3 density valuesfor the coal particle aElementCoal fly ashcalc. conc. (%)Wood fly ashcalc. conc. (%)O a 47 10Si 26 –S 8.3 5Cl – 7K 1.7 20Ca 12.0 2.1Ti 0.9 0.3Cr 0.05 0.1Mn 0.07 0.05Fe 4.8 1.3Ni – 1.8Cu – 0.2Zn 0.05 0.5a Concentration value of oxygen was calculated fromstoichiometric considerations.Table 6.1.3 Trace element concentrations inan individual wood and coal fly ash particle,whose spectra are shown in Figure 6.1.6(a)and 6.1.6(b). In the case of the wood fly ash,a residual matrix consisting of 50 % C anda density of 0.5 g/cm 3 was assumed whilein the case of the coal fly ash a density of1.0 g/cm 3 was usedElementWood fly ashconc. (ppm)Coal fly ashconc. (ppm)Se 21 53Br 238

REFERENCES 459viable in view of the rapid increase of inexpensivecomputing power and because of the availabilityof accurate atomic data for photon–matterinteractions. By considering the three most importantinteraction types in the 1–100 keV energyrange (photoelectric effect followed by fluorescenceemission, Compton and Rayleigh scattering)such models can be used in a general fashion topredict the achievable analytical characteristics offuture (SR)XRF spectrometers and to aid the optimization/calibrationof existing instruments.With an efficient combination of sampling andvariance reduction techniques in a given MCmodel, the complete spectral response of heterogeneousmulti-element samples irradiated with apolychromatic (optionally linearly polarized) X-ray beam can be simulated using a CPU time in theorder of minutes on a typical personal computer.For monochromatic excitation, the calculation timeis in the order of a few seconds.The code illustrated in this subchapter has beenexperimentally verified by comparisons of simulatedand experimental spectral distributions ofsamples of various nature, recorded at differentSRXRF spectrometers. As the code could reliablypredict both the fluorescent and scattered intensitiesin the measured fluorescent spectra, it has beenapplied to determine unknown sample characteristics,such as the sample composition. The latterwas estimated by the (reverse) iterative use of thecode, which provides an alternative for the quantitativeanalysis of unknown samples next to thetraditional FP methods.The code could also be successfully used toestimate unknown primary beam characteristics,such as the degree of linear polarization, which isan interesting application for the characterizationof existing SRXRF instruments.With respect to the simulation of heterogeneoussamples, an example was given for the modelingof XRF tomography experiments. The simulationof such lengthy XRF imaging experimentsis extremely important for performing feasibilitystudies and optimization before the actual measurementis performed.Potential future development for MC codesspecific for EDXRF spectroscopy includes theextension of the simulated energy range below 1keV and the refinement of the employed physicalmodels serving as the engine for the simulationmodel. On the one hand, there is a general necessityto select the most up-to-date atomic constants(X-ray cross-sections, fluorescence yields, emissionrates, etc.) in order to increase the accuracyof the simulated results. And, on the other hand,to improve the validity of background modelingin the case of highly polarized monochromatic X-ray sources.One of the important effects, determining thespectral background in the case of XRF experimentsperformed at third generation synchrotronsources employing highly polarized monochromaticexcitation is the bremsstrahlung emission byenergetic photoelectrons (and to a lesser extentAuger electrons) produced during photoelectricinteractions. The simulation of these processesrequires the modeling of electron transport phenomena,which have been implemented only inthe most general MC codes for particle transportproblems (e.g. EGS4, MCNP). As these generalpurposecodes often cannot be used directly formodeling EDXRF spectra efficiently, there is ageneral need to further develop specific MC codesfor XRF spectroscopy.Next to electron bremsstrahlung, another importanteffect contributing to the spectral responseof samples illuminated with highly monochromaticsynchrotron radiation is resonant RamanX-ray scattering, which is currently under implementationin the simulation model described inthis subchapter.REFERENCESAl-Ghorabie,F.H.H. Radiat. Phys. Chem. 55, 377–384(1999).Al-Ghorabie,F.H.H., Natto,S.S.A. and Al-Lyhiani,S. H. A. Comput. Biol. Med. 31, 73–83 (2001).Ao, Q., Lee, S. H. and Gardner, R. P. Appl. Radiat. Isot. 48,1403–1412, (1997a).Ao, Q., Lee, S. H. and Gardner, R. P. Appl. Radiat. Isot. 48,1413–1423 (1997b).Apostolakis, J., Giani, S., Maire, M., Nieminen, P., Pia, M. G.and Urban, L. GEANT4 Low Energy ElectromagneticModels for electrons and photons. CERN-OPEN-99-034,preprint, 1999.

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6.2 Spectrum EvaluationP. LEMBERGEUniversity of Antwerp, Antwerp, Belgium6.2.1 INTRODUCTIONSpectrum evaluation essentially comprises themathematical procedures to extract relevant informationfrom acquired X-ray spectra. Apart fromsmoothing and peak search methods, the mostimportant aspect is, beyond doubt, the extractionof the analytically important net peak areas of theelement characteristic fluorescence lines.Spectrum evaluation remains a crucial step inX-ray spectrometry and can be considered asimportant as sample preparation and quantification.Due to the relatively low resolution of solid-statedetectors, spectrum evaluation is certainly morecritical to energy-dispersive X-ray spectrometry(ED-XRF) than to wavelength-dispersive X-rayspectrometry (WD-XRF). However, the oftenquotedinferior accuracy of ED-XRF can, to alarge part, be attributed to errors associated withthe evaluation of these spectra. Although ED-XRFlacks the precision of WD-XRF, a correct spectrumevaluation improves the accuracy of ED-XRF tothe same or even higher level than WD-XRF. Thisis also important from an economical perspective,i.e. in many industrial applications the moreexpensive WD-XRF systems might be replaced orbacked-up by cheaper and more versatile ED-XRFinstruments. To achieve this, the precision ofED-XRF is to be improved while the analysis timeshould remain comparable to WD-XRF.As discussed in the chapter on new detectortechnologies, the ever-expanding computer andchip industry has also triggered the developmentof Si-PIN photodiodes and semiconductor driftdetectors (SDD) or drift chambers (SDC). Theversatility of the Integrated Circuits (IC) productionapparatus made it possible to manufacturethese detectors of high quality at low cost. Suchdetectors can handle a much higher count rate thanSi(Li) or HPGe/Ge(Li) detectors (Gatti and Rehak,1984; Murty et al., 1998; Castoldi et al., 2000).At the same time, the introduction of digital signalprocessing (DSP) further improved the countrate and made it possible to operate solid-statedetectors at high dead-times while preserving thepeak shape of the characteristic lines in the spectrum(Jordanov et al., 1994). In the early 1970swhen the first commercial ED-XRF systems basedon Si(Li) detectors became available the maximalcount rate was about 10 kcps. Over the past fewyears, count rates of 50 kcps to 100 kcps are nolonger exceptional.With an increased count rate and hence a betterprecision, more details (e.g. the Lorentz characterof characteristic lines) as well as specificfeatures of the spectrum (e.g. peak tailing andincomplete charge collection) become apparent.The simple fitting model used in the past to evaluatespectra should therefore be improved andextended to describe all the aspects of the spectrum.Until now, such a complex model requiringmany parameters demanded too much processingpower of the computer attached to the instrument.Today, the availability of inexpensive andpowerful personal computers enables the implementationof mature spectrum evaluation packagesbringing sophisticated spectrum evaluationwithin reach.X-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

464 SPECTRUM EVALUATIONThe previous subchapter already indicated thatan ED spectrum is in fact the original spectrum,as it reaches the detector, convoluted with theresponse function of this detector. In this respect,spectrum evaluation is also known as spectrumdeconvolution. The Monte Carlo (MC) simulationcode also relies on an accurate detector responsefunction to deliver, through convolution, a closeagreement between simulated and experimentalspectrum. The ability to simulate X-ray spectrathat agree very well with measured spectra opensthe possibility to use them as standards for newquantification methods.The various methods for spectrum evaluationdiscussed in this subchapter emphasize ED X-rayspectra. Most of the methods are relevant forX-ray fluorescence (XRF), particle-induced X-rayemission (PIXE) and electron beam X-ray analysis(electron probe X-ray microanalysis (EPXMA),scanning electron microscopy - energy dispersiveX-ray analysis (SEM-EDX) and analytical electronmicroscopy (AEM)). A complete and detailed texton every aspect of spectrum evaluation can befound elsewhere (Van Espen, 2002).6.2.2 SIMPLE NET PEAK AREADETERMINATIONFor both WD-XRF and ED-XRF, the concentrationof an element is proportional to the number ofcounts under the characteristic X-ray peak of theelement, corrected for the continuum. Providedthat the resolution is constant, this proportionalityextends to the entire net peak height. Due tothe inherent nature of the ED-XRF to detectX-rays simultaneously, preference is given tothe peak area. In WD-XRF the detection ofX-rays is a sequential process. Acquisition ofthe entire peak profile is very time-consumingand pointless except when detecting low-energyX-rays where the resolution is inadequate dueto the limited ability of the crystal to dispersethe X-rays. In such a case, peak integration isadvisable. For higher X-ray energies, the countrate is measured only at the peak maximum.To utilize the count rate at the 2 angle ofthe peak maximum as the analytical signal, itshould be corrected for the continuum. Thecontinuum is estimated at a 2 position onthe left- and right-hand side of the peak. Thisstraightforward method is sufficiently adequate toobtain both accurate and precise results. For now,improvement of this procedure is not considerednecessary.In ED-XRF, a closely related method to obtainthe net area of an isolated peak in a spectrumconsists of interpolating the continuum underthe peak and summing the channel contents(corrected for the continuum) in a window overthe peak. This method can only be used forpeaks that are free from interferences whilethe continuum should be linear over the extentof the region taken into consideration. Becauseof these restrictions, a simple peak integrationmethod cannot be used as a general tool for theevaluation of ED-XRF spectra and good resultsare obtained in a limited number of applicationsonly. At present, application of this method hasbecome rare.6.2.3 LEAST-SQUARES FITTINGUSING REFERENCE SPECTRAA much more robust technique is the least-squaresfitting method using reference spectra. The referencespectra are measured or calculated spectra ofpure compounds. A spectrum of an unknown sampledescribed as a linear combination of pure elementspectra can be formulated mathematically asy modi =m∑a j x ij (6.2.1)j=1in which yimod stands for the content of channeli in the model spectrum and x ij the content ofchannel i in the jth reference spectrum. Thecoefficients a j represent the contribution of thereference spectra to the unknown spectrum and canbe used for quantitative analysis. The values of thea j coefficients are found via multiple least-squarefitting. During the fit the sum of weighted squareddifferences between the measured spectrum and the

LEAST-SQUARES FITTING USING ANALYTICAL FUNCTIONS 465model are minimized. This object function, χ 2 ,iswritten asχ 2 ==1i 2 − i 1 + 1 − m1i 2 − i 1 + 1 − m∑i 21σ 2i=i 1ii 2∑1σ 2i=i 1i(y i − y modi ) 2(y i −)∑i 22a j x iji=i 1(6.2.2)with y i the content of channel i and σi2 the varianceat channel i, normally taken as σi2 = y i (Poissonstatistics). Channels i 1 and i 2 are the beginning andthe end of the fitting region.The approach assumes that a measuredspectrum can be described as a linear combinationof pure element spectra. This assumption holdsto some extent for the characteristic lines in thespectrum but is not valid for the continuum.Therefore, prior to the least-squares fitting thebackground must be removed. A frequently usedapproach is the application of a digital filter toboth unknown and reference spectra. This variantis known as the filter-fit method (Schamber,1977; Statham, 1978; McCarthy and Schamber,1981). The continuum can also be estimated bypeak stripping or using polynomial functions asdiscussed later.The advantage of using reference spectra is theability to deal with a complex and difficult tomodel continuum. On the other hand, when netintensities of small peaks in the vicinity of verylarge peaks are to be derived, the method is lessoptimal. The filter-fit and related methods are stillavailable in some software packages. Recently,no further research has been done in this area ofspectrum evaluation.6.2.4 LEAST-SQUARES FITTINGUSING ANALYTICAL FUNCTIONSA widely used and certainly the most flexibleprocedure for evaluating complex X-ray spectra, isbased on least-squares fitting of spectral data withan analytical function. The method is conceptuallysimple, but not trivial to implement and use.6.2.4.1 CONCEPT OFSPECTRUM FITTINGIn least-squares fitting of spectral data an algebraicfunction or fitting model, including analyticallyimportant parameters, such as the net areas ofthe fluorescence lines, is used to describe themeasured spectrum. Chi-square, χ 2 ,isdefinedasthe weighted sum of squares over a certain regionof the spectrum, i 1 to i 2 , of the differences betweenthe model and the measured spectrum y i :χ 2 =1i 2 − i 1 + 1 − mi 2∑1σ 2i=i 1i× [y i − y(i,a 1 ,...,a m )] 2 (6.2.3)again with σi2 the uncertainty of the measuredspectrum, and a j are the parameters of the model.The optimum values of the parameters are thosefor which χ 2 reaches a minimum. They can befound by setting the partial derivatives of χ 2 tothe parameters to zero:∂χ 2∂a j= 0 j = 1,...,m (6.2.4)If the model is linear in all the parameters a j ,theseequations result in a set of m linear equations in munknowns a j , which can be solved algebraically.This is known as linear least-squares fitting. If themodel has one or more nonlinear parameters nodirect solution is possible and the optimum valueof the parameters must be found by iteration. Thelatter is known as nonlinear least-squares fitting.The selection of a suitable minimization algorithmis important because it determines to a largeextent the performance of the method. In most ofthe software packages the Marquardt–Levenbergalgorithm is used (Levenberg, 1944; Marquardt,1963).The difficulty with this method is to find analgebraic function that accurately describes theobserved spectrum or at least the spectral regionof interest. This requires a model describing thecontinuum, the element characteristic lines and allother features present in the spectrum. Thoughthe response function of the solid-state detector

466 SPECTRUM EVALUATIONis, to a very good approximation, Gaussian, thedeviation from the Gaussian shape needs to betaken into account. An inaccurate model will resultin systematic errors, which may lead to grosserrors in the estimated peak areas and ultimatelythe element concentrations. On the other hand,the fitting function may not become too complexand preferably use few parameters. Especially fornonlinear fitting, the location of the χ 2 minimum isdemanding on the computing power when a largenumber of parameters is involved.During the last decade much of the researchin this field has been focused on the developmentof a model including a Gaussian and some extrafunctions to describe the deviation from the idealGaussian and has also increased the number ofparameters. This evolution was not possible untilthe availability of cheap and powerful PCs. Before,the deviation from the Gaussian peak shape wastaken into account numerically. This method isonly satisfying when applied for similar detectors.With the availability of detectors different fromthe original Si(Li) and Ge detectors, spectrumevaluation required more flexible models.In general, the fitting model consists of twoparts; the first part describes the continuumwhile the second part deals with the elementcharacteristic lines and other peak-like features:Peaks∑y(i) = y Cont (i) + y P (i) (6.2.5)P =1where y(i) is the calculated content of channel i.6.2.4.2 THE CONTINUUMSeveral functions can be used to describe thecontinuum, depending on the excitation conditionsand on the width of the fitting region. Since itis almost impossible to construct an acceptablephysical model describing the continuum, in mostcases some kind of polynomial expression isused. An exception, worthwhile to be mentioned,is the case of electron microscopy where aBrehmsstrahlung continuum is observed. This canbe modelled with an exponentially decreasingfunction according to Kramer’s formula, correctedfor the absorption by the detector windows and bythe sample. To be physically correct, the absorptionterm must be convoluted with the detector responsefunction, because the sharp edges due to absorptionby detector windows or elements present in thesample are smeared out by the finite resolution ofthe detector.6.2.5 LINEAR AND EXPONENTIALPOLYNOMIALSA linear polynomial is defined asy Cont (i) = a 0 + a 1 (E i − E 0 ) + a 2 (E i − E 0 ) 2+···+a k (E i − E 0 ) k (6.2.6)with E i the energy (in keV) of channel i and E 0a suitable reference energy, often the middle ofthe fitting region. The user is allowed to choosethe degree of the polynomial, k. k = 0 producesa constant while k = 1 produces a straight lineand k = 2 a parabolic continuum. Values largerthan k = 4 are rarely useful because such highdegreepolynomials tend to have physical nonrealisticoscillations. Linear polynomials are used todescribe the continuum over a region of 2 to 3 keVwide. Wider regions usually exhibit too much curvatureand can be modelled by an exponentialpolynomial instead:y Cont (i) = a 0 exp[a 1 (E i − E 0 ) + a 2 (E i − E 0 ) 2+···+a k (E i − E 0 ) k ] (6.2.7)where k is the degree of the exponential polynomial.A value k = 6 or higher might be necessaryto accurately describe a continuum from 2to 16 keV.6.2.6 ORTHOGONAL POLYNOMIALSSteenstrup (1981) proposed the use of orthogonalpolynomials to model the continuum as demonstratedby evaluating energy-dispersive X-raydiffraction spectra. The spectrum is fitted usingorthogonal polynomials, and the weights of the

ENERGY AND RESOLUTION CALIBRATION 467least-squares fit are iteratively adjusted so that onlychannels belonging to the continuum are includedin the fit. The method is generally applicable andcan be implemented as an algorithm that needslittle or no control parameters. Vekemans et al.(1994) used the method for the unsupervised evaluationof spectra collected with a micro X-rayfluorescence (µ-XRF) setup.6.2.6.1 THE FLUORESCENCE LINESThe second part of y(i) is the more importantone since it represents the actual detector responsefunction. As already mentioned, given that theresponse function of solid-state detectors is predominantlyGaussian, all mathematical expressionsused to describe the fluorescence lines involve thisfunction. As will be discussed later, the intrinsicenergy distribution of a characteristic X-ray is ofLorentzian nature. Convolution with the Gaussianbroadening function of the detector actually resultsin Voigtian distribution. However, in most casesthe width of the Lorentzian is negligible in comparisonwith the resolution of the detector so thata Gaussian peak shape model is adequate (Wilkinson,1971; Gunnink, 1977).6.2.7 A SINGLE GAUSSIANA Gaussian peak is characterized by three parameters:position, width and area. The first approximationto the profile of a single peak is given by[Aσ √ 2π exp − (x i − µ) 2 ](6.2.8)2σ 2where A is the peak area (counts), σ is the widthof the Gaussian expressed in channels, and µ thelocation of the peak maximum. The full width athalf-maximum (FWHM) is related to σ by thefactor 2 √ 2ln2 or FWHM= 2 √ 2ln2σ .To describe part of a measured spectrum,the fitting function must contain as many ofsuch Gaussian functions as there are peaks. For10 elements and 2 peaks (Kα and Kβ) perelement, 60 parameters need to be optimized. It ishighly unlikely that a nonlinear least-square willsuccessfully reach a global minimum for the χ 2 .This problem is overcome by writing the fittingfunction in a different way.6.2.8 ENERGY AND RESOLUTIONCALIBRATIONA first step is to drop the idea of optimizing theposition and width of each peak independently. InX-ray spectrometry, the energies of the fluorescencelines are known with an accuracy of 1 eV orbetter. The pattern of peaks observed in a spectrumis directly related to elements present in the sample.Based on those elements, we can predict allX-ray lines that constitute the spectrum and theirenergies. Obviously, a peak function is thereforebest written in terms of energy rather than channelnumber. Defining ‘zero’ as the energy at channel0 and expressing the spectrum ‘gain’ in eV perchannel, the energy of channel i is given by:E i = zero + gain iThe resolution or peak width S jk of an X-ray lineat energy E jk is given by[ ( ) ] 1noise2 2S jk =2 √ + ε Fano E jk2ln2(6.2.9)in which ‘noise’ is the detector system’s electroniccontribution to the peak width (typically 80 to100 eV FWHM) with the factor 2 √ 2 ln 2 to convertto σ units. Fano is the Fano factor (∼0.114 forSi(Li) detectors) and ε the energy required toproduce an electron–hole pair in the solid-statedetector (3.85 eV for Si(Li) detectors).Taking into account the energy and resolutioncalibration, the Gaussian can be written asGaussian (E i ,E jk )[]= gain √ exp − (E i − E jk ) 2S jk 2π 2Sjk2 (6.2.10)in which gain/(S jk√2π) is required to normalizethe Gaussian so that the sum over all channelsis unity. Instead of optimizing the position and

468 SPECTRUM EVALUATIONwidth of each peak the parameters of the energyand resolution parameters are optimized, reducingthe dimensionality of the problem. In the caseof 10 elements with two peaks each, the numberof parameters to be optimized is now 24. Moreimportantly, all the information available in thespectrum is now used to estimate zero, gain, noiseand Fano, and thus the positions and widths ofall peaks. In this way, small overlapping peaksexhibiting low counting statistics can be estimatedmuch more accurately provided that some welldefinedpeaks are available in the fitting region(Nullens et al., 1979).6.2.9 RESPONSE FUNCTIONFOR AN ELEMENTTo further reduce the number of fitting parameters,entire elements are modelled rather than singlepeaks. This way, a number of lines belongingtogether in a logical way, such as the Kα 1 andKα 2 of a doublet or all the K lines of an element,are fitted as one group, with one area parameter Arepresenting the total number of counts in all thelines within the group. This is represented by:[ng∑ np(j )]∑y P (i) = A j R jk Gaussian (E i ,E jk )j=1 k=1(6.2.11)In the above equation, R jk is the relative intensityof an individual line k within a peak group j,E iis the energy of channel i, E jk is the energy ofthe kth line of peak group j. The inner summationruns∑over all lines within the group np(j ) withk R jk = 1. R jk values are available in theliterature. The outer summation runs over all thegroups specified in the spectral region of interest.deviation from the pure Gaussian shape becomessignificant.Figure 6.2.1 shows part of the spectrum of aV thin film standard. The almost flat continuumis higher at the low-energy side of the Kα andKβ peaks than at the high-energy side. Also, atthe low-energy side the peak is broader, this isthe so-called tail which results in an asymmetricpeak shape.As indicated previously, the observer peakshape is partially caused by the non-ideal behaviourof the detector. For low-energy lines (

NUMERICAL PEAK SHAPE CORRECTION 46910 610 5Intensity (counts)10 410 310 2 2 3 4 5 6 7 8Energy (keV)Figure 6.2.1 Part of the spectrum of a V thin film standard detected with a Si(Li) detector. For excitation a Rh X-ray tube isused in combination with a 0.05 mm thick Rh filter. The analysis time was 15 000 s. Main peaks in the spectrum are the V Kαand Kβ peaks, the peaks located at ∼3.1 keV and ∼3.6 keV are the escape peaks. The shelf and tail features are clearly visibleGaussian. The table extends from zero energyup to the high-energy side of the Kβ peak andis normalized to the area of the Kα peak. Thedeviation is obtained from pure element spectrahaving high counting statistics (area Kα ∼ 10 7counts). Preferably, thin films are used to keepthe continuum as low as possible and to avoidabsorption effects. The area, position, and width ofall peaks in the spectrum are determined by fittingGaussians on a constant continuum over the fullwidth at tenth maximum (FWTM) of the peaks.The Gaussian contributions are then stripped fromthe spectrum. The resulting non-Gaussian partis further smoothed and subsequently used asa numerical peak-shape correction. The fittingfunction for the characteristic lines is now given byy P (i) =ng∑j=1np(j )+k=2A j{R jKα [Gaussian (E i ,E jKα ) + C i ]}∑R jk Gaussian (E i ,E jk )(6.2.12)where C i is the numerical peak shape correctionat channel i. Values in the table are interpolated toaccount for the difference between the energy scaleof the correction and the actual energy calibrationof the spectrum.A major advantage of this method is itscomputational simplicity and the fact that no extraparameters are required in the model. However,it is quite difficult and laborious to obtain goodexperimental peak-shape corrections and they are,to some extent, detector dependent. Also, sincethe peak shape correction is only related to thearea of Kα, the peak shape correction for Kβbecomes underestimated when strong differentialabsorption takes place. In addition, it is nearlyimpossible to use this method to describe the Llines. Certainly, numerical peak shape correctionmeant a breakthrough in the early years ofED spectrum evaluation, enabling an efficientway to correct for the deviation from the idealGaussian peak shape. Nowadays, it is replaced bymore flexible methods carrying out the correctionthrough analytical functions.

470 SPECTRUM EVALUATION6.2.12 MODIFIED GAUSSIANSA number of analytical functions have been proposedto account for the true line shape. Nearlyall of them include a flat shelf and an exponentialtail, both convoluted with the Gaussian responsefunction. The original function was first introducedby Philips and Marlow (1976) to describe thepeak shape observed in γ -ray spectra. Later on,other authors adopted, extended and improved thisfunction (Jorch and Campbell, 1977; Gardner andDoster, 1982; Yacout et al., 1986; Vekemans et al.,1994).To account for the deviation from the Gaussianpeak shape, the Gauss function, Gaussian (E i ,E jk )in Equation (6.2.12) is replaced byF(E i ,E jk ,f Sjk ,fT jk ,γ jk)= Gaussian (E i ,E jk ) + f Sjk shelf (E i,E jk )+ f Tjk tail (E i,E jk ,γ jk ) (6.2.13)in which Gaussian (E i ,E jk ) is the Gaussian partgiven earlier while the shelf and tail functionsdenoted by shelf (E i ,E jk ) and tail (E i ,E jk ,γ jk )are given by.Shelf (E i ,E jk ) = gain2E jk× erfcgainTail (E i ,E jk ) =(2γ jk S jk exp( )Ei − E jk√S jk 2− 12γ 2jk( )Ei − E jk× expγ jk S jk× erfc)(6.2.14)(Ei − E jkS jk√2+ 1γ jk√2)(6.2.15)Intensity (counts)10 610 510 410 3SpectrumFitCont.StepTail(a)10 22 3 4 5 6 7 8Residuals(b)12840−4−8−122 3 4 5 6 7 8Energy (keV)Figure 6.2.2 The same spectrum of V as shown in Figure 6.2.1 but now the spectrum is fitted with a modified Gaussian. Alsothe escape peaks are fitted. This is done with a simple Gaussian, the fraction of counts ending up in the escape peaks can becalculated from theory. The continuum is fitted with a first-degree linear polynomial, i.e. a constant value

MODIFIED GAUSSIANS 471In these equations, S jk represents the spectrometerresolution and γ jk is the broadening of theexponential tail. The parameters fjkS and fjkTdescribe the fraction of the photons that end up inthe shelf and the tail respectively. In some studies,the exponential function is slightly different fromthe one presented here. Those authors use β jkinstead of the term γ jk S jk . Here, β jk is defined asa multiple, γ jk ,ofS jk . In this way, the parameterγ jk becomes independent of the resolution of thedetector. However, both β jk and γ jk S jk may beused to describe the slope of the exponential tail.Figure 6.2.2 represents the fitted spectrum of V(already shown in Figure 6.2.1) and demonstratesthat a fitting model based on a modified Gaussiandescribes the data well. A χ 2 value of 7.1 wasobtained which is very good taking into accountthat the intensity at the maximum of V Kα isnearly 10 6 counts. A discrepancy clearly seen atthe high-energy side of the V Kβ peak is due tothe Lorentzian character of the peaks.Figures 6.2.3(a) and 6.2.3(b) show the effect ofusing simple Gaussians instead of modified Gaussians.Here, the spectrum of a brass sample (NISTSRM 1106) is fitted. When simple Gaussians areused, the Ni Kα peak is clearly overestimated sinceit is used to fill up the tail of the Cu lines. When modifiedGaussians are used, a realistic fit is obtained.In the above equations, erfc is the complementof the error function erf and serves to round off theexponential and shelf terms to avoid non-physicalsharp edges. (Actually, the erfc component resultsfrom convoluting an exponential tail or shelf withthe Gaussian detector response function.) Erf anderfc are given by the following expressionserfc(x) = 1 − erf(x) = 1 − 2 √ π∫ x0e −t 2 dt= √ 2 ∫ +∞e −t 2 dt (6.2.16)πxand can be calculated via series expansion.Counts100 k10 k1 k100Fe KCu escNiKaCu KaZn KaCu KbZn KbPb LSpectrumFitContinuum10(a)1100 kStep and tail10 kCounts1 k100(b)101200 300 400 500 600 700ChannelFigure 6.2.3 Part of the spectrum of a brass sample NIST SRM 1106 fitted with simple Gaussians (a) and modified Gaussians(b). The continuum is fitted with a third degree polynomial in both cases. When only simple Gaussians are used, the Ni peaksare overestimated and the continuum is not correctly fitted. Both the Ni peaks and the continuum are used to compensate for thetailing of the Cu and Zn K lines. Reproduced by permission of international centre for diffraction data

472 SPECTRUM EVALUATIONThe parameters fjk S ,fT jk and γ jk vary smoothlywith the X-ray energy of the characteristic peak.Campbell et al. (1985, 1987) conducted manyexperiments employing monoenergetic X-raybeams that were obtained from a curved crystalmonochromator. Deriving the values of thedifferent parameters and relating them to theX-ray energy showed, evidently, no differencebetween Kα and Kβ lines. As already shown byWielopolski and Gardner (1979), this is not thecase when real K X-rays are examined. It is foundthat the parameters are not unique but take ondifferent values for the Kα and Kβ series. Thisis due to the appearance of radiative phenomena(e.g. radiative Auger effects) in the vicinity of theKα and Kβ signals.Fitting real X-ray spectra with modified Gaussiansdramatically increases the number of parametersthat need to be optimized for each peak.Besides the area, A, also the tail parameters,fjk S ,fT jk and γ jk are now involved. In our exampleof 10 elements with two peaks each, the number ofparameters has again increased to 84! In practiceless parameters are needed since not all the peaksin the spectrum have such intensities that peakshape correction through modified Gaussians arerequired. To decrease the number of parameters,the energy dependence of the shelf and tail parameterscan be used. In this way, functions describingthe energy dependence can again reduce the totalnumber of parameters, similar to the energy andresolution calibration.6.2.13 REPLACING THE GAUSSIANBY A VOIGTIANThe fact that a characteristic X-ray has an intrinsicenergy distribution of Lorentzian nature mightinfluence the fitting results. Two aspects areimportant: the Lorentzian width itself and thetailing of the Lorentzian function. For the energyregion usually investigated (1 to 15 keV) thecontribution of the Lorentzian width (1 to 5 eV) isnegligible in comparison with the FWHM of thedetector (100 to 300 eV). As indicated previously,the convolution of the Lorentzian function withthe Gaussian broadening function of the detector,resulting in a Voigt function is usually not takeninto account. Instead, only a Gaussian function isused. If the energy of the characteristic photonis higher than 15 keV, the contribution of theLorentzian width increases rapidly, e.g. for Sn(Kα = 25.27 keV) the Lorentzian width is in theorder of 11 eV, for Ba (Kα = 32.19 keV) 16 eVand for W (Kα = 59.31 keV) 45 eV. In the case ofL lines the effect is even more important since theLorentzian width of these lines is larger at lowerenergies, e.g. 6 eV for W Lα 1 (E = 8.398 keV) and12 eV for W Lβ 3 (E = 9.819 keV) (Campbell andPapp, 1995). If such lines are fitted, the Lorentzianbroadening cannot be neglected. Another moreimportant feature of the Lorentzian distributionis its tailing. Unlike a Gaussian, the Lorentzianfunction falls to zero much less rapidly. Whilethe peak broadening becomes apparent only atcharacteristic photon energies higher than 15 keV,the tailing effect is also observable for photonenergies below 15 keV. Therefore, replacing theGauss by a Voigt profile results in a more accuratedetector response function (Campbell and Wang,1992).The Voigtian is the convolution of a Lorentzianwith a Gaussian distribution and can be written asV(E)=∫ +∞−∞L(E ′ )G(E − E ′ )dE ′ (6.2.17)in which E is the energy along the convolutedspectrum. L(E ′ ) and G(E − E ′ ) are the Lorentziandistribution and the Gaussian distribution, given bythe following expressions:ƔL(E ′ ) =2π( ) Ɣ 2(6.2.18)(E ′ − E jk ) 2 +2G(E i − E ′ ) =Gain √ exp[− (E i − E ′ ) 2 ]S E′ 2π 2SE 2 ′ (6.2.19)in which Ɣ is the Lorentzian width of characteristicline of energy E jk and S E′ is the Gaussianwidth at energy E ′ . Substitution in the expression

REPLACING THE GAUSSIAN BY A VOIGTIAN 473representing the convolution gives:The Voigt function can be written as the real part∫ +∞of the complex error function:ƔV(E i ) =−∞ S E ′2π √ gain( )2πƔ 2((E ′ − E jk ) 2 +2 W(z) = e −z2 1 + 2i ∫ z)√ e t 2 dt = e −z2× exp[− (E i − E ′ ) 2 ]π 02SE 2 dE ′ (6.2.20) erfc (iz) = K(x,a) + iL(x,a) (6.2.28)′Rearranging and adding E i − E i giveswhere z = x + ia.L(x,a) is expressed as follows:∫ +∞1V(E i ) =−∞ 2 √ Ɣ 12 S E′ π √ πL(x, a) = 1 ∫ +∞(x − y)exp(−y 2 )dy (6.2.29)π −∞ (x − y)gain2 + a 2×( ) Ɣ 2[(E i − E jk ) − (E i − E ′ )] 2 + Various computational procedures have been publishedfor the evaluation of the Voigt function,2× exp[− (E i − E ′ ) 2 ]2SE 2 dE ′ K(x,a). They are based upon numerical expansionsin different regions of the x,a space. Proce-′(6.2.21)dures are known that calculate only the real partIntroducing in this expression the following substitutionsevaluate the complete probability function W(z)of the complex probability integral while othersx = E i − E jk(Armstrong, 1967; Humlicek, 1982). The calculationof the complete probability function has the√ (6.2.22)S E ′ 2y = E advantage that the imaginary part can be used fori − E ′√ (6.2.23)the evaluation of the partial derivatives of the VoigtS E′ 2 function. Schreier (1992) gives an overview of thea = 12 √ Ɣavailable computational procedures. Until now, the(6.2.24) best algorithm is the one developed by Poppe and2 S E′Wijers (1990a, 1990b), which is an improved versionof Gautschi’s algorithm (Gautschi, 1969). Thegives for the Voigt profile, symbolized as V(x,a)∫ +∞a √ accuracy of this algorithm is 14 significant digitsthroughout most of the complex plane while2S E′V(x,a)=−∞ π √ πthe speed is comparable with other, less accuratealgorithms.gain×[ √ 2S E ′(x − y)] 2 + ( √ 2S E ′a) 2 Figure 6.2.4 shows the same spectrum asFigures 6.2.1 and 6.2.2 but now a Voigtian is× exp(−y 2 )dy (6.2.25) used in combination with a shelf and tail. Theχ 2 value drops to 3.7 and the misfit at 5.8 keVorV(x,a)= √ gainis now absent.K(x,a) (6.2.26) To conclude this section, Figures 6.2.5 and2πSE ′6.2.6 show the fitted spectra of NIST SRMwhere K(x,a) is in general known as the 1155 and NIST SRM 2710, a stainless steel andVoigt functioncontaminated soil sample, respectively. χ 2 valuesK(x,a) = a ∫of 1.46 and 4.0 are obtained. Notice that almost+∞exp(−y 2 )π (x − y) 2 + a dy (6.2.27) every characteristic peak in the spectrum of the2 soil sample is fitted in the same run.−∞

474 SPECTRUM EVALUATIONIntensity (counts)10 610 510 410 3SpectrumFitCont.StepTail10 22 3 4 5 6 7 8Residuals12840−4−8−122 3 4 5Energy (keV)6 7 8Figure 6.2.4 The same V spectrum is shown as in Figures 6.2.1 and 6.2.2. This time, a Voigtian based fitting function includingshelf and tail is used. The skirts of the Lorentzian distribution of the V K lines, clearly seen at the basis of the V Kβ peak, arenow fitted. This was not the case in Figure 6.2.3. The standardized residuals do not show a systematic deviance anymore around5.7 keV6.2.14 CONVOLUTION OF MCSIMULATED SPECTRAThe previous subchapter gives a detailed overviewof the MC technique as applied to the simulationof XRF spectra. Simulated X-ray spectra can beused for quantitative analysis as well as to studythe behaviour and performance of spectrum processingmethods. The know-how gained via MCsimulations can also be used for the design andoptimization of new instrumental set-ups. In eithercase, the simulated spectrum is one as seen byan ideal detector with infinite resolution or, put inanother way, it is the spectrum as it impinges onthe detector surface. This spectrum still needs to beconvoluted with the detector response function toobtain the familiar pulse-height spectrum. Therefore,apart from a sophisticated MC simulationcode, the method also requires an accurate detectorresponse function.We already identified peak tailing as beinga detector related phenomenon. Obviously, thefeature is not taken into account during the MCsimulation step. During the convolution all thecounts belonging to a characteristic peak areredistributed over a Gaussian (or Voigtian) aswell as the tail and the shelf. Numerical peakshape correction cannot be used here because itwould imply adding extra counts to the systemand altering the peak ratios. The sole plausible

CONVOLUTION OF MC SIMULATED SPECTRA 47510 5SpectrumFitCont. Step Tail10 4Intensity (counts)10 310 210 110 0 432100 2 4 6 8 10 12 14 16 18 20 22 24Residuals−1−2−3−40 2 4 6 8 10 12 14 16 18 20 22 24Energy (keV)Figure 6.2.5 The entire spectrum of a stainless steel sample NIST SRM 1155. The region between 1 keV and 14 keV is fitted.The major peaks are fitted with modified Voigtians. To fit the continuum a first degree linear polynomial is used. Notice that forthis energy region the continuum is nearly absent10 5SpectrumFitCont. Step TailIntensity (counts)10 410 310 210 1 864200 2 4 6 8 10 12 14 16 18 20 22 24Residuals−2−4−6−80 2 4 6 8 10 12 14 16 18 20 22 24Energy (keV)Figure 6.2.6 Spectrum of a contaminated soil sample NIST SRM 2710. All characteristic peaks are fitted simultaneously. Thecontinuum is modelled with a sixth degree exponential polynomial. The L lines of Pb are fitted with Voigtians without shelf andtail. The high intensity K lines are fitted with Voigtians including shelf and tail functions

476 SPECTRUM EVALUATIONmethod is to use a detector response functionbased on modified Gaussians. To obtain a perfectagreement between simulated and experimentalspectra it is necessary to derive the values of theparameters fjk S ,fT jk and γ jk for the detector systemwith which the experimental spectra are obtained.The characteristic element lines, continuum and, ifpresent, the elastically and inelastically scatteredcharacteristic lines of the source are all convolutedwith the same detector response function. Inaddition, also escape peaks and sum peaks aretaken into consideration.An example is given in Figure 6.2.7 where thespectrum of the NIST SRM 1106 brass sampleis simulated and convoluted with the appropriatedetector response function. The experimentallymeasured spectrum is also shown. The standardizedresiduals show that the agreement isnearly perfect.6.2.15 PARTIAL LEAST-SQUARESREGRESSIONAs discussed throughout this subchapter, the aim ofspectrum evaluation is to derive the net intensitiesof the characteristic element lines. In a next step,these net peak intensities are used to determinethe constituent concentrations using one of theempirical, semi-empirical or fundamental quantificationmethods. The procedure of spectrum evaluationfollowed by an independent quantification hasproven to work very well but it remains a rathercomplicated and time-consuming process requiringa high degree of experience and knowledge fromthe operator. This makes it very hard to automatethe process. Moreover, the spectrum evaluationmethod will fail when the encountered peak shapesdiffer too much from the employed peak model.Also, any structures in the spectrum not taken10 810 7Intensity (arbitrary unit)10 610 510 410 310 210 1(a)10 010 9 0 4 8 12 16 20 24 28 32 36 40Energy (keV)Figure 6.2.7 The plots show the simulated and experimentally measured spectrum of NIST SRM 1106. (a) Simulated spectrumbefore convolution with the detector response function. This is the spectrum as seen by an ideal detector with infinite resolutionand detector efficiency equal to 1. (b) Simulated spectrum after convolution with a detector response function based on modifiedGaussians and corrected for the detector efficiency. Together with the simulation the real spectrum is also shown. The standardizedresiduals show that the agreement is almost perfect when the uncertainty due to counting statistics is taken into account

PARTIAL LEAST-SQUARES REGRESSION 47710 610 5MeasuredSimulatedIntensity (counts)10 410 310 210 110 0100 4 8 12 16 20 24 28 32 36 40Residuals(b)50−5−100 4 8 12 16 20 24 28 32 36 40Energy (keV)Figure 6.2.7 (continued)into account by the fitting model (e.g. Comptonpeaks) might pose problems. During the past fewyears new approaches based on multivariate calibrationhave appeared in the field of quantitativeX-ray spectrometry. In what follows we will concentrateon partial least-squares regression (PLS),a technique comprehensively written about in thechemeometrics literature. PLS showed to be veryuseful with quantitative infrared (IR) and ultraviolet(UV) spectrometry where the spectral informationis less selective compared to ED-XRF. Thisselectivity is probably the only reason why PLShad not yet been applied to ED-XRF or WD-XRF.An important advantage of PLS is its ability to takecare of the spectrum evaluation and quantificationin one single step.6.2.15.1 THEORYPLSR is a multivariate calibration method ableto relate element concentrations directly to themeasured XRF spectra (or portions of them). Thespectral variables are collected as a matrix X witha row number equal to the number of samplesand a column number equal to the number ofchannels in the spectra. The Y matrix consists ofthe concentrations with a number of rows equalto the number of samples and the number ofcolumns equal to the constituents of interest. Therelationship can then be written in the form:Y = XB + F (6.2.30)in which F is the matrix containing the residuals(variation not described by the model, e.g. misfitor noise). The regression coefficients B canbe calculated in several ways. One widespreadmethod is multiple linear regression (MLR) inwhich the least squares solution is given by:B = (X ′ X) −1 X ′ Y (6.2.31)However, when the number of x-variables exceedsthe number of samples and/or when there is a high

478 SPECTRUM EVALUATIONdegree of correlation (also known as collinearity)among the variables, the resulting solution is notstable. Mathematically, this means the inverse ofcovariance matrix X ′ X does not exist. This is thecase for ED-XRF where the number of channelslargely exceeds the number of samples and wherethe intensities of neighbouring channels in eachpeak and peaks of the same element are verystrongly correlated.The PLSR method handles this collinearityproblem by compressing the X data matrix X =[x 1 , x 2 ,...,x p ] containing p spectrum channelsfor n samples, into a number of A orthogonallatent variables or scores T = [t 1 , t 2 ,...,t A ]. Intheory, there are as many latent variables asthere are original samples (or variables, dependingon which of the two is smaller). In practice,only the most significant, carrying most of thevariance in the data, are used. In the end, anumber of latent variables usually much smallerthan the original number of variables p areretained. The scores T are employed to fit a setof n observations to m dependent concentrationvariables Y = [y 1 , y 2 ,...,y p ]. Since the latentvariables are orthogonal (linearly independentfrom each other), the inverse can easily beobtained, solving the problem of collinearity.When one PLS model is built per constituent(PLS1), the vectors t are easily found via singularvalue decomposition of the matrix X ′ yy ′ X.Ifmorethan one constituent is modelled with the samePLS model (PLS2), the derivation of the t vectorsis conceptually less straightforward.The PLSR model can be considered as consistingof two outer relations and an inner relation.There is an outer relation for the X matrix:A∑X = TP ′ + E = t a p a ′ + E (6.2.32)aAs well as for the Y matrix:A∑Y = UQ ′ + F = u a q a ′ + F (6.2.33)aIn which P and Q are the loadings of the Xand Y variables block, respectively, E and F arematrices containing residuals. A represents thenumber of latent variables retained in the PLSRmodel. The loadings describe how the original Xand Y variables are related to the scores T and U.The inner relation is written as:u a = b a t a (6.2.34)In essence, the inner relation is a least squares fitbetween the X block scores and Y block scores.When all the necessary scores and loadings arecalculated the final PLSR model can be written as:Y = TBQ ′ +F (6.2.35)Figure 6.2.8 illustrates these relationships graphically.As explained, the PLS method compresses theoriginal variables into a number of latent variables.Validating the PLS model essentially concernsthe selection of the optimal number of PLSdimensions/components. In addition, the validationmethod provides a value for the prediction errorenabling the assessment of the predictive capacityof the model.The determination of the optimum number ofPLS components is mainly done by calculation ofthe root mean squared error (RMSE)n∑(ŷ i − y i ) 2√i=1RMSE =(6.2.36)nin which n denotes the number of observations, yis the given (or ‘true’) value of the constituent ofinterest and ŷ the concentration predicted by thePLS model.Given a certain data set, the RMSE values arecalculated for different numbers of componentsincluded in the PLS model. Normally the RMSEreduces with increasing number of PLS componentsuntil a minimum or constant value is reachedand the corresponding number of components isregarded as optimal. The prediction error is composedof two contributions, the remaining interferenceerror and the estimation error. The formeris the systematic error due to unmodelled interferencein the spectral data and the latter is caused byrandom measurement noise of various kinds or by

PARTIAL LEAST-SQUARES REGRESSION 479pApP′AX (spectra) = T +EpnnnmY(conc.)=UAAQ′m+FmnnnmY(conc.)=TAABAAQ’m+F*mnnnFigure 6.2.8 Graphical representation of the outer and inner models of PLS with n the number of calibration samples, p thenumber of channels in the spectrum, A the number of latent variables retained and m the number of constituents modelled.Reproduced by permission of John Wiley & Sons, Ltdsystematic error not relevant for the modeled analytey. The two contributions to the prediction errorhave opposite trends with increasing complexity ofthe PLS model. The interference error decreaseswith an increased modelling of the systematic varianceby including more PLS components. However,at the same time the statistical uncertaintyerror increases. Including too few PLS componentsresults in underfitting and one risks that importantphenomena are not modelled. Including too manycomponents results in overfitting and this is equivalentto the modelling of noise.Calculation of the RMSE value is mostlydone in either of two ways; leave one out crossvalidation (LOO-CV) or by means of a separatedata set. The LOO-CV technique is generallyused when only a limited number of samples areavailable to set up and validate a calibration. Eachsample is excluded once from the data set anda PLS model is built based on the remainingsamples. Once built, the excluded sample ispredicted and the deviation stored. This is doneuntil all samples have been excluded once. TheRMSE value is the mean of the stored deviations.In the case of a separate data set or predictionset, the PLS model is built from the so-calledtraining set and used to predict the samples of theprediction set.Geladi and Kowalski (1986) published a tutorialon PLSR and its relation to other regressionmethods. A standard work on PLS and multivariatecalibration in general is the book by Martens andNæs (1989). For a thorough discussion of thetheoretical and statistical aspects of PLS, we referto articles by Manne (1987), Lorber et al. (1987),Höskuldsson (1988), de Jong (1993), Phatak et al.(1992), Burnham et al. (1996) and Ter Braak andde Jong (1998).6.2.15.2 APPLICATIONThe PLS method is illustrated with the analysisof cement containing CaO, SiO 2 ,Al 2 O 3 ,SO 3 andFe 2 O 3 . Cement analysis is one of the major applicationsof XRF and most cement production plantsmaintain a quality control programme to assurethat the final product is of constant quality andmeets its preset specifications. Without exception,completely automated WD-XRF set-ups are used

480 SPECTRUM EVALUATIONto determine the constituents of the product. In thisexample a cheap ED-XRF instrument equippedwith a low power Cu anode and a sealed neongas proportional counter with an energy resolutionat Mn Kα of 700 eV is used. Due to the verylow resolution of the instrument compared to Sibased solid-state detectors, a high degree of overlapexists between the characteristic peaks in thespectrum. In such a case, spectrum evaluation willfail. The example will show that for these kindof applications PLS is well suited. More on theanalysis of cement with PLS and low-resolutionED-XRF can be found in an article published byLemberge et al. (2000).The purpose of this PLS calibration is todetermine the concentration of the most abundantcomponent, CaO. In total, 14 certified cementstandards (601A Cement, Japan Cement Association,Research and Development Laboratory,Tokyo, Japan) are measured. Table 6.2.1 gives thecomposition of the samples used in the PLS calibration.Sample preparation consisted of pressing5 g of cement powder into an aluminium samplecup without use of a binder or diluent. Spectrawere recorded with a tube voltage of 12 kVand a measurement time of 150 s. The recordedspectra consist of 2048 channels and span anenergy range going from 0 to 8 keV. Figure 6.2.9Table 6.2.1 Most abundant constituents of the analysed cementsamples (601A Cement, Japan Cement Association, Researchand Development Laboratory, Tokyo, Japan). In addition to thetabulated constituents, the samples also contain MgO, Na 2 O,K 2 O, TiO 2 .P 2 O 5 and MnO are at concentration levels below1% (m/m)Sample no.Concentrations [% (m/m)]CaO SiO 2 SO 3 Al 2 O 3 Fe 2 O 31 63.13 22.09 2.22 5.23 3.012 63.66 21.02 1.83 5.29 2.863 65.12 20.49 3.13 4.54 2.374 65.41 20.69 2.58 4.69 2.805 64.93 20.32 2.97 5.04 2.996 65.14 20.51 2.55 4.88 2.717 63.11 22.42 2.33 4.18 4.018 63.36 23.09 1.85 3.73 4.009 61.07 23.03 2.03 6.25 2.3810 58.33 24.36 1.92 7.35 2.2411 54.31 26.18 1.93 8.91 1.8112 54.46 25.99 1.19 9.16 2.0113 54.76 25.77 2.09 8.56 2.0214 49.25 29.56 1.32 10.70 1.33shows the spectrum for sample 1 with compositiongiven in Table 6.2.1. Since there is only oneconstituent of interest, a PLS1 model for CaOis built. Due to the limited number of cementstandards available it is not possible to split thedata in a training and prediction set. Thereforewe shall use LOO-CV to calculate the RMSEvalue and to determine the optimal number of PLScomponents.In Figure 6.2.10 the RMSE is plotted as afunction of the number of latent variables. Inthis case, the minimum is located at the firstlatent variable and the error slightly increaseswhen more latent variables are included in themodel. The minimum RMSE is equal to 0.29 %(m/m) and a PLS model with one latent variableis retained. Figure 6.2.11 compares the true CaOconcentration with the predicted concentrations forthe data set. The PLS model predicts the CaOconcentrations very accurately in the range of 49 to66 % (m/m). The regression coefficients of the PLSmodel show what parts of the spectrum (spectralvariables or channels) are used by the PLS modelto predict the CaO concentrations. The regressioncoefficients are plotted in Figure 6.2.12 and showthat, as expected, the channels corresponding tothe Ca signal contribute most to the PLS model.In addition, there is also a contribution at theposition of the Si peak but unlike the positivecontribution for Ca the one for Si is negative. Thiscan be explained by observing Table 6.2.1 showingthat the CaO concentration is to a large extentcomplementary to the SiO 2 concentration. Whenthere is less CaO in the cement the SiO content isincreased and vice versa. This information is alsoused by the PLS model to achieve better results.At the same time it makes the model only valid forthis kind of sample and hence, the model becomesless robust.To build an accurate PLS model, a largenumber of standards spanning the concentrationrange of each element or constituent of interestis necessary. This allows the PLS model to takeinto account all interactions occurring. Comparedto the FPM or semi-empirical methods relyingon theoretical principles, the PLS method isempirical and relies entirely on the data given

PARTIAL LEAST-SQUARES REGRESSION 4818070Ca60Intensity [√ (counts)]50403020AlSiSFe1000 1 2 3 4 5 6 7 8Energy (keV)Figure 6.2.9 Low-resolution ED-XRF spectrum of cement sample 1 of Table 6.2.1. Due to the low resolution (FWHM at Mn Kαof 700 eV) a high degree of overlap exists between the element characteristic peaks. Reproduced by permission of John WileySons, Ltd54RMSE [% (m/m)]321002 4 6 8 10No. of PLS componentsFigure 6.2.10 RMSE curve for CaO obtained via LOO-CV. The minimal value is already obtained with one PLS component(also known as latent variable)

482 SPECTRUM EVALUATION6664CV predicted CaO conc. [% (m/m)]62605856545250484850 52 54 56 58 60 62 64 66Certified CaO conc. [% (m/m)]Figure 6.2.11 Predicted versus measured CaO concentrations. Clearly, the PLS model based on one latent variable only accuratelypredicts the CaO concentration. Reproduced by permission of John Wiley & Sons, Ltd1 × 10 −4 08 × 10 −56 × 10 −5b-coefficients4 × 10 −52 × 10 −5−2 × 10 −50 1 2 3 4 5 6 7 8Energy (keV)Figure 6.2.12 The b-coefficients show which part of the cement spectra is used for the determination of the CaO concentration.Large positive values are located at the position of the Ca peak. Evidently the Ca peak contains most of the information topredict the CaO concentration. Next to the Ca peak also the region of the Si peak is used. The negative values around 1.5 keVindicate an inverse relationship between the Si concentration and the Ca concentration. This is explained by the specificity ofthe cement composition. Reproduced by permission of John Wiley & Sons, Ltd

FUTURE PERSPECTIVES 483to it during the calibration. The large numberof calibration samples required and the empiricalaspect related to it, is certainly the major drawbackof PLS for its application in XRF. However,with the availability of excellent MC simulationcodes this problem can be overcome by usingsimulated spectra. Virtually any composition inaccordance with an experimental design can thenbe chosen. Another drawback remains, due tomatrix effects encountered with XRF spectrometry,the relationship between intensities of elementcharacteristic lines and the element concentrationsare in part nonlinear. PLS, being in essence a linearmethod able to handle only a certain degree ofnonlinearity is probably less suited for XRF thanforIRorUVspectrometry.Wang et al. (1990) applied the PLS method forthe analysis of nickel alloy samples employingWD-XRF. The authors used the instrument inscan mode to acquire a spectrum of each sample.Each spectrum consisted of 261 channels andthe total measuring time was 7830 s (30 s perchannel). Adams and Allen (1998) reported on theapplication of PLS to WD-XRF in combinationwith variable selection for the analysis of ironbasedalloys, copper-based alloys and geologicalsamples. Swerts et al. (1993) were the first toapply PLS in combination with ED-XRF for theanalysis of sulfur–graphite mixtures. The PLSmethod was used both for the analysis of sulfurand the explanation of various artifacts observedin the spectra. Later, Urbanski and Kowalska(1995) applied the PLS method to various lowresolutionED-XRF analyses. Lemberge and VanEspen (1999) used the PLS method for thedetermination of Ni, Cu and As in liquid samples.They showed that taking the square root of thedata improves the PLS model and that the PLSmethod extracts information from the scatteredexcitation radiation to describe the matrix effects.PLS has also been applied for EPXMA and µ-XRF analysis of glass samples (Lemberge et al.,2000). The PLS method seemed to perform betterfor EPXMA than for XRF because of smallermatrix effects and hence a reduced nonlinearityeffect in the intensity–concentration relationshipfor EPXMA.6.2.16 FUTURE PERSPECTIVESThough the development of modified Gaussian andVoigtian based detector response functions havebeen going on for over 10 years, it was not possibleto implement them as practical and user-friendlyspectrum evaluation software. The reason for thisis two-fold. The shelf and tail functions add extraparameters to the fitting algorithm and thoughonly peaks with high counting statistics requirethese functions, it becomes more difficult to finda global minimum in the χ 2 space. Preferably,the software should decide automatically whichpeaks require an extended peak model. Next tothis, ordinary PCs were not powerful enoughto fit a spectrum containing many peaks usingonly modified Gaussians or Voigtians. However,new PCs deliver massive amounts of processingpower. Also, the relationship of the shelf and tailparameters as a function of energy is intensivelystudied. Most probably this research will resultin physically meaningful functions describing therelationships, further decreasing the number offitting parameters. With this knowledge, robustand accurate spectrum evaluation software ispossible. The availability of such software willrenew interest in ED-XRF. In the near future,new high performance ED-XRF instruments willbecome available. Together with recent advancesin hardware the precision of such instrumentswill improve considerably. Detection limits tubeexcitedED-XRF instruments will improve fromthe lower p.p.m. range at the moment to sub p.p.m.during the next few years. Hence, ED-XRF willbecome an important competitor of inductivelycoupled plasma (ICP) instruments, especially forsolid samples.PLS and other multivariate methods mightprove important for instruments operating withoutsupervision, e.g. portable instruments used inthe field or on-line systems. In such dedicatedapplications the type of samples are usually ofthe same type, e.g. soil analysis, alloy sorting andthe PLS method will be more than adequate toobtain accurate results. PLS can also be appliedto the analysis of images obtained with microX-ray spectroscopy. The image consists of pixels

484 SPECTRUM EVALUATIONand in each pixel a complete X-ray spectroscopyspectrum is recorded. For a small image of 50 × 50pixels this results in 2500 spectra and all of themneed to be deconvoluted individually. With PLS,the data processing will be much faster providedthat appropriate calibration standards are available.REFERENCESAdams, M.J. and Allen, J.R. Variable selection and multivariatecalibration models for X-ray fluorescence spectrometry.J. Anal. At. Spectrom. 13, 119–124 (1998).Armstrong, B.H. Spectrum line profiles: the Voigt function. J.Quant. Spectrosc. Radiat. Transfer 7, 61–88 (1967).Burnham, A.J., Viverbos, R. and MacGregor, J.F. Frameworksfor latent variable multivariate regression. J. Chemom. 10,31–45 (1996).Campbell, J.L. Si(Li) detector response and PIXE spectrumfitting. Nucl. Instrum. Methods B 109/110, 71–78 (1996).Campbell, J.L. and Papp, T. Atomic level widths for X-rayspectrometry. X-Ray Spectrom. 24, 307–319 (1995).Campbell, J.L. and Wang, J.X. 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Analysis ofcement using low-resolution energy-dispersive X-ray fluorescenceand partial least-squares regression. X-Ray Spectrom.29, 297–304 (2000).Levenberg, K. A method for the solution of certain non-linearproblems in least squares. Quart. Appl. Maths. 2, 164–168(1944).Lorber, A., Wangen, L.E. and Kowalski, B.R. A theoreticalfoundation for the PLS algorithm. J. Chemom. 1, 19–31(1987).Manne, R. Analysis of two partial-least-squares algorithmsfor multivariate calibration. Chemom. Intell. Lab. Syst. 2,187–197 (1987).Marquardt, D.W. An algorithm for least-squares estimation ofnon-linear parameters. J. Soc. Ind. Appl. Math. 11, 431–441(1963).Martens, H. and Naes, T. Multivariate Calibration, Wiley,Chichester, 1989.McCarthy, J.J. and Schamber, F.H. NBS Special Publication604, 1981.Murty, V.R.K., Winkoun, D.P. and Devan, K.R.S. On thecomparison of performance of freoelectric cooled Si(Li) andSi-PIN Peltier cooled detectors. Radiat. Phys. 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Chapter 7New Applications7.1 X-Ray Fluorescence Analysis in Medical SciencesJ. BÖRJESSON 1,2 and S. MATTSSON 11 Malmö University Hospital, Malmö, Sweden and 2 County Hospital, Halmstad, Sweden7.1.1 INTRODUCTION7.1.1.1 ANALYSIS OF ELEMENTCONCENTRATIONMany elements are essential for the function ofthe human body. Others are toxic. There is thus aneed to control their levels in human organs andtissues. This is especially important for occupationallyexposed subjects. Moreover, it is essentialto increase our knowledge of relations betweenobservable toxic effects and element concentrationsin man and his environment. Monitoring andbasic occupational/environmental research rely onmeasurements directly in humans as well as ofsamples from humans and the environment. Thesame technique can also be used to follow, either apure element or an element part of a molecule, afterthey have been administered to patients for diagnosticand therapeutic purposes. This subchapterfocuses on recent advances in in vivo X-ray fluorescence(XRF) methods and their applicationssince 1995, including examples of in vitro use ofthe technique in the medicine field.In Vitro AnalysisIn vitro XRF is primarily used for laboratoryanalysis of, e.g. metals, minerals, samples ofthe environment, food, body fluids and tissuespecimen (Szalóki et al., 2000). Element concentrationsin blood and urine are readily analysedby, e.g. chemical techniques (AAS, atomicabsorption spectrophotometry; ICP-MS, inductivelycoupled plasma mass spectrometry, etc.) andatomic/nuclear techniques (XRF; PIXE, particleinduced X-ray emission, etc.). A disadvantage ofthe PIXE method, compared with XRF, is thatPIXE may destroy the sample due to very highlocal energy absorption (Amokrane et al., 1999).However, with proper conditions fulfilled, even µ-PIXE using a scanning proton microprobe (SPM),can be used to detect most elements above Z ≈ 10with detection limits of 1–10 µg/g. A recent applicationis the identification of atoms in proteins(Garman, 1999).Under certain conditions, element concentrationsin blood and urine can be used to predict theconcentration of the same element in an organ ortissue. In general, however, these relationships arenot simple or well-known. The relations are influencedby, e.g. endogenous and ongoing externalexposure, individual kidney function and variabilityin kinetics.Faeces and hair as well as biopsy and autopsyspecimens have also been used to estimate theX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

488 X-RAY FLUORESCENCE ANALYSIS IN MEDICAL SCIENCESexposure and the amount of the element retained inthe body. A tissue biopsy provides information onthe element concentration. However, it is invasive,involves a risk and may not be possible to repeat.In addition, the concentration in the biopsy maynot necessarily represent the mean concentrationin the organ. Thus, there is an interest to developin vivo methods.In Vivo AnalysisThe two main non-invasive in vivo methods areXRF and neutron activation analysis (NAA).Reviews of in vivo XRF can be found in the literature(Börjesson et al., 1998; Bradley and Farquharson,1999; Chettle, 1999; McNeill and O’Meara,1999) as can reviews of in vivo NAA (Sutcliffe,1996).Neutron activation analysis is possible forelements, which have a high cross-section forneutron capture. The technique has proven usefulfor in vivo studies of nitrogen, calcium, cadmiumand aluminium. Many in vivo NAA studies havebeen concerned with prompt neutron activationof nitrogen in order to determine the whole-bodycontent of protein or of cadmium in kidneys andliver (McNeill and Chettle, 1998; Kadar et al.,2000; O’Meara et al., 2001a).Although useful for non-invasive quantification,both in vivo XRF and in vivo NAA have limitations.The attenuation of photons used to excite theelement and of emitted characteristic X-rays fromthe atom imposes a limit to which element thatpractically can be measured with XRF. In in vivoKXRF, elements must have a Z higher than ≈25.For elements with Z = 25–45, studies are limitedto the most superficial tissues of the body.The first in vivo XRF application was the noninvasivemeasurements of natural iodine in thethyroid (Hoffer et al., 1968). Later, a techniqueto measure iodine in human tissue in vivo fromX-ray contrast agents was reported (Grönberget al., 1983). Measurements of lead in vivo beganin 1971 (Ahlgren et al., 1976, Ahlgren andMattsson, 1979) and since then a number ofalternative XRF techniques have been developed(Somervaille et al., 1985; Wielopolski et al., 1989;Gordon et al., 1993). Descriptions of systemsTable 7.1.1 Application, principal measurement site(s), K absorption energy and characteristic X-ray energies of elements subjectto in vivo XRF (Börjesson, 1996 and references therein). A question mark indicates that the application or measurement site ismore or less speculative and based on scarce informationElement (Z) Application In vivo measurement site(s) K absorptionenergy (keV)K α X-rayenergies (keV)Iron (26) Medical (splinters, disease) Eye, skin 7.11 6.39, 6.40Copper (29) Medical (splinters, disease) Eye, skin 8.98 8.03, 8.05Zinc (30) Medical (splinters, disease) Eye, skin 9.66 8.62, 8.64Strontium (38) Natural abundance Bone 16.11 14.10, 14.17Cadmium (48) Occupational, environmental Kidneys, liver 26.71 22.98, 23.17Iodine (53) Natural abundance, medical (X-ray Thyroid, blood 33.17 28.32, 28.62contrast)Xenon (54) Medical (cerebral blood flow) Brain 34.56 29.46, 29.78Barium (56) Medical (X-ray contrast) Lungs 37.44 31.82, 32.19Platinum (78) Medical (cytotoxic agent) Kidneys, liver, tumours 78.40 65.12, 66.83Gold (79) Medical (anti-rheumatic agent) Kidneys, liver, bone joints 80.73 66.99, 68.81Mercury (80) Occupational, environmental Kidneys, liver?, thyroid?, bone? 83.10 68.89, 70.82Lead (82) Occupational, environmental Bone 88.00 72.80, 74.97Bismuth (83) Medical (treatment of ulcus Stomach?, intestines?, brain90.53 74.81, 77.11duodeni, cytotoxic agent?)tumour?Thorium (90) Medical (previously used X-ray Liver, spleen 109.65 89.96, 93.35contrast)Uranium (92) Nuclear weapons industry, ‘war’,‘crime’ (uranium coveredammunition)Bone, lung 115.61 94.66, 98.44

IN VITRO APPLICATIONS OF XRF IN MEDICINE 489for measurements of cadmium, mercury, gold,platinum, uranium and a number of other elementshave been given through the years (Ahlgrenand Mattsson, 1981; Bloch and Shapiro, 1981;Christoffersson and Mattsson, 1983; Jonson et al.,1985; 1988; Börjesson et al., 1993; Shakeshaft andLillicrap, 1993; Börjesson et al., 1995; O’Mearaet al., 1997). Table 7.1.1 summarizes elements,which have been subjects to in vivo XRF.The In Vivo and In VitroSituations – DifferencesAt first glance one may think that there is nogreat difference between the in vivo and in vitroXRF situations. However, some factors are moreprominent for in vivo XRF. First, volumes areconsiderably larger and situated deeply in thebody. Attenuation of incoming and characteristicX-rays is very pronounced, although the effect isalso seen at in vitro measurements (Streli, 1995).For example, characteristic cadmium X-rays areattenuated by 98 % when passing through 50 mmof water, i.e. a typical distance between the skinand the kidney surface. Moreover, matrix effectscan not be decreased by, e.g. drying.Second, the measurement time is limited fortwo reasons. One is the time that the subject canlay or sit still. The other is the absorbed dose tothe subject. The irradiated volumes are howeverquite small, thus, the energy imparted and meanabsorbed dose to the whole body are low comparedwith other diagnostic procedures in medicine. Forexample, for an absorbed dose to the skin ofthe finger of 3 mGy, the mean absorbed dose tothe whole body, at a finger-bone lead measurement,is two to four orders of magnitude lowerthan that of an ordinary chest X-ray examination(Börjesson, 1996).7.1.2 IN VITRO APPLICATIONS OFXRF IN MEDICINEThis section describes some recent applications ofin vitro XRF for measurement of heavy metals andother elements. It is not intended to completelycover all improvements and applications, rather togive an overview of some areas of research.7.1.2.1 MEASUREMENT OF HEAVYMETALS AND OTHER ELEMENTSMercuryHair mercury correlates with blood mercury at thetime when the hair is formed. Toribara (2001) useda scanning XRF method to investigate the mercurylevel in 1 mm portions of a single hair and couldin an exact way determine when a fatal mercuryaccident had happened (Figure 7.1.1).During dental intervention, amalgam particlesmay become absorbed in the oral mucosa; an‘amalgam tattoo’. Small amounts of mercury arebelieved to find their way to the blood. Forsellet al. (1998) found correlations between inflammatoryeffects and the mercury content in tissuebiopsies in the surroundings of tattoos.Autoclave sterilisation of extracted teeth, whichare used for educational purposes, possesses apotential health hazard. A LXRF study of mercuryon the inside of the autoclave bag suggested thatmercury is transported to a vapour phase during theprocedure and that vapour escapes and is finallyreleased into the room (Parsell et al., 1996).Chromium and LeadSmall airway epithelial cells may be targets forchromium-induced lung cancer (Singh et al., 1999).Phagocytosed lead chromate particles and intracellularlead inclusion bodies were observed by electronmicroscopy and confirmed by XRF (beam size0.5 µm × 0.5 µm). Interaction of chromium andlead with DNA may be involved in lead–chromatecarcinogenesis.It is well-known that heavy metal compounds,e.g. lead chromate, may leach from crystal glassand ceramic glazes and imply a health risk. XRFtechniques may be valuable to separate ceramic

490 X-RAY FLUORESCENCE ANALYSIS IN MEDICAL SCIENCES12001000800ng Hg/mg hair6004002000January1997December1996OctoberAugustData of measurementJuneFigure 7.1.1 XRF analysis of hair collected 31 January 1997 (Toribara, 2001). In August 1996, a fatal mercury accident occurred.Reproduced by permission of Arnold Publishershousehold utensils with high concentrations oftoxic elements from those with low levels (Andersonet al., 1996).In situ measured lead in remaining, scatteredbones, recovered 1993 from a purported campsiteof the 1845 Franklin expedition 1 was seen to rangeup to 1800 µg/g bone mineral (Keenleyside et al.,1996; Figure 7.1.2). Correlations between lead atdifferent bone sites were used to identify missingbones, i.e. bones could be associated to the sameindividual. Improperly soldered tin containers werebelieved to have been a major source of leadexposure for the expedition members.1 The purpose of the expedition was to map out the North-WestPassage from Europe to Asia, a sea route linking the Atlantic and PacificOceans. It lies above the Arctic Circle between Canada and Greenlandand the Arctic itself. The sea in this region is frozen over for most ofthe year. Temperatures in winter fall below −50 ◦ C. During the winterof 1846–1847, the ships became trapped in thick ice. After leaving theships and trying to find help the crew broke up in small groups butfinally all men died.IodineIn animals and man iodine is concentrated in thethyroid gland as a constituent of thyroid hormones.Iodine deficiency may lead to neurological syndromes,e.g. cretinism. Liu et al. (2001) showedthat iodine supplementation to iodine-deficient ratsimproved thyroid hormone metabolism, whereasthe trace elements bromine in brain (increased) andzinc (decreased), manganese (decreased) and copper(decreased) in erythrocytes, were affected bythe iodine supplementation. The data stimulate furtherstudies of the role of trace elements in thecentral nervous system (CNS) and their possiblelinks to neurological defects. Moreover, Majewskaet al. (2001) showed that the zinc concentration inTXRF (total reflection XRF) measured samples ofthe thyroid was lower in patients with thyroid cancer(23 µg/g) compared with patients with Grave’sdisease (42 µg/g). In blood samples, the reverserelation was obtained. Regarding whether elevated

IN VITRO APPLICATIONS OF XRF IN MEDICINE 491Bone lead [µg Pb (g bone mineral) −1 ]180016001400120010008006004002000VertebraCalcaneusPelvisMandibleBoneRadiusSkullHumerusFemurUlnaTibiaFigure 7.1.2 Bone lead content for all Franklin expedition bones measured (Keenleyside et al., 1996). Reproduced by permissionof Academic Pressblood zinc concentration is an indicator of thyroidcancer is a question for further studies.Most X-ray contrast agents contain iodine.Such substances can also be used as markersfor glomerular filtration rate (GFR). The contrastagent Iohexol has been compared with the mostcommonly used GFR marker for clearance measurements,51 Cr-EDTA (ethylenediaminetetraaceticacid). Both substances were injected in patients andsubsequent blood samples were analysed for iodinewith XRF technique (Brändström et al., 1998) andfor 51 Cr with γ -spectrometry. The observed strongcorrelation between Iohexol and 51 Cr-EDTA clearancesimplied compatibility between GFR markers.Measurement of urographic iodine contrast mediacan also be used to estimate the residual renal functionand the efficiency of haemodialysis (Sterneret al., 2000).ThoriumThorotrast (25 % thorium oxide), another contrastmedium, was used from the late 1920s until about1950. After i.v. injection, high concentrationsof thorium were seen in spleen (10–50 mg/g),liver (1–10 mg/g), bone marrow and lymph node.With respective biological and physical half-livesof 400 and 1.4 × 10 10 years, internal organs areirradiated by α-particles for the rest of the subject’slife. Increased occurrences of liver cancer, livercirrhosis and leukaemia have been reported. Usinga µ-beam XRF technique (beam ∅160 µm, Si(Li)detector for thorium L α line) the microdistributionof thorium was seen to form conglomerates in theliver, whereas it more looked like a belt in thespleen (Muramatsu et al., 1999). XRF can givecomplementary information to results gained byγ -spectrometry and α-autoradiography.PlatinumPlatinum, in the chemical form of cisplatin, maybe used to cure cancer. The drug has been inuse for about 30 years and it has shown verygood results in the treatment of, e.g. testicularcarcinoma. Cisplatin’s adverse effects, however,limit the amount which can be administered topatients. In animals, treated with cisplatin fortumours, increased levels of trace elements, e.g.iron, copper, zinc, ruthenium and bromine, inaddition to platinum, was observed in the kidneysand liver and suggested that platinum toxicity is aresult of the overall accumulation of trace elementsin these organs and not only high platinum levels(Shenberg et al., 1994). Administered amounts ofselenite reduced the trace element levels, hence,selenium might have a future as chemoprotector.It has also been shown that rubidium, bromine,

492 X-RAY FLUORESCENCE ANALYSIS IN MEDICAL SCIENCESselenium, zinc, copper and iron concentrationsin blood, liver, kidneys, colon, and skin weresignificantly different in tissue samples obtainedfrom mice inoculated with tumours and normalmice (Feldstein et al., 1998). The rubidium levelin a tumour was one order of magnitude higherthan in normal tissue.CalciumCoronary heart disease (CHD) is common, especiallyin the Western countries. Inverse relationshave been found between health district standardisedmortality ratio (SMR) and the mean hair calciumconcentration (MacPherson and Bacsó, 2000;Figure 7.1.3). Part of the explained variance wasenvironmental factors believed to influence calciummetabolism, e.g. water hardness and numberof sunshine hours. For example, the south-east partof England had the highest hair calcium, the hardestwater and the most sunshine hours and thelowest mortality from CHD. The converse was trueof Scotland. Additionally, the authors point out thatconfounding socio-economic conditions may havebeen more beneficial to the south-east part than toScotland, thus reducing the SMR.Synchrotron radiation XRF may be a suitablemethod to study the interface between bone andbiomaterials, i.e. substitutes for autogenous bonegrafts, with regard to mineral content. Circulardefects (∅ 4 mm), made in tibias of rabbits, wereaugmented with a composite of hydroxyapatite(HA) granules. The calcium distribution, studiedwith µ-XRF line scans, suggested that calciumphosphate compositions, e.g. HA, have interestingproperties as bone substitutes (Liljenstenet al., 2000).NickelIn order to detect allergen metals, XRF is used indentistry and dermatology. Suzuki (1995) reported150Mean SMR for CHD100502.52.6 2.7 2.8Log district hair Ca (ppm)2.9 3 3.1Figure 7.1.3 The relationship between the mean district SMR for CHD and log district hair calcium concentration (MacPhersonand Bacsó, 2000). Reproduced by permission of Elsevier Science

SYSTEM DEVELOPMENT OF IN VIVO XRF IN MEDICINE 493successful allergen elimination in patients withmetal allergy from dental restoration work.Detected nickel and gold in skin specimens, takenfrom lesions in pierced earlobes, suggested thatsmall metal fragments remain in lesions for along time, even after the studs have been removed(Suzuki, 1998). This causes irritation and cutaneousreactions.BromineThe determination of extracellular water, using82 Br dilution technique, has drawbacks, e.g. radiationdose and the short physical half-life of 82 Br.An approach with administered stable brominedetected with 109 Cd sources and a Si(Li) detectorin vitro indicated that measurements of bloodbromine may be substituted with bromine in urineand saliva, which imply less discomfort to thepatient (Zaichick, 1998a,b).PalladiumThe increasing pollution of palladium in theenvironment, as well as in the body of livingspecies is discussed controversially. Sures et al.(2001) showed, with TXRF technique, that automobilecatalyst emitted palladium is bioavailablefor aquatic animals. Also, the production and recyclingof palladium-containing materials, as well asthe use of palladium in dental restorative alloys,may be a source of toxic/allergic reactions.Palladium in body fluids can be analysed withICP-MS, however, for environmental samples,e.g. road dust, the technique is less suitable(Messerschmidt et al., 2000). Therefore, a TXRFmethod was developed for analysis of palladiumand gold in environmental samples (detectionlimits 2.5 ng/l and 2.0 ng/l, respectively). Themethod is sensitive but time consuming, hence itwas suggested to serve as ‘gold standard’.GoldMechanisms of drowning were studied usingan immersion fluid, containing small gold tracers(12–48µm), which were introduced into theairways of rats (Bajanowski et al., 1998). Microanalysesafter the animals had died showed thatsmall diameter tracers had penetrated the intercellulargaps of the alveolar epithelium, while largertracers were incorporated into the epithelial andendothelial cells. An active post-mortem transportproceeded in alveolar pneumonocytes andmacrophages and functioned for a time period evenafter death and cessation of circulation.Multielement StudiesImproved element-specific (iron, cobalt, copperand zinc), detection in capillary electrophoresis,with monochromatic 10 keV synchrotron radiationXRF was seen to be superior compared with ICP-MS and PIXE methods (Mann et al., 2000). Thepresent detection limit was ≈0.5 ng and furtherdevelopment seems possible.Synchrotron radiation XRF has also been usedto study the myocardial blood flow by means ofheavy element microspheres (Mori et al., 1995).Elements studied were bromine, yttrium, zirconium,niobium, iodine, and barium and 20 and50 keV SR energy was used.Multielement studies of human placenta haveindicated that most element concentrations are thesame, regardless of the mother’s state (‘normal’,undernourished, smoker or hypertension) (Meitínet al., 1999). However, strontium levels for thelatter three states were markedly lower than forthe ‘normal’ state.7.1.3 SYSTEM DEVELOPMENTOF IN VIVO XRF IN MEDICINE7.1.3.1 PHOTON SOURCESGEOMETRIESPhotons from an X-ray tube or from a γ -emittingradionuclide source may be used to excite elementsin vivo. In some cases it is possible to find radionuclidesources with suitable energy, negligible orfilterable emission of other γ - and β-radiation,high yield and high specific activity at a reasonable

494 X-RAY FLUORESCENCE ANALYSIS IN MEDICAL SCIENCEScost. Sources used or proposed for in vivo studiesare among others 57 Co, 99 Tc m , 109 Cd, 133 Xeand 241 Am. An advantage is the stable output,compared with the X-ray tube output, which mayvary to some extent over time and thus need tobe continuously monitored by a separate detector.A radionuclide source is also compact and transportable.On the other hand, it may have a shorthalf-life, be expensive and give a low photon fluencerate.A limitation of the XRF technique is the amountof scattered photons that are detected. Since thehuman body mainly consists of low Z elements,incoherent scattering is the dominating photoninteraction process. Scattering in low Z matricesleads to a broad and large background in measuredpulse height distributions. The concentration of theelement of interest is generally low, on the orderof µg/g, which implies a low signal-to-backgroundratio as the small characteristic X-ray peaks aresuperimposed on a high background distributionof scattered radiation. Thus, it is essential toimprove this ratio by increasing the net signaland/or decreasing the background. One should,however, be aware that incoherently scatteredphotons can be used constructively. For mostbiological materials, the amount of incoherentlyscattered photons is proportional to the mass ofthe analysed volume, thus, a normalisation canbe made. Moreover, coherent scattering can beused for bone mineral measurements and fornormalisation to bone mineral content when leadin bone is determined.Polarised Photons from an X-ray TubeBackground reduction may be achieved by usingpartly plane-polarised photons, e.g. produced byincoherent scattering of primary photons in 90 ◦ .Other methods to produce a beam of planepolarisedphotons are synchrotron radiation (SR),thin-anode transmission X-ray tubes and Braggdiffraction. However, incoherent scattering hasbeen described as one of the best ways toimprove the ratio between fluorescent and scatteredradiation for low Z matrices (Heckel, 1995).Briefly, the detector is put in the plane definedby the electric vector of the polarised photon.A reduced fluence rate of scattered photons willresult if the detector axis is parallel to theelectric vector. The differential collision crosssection(d e σ /d) ratio for the photon fluencerate in the directions of minimum and maximumscatter is 1.6 % at a photon energy of 100 keV(Evans, 1955). However, collimation and multiplescattering largely reduce the benefit of polarisation,e.g. an in vivo method for platinum had a ratio of40 % (Jonson et al., 1988).The tube potential significantly impacts thedetection limit since the number of photons, capableof exciting the element increases, and the overallnumber of photons also increases when thevoltage of the tube is increased (Figure 7.1.4).Theoretical analyses of system parameters for arenal mercury measurement set-up indicate that adecreased detection limit is within reach (O’Mearaet al., 2000). An improvement might be possiblethrough a higher accelerating potential (250 kVp)than was used by Börjesson et al. (1995). However,this has to be tested experimentally.Development of tube design leads to considerablechanges in spectral shape and possiblyto lower MDCs. The feasibility of a nearlymonochromatic X-ray tube, with a gold anodeand a secondary target of tantalum for measuringcadmium in vivo, was studied by Börjessonet al. (2000). However, characteristic tantalumX-rays (56–67 keV) and a low fluence rate ofbremsstrahlung did not offer an improved detectionlimit. In the future, interchangeable targetsmay facilitate a better match between the studiedelement’s absorption edge and the primaryphoton energy. A recent Monte Carlo simulationof a monochromatic X-ray tube seems promising(O’Meara et al., 2002) for decreasing the detectionlimit.Radionuclide SourcesBesides the aforementioned in vivo methods foriodine and lead, developed during the 1960s and1970s (Hoffer et al., 1968; Ahlgren et al., 1976;Ahlgren and Mattsson, 1979), another KXRF

SYSTEM DEVELOPMENT OF IN VIVO XRF IN MEDICINE 495160140120MDC (µg/g)10080604020090100 110 120 130 140 150Tube potential (kVp)160 170 180 190 200Figure 7.1.4 The minimum detectable concentration (MDC) for mercury in the kidney for different X-ray tube voltages (kVp)(Börjesson, 1996)technique based on a 109 Cd source was developedfor bone lead measurements. In the beginning, anannular source was used (Somervaille et al., 1985)but was later replaced by a point-source, placed infront of a large area detector. This resulted in animproved precision (Gordon et al., 1993).A third technique, uses low photon energyLXRF from bone lead excited from a 109 Cdsource or an X-ray tube (Ao et al., 1997b; Rosen,1997; Figure 7.1.5). Methodological differencesin KXRF and the ‘short-sighted’ LXRF presumablyimply that the KXRF and LXRF methodsprovide complementary information. Recently,Todd (2002a,b) reviewed the LXRF method andshowed that predicted bone lead and measurementuncertainty were influenced by the choiceof linear attenuation coefficient, with which tocorrect for overlying tissue. Inter-individual variabilityin body composition, methodological uncertaintyin the ultrasound measurement of overlyingtissue thickness as well as discrepancy betweenthe site of LXRF and the site of ultrasound measurementwere also important factors. Interferencefrom lead in non-bone tissues may not be negligible.A combination of radionuclide KXRF andtube LXRF has been proposed, however, Toddet al. (2002a) found that the variability of themethod was large enough to give concerns regardingthe application of this method at all for in vivouse. Feasibility studies of various sources ( 99 Tc m ,133 Xe, etc.) for measurements of platinum andgold have also been presented, but will not bereviewed here.7.1.3.2 DETECTOR ANDELECTRONICSIt is essential to optimise the detector for variouselements studied as illustrated by the reduced(50 %) detection limit when switching from agermanium detector to a silicon detector for in vivocadmium measurements (Nilsson et al., 1990).The combination of a large-area detector anda fast analogue-to-digital converter (ADC) hasalso proven advantageous. The new ‘clover-leaf’detector is also of special interest (Nie et al., 2002).It consists of several detectors with separate setsof electronics. Consistency between simulationsand experiments and a greatly reduced detectionlimit (70 % lower than with standard detector) werereported for bone lead KXRF.Furthermore, digital spectroscopy systems mayoffer important advantages, due to their increasedthroughput of pulses from photon interactionsin the detector (Fleming, 1998, 1999). Insteadof conventional pulse shaping circuits, the newspectrometer filters and shapes the pulses digitally.

496 X-RAY FLUORESCENCE ANALYSIS IN MEDICAL SCIENCESPolarising scattererand/or secondary targetPrimary pathfilter locationUnpolarisedPrimary pathX-ray source90°Secondary filterSecondary pathPrimary pathfilter locationPartially planepolarised90°SampleTertiary pathTertiary filterDetectorFigure 7.1.5 Schematic representation of experimental configuration for LXRF of bone lead (Todd, 2002b). The sketch showsthe X-ray source, scatterer with filters, sample and detector with filter. Notice the state of polarisation at various positions alongthe beam line. Reproduced by permission of IOP PublishersImproved energy resolution, detection limit andprecision, the latter up to 27 %, have beenrecorded (Bateman et al., 2000). The detectionlimit for tibia bone lead was 2.2 µg/g bone mineral,corresponding to about 1.3 µg/g wet bone (Flemingand Forbes, 2001). The in vivo performance is tobe explored.Portable XRF systems, with generators producing35 kV and 0.1 mA, and thermoelectricallycooled cadmium zinc telluride detectors are todayavailable on the market. Primarily, they seemapplicable to in vitro studies, e.g. for measurementof mercury and lead contamination of surfaces, ata detection limit of 0.1 mg/cm 2 , but may have afuture potential for in vivo XRF.7.1.3.3 MONTE CARLO SIMULATIONThe detection limit in vivo is often higher or comparablewith the concentration of the element in thesubject. Thus, improving the sensitivity by modificationsof the set-up parameters are desirable. Thegenerally large number of parameters (e.g., tubevoltage, collimation, angles, filters, detector) thatcan be changed makes this time consuming andcostly. However, modern computers make it possibleto simulate the measurement situation, usinga Monte Carlo code. Several such codes are nowavailable and need only small modifications. Wewill briefly review some recent publications in thefield. Some codes account for Compton momentum

SYSTEM DEVELOPMENT OF IN VIVO XRF IN MEDICINE 497broadening and photon polarisation (Tartari et al.,1991; Fernandez et al., 1993; Tartari et al., 1999).It has to be stressed that the ultimate test of a simulatedresult is to apply the optimised system to anin vivo measurement to verify that the optimisationworks in reality.Wielopolski et al. (1983, 1989) used an X-raytube for bone lead LXRF analysis. Later, Ao et al.(1997a,b) and Gardner et al. (1999a,b) developedthe CEARXRF code to improve three set-ups withKXRF ( 109 Cd source) and LXRF ( 109 Cd and X-ray tube source). The lowest detection limit wasfound for a polarised X-ray tube source. For theLXRF technique, L α and L β X-rays provide amethod for minimising the skin thickness effect.The code may be used for tasks such as theproposed combination of KXRF and LXRF (seesection on ‘Radionuclide sources’). It was alsoshown that the normalisation of bone lead tocoherent scatter improves the accuracy for theKXRF system, in accordance with Somervailleet al. (1985) and Bradley et al. (1999).The code developed by O’Meara et al. (1997,1998a) for simulation of source-excited in vivoXRF of heavy metals showed agreement in mostparts of the spectrum, whereas, in the low energytail of Compton scattered photons, agreementwas less. Simulations of a 57 Co source in abackscatter geometry (Figure 7.1.6), to measurebone uranium showed that the uranium concentrationin tibia was insensitive to variations insource–sample geometry, thickness of overlyingtissue and tibia size.O’Meara et al. (1999, 2001b) also presentedsimulation results of the original set-up with the57 Co technique (Ahlgren and Mattsson, 1979) tomeasure finger-bone lead. As for the 109 Cd set-up,the 57 Co may also benefit from using the coherentscatter peak normalisation, as an alternative to howit presently is made by radiographs of the subject’sfinger, which increase the absorbed dose.Al-Ghorabie (2000) used the EGS4 MonteCarlo code to simulate a measurement situationwith a 133 Xe source in a backscatter geometry,and found detection limits of 15–60 µg/g forcadmium KXRF in kidneys situated at a depthof 30–60 mm. Further optimisation and in vivoresults are expected.A version of the EGS4 code (Kilic, 1995)has also been used to optimise a set-up with apolarised source (X-ray tube) for in vivo XRF ofplatinum (Lewis et al., 1998). Good agreementbetween simulation and experiment was observed(Figure 7.1.7). Another version of EGS4, alsointended to model platinum in vivo measurements,was presented by Hugtenburg et al. (1998). Incontrast, analytical methods, e.g. the fundamentalparameter method, for describing the in vivoKXRF of platinum measurement situation havebeen suggested (Szaloki et al., 1999).7.1.3.4 SPECTRUM ANALYSISAt most in vivo XRF measurements, a small netsignal is analysed in the presence of a largebackground of scattered photons. More or lesscomplex fitting algorithms may be applied forextraction of the net peak area. The commonlyused straight line approximation (least-squaresmethod) of the background under the peak iseasy to apply and works well in situations witha ‘straight’ background. However, this is oftennot the case and the background may be betterdescribed with a polynomial.There are also nonlinear regression methodsthat model both background and signal, e.g.the Marquardt algorithm and sequential quadraticprogramming. These methods find the optimal fitby iteratively changing the parameters in smallsteps, starting with initial data supplied by theuser. The algorithm may, for example, be the sumof a polynomial background and Gaussian shapedpeaks. Iterative methods are sensitive to the supplyof ‘correct’ seed values at the start of fitting,otherwise the procedure may capsize.For those interested in spectrum analysis andfitting, especially regarding ‘outliers’, the publicationby Reich (1992) is recommended. The authordiscusses, among other things, the use of absolutevalues of the deviations instead of the squareddeviations. The proposed technique might producemore stable fits in spectra with outliers. These outliershave a destructive effect on the whole fit as

498 X-RAY FLUORESCENCE ANALYSIS IN MEDICAL SCIENCESGe crystal(variabledimensions)g-ray source(variabledimensions)Source−phantom separation(variable)Bone offset(variable)Bone diameter(variable)(a)Tissue diameter(variable)g-ray sourceGe crystal(variabledimensions)Detector−phantomseparation(variable)Source−phantom separation(variable)Bone offset(variable)Bone diameter(variable)(b)Leg diameter(variable)Figure 7.1.6 A schematic of the geometries used for simulating the (a) 180 ◦ backscatter and (b) 90 ◦ scatter systems. Notethe alignment of the detector with the centre of the bone cylinder (O’Meara et al., 1998a). Reproduced by permission of IOPPublishers

SYSTEM DEVELOPMENT OF IN VIVO XRF IN MEDICINE 4996000Pt Ka 2Pt Ka 1Pb Ka 2,1Pb Kb 1,2Counts40002000ExperimentSimulation0500Channel number10001500Figure 7.1.7 Simulated and measured XRF spectra using a 1000 µg/g platinum solution (Lewis et al., 1998)their impact become very strong due to the squaringwhen minimising the deviations. In the end, itis up to the individual scientist to determine themethod to use (Kondrashov et al., 2000). Moreover,it is wise to check the accuracy and precisionof the fitting procedure by, e.g. fitting a large numberof background distributions (no phantom) anddetermine the mean net number and the coefficientof variation.New algorithms for fitting data have evolvedand one of them uses a least moduli approach.Compared with the least-squares method the ‘new’approach is more effective for ‘strong’ peaks on alow background, i.e. calibrations peaks, whereasthe least-squares method is more effective for aweak peak situated on a large background, i.e.the in vivo situation (Kondrashov et al., 2000).Moreover, a doublet deconvolution technique forcorrecting the peak of coherently scattered photonsfor the K β2 signal in the bone lead set-upwas suggested by Kondrashov and Rothenberg(2001a). Kondrashov and Rothenberg (2001b)presented mathematical proof that the estimateof bone lead uncertainty in measurements with109 Cd needs revision. Authors also suggested areduced detector–target distance to improve themeasurement. A shorter distance may, however,lead to pile-up of pulses and this effect has beenstudied by simulations (Gardner et al., 1999a).7.1.3.5 CALIBRATIONCalibration of an in vivo measurement techniquefor quantitative analysis of element tissue concentrationis not an easy task. Often there is no ‘goldstandard’ and phantoms have to be used. One mayalso make an in vivo XRF measurement and chemicallydetermine the element concentration in abiopsy of the measured volume. Another variant isto measure the concentration in situ, usingXRF,inautopsy material and then analyse the material by,e.g. AAS. Yet another way is to use animal organs,e.g. animal kidneys immersed in water for simulationof in vivo XRF of kidney cadmium. Onemust, however, always be aware of the strengthsand weaknesses the actual calibration method has.In the last example, clearly visible horse kidneys,

500 X-RAY FLUORESCENCE ANALYSIS IN MEDICAL SCIENCESat an accurately known depth in water, is not thesame as a kidney at an unknown depth in a nontransparenthuman being.In the following section we will limit the discussionto calibration of bone lead systems. Regardingthe phantom, it has traditionally been made of silicaparaffin wax and plaster-of-Paris, a powdery,slightly hydrated, calcium sulfate made by calcininggypsum. However, phantoms of polyurethanesand calcium carbonates are claimed to be muchmore uniform in density and composition andto better describe the in vivo situation regardingscatter, attenuation, positional dependency anddead-time loss (Spitz et al., 2000). Another phantom,a synthetic apatite matrix was proposed byTodd (2000a). Todd concluded that the effect onthe coherent conversion factor, which convertsbetween calibration standard and human bone,from impurities in plaster, coherent scatter fromnon-bone tissues and the subject’s measurementgeometry were all of minor effect. Furthermore,validation using non-human bones may introduce‘new’ uncertainties due to changes in spectralshape (Todd et al., 2001d).Contamination of subjects, measurement systemsand phantoms has occurred, and may happenagain, unless measures are taken to prevent it. Forexample, measurement of bone lead on the groundsof a lead plant demands that the measurement roomis clean from environmental lead. It means thatworkers are to enter the room without bringing leadwith them and that lead on skin at the measurementposition is carefully removed. The effects ofcontamination may be considerable (Todd, 2000b;Todd et al., 2000b).7.1.3.6 DETECTION LIMITVarious definitions of the MDC have been presented(Currie et al., 1994; Todd, 2002b). Forexample, the MDC may be defined asMDC = 3 ∗ C√ N bgN netwhere N bg is the background counts under thecharacteristic X-ray peaks, N net the net countsin the peaks and C the element concentration.N bg and N net linearly depend on the measurementtime, thus the MDC is inversely proportional tothe square root of the measurement time. TheN net varies, according to, e.g. attenuation of theemitted characteristic X-rays. Hence, the MDCvaries strongly with depth (Figure 7.1.8). Photonattenuation in lateral direction results in MDCvariability for a given dorsal kidney depth. It is200MDC (µg/g)10080604020108643035 40 45 50 55 60Dorsal depth to kidney surface (mm)65 70 75 80 85 90 95Figure 7.1.8 The MDC for cadmium (ž and Ž) and mercury () in the kidney cortex plotted as a function of the dorsal kidneydepth (Börjesson, 1996)

SYSTEM DEVELOPMENT OF IN VIVO XRF IN MEDICINE 501important that all data are used and not discarded inthe analysis. For example, excluding all data pointswith concentrations under the detection limit willlead to errors in the calculation of mean values andstandard deviations (Kim et al., 1995).7.1.3.7 PRECISION AND ACCURACYIt is essential that the measurement presents aresult close to the ‘true’ value. If the in vivo XRFmeasurement may be repeated with the same setup,a low precision may be acceptable as long asthe mean value of the series of measurements isaccurate. However, if only a single measurement ispossible, which is usually the case in in vivo XRF,precision must be high. Accuracy and precision arediscussed from a KXRF bone lead point of view.The high precision for repeated measurementsat the same bone site and the bone lead heterogeneity,i.e. potential differences in bone lead at varioussites of the studied bone, need to be controlled. In1995, Hoppin et al., after measuring with a 109 CdKXRF technique, concluded that it ‘...may not yetbe a useful diagnostic tool for individual subjects,but it may be of great use to environmental scientiststrying to characterise long-term lead exposureand dose in the general population or specificsubpopulations.’ Hoppin et al. (2000) later demonstrateda considerable variability in bone lead formeasurement locations only 10 mm from the centreof the tibia. This may, according to the authors,limit the interpretation of bone lead.On a group level, the 109 Cd KXRF techniqueis capable of revealing bone lead differencesof 5 µg/g bone mineral (i.e. 2.9 µg/g wetbone; conversion factor from bone mineral to wetbone 1/1.72) or less (McNeill, 1999; McNeillet al., 1999). However, the individual measurementuncertainty is significantly affected by age,sex, and subject obesity (Figure 7.1.9). Womenhave poorer precision than men because of smallerbone mass. Obese subjects have tissue overlaythicknesses that attenuate the signal, thus, precisioncan be poor (>10 µg/g bone mineral; >5.8 µg/gwet bone). A precision better than 2 µg/g bonemineral (1.2 µg/g wet bone) may be necessaryfor meaningful evaluations of individual measurements(Bradley and Farquharson, 1999). Theuncertainty at measurements in young individualswas shown to be marginally worse than inadults (Todd et al., 2001a). This is important sincemeasurement in children and adolescents is of specialinterest.Ideally, the uncertainty assigned to an individualbone lead measurement would be the standarddeviation of multiple measurements made in thesubject. Regarding 109 Cd KXRF measurements,Todd et al. (2000a) studied factors that mightexplain why the observed uncertainty underestimates(up to 18 % deviation) the standard deviation43In (precision)2100.100.20 0.30 0.40 0.50 0.60Body mass index (kg/cm 2 (E-2))Figure 7.1.9 The natural logarithm of the precision against body mass index for female subjects (McNeill et al., 1999a).Reproduced by permission of IOP Publishers

502 X-RAY FLUORESCENCE ANALYSIS IN MEDICAL SCIENCESof replicate tibia lead measurements. Changes overtime, e.g. source decay, degradation in detectorresolution and efficiency, may partly be responsiblefor the observed discrepancy. Repositioning ofthe sample, as suggested by Hoppin et al. (2000),seemed however not to add to the uncertainty.Macroscopically, lead is fairly homogeneouslydistributed within the skeleton. Microscopically,lead-to-bone mineral concentration ratio ishomogenous in the endosteum but peaked in theperiosteum region (Jones et al., 1990; Schidlovskyet al., 1990). Bone lead in cadaver legs showhigher concentrations (5–8 µg/g bone mineral;2.9–4.7µg/g wet bone) in surface compared withcore tibia bone (Todd et al., 2001b,e). These findingswill have an impact on the evaluation ofKXRF and LXRF since the former technique samplesmore than just the superficial 1–2 mm of thetibia. Thus, it is not expected that the results of thetwo techniques should agree. Moreover, comparisonwith AAS showed that the KXRF method islikely to overestimate the core lead level by about5–8µg/g bone mineral (2.9–4.7 µg/g wet bone)(Todd et al., 2002b).Besides tibia and calcaneus, the two mostwidely used sites for 109 Cd KXRF measurements,also the patella has been used. The questionwhether orientation of the patella affects the measurementwas looked into by Todd et al. (2001c),who reported no obvious effect on lead concentration,whereas uncertainty was significantlychanged. Contributions from non-patellar lead indistal femur, proximal tibia and synovium couldnot be excluded.Aro et al. (2000) validated the 109 Cd KXRF byinitial measurements in patella and tibia in cadavericlegs with surrounding tissues intact. KXRFwas repeated after all soft tissue had been stripped.The bone was then isolated and measured by ICP-MS. Results showed strong correlations betweenKXRF and ICP-MS bone lead. The study indicatedthat KXRF measurement is not influencedby interference from surrounding soft tissue.The relationships between indicators of leadexposure have mainly been studied by linearregression methods. However, there are basicunderlying assumptions associated with this technique,e.g. that the uncertainty in the X values iszero, which as a rule is not true. For example,the relationship between bone lead (Y) and bloodlead (X) assumes that blood lead is determinedwith a 100 % accuracy, which is not realistic.Thus, the regression line would be different if wewould change the X and Y variables. To take intoaccount the uncertainty in both variables one mayuse ‘structural analysis’ (Brito et al., 1999).7.1.4 SUMMARY OF IN VIVOAPPLICATIONS OF XRF IN MEDICINE7.1.4.1 LEADLead has found a range of modern applicationsin which occupational exposure mayoccur (Tables 7.1.2 and 7.1.3). For the generalTable 7.1.2 Sources of exposure and uptake of cadmium, mercury and lead (Börjesson, 1996, references therein and paperswithin this review)Element Exposure Uptake (%)Occupationally exposed General public Gastrointestinal InhalationCadmiumMercuryLeadProduction and recycling of Ni-Cdbatteries. Use of alloys, solders,pigments, fertilisersMercury and gold mining.Chloralkali and thermometerfactories. Dental amalgamhandlingProduction and recycling of leadbatteries, ammunition, paint,plumbing, cable cover, radiationshieldFood, smoking ≈5 0.1–50Food, dentalamalgamFood, water, lead ingasoline

SUMMARY OF IN VIVO APPLICATIONS OF XRF IN MEDICINE 503Table 7.1.3 The estimated biological half-life and tissue levels for cadmium, mercury and lead. Note that multiple half-lifecomponents may be found in, e.g. blood, and this mirrors the excretion of an element from various organs and tissuesElement Biological half-life (d = days, y = years) Typical levels in tissues (µg/g)Blood Urine Tissue Occupationally exposed General publicCadmiumMercury75–130 dand7–16y3–4 d and45 dLead 1 d,30–50d,1–5yand 13 yNo studiesfound26 y (whole body) 1 d and30–60 d (lungs), 10–30 y(kidney), 5 y (liver)40–90 d 42–58 d (whole body),64 – 180 d (kidney), 21 d(brain) (Long-termcomponents not known)150 d andprobably alongercomponent5–30 y (cortical/trabecularbone) 30 d (soft tissue)Up to 600 (kidney), Up to120 (liver)Up to 70 (kidney),

504 X-RAY FLUORESCENCE ANALYSIS IN MEDICAL SCIENCES1 2 3 4Figure 7.1.11 Schematic diagram of the in vivo XRF of leadin teeth (Zaichick and Ovchjarenko, 1996). 1, Detector casing;2, Si(Li) detector; 3, annular 109 Cd radionuclide source; 4,shielding and collimation. Reproduced by permission of MarcelDekker, IncBone lead XRF has mostly been applied tooccupationally exposed subjects. Retired smeltersmay have much higher bone lead levels than activesmelters. This is ascribed to the long exposureduration and high exposure levels during earlieremployment periods, in combination with the slowbone lead excretion.A positive correlation between blood and bonelead concentrations is often found for retiredsmelters, confirming the skeleton as an endogenoussource of lead. The fraction of blood lead thatcomes from the skeleton may be up to 70 %.In active workers, the influence from ongoingexposure masks the relation between blood andbone lead.Re-measurements of bone lead in smelter workershave indicated a shorter bone lead half-life,about 5 years, in younger persons (10 % and in some cases possibly >30 % (Gulsonet al., 1999). However, the changes in bone leadwould be unlikely to be detected by current boneXRF methods. The most influencing factors onmaternal plasma lead seem to be maternal bonelead stores, air lead exposure and recent cookingwith lead-glazed ceramics (Chuang et al., 2001).The breastfeeding practice also seems to be animportant predictor of blood lead concentration(Tellez-Rojo et al., 2002). Women who exclusivelybreastfed their infants had blood lead levels thatwere increased by 1.4 µg/dl and women whopractised mixed feeding had levels increased by1.0 µg/dl, in relation to those who had stoppedlactation. These results support the hypothesis thatlactation is related to the amount of lead releasedfrom bone.Apart from the acute threat of being killed bya gunshot, retained lead bullets tend to increaseblood lead and the situation is probably aggravatedif a bone fracture is caused by the gunshot(McQuirter et al., 2001).KXRF indicated a correlation between uricacid level and bone lead, whereas no obviousassociation between gouty arthritis and lead, atenvironmental exposure levels was seen (Shadicket al., 2000).For the reader interested in kinetics/toxicologywe refer to papers published within the last decode(Cake et al., 1996; Börjesson et al., 1997b; Chettleet al., 1997; Fleming et al., 1997; Bergdahlet al., 1998; Hernandez-Avila et al., 1998; Elreedyet al., 1999; Fleming et al., 1999; Schwartz et al.,

SUMMARY OF IN VIVO APPLICATIONS OF XRF IN MEDICINE 5051999; Skerfving et al., 1999; Suarez et al., 1999;Ambrose et al., 2000; Olsson et al., 2000; Erfurthet al., 2001; Markowitz and Shen, 2001; McQuirteret al., 2001; Schütz et al., submitted).Low-level lead exposure in early developmentand childhood may be linked with disturbancesin physical and mental development (Needlemanet al., 1996). Central and peripheral neurologicaleffects were found in young adults some20 years after childhood environmental lead exposure(Stokes et al., 1998). However, an associationbetween neurological outcomes and bone leadwas absent, due to a presumably low precisionof the bone lead measurement. Furthermore, datasuggested that cognitive function (verbal memoryand learning, visual memory, etc.) may progressivelydecline due to past occupational exposure(Schwartz et al., 2000). An increased tibia lead of16 µg/g was equivalent to 5 more years of age.7.1.4.2 CADMIUMOccupational cadmium exposure takes place invarious sites of industry (Tables 7.1.2 and 7.1.3).The total uptake of cadmium in the normal populationmay typically range 0.5–3 µg/day. The naturalcadmium content in soil varies and agricultural useof phosphate fertilisers and sewage sludge lead tosoils with increased cadmium content. Acid precipitationfacilitates mobilisation of cadmium insoil. Hence, elevated cadmium levels in vegetablesand animal food may be anticipated. Thiseventually results in an increased human exposure(Chan et al., 2000). Increasing levels of cadmiumin humans have been observed during the 20thcentury (Drasch, 1983). In kidney specimens from1897–1939 (year of death), subjects from the normalpopulation of that period had 50 times lowercadmium concentrations compared with specimensfrom the 1980s. However, kidney cadmium, asmeasured with KXRF in groups of non-smokingfarmers with high and low pH in their drinkingwater did not differ between groups (Nilsson et al.,2000). Neither did two groups with high and lowblood cadmium levels differ in their kidney cadmium.On the other hand, for the pooled groupof farmers a correlation was seen between urinarycadmium and decreasing drinking water pH.Cadmium is virtually absent in new-borns, butthe element’s long biological half-life may lead toa considerable increase in the body burden duringlife. Kidney cadmium increases progressivelywith age up till 50–60 years and then tends todecline, whereas a decline is not observed for livercadmium (Torra et al., 1995). The renal cortex cadmiumconcentration in non-occupationally exposedsubjects generally ranges 10–100 µg/g (Friis et al.,1998; Barregård et al., 1999a; Benedetti et al.,1999).Cadmium in kidneys and liver is readilymeasured using KXRF, but many studies havealso been made using in vivo NAA. Both techniqueshave advantages and drawbacks regardingabsorbed dose, sensitivity, radiation shielding, etc.The polarised KXRF system is devoted to measurementsnot only in occupationally exposed subjectsbut also in the general population. NAAand XRF studies have shown that the relationbetween kidney and liver cadmium is broadlyconsistent, regardless of method used (Börjessonet al., 1997a).The toxic effects of cadmium exposure includeacute and chronic poisoning (Järup et al., 1998;Skerfving et al., 1999). The kidney is consideredthe critical organ for chronic poisoning and anestablished damage seems irreversible and mayprogress even though the exposure has ceased.Low-level exposure may be linked with tubularproteinuria, i.e. an increased excretion of proteins,at a considerably lower U–Cd, 1.0 nmol/mmol creatinine,than earlier expected (Järup et al., 2000).Low-level exposure may also be associated withosteoporosis (Staessen et al., 1999; Alfvén et al.,2000) and end-stage renal disease (Hellströmet al., 2001).7.1.4.3 MERCURYMercury is naturally introduced into the biosphereby degassing from the earth’s crust and the oceans.It is also released by combustion of fossil fuels,cremation of people with amalgam fillings and bya number of other human activities (Tables 7.1.2

506 X-RAY FLUORESCENCE ANALYSIS IN MEDICAL SCIENCESand 7.1.3). In chloralkali plants, mercury cathodesmay be used for the production of caustic sodaand chlorine gas from brine. Another applicationis the primitive extraction of gold in mining,using mercury amalgamation. In general, theoccupational exposure levels may be about 10–20times higher for chloralkali and thermometerworkers than for dental personnel. Food and dentalamalgam dominate the mercury exposure for thegeneral population (Barregård et al., 1995).Absorbed mercury is quickly distributed to mostregions of the body with the kidneys as the majordepot. The kidneys and the central nervous systemmay be regarded as risk organs. For a reviewof mercury kinetics/toxicology see, e.g. Skerfvinget al. (1999).Our group seems to be the first to havepublished in vivo KXRF measured kidney mercuryconcentrations in occupationally exposed subjects(Börjesson et al., 1995). The average concentrationwas 24 µg/g (maximum 54 µg/g; Figure 7.1.12).The results were in accordance with literaturedata on chemically measured kidney mercuryconcentrations (Barregård et al., 1999b). Mercurymeasured in liver, thyroid, tibia and bone werebelow the respective detection limits.Repeated measurements in subjects over afew months non-occupational exposure indicateda decrease in kidney mercury, although measurementscontained substantial uncertainty. Theestimated mean biological half-life was 115 days(range 55–173 days; Figure 7.1.13), thus longerthan that reported from whole-body counter measurementsafter short-term exposure (Rahola et al.,1973; Hursh et al., 1976). However, long-termoccupational exposure may lead to a considerableaccumulation of mercury in the kidneys,thus, components with long half-lives may possiblybe observed.7.1.4.4 IRONThose who suffer from thalassaemia, an inheritedchronic blood disorder, are unable to produce sufficientamounts of haemoglobin, hence regular bloodtransfusions are required (Bradley and Farquharson,1999). A build-up of residual iron in liver,heart and other organs may in turn lead to coronaryproblems, etc. A KXRF system (X-ray tubeusing 20 kV and 20 mA and a germanium detector;Figure 7.1.14) was developed for indirect determinationof organ iron stores via measurements on theskin (Farquharson and Bradley, 1999; Farquharsonet al., 2000). A quasi-monoenergetic beam of8.4 keV, which is just above the absorption edgeof Fe (7.11 keV), produced a detection limit of1210Number of persons86420

SUMMARY OF IN VIVO APPLICATIONS OF XRF IN MEDICINE 507Kidney Hg (µg/g)605040302010987654−20 0SubjectPMLIA20 40 60 80 100 120 140 160Time (days since first measurement)Figure 7.1.13 Retention of mercury in kidneys (Kidney Hg; log scale) of occupationally exposed subjects, during a period ofnon-occupational exposure. Straight lines fitted for subjects having initial kidney Hg above the detection limit (Börjesson, 1996)DetectorLeadshieldingX-ray tubeSkinphantomCopperfilterFigure 7.1.14 Schematic diagram of the experimental set-up for in vivo iron measurement (Bradley and Farquharson, 1999).Reproduced by permission of John Wiley & Sons, Ltd

508 X-RAY FLUORESCENCE ANALYSIS IN MEDICAL SCIENCES≈15 µg/g. This implies a step forward in beingable to measure iron in vivo. A strong correlationbetween skin and liver iron concentrations wasdemonstrated in rats.7.1.4.5 IODINEIn an in vivo K-XRF study, a mean iodine concentrationof 325 µg/g was noted in healthy persons,whereas decreased concentrations were found ineuthyroid goitre patients and hyperthyroid patientswith focal functional autonomy or Graves’ disease(Reiners et al., 1996). The method was reportedto be well suited for individual follow-up studiesbecause of its sensitivity, high reproducibility andlow radiation exposure.7.1.4.6 PLATINUMA method for non-invasive determination of theplatinum concentration in tumours is desirable inorder to collect more information on cisplatinumuptake, retention and metabolism in tumours andrisk organs. A plane polarised XRF system for platinummeasurement in head and neck tumours wasdeveloped and optimised by Monte Carlo methods(Ali et al., 1998a,b; Kadhim et al., 2000). Aradiotherapy treatment unit operated at 220 kV, afilter and a bi-layer polariser produced a detectionlimit of 5.6 µg/g for a tumour depth of 20 mm anda skin dose of 3 mGy. This system is similar tothat developed by Jonson et al. (1985) and usedfor platinum measurements in tumours and kidneysafter cisplatinum therapy.7.1.4.7 GOLDGold salt is used in the treatment of rheumatoidarthritis. In vivo XRF of gold has been made byat least two groups. The Bath group (Shakeshaftand Lillicrap, 1993) put their efforts into a systembased on a 153 Gd source and a 32 mm diametergermanium detector placed in 90 ◦ geometry. Thekidney gold levels in the 12 patients measuredwere broadly consistent with those reported byBörjesson et al. (1993). There was no strongcorrelation between measured concentrations andadministered amounts of gold.7.1.4.8 URANIUMBone uranium has been measured in vivo byO’Meara et al. (1997, 1998b) using a 57 Co sourcein a backscatter geometry. The MDC of 20 µguranium per g bone mineral in tibia and resultsfrom 10 measured subjects indicated that thecurrent technique is not sensitive enough formeasurements in occupationally exposed subjects,in which bone uranium seems to be at least anorder of magnitude less.7.1.5 FUTURE ASPECTS ANDPOTENTIALSThis subchapter reviews some of the methods usedfor quantification of various elements using in vitroand in vivo methods. Nondestructive in vitro XRFmethods are well established and the detectionlimits imply that low concentrations of manyelements can be measured in samples of minerals,food, body fluids, tissue specimen, etc. Issues ofmedical interest include studies of heavy elementsin blood, urine, sweat, skin, hair, teeth, biopsiesof tissues and organs, breathing air and drinkingwater. Carcinogenic and anti-tumour substances aswell as elements causing allergic reactions havebeen studied.Due to a decreased use of lead in petrol anddecontamination of lead-based paint, although takingtime and with delayed effects, lead concentrationsmay decrease over the coming decades.On the other hand, elements like palladium andcadmium may become more important due to theuse of automobile catalysors and long-term use offertilisers in modern agriculture, respectively. Epidemiologicalstudies of elements like calcium maybe of interest in order to establish presumed relationswith coronary failure. Ancient bones, studiedin connection with prehistoric finds of e.g. pottery,give us ideas of lead intake a long time ago.Progress in the in vivo field has producedoriginal techniques for measuring the toxic

REFERENCES 509elements cadmium, mercury and lead. For all threeelements the in vivo studies made so far have suppliedus with important data on element concentrationsand kinetics. This information is of greatvalue to researchers in the environmental and occupationalarea. Lead is the one that has been moststudied at a number of research centres around theworld. Studies of bone lead in relation to occupationalexposure, hormonal alterations and fracturesare important.XRF is the only known in vivo method to quantifybone lead. The XRF technique can be utilisedfor determining the bone lead concentration and itsrelation to more traditional indices of lead exposure(lead in blood and urine). In cases of suspectedlead intoxication and in more basic studies, determinationsof lead in bone are important. At leadintoxication the technique gives hints on how muchof the lead that has been retained in bone, showingthe risk of future endogenous exposure frombone lead.XRF set-ups for cadmium and mercury arestill limited but their number will presumablyincrease. The cadmium method has the lowestMDC and may already be used for measurementsin the general population. For mercury the situationis more troublesome, since only subjects withvery high exposure may have detectable levels.However, the MDC may be improved by changesin the set-up; a process guided by Monte Carlosimulation. Moreover, novel techniques to studyiron, iodine, platinum, gold and uranium havebeen presented and applied to volunteers orpatients. Some of the methods’ significance needsfurther evaluation.The use of fast computers and simulationprograms may greatly help to study the influence ofparameters changed in efforts to optimise methods.The new generation of synchrotron radiationsources needs to be investigated further, also inconnection with in vivo applications, although thepractical aspects of measurements need to beconsidered. Improvements in radiation sources,e.g. semi-monoenergetic X-ray tubes and filteredbeams, are worth looking into in more detail. Theuse of new electronics and detector configurationshave already proven valuable.For both in vivo and in vitro methods, calibrationprocedures need to be rigorous and phantomsneed to be constructed with careful considerations.Detection limits must be stated clearlyand the effects of a matrix or overlying tissueneed to be controlled for. Figures for accuracyand precision should be mentioned, preferably forthe in vivo situation rather than just for the phantommeasurement. Intercomparison programs, withthe elements in various types of structures, shouldbe stimulated.REFERENCESAhlgren, L., Lidén, K., Mattsson, S. and Tejning, S. X-rayfluorescence analysis of lead in human skeleton in vivo.Scand. J. Work Environ. Health 1976;2:82–6.Ahlgren, L. and Mattsson, S. An X-ray fluorescence techniquefor in vivo determination of lead concentration in a bonematrix. Phys. Med. Biol. 1979;24:136–45.Ahlgren, L. and Mattsson, S. Cadmium in man measuredin vivo by X-ray fluorescence. Phys. Med. Biol.1981;26:19–26.Alfvén, T., Elinder, C.G., Carlsson, M.D., Grubb, A., Hellström,L., Persson, B., Pettersson, C., Spång, G., Schütz, A.and Järup, L. Low-level cadmium exposure and osteoporosis.J. Bone Miner. Res. 2000;15:1579–86.Al-Ghorabie, F.H. Evaluation of 133 Xe for X-ray fluorescenceanalysis of cadmium in vivo: a Monte Carlo study. Radiat.Environ. Biophys. 2000;39:141–5.Ali, P.A., Al-Hussany, A.F., Bennett, C.A., Hancock, D.A.and El-Sharkawi, A.M. Plane polarized X-ray fluorescencesystem for the in vivo measurement of platinum in head andneck tumours. Phys. Med. Biol. 1998a;43:2337–45.Ali, P.A., Bennet, C., El-Sharkawi, A.M. and Hancock, D.A.Optimisation of a polarised X-ray source for the in vivomeasurement of platinum in head and neck tumours. Appl.Radiat. Isot. 1998b;49:647–50.Ambrose, T.M., Al-Lozi, M. and Scott, M.G. Bone lead concentrationsassessed by in vivo X-ray fluorescence. Clin.Chem. 2000;46:1171–8.Amokrane, A., Gamaz, F., Bouchagra, T. and Heitz, C. Possibilitiesfor the determination of trace elements in blood byPIXE and NAA. In Proceedings of the European Conferenceon Energy Dispersive X-ray Spectrometry EDXRS-98(Fernandez, J.E and Tartari, A., eds), Editrice Compositori,Bologna, 1999, pp. 191–6.Anderson, D.L. and Cunningham, W.C. Nondestructive determinationof lead, cadmium, tin, antimony, and barium inceramic glazes by radioisotope X-ray fluorescence spectrometry.J. AOAC Int. 1996;79:1141–57.Ao, Q., Lee, S.H. and Gardner, R.P. Development of thespecific purpose Monte Carlo code CEARXRF for the design

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REFERENCES 515in a battery-making work-force. Environ. Res. 2000b;84:282–9.Todd, A.C., Godbold, J.H., Moshier, E.L. and Khan, F.A.Patella lead X-ray fluorescence measurements are independentof sample orientation. Med. Phys. 2001c;28:1806–10.Todd, A.C., Moshier, E.L., Carroll, S. and Casteel, S.W. Validationof X-Ray fluorescence-measured swine femur leadagainst atomic absorption spectrometry. Environ. Health.Perspect. 2001d;109:1115–1119.Todd, A.C., Buchanan, R., Carroll, S., Moshier, E.L., Popovac,D., Slavkovich, V. and Graziano, J.H. Tibia lead levelsand methodological uncertainty in 12-year-old children. Environ.Res. 2001a;86:60–5.Todd, A.C., Carroll, S., Godbold, J.H., Moshier, E.L. andKhan, F.A. The effect of measurement location on tibia leadXRF measurement results and uncertainty. Phys. Med. Biol.2001b;46:29–40.Todd, A.C., Carroll, S., Geraghty, C., Khan, F.A., Moshier,E.L., Tang, S. and Parsons, P.J. L-shell X-ray fluorescencemeasurements of lead in bone: accuracy and precision. Phys.Med. Biol. 2002a;47:1399–1419.Todd, A.C., Parsons, P.J., Tang, S. and Moshier, E.L. Individualvariability in human tibia lead concentration. Environ.Health. Perspect. 2001e;109:1139–1143.Todd, A.C., Parsons, P.J., Carroll, S., Geraghty, C., Khan,F.A., Tang, S. and Moshier, E.L. Measurements of lead inhuman tibiae. A comparison between K-shell X-ray fluorescenceand electrothermal atomic absorption spectrometry.Phys. Med. Biol. 2002b;47:673–687.Toribara, T.Y. Analysis of single hair by XRF disclosesmercury intake. Hum. Exp. Toxicol. 2001;20:185–8.Torra, M., To-Figueras, J., Rodamilans, M., Brunet, M. andCorbella, J. Cadmium and zinc relationships in the liver andkidney of humans exposed to environmental cadmium. Sci.Total. Environ. 1995;170:53–7.Wielopolski, L., Vartsky, D. and Cohn, S.H. In vivo elementalanalysis utilizing XRF techniques. Neurotoxicology1983;4:173–6.Wielopolski, L., Rosen, J.F., Slatkin, D.N., Zhang, R., Kalef-Ezra, J.A., Rothman, J.C., Maryanski, M. and Jenks, S.T.In vivo measurement of cortical bone lead using polarisedXrays.Med. Phys. 1989;16:521–8.Zaichick, V. Estimation of extracellular water by means ofstable bromine and X-ray fluorescence analysis. Appl.Radiat. Isot. 1998a;49:635.Zaichick, V. X-ray fluorescence analysis of bromine forthe estimation of extracellular water. Appl. Radiat. Isot.1998b;49:1665–9.Zaichick, V.Y. and Ovchjarenko, N.N. In vivo X-ray fluorescentanalysis of Ca, Zn, Sr and Pb in frontal tooth enamel.J. Trace Microprobe Tech. 1996;14:143–52.Zaichick, V. and Ovchjarenko, N. In vivo X-ray fluorescencefor estimation of essential and toxic trace elements in teeth.Appl. Radiat. Isot. 1998;49:721.Zaichick, V., Ovchjarenko, N. and Zaichick, S. In vivo energydispersive X-ray fluorescence for measuring the content ofessential and toxic trace elements in teeth. Appl. Radiat. Isot.1999;50:283–93.

7.2 Total Reflection X-ray Fluorescencefor Semiconductors and Thin FilmsY. MORIWacker-NSCE Corp., Yamaguchi, Japan7.2.1 INTRODUCTIONFor many years, only a few materials have beenused in the manufacturing of silicon semiconductordevices: SiO 2 for gate oxide, Si 3 N 4 for capacitors,polycrystalline Si for electrodes, and Al forwiring. In the past decade, the simple shrinkageof unit transistors in large-scale integrated(LSI) circuits increased manufacturing difficultybecause of the physical restrictions imposed bythe smaller size. Consequently, a large number ofalternative elements have been tested and actuallyadopted to keep pace with the reduced size.Some examples include ZrO 2 and HfO 2 for gateoxides, Ta 2 O 5 and (Ba,Sr)TiO 3 (BST) for capacitors,SrRuO 3 (SRO) for electrodes, and Cu forwiring. 1 At the same time, in order to reduce thecost of LSI devices, large-diameter silicon waferswere adopted by leading-edge semiconductor manufacturers.Shipment of 200-mm φ wafers is mainstreamat present, and the shipment of 300-mm φwafers is increasing. 2 In the semiconductor manufacturingprocess using such large-diameter wafers,controlling the film composition as well as reducingundesirable contaminants over the surface isincreasingly significant for stabilizing yield.Because of the technological transitions mentionedabove, two characteristics have becomethe keys to current semiconductor analysis. Thesekey characteristics are (1) the expansion of thenumber of analysable elements to evaluate thenew materials and (2) the capability of distributionanalysis for large-diameter wafers. High throughputand ease of operation are also indispensablein the highly competitive semiconductor industry.X-Ray analyses such as the methods of totalreflectionX-ray fluorescence (TXRF) spectrometryand X-ray reflectivity (XRR) meet these requirements,and significant improvements to these techniqueshave been seen in recent years.In this subchapter, progress in the industrialTXRF technique will first be shown. The useof TXRF for semiconductor analysis started atthe end of the 1980s, and came into popularuse in the 1990s. Today, more than 300 TXRFspectrometers are installed in this industry worldwide,meaning that almost all leading-edge semiconductorfactories have introduced TXRF. Sincethe main purpose of TXRF is trace contaminationanalysis, improvements in detection ability aswell as reliability will be discussed. In addition,XRF and XRR/XRF analysers for the characterizationof thin films made from new materials willbe introduced.7.2.2 IMPROVEMENTS IN TXRFINSTRUMENTATION7.2.2.1 EXPANSION OF ANALYSABLEELEMENTSThe conventional TXRF uses W Lβ (9.67 keV) asan excitation source to analyse the elements suchas Cr and Fe that are critical to the propertiesX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

518 TOTAL REFLECTION X-RAY FLUORESCENCE FOR SEMICONDUCTORS AND THIN FILMSof LSIs. As a number of new metals havebeen introduced or are being tested as alternativematerials in recent LSI manufacturing, the WLβ source ceased to be satisfactory due to itsnarrow excitation window ( 16 S − 30 Zn by K lines).Although some TXRF manufacturers used Mo Kα(17.45 keV) as an alternative source, they could notanalyse materials such as Zr, Mo, and Ru that havehigh K-absorption edge energy. To analyse thesenew elements, new types of excitation sources havebeen introduced. One type is Ag Kα (22.11 keV)excitation, which can excite the K shells of up toRu. TXRF with a sealed Ag X-ray tube is actuallyused to evaluate the cleaning efficiency of Ru. 3Figure 7.2.1 is a sample spectrum of 10 12 atomscm −2 Ru on a silicon wafer.Another interesting approach is to utilize continuousX-rays that had at one time been consideredto be useless in semiconductor TXRF. Figure 7.2.2is a sample spectrum of 5 × 10 11 atoms cm −2 Moon a silicon wafer excited by ca. 22 keV X-raysthat are monochromatized from continuous X-rays.Because of the relatively high intensity of continuousX-rays from the rotating anode and theimprovements in the multilayer monochromator,the system shows a detection limit of ca. 1.5 ×10 10 atoms cm −2 for Mo. This system is also applicableto Ru analysis.Besides the heavy elements mentioned above,the analysis of light elements (Na, Mg, Al) byTXRF has been an issue of interest from thebeginning of semiconductor application. Becauseconventional TXRF systems with medium-energyexcitation sources such as W Lβ or Mo Kα donot have enough excitation efficiency for light elementssuch as Na and Al, the detection limit waspoor. The low detection ability of light elements isone of the major drawbacks of TXRF when comparedwith atomic absorption spectrophotometry(AAS) and inductively coupled plasma mass spectrometry(ICPMS). Several researchers attemptedto improve the capability of light element analysis.One such system is a straight-TXRF with W Mα(1.78 keV) excitation, which is now commerciallyavailable. 4 The monochromatic W Mα, generatedby a W rotating anode, can effectively excite lightelements up to Al. In addition, the energy of W Mαis lower than the Si K absorption edge (1.84 keV),2Si–Ka1.5Ru–KaIntensity (cps)1.50Cl–Ka Mn–KaS–KaP–Ka Ti–Ka Fe–Ka Zn–KaAl–Ka Ca–KaCr–Ka Cu–KaK–Ka V–Ka Ni–KaBr–Ka0 5 10 15 20Energy (keV)Figure 7.2.1 Sample TXRF spectrum of 10 12 atoms cm −2 Ru on a silicon wafer excited by Ag Kα (22.11 keV). Courtesy ofTechnos Corp., Japan

IMPROVEMENTS IN TXRF INSTRUMENTATION 51930(Br Kα, Kβ)Intensity (counts)Si KαMo Kα001 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Energy (keV)Figure 7.2.2 Sample TXRF spectrum of 5 × 10 11 atoms cm −2 Mo on a silicon wafer. The excitation source is a monochromaticca. 22 keV X-ray from continuous X-rays generated by an Au rotating anode (35 kV–255 mA)so the spectral background caused by Si Kα fromthe substrate is reduced. The detection limit of thissystem, however, is not very good (i.e. 10 11 –10 12atoms cm −2 level) because the W Mα emissionis not strong and the sensitivity of the solid statedetector (SSD) in the low energy region is not highenough to allow determination at the 10 9 atomscm −2 level. To achieve a higher level of sensitivityon this system, a combination of chemical preconcentrationwas examined. 5–7 The results will bediscussed in another subsection.7.2.2.2 LOW BACKGROUND OPTICSThe lower limit of detection (LLD) of TXRF isgenerally expressed by the equationLLD = 3I 1/2BG C STD/I STD (7.2.1)where I BG is the background count of a blanksample, C STD is the nominal concentration of astandard sample, and I STD is the fluorescent X-rayintensity of the standard sample. At the initial stageof TXRF development for semiconductor application,increasing I STD by intensifying the primaryX-ray was a common effort to improve LLD. Atfirst, a rotating anode was introduced instead ofa sealed tube, and then an artificial multilayermonochromator was installed. In recent TXRFmachines, however, the intensification of the primaryX-ray is becoming impractical, because ofthe increasing dead time of the detection systemand the impurity peaks caused by imperfectionsof the artificial multilayers. 4 Therefore, the nextstrategy to improve LLD should be the reductionof I BG , and some significant improvements havebeen achieved.The first improvement was the introduction ofa dual-crystal monochromator. Because an artificialmultilayer is not a perfect monochromator,parts of white X-rays sometimes passed through tocause impurity peaks in the background spectrumof single-crystal systems. To reduce the intensity ofthese impurity peaks, a dual-multilayer monochromatorwas proposed. 4 Figure 7.2.3 compares theblank spectra for single- and dual-crystal opticsof Au Lβ excitation. Impurity peaks in the formersystem, which appeared at around 6 keV and8.4 keV, disappeared in the dual-crystal system.Accordingly, the detection ability has improvedsubstantially.The second improvement is the implementationof an x –y stage instead of the traditional

520 TOTAL REFLECTION X-RAY FLUORESCENCE FOR SEMICONDUCTORS AND THIN FILMS50Single multilayerDual multilayerCounts00 1 2 3 4 5 6 7 8 9 10 11 12Energy (keV)Figure 7.2.3 Comparison of blank spectra for single- and dual-crystal optics of Au Lβ excitation TXRFr –θ stage. Because a silicon wafer is a singlecrystal, the diffraction of irradiated primary X-rays occurs at a certain azimuthal angle against thewafer, raising the overall background of the spectrum.During mapping measurements on an r –θcontrolled stage, the diffraction cannot be avoidedbecause the azimuthal angle is not selectable. 8Hence, the necessity of an x –y –θ stage hadbeen suggested, 9 and such a stage was actuallyimplemented. 4 Because of the additional third axis,any arbitrary azimuthal angle can be set at anymeasurement spot on the sample to avoid thediffraction in mapping analysis.The third improvement is in the SSD. Spuriouspeaks originating in impurities in the detectionsystem had been known to raise the backgroundlevel to degrade the LLD. The principal causeof such spurious peaks were found to be theimpurities in the Be window, 9,10 but this is notthe only source according to our research. Now,a manufacturer has reported the almost completeremoval of impurity peaks. Figure 7.2.4 comparesthe impurity peaks of Fe for conventional andimproved detectors.The fourth improvement is concerned withthe alternative excitation source. Recently, crosscontaminationby Cu has become a critical issue inthe Cu wiring process in manufacturing high-speedLSI devices, and trace Cu detection is becomingincreasingly important. The traditional W Lβexcitation TXRF, however, includes a backgroundproblem in trace Cu detection. An escape peakinevitably appears at 7.93 keV in the W Lβexcitation-Si(Li) SSD system, which is unfortunatelyvery close to Cu Kα (8.04 keV). The escapepeak not only raises the background of Cu but alsomakes the peak separation of small Cu Kα difficult,resulting in a degradation of the ability to detectCu. Au Lβ (11.44 keV) might be one solution tothis problem while retaining the ability to detectother elements such as Fe and Ni. 11,12 Figure 7.2.5compares the blank spectra of W Lβ andAuLβexcitation. Since the escape peak in Au Lβ excitationappears at 9.70 keV, no interference with CuKα is observed. The ability to detect trace Cu by WLβ andAuLβ excitation was experimentally compared(Figure 7.2.6). In this experiment, identical5-point mapping analyses were performed with thetwo systems for 6-level Cu-contaminated wafers.In W Lβ excitation, although the linearity reachesthe level of 10 9 atoms cm −2 , the dispersion of 5-point mapping is large, because of interference bythe escape peak. In comparison, the data dispersionin Au Lβ excitation is very small even at the lowerlevel of 10 9 atoms cm −2 .

TXRF WITH CHEMICAL PRECONCENTRATION 5211,4001,200W–Lb1Fe–Ka0.70.6W Lβ intensity (cps)1,0008006004000.50.40.30.2Fe Kα intensity (cps)2000.1(a)00 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345Incident azimuth angle (deg)0.03,5003,000W–Lb1 cpsFe–Ka cps1.00.90.8W Lβ intensity (cps)2,5002,0001,5001,0005000.70.60.50.40.30.20.1Fe Kα intensity (cps)(b)00 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345Incident azimuth angle (deg)0.0Figure 7.2.4 Incident azimuth dependence of Fe impurity peak intensity for (a) conventional SSD and (b) improved SSD.Courtesy of Technos Corp., Japan7.2.3 TXRF WITH CHEMICALPRECONCENTRATION7.2.3.1 AUTOMATIONOF PRECONCENTRATIONThe potential of TXRF with chemical preconcentration(generally called vapor phase decomposition(VPD)-TXRF) was pointed out at anearly stage of semiconductor-oriented TXRF. 13The enrichment factor, [wafer area]/[detector viewarea] ratio, equals about two orders of magnitude,resulting in an ultra-low detection limit comparableto VPD-ICPMS. Until the middle of the1990s, however, the chemical preconcentrationwas performed manually by persons with specialtechnical skills, so routine VPD-TXRF analyses

522 TOTAL REFLECTION X-RAY FLUORESCENCE FOR SEMICONDUCTORS AND THIN FILMS100WLβAuLβCountsEscapepeak001 2 3 4 5 6 7 8 9 10 11 12Energy (keV)Cu ZnFigure 7.2.5 Comparison of blank wafer spectra for W Lβ andAuLβ excitation. The applied power is 9 kW for each. Courtesyof Rigaku Corp., Japan0.600.350.500.30Cu (cps)(W Lβ excitation)0.400.300.20Cu (cps)(Au Lβ excitation)0.250.200.150.100.100.050.000.00.5 1.01.5 2.00.000.00.5 1.01.5 2.0(a)Cu (× 10 10 atoms cm −2 )(VPD-AAS)(b)Cu (× 10 10 atoms cm −2 )(VPD-AAS)Figure 7.2.6 Correlation of Cu between VPD-AAS and TXRF with (a) W Lβ excitation and (b) Au Lβ excitationfor semiconductor process characterization wereactually difficult to implement. To solve this problemso as to meet the coming age of large-diameterwafers, the automation of VPD had been steadilydeveloping. Now, such instruments are commerciallyavailable. 14–16 Figure 7.2.7 is an exampleof one of those instruments. The basic function ofsuch instruments is as follows: loader/unloader forwafer cassette, VPD reaction chamber(s) to makethe wafers hydrophobic, a scanning unit to collectthe surface impurities into a small droplet,and a stage for drying the droplet to deposit a

TXRF WITH CHEMICAL PRECONCENTRATION 523Figure 7.2.7 Photograph of an automatic VPD system (WSPS, Wafer Surface Preparation System). Courtesy of GeMeTecCorp., GermanyLoad/UnloadVPDRobotScanning/dryingFigure 7.2.8 Overview of an automatic VPD system integration. Courtesy of SES Corp., Japanresidue on a wafer. These combined processes takeplace in a clean draft chamber, and each samplewafer is sequentially transferred from unit tounit by a robotic system (Figure 7.2.8). The automaticVPD instrument significantly reduced thelabor and time required for chemical preconcentration.In addition, isolation from the laboratoryenvironment achieved a drastic reduction in unintentionalcontamination, and the automatic roboticmotions improved the reproducibility of the overall

524 TOTAL REFLECTION X-RAY FLUORESCENCE FOR SEMICONDUCTORS AND THIN FILMSpreconcentration process, 17 resulting in a higherdegree of reliability of the analytical data for tracemetal contamination.7.2.3.2 LIGHT ELEMENT ANALYSISAs mentioned above, the capability of light elementanalysis by straight-TXRF with W Mα excitationis not satisfactory for critical applications.To improve the detection limit, the combinationof chemical preconcentration was examined.Figure 7.2.9 is a set of sample spectra for straightandVPD-TXRF. 7 Because of the concentratingeffect, the latter shows clear Na Kα and Al Kαpeaks. The detection limits of Na and Al reach3 × 10 10 atoms cm −2 and 2 × 10 9 atoms cm −2 for150 mm φ wafers, respectively. These detectionlimits correspond to ca. 8 × 10 9 atoms cm −2 and5 × 10 8 atoms cm −2 , respectively, when convertedIntensity (kcps)(a)Intensity (kcps)(b)10.05.002.01.000 0.5 1.0 1.5 2.0 2.5Energy (keV)Na KaAl KaAl Ka0 0.5 1.0 1.5 2.0 2.5Energy (keV)W MaW MaFigure 7.2.9 (a) Straight-TXRF spectrum of a wafer on which1 × 10 11 atoms cm −2 Na and Al are added and (b) spectrumafter VPD preconcentration for the same wafer. 6 The excitationsource is W Mα. Reproduced by permission of John Wiley &Sons, Ltdto those of leading-edge 300 mm φ wafers. Thislevel of detection is satisfactory for conductingsemi-quantitative analysis of current semiconductorsurfaces. For Na, however, ca. one-orderimprovement of the detection limit may still bedesirable to meet critical use.7.2.4 STANDARDIZATION OF TXRFAND OTHER METHODS7.2.4.1 CROSS-CHECK ACTIVITIESAlong with the improvement of LLD, the standardizationof TXRF analysis for semiconductorshas been attracting more attention in recentyears. On the background of previous two crosscheckworks, 18,19 ISO/TC201/WG2 was organizedto establish international standards of TXRF measurementin 1993, primarily for the semiconductorindustry. After an international round-robintest (RRT) and its data analysis, the first internationalstandard, ISO14706:2000 (‘Surface chemicalanalysis–Determination of surface elementalcontamination on silicon wafers by total-reflectionX-ray fluorescence (TXRF) spectroscopy’) waspublished. The ISO/TC201/WG2 then decided tostandardize chemical preconcentration methods forVPD-TXRF as its second major task, and thework started in 1998. This work consisted of twointernational RRTs. In the first RRT, the experimentalconditions were left to each participant’sdiscretion, which brought about poor interlaboratoryreproducibility. The lesson learned from thefirst RRT contributed to the conduct of the secondRRT. In the second RRT, both the VPD-TXRF andVPD-wet (e.g. ICPMS) methods were tested, andbasic experimental conditions and calculation procedureswere carefully provided by the organizer.For example, internal addition of V or Sc wasapplied to normalize the fluorescence intensitiesbetween different dried residues, and 2 % HF +2% H 2 O 2 was specified as the scanning solution.Figure 7.2.10 summarizes the results of thefirst and second RRT for Ni. 20 The careful controlof experimental conditions and calculation proceduresin the second RRT accomplished significant

STANDARDIZATION OF TXRF AND OTHER METHODS 525Ni, relative srj (%)20151050srjF1 wholeF1 TXRFF1 wetF2 wholeF2 TXRFF2 wetH1 wholeH1 TXRFH1 wetH2 wholeH2 TXRFH2 wetB1 wholeSecond RRTSRjB1 TXRFB1 wetB3 wholeB3 TXRFB3 wetFirst RRTFigure 7.2.10 Summary of the international RRT results conductedby ISO/TC201/WG2. ‘SRj’ (right axis) and ‘srj’ (leftaxis) indicate interlaboratory reproducibility and intralaboratoryrepeatability, respectively. B1 to H2 are the sample names,and the B series are of the first RRT, while the F and H seriesare of the second RRT. ‘wet’ means the result of VPD-AASor ICPMS, and ‘whole’ means the overall dispersion of theVPD-TXRF and VPD-wet method. 20 Reproduced by permissionof The Japan Society of Applied Physics403020100Ni, relative SRj (%)improvements in repeatability and reproducibility.Based on the results of the second RRT, an ISOdraft was prepared by ISO/TC201/WG2 in 2001,and the final document is scheduled to be publishedin 2004.7.2.4.2 STANDARD SAMPLE ISSUEThere are many error factors in TXRF quantification.21 One of the critical factors is the depthprofile of the analyte element; the fluorescentX-ray intensity in TXRF is highly sensitive tothe depth profile of the analyte. Figure 7.2.11schematically demonstrates this fact. Two typesof depth profiles for the same amount of analyteare assumed: (a) a near-surface analyte; and (b) animplanted analyte. The primary X-rays attenuate asthey penetrate into the substrate, as illustrated inNear-surface analyte0AnalyteIntensity,concentration0Intensityx concentrationPrimary X-rayintensityFluorescent X-rayintensity(a)DepthDepthImplanted analyte0Intensity,concentration0Intensityx concentrationFluorescent X-rayintensityAnalytePrimary X-rayintensity(b)DepthDepthFigure 7.2.11 Schematic illustrations explaining the differences in the intensity of X-ray fluorescence for two types of analyteswith different depth profiles

526 TOTAL REFLECTION X-RAY FLUORESCENCE FOR SEMICONDUCTORS AND THIN FILMSFigure 7.2.11 on the left. The intensity of the fluorescentX-ray is proportional to the integrationof the product of concentration and the excitationX-ray intensity along the depth, which is illustratedin the figures on the right. The differencesof the areas indicate that different depth profilesgive different fluorescent X-ray intensities eventhough the amount of analyte is the same. Suchan effect was actually found in standard samplesfor TXRF. Figure 7.2.12 shows the angle scansof Ni for two spincoat 22 standard samples preparedby following the same process. Althoughtheir targeted concentrations were the same, theirangle scans were apparently different. At 0.10 ◦ ,which is the typical measurement angle in actualuse, the difference in fluorescent X-ray intensityis more than double. Similar differences wereobserved for standard microdrop 23 samples. Thesefindings imply that controlling the depth profileat nanometer-level resolutions in physisorption isdifficult, and a method that employs chemisorptionwas proposed. The method is named ‘Immersion inAlkaline Hydrogen Peroxide Solution’ (IAP). 24,25This method utilizes a mixture of ammonia, hydrogenperoxide, and water, which is a very commoncleaning solution for removing particles from siliconwafers. If metal ions are contained in thissolution, they adsorb onto the surface of siliconwafers, 26 and the IAP method makes use ofthis chemisorption. In this method, cleaned siliconwafers are immersed in the solution that isintentionally doped with a certain amount of metalions such as Fe, Ni, and Zn. A schematic illustrationof the reactions in the solution is shownin Figure 7.2.13. During immersion, the SiO 2 formationby hydrogen peroxide and the etching ofSiO 2 by ammonia balance each other out, continuouslyleaving ca. 1 nm SiO 2 layer, and metalions adsorb to the SiO 2 layer based on chemicalequilibrium. The ‘adsorption isotherms,’ the200Fluorescent X-ray intensity (cps)1501005000.05 0.1 0.15 0.2 0.25 0.3 0.35Glancing angle (deg.)Figure 7.2.12 Angle scan profiles of two spincoat samples (Ni, 5 × 10 13Discussion Group of X-Ray Analysis Japanatoms cm −2 ). Reproduced by permission of The

STANDARDIZATION OF TXRF AND OTHER METHODS 527M n+ M n+ M n+M n+ M n+~1 nmSiO 2M n+ M n+SiO 2SiSiSiSi + 2H 2 O 2 → SiO 2 + 2H 2 OSiO 2 + OH − → HSiO 3−Si + 2H 2 O 2 → SiO 2 + 2H 2 OFigure 7.2.13 Schematic models of surface reactions on a silicon wafer in alkaline hydrogen peroxide solution10 0001000Surface metal concentration( × 10 10 atoms cm −2 )10010FeZnMnCa1NiCuCo0.10.1 1 10Concentration in the solution (ppb)100 1000 10 000Figure 7.2.14 Adsorption isotherms of several metal ions in alkaline hydrogen peroxide solution (2.2 M NH 3 and 1.4 M H 2 O 2 ,80 ◦ C, 10 min). Reproduced by permission of The Discussion Group of X-Ray Analysis Japanamount adsorbed versus the concentration of dissolvedmetal at a fixed temperature, are shownin Figure 7.2.14 for several metals. 25 The IAPmethod can be applied to these important elementsin the range of at least 10 9 to 10 13 atoms cm −2 .In addition, this method can also be applied to Aland Mg, although they are omitted here becausethey cannot be analysed with ordinary TXRF. Itshould be mentioned, however, that alkaline metals(Na and K) and some heavy metals (Cr, W,

528 TOTAL REFLECTION X-RAY FLUORESCENCE FOR SEMICONDUCTORS AND THIN FILMSNormalized fluorescentX-ray intensity (a.u)2.9 × 10 127.3 × 10 121.4 × 10 1300.04 0.12 0.20Glancing angle (deg.)0.28 0.36Figure 7.2.15 Comparison of angle scan profiles for three IAP wafers (Ni, different concentrations). Reproduced by permissionof The Japan Society for Analytical Chemistryand Ta) were not adsorbed. The reproducibility ofthe depth profiles was examined by measuring theangle scans of the analyte elements on IAP wafers.Figure 7.2.15 compares the angle scans for IAPwafers that have different concentrations of Ni. 24The angle scan profiles agreed well, indicating thatthe depth profile is independent of the adsorbedconcentration. Figure 7.2.16 compares the anglescans between three elements – Fe, Ni, and Zn. 24The results agreed well with each other, indicatingthat the depth profile is independent of the element.From a standpoint of use as a standard sample,uniformity of adsorption is also a critical factor.Table 7.2.1 shows the spatial uniformity of metaladsorption evaluated by conducting 9-point TXRFmapping. The uniformity was typically 10 % orless by relative standard deviation (RSD), which iscomparable to that of traditional spincoat wafers. 22Table 7.2.2 lists the in-batch uniformity ofadsorbed concentration. In this experiment, ninewafers were immersed in a single solution atTable 7.2.1 Summary of spatial uniformity test for IAP wafersElementConcentration(atoms cm −2 )Relative standarddeviation (%)9.0 × 10 11 7.7Fe 4.5 × 10 12 3.51.7 × 10 13 4.03.5 × 10 11 12.3Ni 3.3 × 10 12 19.61.0 × 10 13 4.37.3 × 10 11 9.3Zn 3.0 × 10 12 3.46.0 × 10 12 4.8Reproduced by permission of The Japan Society for AnalyticalChemistry.one time, and the wafer-to-wafer uniformity wasevaluated by analysis with TXRF or AAS. Thedispersion was very small–less than ca. 6 % byRSD. Good in-batch uniformity, as well as spatialuniformity, is advantageous in standard or crosschecksamples for the contamination analysis ofsemiconductor surfaces. The maximum numberof IAP wafers made from a single solution was

FILM ANALYSIS 529Normalized fluorescentX-ray intensity (a.u)Fe 2.8 × 10 13Ni 7.3 × 10 12Zn 1.6 × 10 1200.04 0.12 0.20Glancing angle (deg.)0.28 0.36Figure 7.2.16 Comparison of angle scan profiles for IAP wafers on which Fe, Ni, or Zn was adsorbed. Reproduced by permissionof The Japan Society for Analytical ChemistryTable 7.2.2 Wafer-to-wafer uniformity of adsorbed metal concentrationfor IAP wafer, prepared in each single batchElementConcentration(atoms cm −2 )Relative standarddeviation (%)Fe 4.5 × 10 12 0.96Ni 1.6 × 10 12 5.9Zn 3.0 × 10 12 5.4Reproduced by permission of The Japan Society for AnalyticalChemistry.typically limited to 25 (i.e. one cassette), but thesequential reuse of a single solution for more thanone cassette of wafers increased the maximumnumber to more than 50. 27 Along with spincoatsamples, the IAP wafers were used as crosscheckstandard samples in the ISO/TC201/WG2international RRT mentioned above. 207.2.5 FILM ANALYSISAs discussed in the Introduction, many new elementsare being introduced or tested as alternativematerials for recently developed semiconductordevices. Usually, the elements are deposited on thewafer surface to form a thin film layer. Controllingthe chemical composition, thickness, and densityof each layer is very important for stabilizing thedevice properties and enhancing the yield. X-Rayanalysis is a suitable means of control becauseof its advantages of nondestructive and mappingcapabilities, among others. As for chemical composition,conventional XRF is applicable. In XRF,an r –θ stage is thought not to be suitable for themapping analysis of certain kinds of films such asBST, or (Ba,Sr)TiO 3 , because of diffraction, and anx –y –θ stage was introduced to avoid diffraction. 28The conventional XRF, however, cannot be usedfor stacked films which include a common element.BST deposited on SRO, or SrRuO 3 , is onesuch example. To analyse such films, two-anglegrazing incidence XRF (GIXRF) was proposed. 29At first, only the top layer is analysed by conductinga low-angle measurement, and then all thelayers are analysed by a high-angle measurement.

530 TOTAL REFLECTION X-RAY FLUORESCENCE FOR SEMICONDUCTORS AND THIN FILMSThe composition of the lower layer can be calculatedby subtraction. As for film thickness, bothXRF and XRR are applicable. In the XRF method,the fluorescent intensity is converted to film thicknessby applying calibration curves, whereas inthe XRR method, the thickness is calculated fromthe oscillation data of reflectivity, as illustratedin Figure 7.2.17. Of the two methods, XRR ismore convenient because the thickness can bedetermined without the use of reference standardsamples. In addition, advanced theoretical fittingto the XRR oscillation data enables simultaneousdetermination of stacked layers. 29 Besides the filmthickness, this method can directly determine thedensity of the first layer from the critical angleat which the reflectivity shows the first inflection.A combined method of GIXRF and XRR forthe semiconductor industry was developed for thispurpose. 29 A schematic illustration of the instrumentis shown in Figure 7.2.18. Many applicationsusing this system are proposed including insulators(TaO 2 , etc.), wirings (Cu, Al + Cu, etc.), electrodes101Critical angle→ densityReflectivity0.10.010.001Oscillation→ thickness0.00010.000010 0.2 0.4Incident angle (deg)0.6 0.8Figure 7.2.17 Sample curve of incidence angle dependence of X-ray reflectivity. Courtesy of Technos Corp., JapanDetector #2(for angleadjustment)X-ray tube #1Monochromator #1Analyte waferDetector #1(for XRR)X-ray tube #2Monochromator #2SSD(for XRF)Figure 7.2.18 Schematic illustration of the X-ray optics of an XRR/XRF film analyser (SMAT210, Technos Corp)

REFERENCES 531(W-Si, Mo-Si, etc.), barrier films (Ti/Ti-N, etc.),and dielectrics (BST on SRO).ACKNOWLEDGEMENTSThe author wishes to acknowledge and thankGeMeTec Japan Corp., Rigaku Corp., SES Corp.and Technos Corp. (in alphabetical order) forkindly providing us with their data and originalillustrations for this contribution.REFERENCES1. Front End Processes, in International Technology Roadmapfor Semiconductors, 2001 Edition, p. 26; http://public.itrs.net/Files/2001ITRS/FEP.pdf.2. Front End Processes, in International Technology Roadmapfor Semiconductors, 2001 Edition, p. 6; http://public.itrs.net/Files/2001ITRS/FEP.pdf.3. Futase, T., Itoh, M. and Katsuyama, K. Wafer back sideand edge cleaning to remove metal contamination (4).Removal of Ru at wafer edge. Extended Abstracts (The48th Spring Meeting 2001), The Japan Society of AppliedPhysics and Related Societies, Meiji University, 2001,p. 831 (29a-D-6).4. Funabashi, M., Utaka, T. and Arai, T. Improvement ofTotal Reflection X-ray Fluorescence (TXRF) spectrochemicalanalysis for silicon wafers. Spectrochim. Acta B, 52,887–899 (1997).5. Funabashi, M., Matsuo, M., Kawada, N., Yamagami, M.and Wilson, R. Enhanced analysis of particles andvapor phase decomposition droplets by total-reflection X-ray Fluorescence. Spectrochim. Acta B, 54, 1409–1426(1999).6. Yamagami, M., Nonoguchi, M., Yamada, T., Shoji, T.,Utaka, T., Mori, Y., Nomura, S., Taniguchi, K., Wakita, H.and Ikeda, S. Analysis of light elements on Si wafer byvapor-phase decomposition/total reflection X-ray fluorescence.Bunseki Kagaku, 48, 1005 (1999).7. Yamagami, M., Nonoguchi, M., Yamada, T., Shoji, T.,Utaka, T., Nomura, S., Taniguchi, K., Wakita, H. andIkeda, S. VPD/TXRF analysis of trace elements on asilicon wafer. X-ray Spectrom., 28, 451–455 (1999).8. Yakushiji, K., Ohkawa, S., Yoshinaga, A. and Harada, J.Main peak profiles of total reflection X-ray fluorescenceanalysis of Si (100) wafers excited by monochromatic X-ray beam W-Lβ (I). Jpn. J. Appl. Phys., 31, 2872–2876(1992).9. Yakushiji, K., Ohkawa, S., Yoshinaga, A. and Harada, J.Main peak profiles of total reflection X-ray fluorescenceanalysis of Si (100) wafers excited by monochromaticX-ray beam W-Lβ (II). Jpn. J. Appl. Phys., 32, 1191–1196(1993).10. Kozono, S., Itoh, T., Yoshinaga, A., Ohkawa, S. andYakushiji, K. Trace analysis of a beryllium window for asolid state detector system by inductively coupled plasmamass spectrometry. Anal. Sci., 10, 477–480 (1994).11. Yamada, T., Shoji, T., Funabashi, M., Utaka, T., Arai, T.and Wilson, R. Tungsten analysis with a total reflection X-ray fluorescence spectrometer using a three crystal changer.Adv. X-Ray Chem. Anal. Jpn., 26s, 53–56 (1995).12. Yamada, T., Matsuo M., Kohno, H. and Mori, Y. Sensitivedetection of trace copper contamination on a silicon waferby total reflection X-ray fluorescence using W-Lβ or Au-Lβ excitation source. Spectrochim. Acta B, 56, 2307–2312(2001).13. Huber, A., Rath, H. J., Eichinger, P., Bauer, T., Kotz, L.and Staudigl, R. Sub-ppm monitoring of transition metalcontamination on silicon wafer surfaces by VPD-TXRF.ECS Proceedings, PV88-20, The Electrochemical Society,Pennington, NJ, 1988, pp. 109–112.14. Pahlke, S., Kotz, L., Ehmann, T., Eichinger, P. andHuber, A. WSPS: wafer surface preparation system. Anovel modular automated method capable of the ultratraceanalytical inspection of 300 mm silicon wafer surfaces.ECS Proceedings, PV98–1, The Electrochemical Society,Pennington, NJ, 1998, pp. 1524–1525.15. http://www.gemetec.com/16. http://www.ses-corp.co.jp/en/17. Fabry, L., Pahlke, S., Kotz, L., Wobrauschek, P. andStreli, C. Novel methods of TXRF analysis for siliconwafer surface inspection. Fresenius J. Anal. Chem., 363,98–102 (1999).18. Hockett, R. S., Ikeda, S. and Taniguchi, T. TXRF roundrobin results. ECS Proceedings, PV92-12, The ElectrochemicalSociety, Pennington, NJ, 1992, pp. 324–337.19. UC Standardization Committee. UC Standard: Test methodfor measuring surface contamination on silicon wafersby total reflection X-ray fluorescence spectroscopy, UltraClean Technology, 8, 44–82 (1996).20. Horie, S. et al. Progress of ISO standardization activity onTXRF method −1: Report on RRT2 (Collecting methodof surface metal). Extended Abstracts (The 48th SpringMeeting 2001), The Japan Society of Applied Physicsand Related Societies, Meiji University, 2001, p. 839(31a-D-1).21. Mori, Y. and Uemura, K. Error factors in quantitative totalreflection X-ray fluorescence analysis. X-Ray Spectrom.,28, 421–426 (1999).22. Hourai, M., Naridomi, T., Oka, Y., Murakami, K.,Sumita, S., Fujino, N. and Shiraiwa, T. A method ofquantitative contamination with metallic impurities ofthe surface of a silicon wafer. Jpn. J. Appl. Phys., 27,L2361–L2363 (1988).23. Kondo, H., Ryuta, J., Morita, E., Yoshimi, T. and Shimanuki,Y. Quantitative analysis of surface contaminations

532 TOTAL REFLECTION X-RAY FLUORESCENCE FOR SEMICONDUCTORS AND THIN FILMSof Si wafers by total-reflection X-ray fluorescence. Jpn. J.Appl. Phys., 31, L11–L13 (1992).24. Mori, Y., Shimanoe, K. and Sakon, T. A standard samplepreparation method for the determination of metal impuritieson a silicon wafer by total reflection X-ray fluorescencespectrometry. Anal. Sci., 11, 499–504 (1995).25. Mori, Y. and Shimanoe, K. Standard sample preparationfor the analysis of several metals on silicon wafer. Anal.Sci., 12, 141–143 (1996).26. Mori, Y., Uemura, K., Shimanoe, K. and Sakon, T. Adsorptionspecies of transition metal ions on silicon waferin SC-1 solution. J. Electrochem. Soc., 142, 3104–3109(1995).27. Mori, Y. and Uemura, K. Multi-batch preparation ofstandard samples from a single doped solution forcross-checking in surface metal analyses of silicon wafers.Anal. Sci., 16, 987–989 (2000).28. Funahashi, M., Kuraoka, M., Fujimura, S., Kobayashi, H.,Kohno, H. and Wilson, R. BST thin film evaluation usingX-ray fluorescence and reflectivity methods. Adv. X-RayAnal., 42, 109–118 (1999).29. Terada, S., Furukawa, H., Murakami, H. and Nishihagi, K.A grazing incidence X-ray fluorescence analysis ofthe composition of (Ba,Sr)TiO 3 (BST), and SrRuO 3(SRO) stacked films. Adv. X-Ray Anal., 43, 504–509(2000).

7.3 X-Ray Spectrometry in ArchaeometryA. ZUCCHIATTIIstituto Nazionale di Fisica Nucleare, Genova, Italy7.3.1 INTRODUCTIONAny human artefact bears the history of its making,use, and conservation. Fossils as well bear thehistory of their birth, of their life, of the aggressionof nature after their death. Reading this history isthe ultimate goal of all the scholars and sciencesthat operate in the broad environment of thecultural heritage. Part of the history is visible.The expert eyes of an art historian, trained bythousands of examinations and supported by asound knowledge of an historic period, can detectin the form of bodies, in the shades of colours,in the length and thickness of brush-strokes, theunmistakable signature of a master. A large partof the history is however hidden, lying below thesurface, trapped in the texture of the object ordeeper in the constituent atoms and molecules.The preparatory drawing of a painting, the artist’ssecond thoughts and remakes, the technology ofpreparing a colour, of firing pottery, of solderingmetals, the signs of climate in a fossil, all requireinstruments to be read. These are the foundationsof archaeometry.In principle any materials science analyticaltechnique can be transferred to archaeometry if itcan meet a few decisive requirements: it should benondestructive, flexible to accommodate a varietyof artefacts and samples and to analyse differentobject structures, fast, accurate and hopefullyquantitative. Techniques using an X-ray beamas the analytical probe or detecting X-rays asthe analysis product meet almost generally theserequirements.The use of X-rays in the broad domain of culturalheritage is almost as old 1 as the discoveryof this kind of radiation and has progressed incoincidence with the technical and instrumentaldevelopments that have marked X-ray productionand detection. X-Rays allow the characterizationof an ancient material, in terms of the elementalcomposition (X-ray fluorescence, XRF; protoninducedX-ray emission, PIXE; scanning electronmicroscopy with energy-dispersive spectrometry,SEM-EDS; synchrotron radiation – X-ray fluorescence,SR-XRF), of the constituent minerals (Xraydiffraction, XRD; SR-XRD; small-angle X-rayscattering, SAXS), of the oxidation state of theatomic species (X-ray absorption near-edge spectroscopy,XANES). Looking at the recent literaturewe observe the constant progress (40–50 %in 2001, source Archaeometry) of techniques likeXRF, XRD, SEM-EDS that can be performed withbench or even portable (XRF) equipment. Theirprinciples are well established, and widely coveredin textbooks 2,3 or review articles. 4 The extendeduse and technical development of traditional techniquesdeserve recording on their own. However,looking at recent developments, it is the progress ofportable instrumentation (including X-ray based)that has brought the best benefits increasing theaccessibility to artefacts and improving considerablythe quality of in situ analyses.Accelerator based techniques represent a rapidlyevolving alternative to bench instrumentation. Interms of elemental sensitivities (ppb level in SR-XRF) they can compete with neutron activationanalysis (NAA) and inductively coupled plasmaX-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

534 X-RAY SPECTROMETRY IN ARCHAEOMETRY(ICP) and offer space-resolved elemental andchemical analysis and an extended accessibility. 5Ion beam analyses in archaeometry 6 have beenbetween 5 and 10 % of the total in recent renownedtopical conferences, an appreciable figure in a fielddominated, quite obviously, by the analysis ofmodern industrial materials. Applications of SR,have been until recently limited to the occasionaluse of a general-purpose beam line. However, theoutstanding performance of second and third generationsynchrotrons now begins to be used ina more systematic way even in dedicated facilities,like the newly established archaeometry laboratoryat Daresbury. 7 Ancient valuable samplesare far from being ideal for the accelerator analyst.They often impose stringent exposure conditionsto avoid any form of beam damage andan experimental geometry which conflicts withthe need of optimising the measurement sensitivity.Important recent evolutions have concernedthe methodology with the aim of assuring quantitativewell-controlled characterization of ancientartefacts, and of describing their texture.7.3.2 ACCESSIBILITY OFTECHNIQUES: PORTABLE SYSTEMSArtefacts of a historical and artistic nature necessarilyattract the attention of art historians andcurators so that the opportunity for instrumentalinvestigations is normally inhibited. If the curatorhas a personal view of what is consideredacceptable damage levels, this can typically leadto a prohibition on sampling and consequently theimpossibility of meaningful laboratory analyses.Portable XRF equipment 8 has been a traditionalresource in archaeometry. Although limited insensitivity and in many cases only qualitative, itcan nevertheless give a rather complete view ofthe object conservation state, assist the restorationprocess and guide the sampling to the areaswhere a precise quantitative characterization cangive the most useful information to restorers andart historians. 9 In some cases (XRF of metalalloys) appropriate algorithms make possible thequantitative analysis 10 to characterize an object indetail. Even if a certain number of radioactivesources can be used to produce the primaryX-ray, 10 X-ray tubes are normally preferred forthese have higher intensity and are not boundto transport regulations. Several portable XRFsystems have managed to combine sensitivity andportability. A light (5 kg) system based on a30 kV, 0.1 mA, air-cooled tungsten tube and on aPeltier-cooled SDD (silicon drift diode) assures 11minimum detection limits (MDLs) of 0.15 % forFe Kα and 0.2 % for Sn Lα. A high power(60 kV, 4 mA), water-cooled tungsten tube coupledto a HPGe detector, liquid nitrogen (LN2) cooled,weighs four times more but has MDLs of 0.1 % forFe and Pb and 0.01 % for Ag, Sn, Sb. 9 Good MDLshave been reported for an air-cooled rhodiumtube operated at 50 kV and 0.35 mA coupled toan LN2 cooled Si(Li) detector and capable ofdetecting down to 0.05 % of Fe, 0.01 % of Ni,0.5 % of As (0.01 % in samples with low Pbcontent), 0.5 % of Zn, 0.001–0.006 % of Ag, Snor Sb. 12A recent device 13,14 makes use of a radioactivealpha source which, combined with a portableX-ray detector and electronics, constitutes a compactand versatile field instrument for quantitativePIXE analysis at the 1 % level. Since the sourceactivity must remain below law enforced limits,the price paid is evidently the increase of MDLs,and the limited penetration depth of an alpha particlecompared to a proton. Nevertheless evenlimited information can be conveniently exploitedas proved in several campaigns. 15–18 The sourceholder is made of Mylar and has a conical shape(Figure 7.3.1) so as to produce a concentration ofalpha particles on the target. The irradiated surfaceis of the order of 1 cm 2 . Alpha particles, emitted atabout 5 MeV, before reaching the target will crossa sealing epoxy resin layer, one of the kapton windowsand a negligible air layer, which is replacedby a helium flow in the most recent configuration.The whole system is very compact and can be usedin close contact to the sample, for minimum energyloss and maximum detection efficiency. 210 Po has ahalf-life of 138.4 days and the source initial activityis 16.6 × 10 7 Bq/g. Only 3.7 × 10 7 Bq of 210 Po is

ACCESSIBILITY OF TECHNIQUES: PORTABLE SYSTEMS 535TargetKapton +Nylon gridEpoxyDepositionMylar structureMylarSilverPoloniumBe windowSi(Li) detectorFigure 7.3.1 A schematic cross-section view of the polonium source with target and detectorsufficient to produce in 30 min peaks, which givesrise to a statistical error below 5 %. 197.3.2.1 X-RAY ENERGY DISPERSIVEDETECTORSThe remarkable performance of portable systems isdue also to the development of energy dispersivespectrometers. (Table 7.3.1). Today they offerresolution and efficiency comparable to that ofprevious laboratory instruments with, in addition,compactness and, in the case of SDD detectors, 11also high speed. In analysis one wants the lowestpossible MDL (Equation 7.3.1) and therefore triesto obtain the largest possible integrated sourceintensity Q, detector solid angle , efficiency εand the smallest possible FWHM resolution.w MDLZ∝√ FWHMR√ Qε(7.3.1)In the case of art objects the source intensitymight be limited by the risk of damage and thesolid angle subtended by the solid surface, whichconfiguration could be quite complex around thedetector. In a very general way we can assumethat the space available to the detector is a coneof full aperture θ as in Figure 7.3.2. In such acase, the maximum solid angle will be obtainedwhen the angular sector is entirely covered by thecryostat and this corresponds to a value:( ) d 2fπS MAX =(D + t) = 2 2 [( ) dctg ϑ2 2 + g d ] 22( ) d 2fπ2= ( ) d 2 (ctg ϑ ) 22 2 + gf= π (ctg ϑ ) 2(7.3.2)2 + g

536 X-RAY SPECTROMETRY IN ARCHAEOMETRYSampleD∆qFilterBeamtSdCryostatFigure 7.3.2 A schematic view of a typical beam–sample–detectorset-up for the analysis of an irregularly shaped artefactwhere d is the detector diameter, S the active area,t the semiconductor–filter distance, g = 2t/d,f = 4S/πd 2 .Givenθ the solid angle dependsonly on f and g, which are critical parametersgiven in Table 7.3.1.7.3.3 SYNCHROTRON RADIATIONIN ARCHAEOMETRYThe advantage that SR has in comparison toeven the most powerful X-ray tube is an intensity10 10 times higher (Figure 7.3.3a), a continuousspectrum (Figure 7.3.3b) rich in hard components(40–100 keV), low background 20 and good emittance.These allow a broad range of preparations(ESRF has 48 beamlines, Hasylab 43, Daresbury44) that can produce on the sample high brilliancemonochromatic microbeams. Since the energy istunable, the penetration depth and the excitationcross-sections are widely controllable. SR offerssuperior spatial and angular resolution, high XRFsensitivity from low to high Z elements and abroad range of complementary techniques (µ-XRF,µ-XRD and µ-XANES). Let us consider two of theseveral SR arrangements, which have been usedrecently in archaeometry. 21–25The SR-XRF microprobe set-up at beamlineL in Hasylab is used for simultaneousmulti-elemental analysis of micro-samples. Theexperimental set-up is schematically shown inFigure 7.3.4. The beam 26,27 is collimated by a systemof 3 mm thick tungsten cross slits to a sizeof 30 × 30 µm 2 and passes an optional absorber toreduce the low energy part of the white spectrum,if a better sensitivity is wanted for higher Z elements.To further reduce the beam spot straightcapillaries or ellipsoidal capillaries can be usedgiving a minimum beam diameter of 2 µm. Thesample is mounted on an XYZ θ table with reproduciblepositioning of about 0.5 µm and 0.1 ◦ .FluorescenceX-rays are collected by a 30 mm 2 ,5mmthick HPGe detector covering a solid angle of 10 −3Sr. The sample is aligned to the beam with aresolution of 3 µm by means of a long distancezoom microscope, coupled to a charge-coupleddevice (CCD) camera. The synchrotron beam isTable 7.3.1 Parameters of recent solid state detectorsDetectorCryostatdiameter(mm)Activearea(mm 2 )f[%]Filterdistance t(mm)g(%)Be(µm)Resol.FWHM(eV)ActiveDepthof S(µm)1 Si(Li) 25.4 12.6 2.5 8 63 8 164 a 34902 Si(Li) 25.4 78 15.5 6 47.2 25.4 184 a 54703 Si-PIN Peltier cooled 14 25 16.2 1.52 21.7 25.4 280 b 5004 SDD Peltier cooled 19.2 10 3.5 1 10.5 8 175 c 3005 HPGe 22 95 25 5 45.5 25.4 155 d 50006 UltraLeGe 25.4 100 19.7 7 55.1 25.4 145 d 50007 Si(Li) 25.4 80 15.8 7 55.1 25.4 180 50008 Si(Li) without internal collimator 19 80 28.2 3 31.6 25 150 e 50009 Si(Li) 25.4 80 15.8 5.5 43.3 25 150 e 5000a Quoted FWHM resolution with 6 µs pulses at 3–4 kHz.b Quoted FWHM resolution with 6 µs pulses and rate below 3 kHz.c Quoted FWHM resolution with 0.5 µs pulses at 50 kHz.d Quoted FWHM resolution with 4 µs pulses and rate below 10 kHz.e Quoted FWHM resolution with 40 µs pulses at 1 kHz.

SYNCHROTRON RADIATION IN ARCHAEOMETRY 537Brilliance(photons/s/mm 2 /mrad 2 /0.1 % BW)Free electronlasers10 2310 2210 2110 2010 1910 1810 17ThirdgenerationDiffractionlimitESRF (future)ESRF (2000)ESRF (1994)10 1610 1510 1410 1310 1210 1110 1010 910 810 7Second generationFirst generationX-raytubesSynchrotronradiation10 6 1900 1920 1940 1960 1980 2000(a)Years10 21EnergyCurrentEmitt. hor.Emitt. ver.Gap6 GeV200 mA4 nm30 pm11 mmBrilliance (photons/0.1 %/mm 2 /mr 2 )10 2010 19U35 × 5 mHigh Beta IDW70 × 1.6 mLow Beta ID10 1810 17 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9(b)1 10Photon energy (keV)100Figure 7.3.3 Comparison of X-ray sources brilliance (a) and some possible selections of the SR spectrum at the EuropeanSynchrotron Radiation Facility (ESRF) (b). Courtesy of the ESRF information office

538 X-RAY SPECTROMETRY IN ARCHAEOMETRYHPGe detector(optional Si(Li)Pb shieldingMicroscopeCCD cameraBeammonitor45°CapillaryopticCrossslitsAbsorberDORIS-IIIBeamstopXYZsamplestage45°BendingmagnetWhite SR(optional monochromatic)Figure 7.3.4 A schematic layout of the micro-XRF beam of line L at Hasylab. Courtesy of Dr Gerald Falkenbergmonitored after the cross slits and after the sampleby ionisation chambers and is finally stopped ina lead block. The fluorescent excitation of K linesis used for element identification and quantificationfrom Z = 19 (K) to Z = 82 (Pb). MDLs are downto 0.1–1 ppm for 19

PROBING THE TEXTURE OF ANCIENT MATERIALS 539~1 mm(a)(b)(c)(d)Figure 7.3.5 Some examples of the texture of ancient artefacts as seen in polished cross-sections. (a) A multilayered paintingon a German fourteenth century polychrome wooden sculpture. © C2RMF photo S. Colinart. (b) The cross-section of a fourthcentury bronze vase showing superficial corrosion layers of even very large depth. © C2RMF photo B. Mille. (c) A portion ofa fourth century pottery with well evident mineral grains and crushed sea shells. © C2RMF photo A. Leclair. (d) A nineteenthcentury blue glaze shows the presence of unfused thenard blue grains. © C2RMF photo A. Bouquillonof the object composition at the sub-micron level.Whenever the object integrity is strictly imposed,radiography (X-ray, neutron) is capable of detectingstructural details 30 with spatial resolution of theorder of 1 mm and can be used for the investigationof whole objects (Figure 7.3.6). With fully nondestructiveprocedures elemental surface maps inthe 10 µm range and depth profiles in the 100 µmrange are now possible.7.3.4.1 RECENT ADVANCES IN PIXEDEPTH PROFILINGRutherford backscattering spectroscopy (RBS) isthe most appropriate, nondestructive, Ion beamanalysis (IBA) technique for element depthprofiling. Whenever RBS is not applicable 31 theanalysis of fluorescence X-rays can be used,despite a poorer depth resolution, to detect theordering of layers and have a clue of theirthickness, especially when each layer may becharacterized by a different most abundant (key)element and when the elements to profile havemedium to high Z.A methodology using 68 MeV protons 32,33 hasbeen demonstrated on a set of test paint layers, preparedby the Kunsthistorisches Museum in Vienna,in resemblance of sixteenth–seventeenth centuryItalian and Flemish paintings and characterized bypigments containing mostly medium and high Zelements (Cu, Hg, Pb). The penetration depth of68 MeV protons in matter is of the order of a few

540 X-RAY SPECTROMETRY IN ARCHAEOMETRYFigure 7.3.6 A three-dimensional CAT scan of Egyptian mummy hands, from a study of the Radiology Department of theUniversity and ‘Le Molinette’ hospital of Turin (Italy). Courtesy of Soprintendenza al Museo Delle Antichità Egizie – Ministeroper i Beni e le Attività Culturali. Imaging by Dr Federico Cesaranimm and the X-ray production cross-section is 100times larger than at 3 MeV, so that still 10 % ofthe Kα X-rays of lead will reach the detector from3 mm below the surface. For several elements thedifferent absorption of two X-ray lines in their passagethrough the matrix gives a yield ratio (e.g.Pb Lα/Pb Kα) related, in layered samples, to theaverage depth at which the element is present.The depth can be quoted as an equivalent CaCO 3thickness since this material should match theaverage absorption coefficients of the real matrix.The unperturbed peak intensity ratios are extractedfrom thin pure foils of Cu, Ag, Au and Pb. Twosamples were prepared on a Cu backing with aslightly different layers sequence: Au foil, cinnabar(HgS), yellow ochre, lead-tin yellow (Pb 2 SnO 4 ),azurite (2CuCO 3 .Cu(OH) 2 ) and, in the secondsample, an extra lead-white (PbCO 3 .2Pb(OH) 2 )layer after the gold foil. As seen in Figure 7.3.7 thesequence is well reproduced, which is more significantinformation than the layer’s actual thickness(doubled by the method!) since the latter changesconsiderably with the brush strokes. The layermarking elements can be used to attempt an identificationof the pigment; however, in the case of twodifferent layers, characterized by the same majorelement, this method produces only one averagedepth and the two levels cannot be disentangled inthe sequence.Another way of probing a material at differentdepths consists of using on the same spot aset of different beam energies. 34 In gold alloysseveral conditions are met that make possible eventhe quantitative determination of a surface layerthickness. An example 5,31 concerns the so-calledtumbaga, a Cu–Ag–Au alloy, rich in copper (upto 40 %), produced by pre-Columbian goldsmithswith processes that reduced the copper content atthe surface thus giving the alloy a colour veryclose to that of pure gold and a durable protectionfrom corrosion. At a given proton energy, E p =1.6MeV, the Cu Kα/Au Lβ yield ratio of 7.8 willbe compatible (Figure 7.3.8) with a homogeneousalloymadeofCu40%,Au54%,Ag6%,but

PROBING THE TEXTURE OF ANCIENT MATERIALS 541350Microns from surface300250200150100Cu BackingLead whiteAu foilCinnabarYellow ochreLead-tin YellowAzuritePbAuHgFePbSnCuPbAuHgFePbSnCu500300Microns from surface250200150100Cu BackingAu foilCinnabarYellow ochreLead-tin YellowAzuriteAuHgFePbSnCuAuHgFePbSnCu500SEM Point 1 Point 2Figure 7.3.7 The depth of two sequences of paint layers observed by SEM, compared with conventional depths deduced from68 MeV PIXE analyses. Two points per sample were analysed. Constructed with the data of Denker and Maier 3298(a)Cu Ka/Au Lb76(a) Cu 40 % Au 54 % Ag 6 %(b)(b) 0.55 µm (Cu 10 % Au 81 % Ag 9)on Cu 50 % Au 45 % Ag 5 %5 (c)(c) 1.5 µm (Cu 30 % Au 63 % Ag 7 %)on Cu 50 % Au 45 % Ag 5 %40.5 1 1.5 2 2.5 3Proton energy (MeV)Figure 7.3.8 The behaviour with proton energy of CuKα/AuLβ yield ratio. Three different curves are given for possible layeredstructures in the examined sample. Reworked from the data of Demortier and Ruvacalba-Sil 32

542 X-RAY SPECTROMETRY IN ARCHAEOMETRYalso with a 0.55 µm surface layer of Cu 10 %,Au 81 %, Ag 9 % on top of a homogeneousbulk material containing Cu 50 %, Au 45 %, Ag5 % or even with a 1.5 µm surface layer of Cu30 %, Au 63 %, Ag 7 % on top of Cu 50 %, Au45 %, Ag 5 %. The ambiguity can be resolved bymeasurements at other energies around 1.6 MeVsince the yield ratio will follow a different curveaccording to the layer’s structure. Since in metalalloys, there is no beam damage the count ratecan be kept high enough to obtain in a short timestatistical errors lower (1 %) than the separationof the curves. The outermost layer composition isdetermined by PIXE analysis with 1 MeV alphaparticles and is used as the starting point for thecalculation of depth profiles. The Cu, Au, Agconcentrations measured on a tumbaga pendant of44 mm diameter, show (Figure 7.3.9) very clearlythe progressive decrease of gold from the surfaceto a bulk material that contains 28 % of copper.7.3.4.2 EXTERNAL MICROBEAMSFOR PIXECharged particle microbeams extracted in airhave a spatial resolution of the order of 10 µm,larger than the 1 µm obtainable in vacuum, buttheir flexibility gives access to microstructures(inclusions, composition gradients, ...)inalargevariety of samples including valuable artefacts,polished sections, fragments. A very effectiveone is that developed at the ALGAE acceleratorof the Louvre museum, 35 based on the nuclearmicroprobe system of Oxford Microbeams coupledto a special design of the beam-line exit nozzleand to an appropriate choice of the exit window.The window material is silicon nitrate (Si 3 N 4 ),which can be produced in 0.1 µm films, andassures good resistance to pressure, to moderatemechanical shocks and to radiation damage. TheSi 3 N 4 window is set at 45 ◦ to the beam. Acollimated exit provided with a 8 µm kaptonfoilgives access to a Peltier-cooled Si(Li) detector tocount the Si 1.740 keV X-rays as a beam monitor(Figure 7.3.10a). The window is highly stableunder the particle beam, and this monitor is quitereliable. A specific brass collimator suppresses thecontribution of beam halo to the beam monitoring.Figure 7.3.10(b) represents in detail the 110 mmlong nozzle. A 3 MeV proton beam emerges fromthe window with an energy loss of 8.5 keV andan energy straggling of 4.5 keV, while a 3 MeValpha beam emerges with an energy loss of 94 keVand an energy straggling of 31 keV. These figuresmake possible RBS and NRA and obviously PIXE120CuAuAgWeight concentration (%)100806040SurfaceLayer 1Layer 2Layer 3Layer 4Layer 5Bulk200Figure 7.3.9 The concentration of Cu, Au, Ag in different layers of a tumbaga pendant. Constructed from the data of Demortierand Ruvacalba-Sil 54

PROBING THE TEXTURE OF ANCIENT MATERIALS 543Si(Li)High ZSi(Li)Low ZSi3N4WindowExit Nozzle(a)Monitor(b)Monitor1 cmFigure 7.3.10 (a) The layout of the ALGAE microbeam showing the two detectors system. (b) The cross-section of the exitnozzle. Shown are the Si 3 N 4 window, the anti-halo collimator and the exit to the Peltier-cooled Si(Li) detector acting as a beammonitor. Courtesy of B. Moignard C2RMFthat is not as sensitive to possible alterationsof the beam quality. The spatial resolution hasbeen quantified by scanning, as a reference, withprotons, deuterons and alphas a calibrated coppergrid. It is 10, 20 and 50 µm FWHM for proton,deuteron and alpha beams, respectively.7.3.4.3 PIXE MICRO-MAPPING OFFLINT TOOLSOf great interest is the information on the wearmechanism of archaeological flint tools. Its archaeologicalimportance is in the presence of remnantsbelonging to the worked material that allows theanthropologists to classify the tools and gatherinformation on the human activities in the area offinding. Flint is a mixture 36 of quartz spherules,averaging 12.5 µm in diameter, embedded in amicrofibrous chalcedony cement. The edge chippingthat was used to manufacture cutting toolsis essentially a fracture of the chalcedony cementand goes around the spherules giving rise to amicroscopically rough surface. The tool’s surfaceis modified by continuous use and a polish appearsat the cutting edges. The origin of this polish hasbeen debated at length. 37 The microanalysis of testtools has added essential information to the debate.The chipped edges have been implanted with Cumarker ions at a depth of only 0.1 µm with a doseof 5 × 10 16 ions/cm 2 for a resulting Cu Kα countrate of 15 Hz. After intense use on bone, linearmicroscans of the edge region (both parallel andperpendicular to the edge profile) were performed.The results prove that no loss of the Cu marker isexperienced, while the edge area is enriched in Ca.Due to the low Cu implantation depth compared tothe spherules diameter it seems therefore excludedthat the use of the tool results in ejection of thequartz spherules from the surface. The formationof polish should therefore be due to the depositionof material from the worked body in the intersticesof the flint tool.The micro-mapping of a set of archaeologicalMesolithic flints 38 reveals again a deposition ofexternal materials confined in the flint edge andcharacteristic of the worked object: bone, wood,skin, meat as in the diagrams of Figure 7.3.11. 39The accumulation of Ca, S, and to a minor extentP and K on the tool edge (Figure 7.3.11) indicates

544 X-RAY SPECTROMETRY IN ARCHAEOMETRYPSKCaPSKCaFigure 7.3.11 PIXE micro-mapping of two 1.2 × 1.2mm 2 areas of two archaeological flint tools. The tool that produced the topmaps was probably used for cutting bone while the other one was used for hide scraping. Reproduced from Smit et al. 39 Withpermission from the European Commissionthat the tool was used for cutting hard material likebone. The absence of Ca but the increase of K andP (Figure 7.3.11) might indicate that the tool wasused for hide scraping.7.3.5 RADIATION DAMAGEIt can never be stressed enough that the nondestructivenature of the X-ray based techniques has

RADIATION DAMAGE 545been the key of their expansion in the domainof cultural heritage. It is extremely important toguarantee safe procedures throughout the analysisprocess to control in a quantitative way thebeam–sample interaction.7.3.5.1 THE RADIATION DAMAGEON GLAZESThe irradiation of pottery glazes with ion beams isknown to produce chromatic alterations visible bythe naked eye even after a short exposure. Thebeam can induce atomic dislocations leading tothe formation of peroxide groups (the coupling oftwo oxygen atoms) and centres (sites where anoxygen bound is lost). The absorption spectrumof the medium and consequently the colour ofthe irradiated sample could change. Althoughself-annealing takes place within hours or daysthe effect is unwanted and must be controlled.Chromatic alterations have been quantified forthe first time 40,41 in white and blue glazes ofthe Italian renaissance. Digital macro-images ofthe irradiated area, are analysed with commercialsoftware and each pixel is assigned the so-calledLab colorimetric coordinates (L, a, b), which aimat reproducing the human perception of colours.L is the lightness and may vary from 0 (totallyblack surface) to 100 (perfectly white surface). aand b account, respectively, for the red–green andyellow–blue balances. The Lab coordinates definea vector E corresponding to a given colour inthe colorimetric space and the chromatic distancebetween two points is represented by:|E| = √ a 2 + b 2 + L 2 . (7.3.3)The colorimetric analysis was performed for aseries of rings of increasing radius even beyondthe visible beam spot (2 × 10 −3 cm 2 ) well intothe non-irradiated unaltered surface. The colourchange E, with respect to the outermost ring, wasmeasured as a function of the radius for a broadrange of beam currents and accumulated charges.A safety value E = 1 was assumed since thehuman eye can only appreciate E ≥ 1. Originalrenaissance and modern white or blue glazes havebeen studied with similar results. In white glazesboth the amount of the damage and its surfaceextension increase with the accumulated charge,as shown in Figure 7.3.12 for a beam currentof 4 pA. The maximum variation, E ≈ 12, isreached close to the beam axis (smallest radius) atan accumulated charge of about 1 nC. Afterwardsthe colour change saturates at the spot centrewhile a further increase of the accumulated chargeproduces a growth of the E values at large radii,in other words an increase of the FWHM of theradial distribution (Figure 7.3.13).∆E141210862.4 nC1.0 nC0.2 nC0.1 nC4200 100 200 300 400 500 600 700 800 900Ring average radius (µm)Figure 7.3.12 The radial distribution of the colour change in white glazes as a function of the collected charge for a beam currentof 4 pA. Constructed from the data of Migliori 40

546 X-RAY SPECTROMETRY IN ARCHAEOMETRY∆ E1614121086422400200016001200800400FWHM (microns)000.1 1 10 100 1000Charge (nC)Figure 7.3.13 The maximum E colour change of white glazes at the spot centre as a function of the total collected charge fordifferent choices of the beam current (dashed band). The FWHM of the colour distribution (dotted curve). Reworked from thedata of Migliori 40Table 7.3.2 Safe limits for IBA of some ancient materialsMaterial Beam Energy(MeV)Current Spot CurrentdensityGlaze Proton 3 4 pA 0.2 mm 2 20 pA/mm 2 0.1 nC 40Glaze Proton 4 0.2 nA 1 mm 2 0.2 nA/mm 2 10 nC 52Paper Proton 4 1 nA 4 mm 2 0.25 nA/mm 2 5nC 34Paper Proton 3.5 – – 10–150 pA/mm 2 12 nC/mm 2 53Paper Proton 2.5 – – 10–150 pA/mm 2 8nC/mm 2 53Paint layers Proton 4 0.5 nA 1 mm 2 0.5 nA/mm 2 30 nC 34Paint layers Proton 68 0.1–1 pA 0.5 mm 2 0.2–2 pA/mm 2 200 nC 54Glass Proton 2 3.5 nA 12 µm 2 300 pA/µm 2 2.4 µC 55SafelimitRef.In blue glazes the behaviour of the colourchange is similar. However E values higherthan 30 have been reached at a charge of 2.4 nC,still without signs of saturation. The perceptionof damage on an irradiated glaze limits thereforethe total integrated charge to values below 0.1 nC.This must be delivered to the sample in controlledconditions 40 operating with currents of 1–2 pA for50–100 s.Limits for safe IBA of various materials havebeen reported in the literature and are summarizedin Table 7.3.2.7.3.5.2 DAMAGE WITH X-RAYPRIMARY BEAMSX-Rays deposit energy in a sample over a volumemuch larger than in the case of particles atequal penetration depth. The effects on the objectappearance and integrity should be negligible.Organic materials could be darkening and becomefragile earlier than other materials. However,no damage has been observed, 41 whatever theexamined material, in years of practice in XRFeven at tube settings of 2.5 kW and 60 kV withmost measurements taken at 0.5 mW and 50 kVand 30 s irradiation.The high photon flux in SR facilities deservessome attention. In the SR-XRF analysis of parchmentscare must be taken 25 to assess the significanceof ionisation and the creation of free radicalswhich have effects on the sample integrity, especiallythose with high moisture content. In inkstudies with SR-XRF with a 0.5 × 1mm 2 polychromaticSR beam the energy deposited in 300 sruns on paper is of the order of 15 µW/cm 2 almost

RECENT PIXE AND µ-PIXE APPLICATIONS 547a factor 100 below solar maximum irradiation 42and therefore the creation of radicals shouldbe negligible.7.3.6 RECENT PIXE AND µ-PIXEAPPLICATIONS7.3.6.1 STUDY OF RENAISSANCEGLAZED TERRACOTTA SCULPTURESGlazed, coloured terracottas, are very distinctiveof the Italian artistic Renaissance and enrich thecollections of the world major museums. Arthistorians are confronted by a rich and compositeensemble of hundreds of objects. PIXE canidentify the elemental content as a fingerprintof each glaze and help to identify similaritiesamongst objects and to strengthen hypotheses onartist attribution. Appropriate analytic procedures 42have been implemented to deal with the nonhomogeneousnature of Renaissance glazes, to treatconsistently the three kinds of samples available(polished cross-sections, fragments and wholesculptures), to correlate data from two facilities(ALGAE 43 and INFN Florence 44 ), to estimate nonstatistical errors which are between 3 and 8 % formany elements and exceed 10 % only for low Zelements (Na,Al) or for elements well below 1 %in weight.The nature of samples requires some considerations.Plaster, dust or paint, could create a surfacelayer on whole sculptures and even more onfragments, which are sampled for evident reasonsfrom peripheral ‘dirty’ areas. The extra layer couldexhaust a non-negligible fraction of the total protonrange and therefore increase the concentrationof contaminant elements, such as Al, K, and Ca incomparison to a polished SEM section. Other discrepanciescould be due to the glaze texture. Forexample the high amounts of CaO found by PIXEon a micro-sample were explained by SEM images.The interface, characterized by the developmentof newly formed crystals of calcium silicate wasexceptionally thick, 42 more than 100 µm, due tolocal over-firing inside the Renaissance kiln. Alarge number of measurements on the same artefactare therefore recommended to avoid possiblemisinterpretations. Even anomalous analyses canbe taken to further statistical treatment since theygive complementary information on the artefactmanufacture and conservation.Almost 700 PIXE measurements have been performedon 54 artefacts. Detailed comparisons canbe made on groups of objects similar in shape, styleand use. The sculpture department of the Louvremuseum hosts two pairs of kneeling angels usedas candleholders, stylistically quite different (cataloguenumbers C52-C53 and RF1533-RF1534).The first is typical of the Buglioni’s or some minorFlorentine workshop, the second seems convincinglya product of the Della Robbia ‘bottega’ executedby an apprentice rather than by the masters(the ageing Luca or Andrea).The glazes have been analysed on the sculpturesas well as on cross-sections. All are leadsiliceousglazes, slightly enriched in K 2 OandCaO,opacified by tin oxide and coloured with differentmetallic oxides: cobalt for blue, manganesefor purple, lead antimoniate for yellow, copperfor green. The microstructure of the glazes (SEMimages) is quite typical: a homogeneous glassymatrix (∼150 µm thick for both pairs) with unmeltedquartz grains or feldspar, heterogeneousre-partition of tin oxides crystals and bubbles. Theglazes are very similar for the two angels of thesame pair and their compositions are compatiblewith the Renaissance recipes published in oldceramics treatises. If the blue glazes are considered,the two pairs differ sharply (Figure 7.3.14).Cobalt is usually associated with other metallic elementsthat reflect the origin of the ores as well asthe different methods of purification of the metal.Cobalt is associated with Ni, Cu, Fe for the pairRF1533-RF1534, whereas appreciable amounts ofAs 2 O 3 are measured in the blue glazes of the otherpair. Studies aiming at tracing the ancient commercialroutes of cobalt in Europe 37,45,46 suggest acompositional change of raw material at the boundaryof fifteenth–sixteenth century, with increasedamounts of As, probably due to a different refinementprocess of the mineral ores. The two pairs ofangels seem to fit in this scheme: the Della Robbiabottega was founded around 1440 while the

548 X-RAY SPECTROMETRY IN ARCHAEOMETRY6000Counts50004000300020001000Arsenic K b11.726 keVRF-1533C52011 11.5 12 12.5 13 13.5X-Ray energy (keV)Figure 7.3.14 The X-ray spectra of samples C52 and RF1533 show clearly the discriminating presence of the As Kβ line in oneof themBuglioni’s were active from the beginning of thesixteenth century.7.3.7 RECENT APPLICATIONS OFSYNCHROTRON RADIATION7.3.7.1 ANALYSIS OF EGYPTIANCOSMETICS WITH SR-XRDCosmetic recipes and details of make-up manufacturingin ancient Egypt have been revealed thanksto powder SR-XRD. 47,48 In a series of experimentsperformed at line BM16 of ESRF, a large numberof cosmetics, used in Ancient Egypt and conservedin the Louvre museum, have been analysed showinghow great was the variety of compositionsusing lead compounds and how advanced was atthat time (2100–1100 BC) the know-how in chemicalsynthesis. 49,50The Rietveld refinement of powder diffractionpatterns (Figure 7.3.15) has identified fourlead-based main phases: the black galena (PbS)3.0 × 10 42.5 × 10 4Intensity (counts)2.0 × 10 41.5 × 10 41.0 × 10 45.0 × 10 30.0−5.0 × 10 31 2 3 4 5d (Å)Figure 7.3.15 The XRD intensity pattern of sample E11047 of Egyptian cosmetic powder (black curve), and Rietveld refinement.Open circles represent the calculated diagram and the experimental-calculated difference is in grey. Courtesy of Ph. Walter C2RMF

CONCLUSIONS 549and three white products, cerussite (PbCO 3 ),phosgenite (Pb 2 Cl 2 CO 3 ) and laurionite PbOHCl.Galena (greyish black) and cerussite are wellknown lead ores mined in antiquity along the Redsea coast. They were mixed to give a varietyof grey shades. Laurionite and phosgenite (bothwhite) are synthetic compounds produced by wetchemistry, according to recipes that were documentedby Greco-Roman authors, and were addedquite surely because of their remedial effects.The study has been extended into the analysis ofthe Bragg line profiles, which are influenced, bythe microstructure, size and distortions of the mineralgrains. The profile of archaeological galena(PbS) was compared with that of a geologicalgalena hand-ground with a pestle and mortar andthen selected through a 63–125 µm sieve. Thelattice distortion is found higher in the archaeologicalpowder than in the geological powder. Thearchaeological powder has been finely ground: theSEM observations reveal a heterogeneous assemblyof small cubes ranging from 20 µm to 150 µmlong, with a significant fraction of smaller grains.Other archaeological galena powders show thatthey were finely ground by the Egyptians andsorted as a function of size, to obtain either ablack mat powder, or grey powders with metallicovertones. Already 4000 years ago, people wantedtheir cosmetics to do more than simply highlightingthe eyes!7.3.7.2 XRF AND XANESMICRO-MAPPING OF CORRODEDGLASSESThe problem of glass corrosion in ancient Romanglass fragments 22,51 has been studied with SRusing both µ-XRF and µ-XANES on the samesample. The severe glass alteration manifests itself,on a microscopic scale, as a series of corrosionlayers at progressive depths down to 400 µm,accompanied by a precipitation crust at the surfaceand separated by interstitial cavities. Such analteration seemed due to a more complex processthan a continuous leaching of alkaline ions, like Naand Ca and their replacement by other ions broughtin by the humid environment. Rather, severalcycles of leaching and layer separation seemed tohave taken place. This hypothesis was confirmedby µ-XRF scans along the depth of the corrosionlayers 51 and by µ-PIXE measurements. 22 Themigratory patterns of major and minor elements,which are related to the size of the ions andtheir chemical bonds in the glass network, werereconstructed. While the Ca leaching is evidentwith a concentration that decreases by a factor 10,some of the elements (K, Ti, Fe, Br) are enrichedand uniformly distributed over the corrosion layer.Most trace elements are also enriched in thecorrosion layers, except those (Sn, Zr) whichare part of the glass network and remain almostconstant. Manganese has a more differentiatedprofile, with maxima and minima within thecorroded area. During the mechanical separationof the leached layer from the glass bulk, oneexpects in the interstices some precipitation ofMn, possibly accompanied by the concentration oftrace elements brought in by ground water. Thishas been clarified by the µ-XANES technique.The K absorption edge of Mn shifts upwardsby several eV if the oxidation state of Mnchanges from 2+ to 4+. Selective mapping ofMn can be done by looking at the SR-XRF mapsperformed at two beam energies: 6.550 keV, whichis only just above the absorption edge of Mn 2+and 6.564 keV where also Mn 4+ is above theabsorption edge. By difference, the chemical Mn 4+(MnO 2 ) map is obtained (Figure 7.3.16). MnO 2 isconcentrated only in cavities that have separatedtwo subsequent corrosion layers formed in therepetitive leaching sequence.7.3.8 CONCLUSIONSThere is growing attention to the problems of studyand conservation of our cultural heritage. Manyscientific initiatives, on an international scale, havepromoted new technologies. The three actions ofthe European Cooperation in the field of Scientificand Technical Research (COST) concerning‘Application of ion beam analysis to art or archaeologicalobjects’, ‘Advanced artwork restoration

550 X-RAY SPECTROMETRY IN ARCHAEOMETRY(a) (b) (c)Figure 7.3.16 Fluorescence micro-maps on leached Qumram glass, performed at two primary beam settings at the Mn 4+ crest (a)and above the Mn 2+ edge (b). By difference, the map of MnO 2 (c) is obtained. Reworked from Jannsen et al. 51 by permissionof John Wiley & Sons, Ltdand conservation methods using laser technology’,‘Non-destructive analysis and testing of museumobjects’ and the network of ‘Laboratories on Scienceand Technology for the Conservation of EuropeanCultural Heritage’ (LabS TECH) are goodexamples of research promotion. X-Ray basedtechniques continue to be one of the fundamentaltools of archaeometry research. A much largeravailability of facilities and several technologicaladvances have produced an impressive number ofscientific examinations of artefacts with X-rays indedicated laboratories, in multi-disciplinary centresand in situ, making archaeometry a very dynamicfield today and an even greater research opportunityfor tomorrow.ACKNOWLEDGEMENTSI would like to thank the many colleagueswho have helped me with comments, reprints,documents, data and photos. I am pleased toacknowledge the warm and friendly hospitalityof the colleagues at the Centre de Rechercheet Restauration des Musées de France (C2RMF)during my many visits to the Louvre. Finally, Iwould like to dedicate this work to the late Prof.Friedel Sellschop who first addressed my attentionto IBA and applied sciences.REFERENCES1. Wilhelm Roentger Museum. Conrad Roentgen, una scopertache ha cambiato il mondo. Catalogue of the specialexhibition of the Roentgen Museum, Remscheid, Germany,1995.2. R.E. Van Grieken and A.A. Markowicz (Eds), Handbookof X-ray Spectrometry, Dekker, New York, 1993.3. R. Jenkins, X-ray Fluorescence Spectrometry, 2nd edition,John Wiley & Sons, Ltd, New York, 1999.4. D.E. Cox, in Handbook of Synchrotron Radiation (EdsG.S. Brown and D.E. Moncton), North Holland, Amsterdam,pp. 155–200, 1991.5. G. Demortier and A. Adriaens (Eds), Ion Beam Study ofArt and Archaeological Objects, Eur. Comm. EUR19218,2000.6. M.A. Respaldiza and J. Gomez-Camacho (Eds), Applicationof Ion Beam Analysis to Arts and Archeometry, Secretariadode Pubblicaciones, Universidad de Sevilla, 1996.7. M. Pantos, Synchrotron Radiation Special Interest Group,http://srs.dl.ac.uk/arch and links therein.8. E.T. Hall, F. Scwezer and P.A. Toller, Archaeometry 15,53–78, 1973.9. M. Ferretti, M. Miazzo and P. Mo’ioli, Stud. Conserv. 42,241–246, 1997.10. M. Milazzo and C. Cicardi, Archaeometry 40–2, 351–360,1998.11. A. Longoni, C. Fiorini, P. Leutenegger, S. Sciuti, G. Fonterottaand L. Strudel and P. Lechner, Nucl. Instrum.Methods A409, 407–409, 1998.12. J. Lutz and E. Pernicka, Archaeometry 38–2, 313–323,1996.13. G. Pappalardo, J. de Sanoit, A. Musumarra, G. Calviand C. Marchetta, Nucl. Instrum. Methods B109-110,214–217, 1996.

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7.4 X-Ray Spectrometry in Forensic ResearchT. NINOMIYAHyogo Prefectural Police Headquarters, Kobe, Japan7.4.1 INTRODUCTIONIn the field of forensic sciences, various analyticaltechniques are used in order to solve crimesor offenses. Total reflection X-ray fluorescence(TXRF) analysis, which is a variant of X-ray fluorescence(XRF) analysis, was first presented byYoneda and Horiuchi as a trace elemental analyticaltechnique. 1 TXRF is a very useful technique fortrace forensic samples because it is nondestructive,and has high sensitivity for trace elements. Klockenkämperreviewed this technique. 2 In the courseof the investigation on forensic elemental analysis,Prange et al. reported the characterization of singlefibers as a forensic application case of TXRF 3 andDuwel et al. reported quantitative elemental microanalysisof thermoplastic remains using TXRF. 4The author has applied TXRF to various forensicsamples, for example, cloth, 5 mineral water, 6pigment, 7 plastic, 8 arsenic material, 9 blood, 10toner, 11 drugs, 10,12–15,18 lipstick, 10 a copied letter,11 counterfeit bills, 14,15 vinyl tape, 14,15 semen,14,15 fingerprints, 14,15 soil, 16 liquor, 16 ivoryand mammoth tusk, 17 fiber 19 and gunshot residue. 19The author has also developed a specific instrumentwith both TXRF mode and fine beam X-rayanalysis mode for forensic samples. 14,15 In addition,a successful application of TXRF to a singlefiber concerning a murder case has been reported 20and synchrotron radiation-elemental mapping analysisof a fingerprint has been reported. 21In this paper, recent laboratory TXRF applicationsand synchrotron radiation-XRF applicationsat SPring-8 are presented.7.4.2 FORENSIC APPLICATIONSOF LABORATORY TXRF7.4.2.1 POISONED FOODIn 1998, a murder case, which involved poisoningcurried food, happened at Wakayama Prefectureand after this triggering case, many food poisoningcases occurred in Japan. TXRF was used toexamine suspicious foods and beverages quicklyand nondestructively. 22A droplet of 1 µl of a canned coffee samplewas spotted on a Si wafer and after drying,a residue sample was measured under conditionsof 40 kV and 30 mA excitation and a monochromatedMo Kα X-ray was incident onto a samplesurface at 0.06 ◦ incident angle for 1000 s.Figure 7.4.1(a) shows a TXRF spectrum of a suspiciouscanned coffee sample A and Figure 7.4.1(b)shows that of a normal canned coffee sample B.Phosphorus and chlorine are clearly detected inFigure 7.4.1(a), while in Figure 7.4.1(b), no phosphorusis detected and a weak peak of chlorineis observed. The peak of silicon is due tothe Si wafer. The difference between spectra in(a) and (b) suggests that some poisoning agentscontaining both phosphorus and chlorine wereadded to sample A. By detailed chemical analysisusing gas chromatography-mass spectrometry(GC-MS), dichlorvos (DDVP) was detected insample A. DDVP is a type of insecticide withmolecular formula (CH 3 O) 2 P(O)CH=CCl 2 . Thepeaks of phosphorus and chlorine in the spectrumin Figure 7.4.1(a) reflect the formula of DDVP.X-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

554 X-RAY SPECTROMETRY IN FORENSIC RESEARCH1000SiClArK800PIntensity (counts)600400K, Ca200CaRb(a)00 2 4 6 8 10 12 14Energy (keV)1000SiArK800K, CaIntensity (counts)600400200ClCaRb(b)00 2 4 6 8 10 12 14Energy (keV)Figure 7.4.1 TXRF spectra of two canned coffee samples: (a) sample A (suspicious); (b) sample B (normal)This TXRF technique can also be appliedto examine the chemical terrorism weapons,sarin, soman, tabun, VX gas and their hydrolysedresidues in water, because these chemicalshave phosphorus elements in their molecularstructures.7.4.2.2 LIQUORResidues of liquors are often discovered as evidentialmaterials at crime scenes. TXRF wasused to examine elemental ingredients containedin liquors.Figure 7.4.2 shows TXRF spectra of four kindsof liquors: sample A (sake, Japanese liquor,alcohol content: 14 %); sample B (beer, alcoholcontent: 5 %); sample C (Chinese liquor, alcoholcontent: 17 %); and sample D (red wine, alcoholcontent: 14 %). Each droplet of 10 µl of liquorwas spotted on a Si wafer and after drying wasmeasured. X-Ray excitation conditions were 40 kVand 40 mA. Other analytical conditions were thesame as for the previous example.

FORENSIC APPLICATIONS OF LABORATORY TXRF 555Intensity (counts)(a)Intensity (counts)(c)40003500300025002000150010005004000350030002500SiClSArKCaMnZn00 2 4 6 8 10 12 14 16KSi ArK, CaEnergy (keV)2000ClRbZn1500CaS1000MnFe500BrZnP00 2 4 6 8 10 12 14 16Energy (keV)Intensity (counts)(b)Intensity (counts)(d)40003500300025002000SiSi KClK, Ca1500Br1000CaRb500P S00 2 4 6 8 10 12 14 164000350030002500200015001000500SiArClSKK, CaCaEnergy (keV)FeMnZn00 2 4 6 8 10 12 14 16Energy (keV)BrSrFigure 7.4.2 TXRF spectra of liquors: (a) sample A (Japanese liquor, sake); (b) sample B (beer); (c) sample C (Chinese liquor);(d) sample D (red wine)On comparing the spectra shown in Figure 7.4.2,the spectral patterns of the four liquors were alldifferent. That is, S, Cl, K, Ca, Mn and Zn weredetected as characteristic elements in sample A, P,S, Cl, K, Ca, Br and Rb were detected in sampleB,P,S,Cl,K,Ca,Mn,Fe,Zn,BrandRbweredetected in sample C and S, Cl, K, Ca, Mn, Fe, Zn,Br and Sr were detected in sample D. The peak ofsilicon was due to the Si wafer. As a result, the fourliquors can be distinguished from each other on thebasis of TXRF data.7.4.2.3 BRANDYIt was reported elsewhere 14,15 that a counterfeitVSOP cognac had been proved to contain sulfurabundantly by TXRF and to be circular dichroism(CD) inactive by CD analysis, while genuineVSOP cognacs had no sulfur and were CD active.Elemental analyses of four kinds of genuinebrandies were examined by TXRF.Each droplet of 10 µl of brandy was spotted ona Si wafer and the TXRF measurement conditionswere the same as for the case of liquors. TXRFspectra of four genuine brandy samples (A, B, Cand D) are shown in Figure 7.4.3.As a characteristic element, Cu was detectedin common in Figure 7.4.3(a)–(d) and no sulfurcould be detected in Figure 7.4.3(a)–(d). On theother hand, the spectrum of a red wine sampleshown in Figure 7.4.2(d) gave no Cu peaksalthough many other elements (S, Cl, K, Ca, Mn,

556 X-RAY SPECTROMETRY IN FORENSIC RESEARCH2000SiAr2000SiArIntensity (counts)15001000500CuCuIntensity (counts)15001000500CuZnPbPb(a)0 00 2 4 6 8 10 12 14 160 2 4 6 8 10 12 14 16Energy (keV)(b)Energy (keV)2000SiAr2000SiArIntensity (counts)15001000500CuZnIntensity (counts)15001000500FeCu(c)0 00 2 4 6 8 10 12 14 160 2 4 6 8 10 12 14 16Energy (keV)(d)Energy (keV)Figure 7.4.3 TXRF spectra of brandies: (a) sample A; (b) sample B; (c) sample C; (d) sample DFe, Zn, Br and Sr) were observed in the spectrum.It is well known that brandy is made by gentledistillation of a large amount of wine. Therefore,the Cu in the four brandies might originate fromthe distillation procedure. Also, compared withthe spectra shown in Figure 7.4.3(a)–(d), everyspectral pattern is different from each other. Thatis, Cu is observed as a main element in sample Aand Cu, Zn and Pb are detected in sample B andboth Cu and Zn are detected in sample C, and bothFe and Cu are detected in sample D. The lead inFigure 7.4.3(b) is supposed to be derived from theglass bottle.7.4.2.4 WASTE WATERFigure 7.4.4 shows the TXRF spectrum of 1 µlof waste water from a factory. Sulfur and nickelwere detected clearly as shown in Figure 7.4.4and the nickel concentration was estimated to be170 mg/l by quantitative analysis of TXRF. In thisfactory, recovery of nickel was usually in operationusing a NiS precipitation process. However, theprecipitation process could not function perfectlyand could not recover efficiently the valuablenickel resources from the waste water. As a result,the waste water still contained valuable nickel afterthe precipitation process.7.4.2.5 SEAL INKIn Japan, traditionally seal impressions are oftenused as certification marks instead of signatures.Nowadays various kinds of seal inks are used inJapan and they appear vermilion in appearance,

FORENSIC APPLICATIONS OF LABORATORY TXRF 55740003500SiSIntensity (counts)3000250020001500ArNi1000500NiFigure 7.4.4 TXRF spectrum of waste water00 2 4 6 8 10 12 14 16Energy (keV)while the elements contained in them are oftendifferent. In disputed documents seal impressionsare often examined. Even if counterfeit sealimpressions have been used, genuine original sealinks can be differentiated from illegal-used sealinks using TXRF.Figure 7.4.5 shows TXRF spectra of five kindsof seal inks (samples A–E) which are vermilion inappearance. Both samples A and B are low priced,while sample C is moderately priced and bothsamples D and E are considerably more expensive.The spectral patterns differ from each other. Thatis, in sample A, Cl, Ti and Zn were detected andin sample B, Pb, S, Ba, Cr and Sr were detectedand in sample C, Ca, Fe, Hg and Sr were detectedand in sample D, Hg, S, Sb and Pb were detectedand in sample E, Hg, S and Ba were detected.Hence, each seal ink could be differentiated fromone another by the TXRF data.7.4.2.6 METHAMPHETAMINEAbuse of drugs is one of the most serious socialissues. Drugs of abuse, such as methamphetamine,amphetamine, heroin, cocaine and other drugs,usually contain trace intrinsic ingredients dueto the synthetic and purification processes ormethods of smuggling. Those ingredients can beused as tagging factors to indicate clandestinesynthetic laboratories or illegal import routes.Impurity profiling analysis has been investigatedfor the characterization and classification of illicitdrug samples. Trace organic ingredient analysesof methamphetamine salts or amphetamine saltshave been reviewed by Verweij 23 and Inoue 24and have been reported by other authors. 25–31Inorganic ingredient analyses of methamphetaminesalts or amphetamine salts by neutron activationanalysis (NAA), 32,33 inductively coupled plasmamassspectrometry (ICP-MS) analysis 34–36 andatomic absorption spectrometry 37 have also beenreported. In those methods, they have used sampleamounts of 2–50, 10–100 mg, and so on, anddetected ppm levels of each trace element. Further,the above methods need complicated pretreatmentof samples and are often destructive.TXRF was applied to examine trace elementsin methamphetamine salts and nanogram levelsof detection of each trace element in 1 mg ofmethamphetamine salts has been reported. 18Figure 7.4.6 shows TXRF spectra of two seizedmethamphetamine HCl salts (samples A and B).Both samples A and B were previously proved to

558 X-RAY SPECTROMETRY IN FORENSIC RESEARCHIntensity (counts)(a)Intensity (counts)(c)80000600004000020000010000080000600004000020000ClTiTiZn0 2 4 6 8 10 12 14 16CaEnergy (keV)FeHgHg00 2 4 6 8 10 12 14 16Energy (keV)SrIntensity (counts)10000PbBaBaSrPb,S Cr00 2 4 6 8 10 12 14 16(b)Energy (keV)60000Hg50000Hg400003000020000SbPb10000PbHgHg,SHg00 2 4 6 8 10 12 14 16(d)Energy (keV)Intensity (counts)40000PbPb300002000060000HgIntensity (counts)50000400003000020000Hg10000HgHgHg,S Ba00 2 4 6 8 10 12 14 16(e)Energy (keV)Figure 7.4.5 TXRF spectra of seal ink samples: (a) sample A; (b) sample B; (c) sample C; (d) sample D; (e) sample Ebe chemically pure by melting point analyses. InFigure 7.4.6(a), Ca, Fe, Ni, Cu, Zn and Br weredetected. Bromine is supposed to be derived fromthe impurities of the methamphetamine HCl saltand Fe, Ni, Cu and Zn are supposed to be from themetallic vessels or tools used during the synthesisprocesses or handling. In Figure 7.4.6(b), iodineand mercury are detected as specific elements,

FORENSIC APPLICATIONS OF LABORATORY TXRF 5591000SiClIntensity (counts)500CaFeNiCuZnBrBr(a)00 2 4 6 8 10 12 14 16Energy (keV)1000SiClIntensity (counts)500IHgHg, BrFe(b)00 2 4 6 8 10 12 14 16Energy (keV)Figure 7.4.6 TXRF spectra of seized methamphetamine HCl salts: (a) sample A; (b) sample Band these elements are supposed to originate fromthe chemical reagents in the methamphetaminesynthesis processes.7.4.2.7 METEORITEOn 26 September 1999, a rock-like materialpenetrated a house in Kobe city. The rock-likematerial broke into 20 pieces, and these pieceswere sent to the forensic laboratory at HyogoPrefectural Police Headquarters for analysis toconfirm whether they were from a meteorite or not.The pieces weighed 135.197 g and were examinedby many nondestructive analytical techniques.Figure 7.4.7 shows the grazing incidence XRFspectra of a small fragment (D) from the samplepieces; in fragment D both Fe and Ni are detectedclearly. It is known that meteorites contain bothFe and Ni, so that the spectra suggest the samplemight be from a meteorite.On the basis of many kinds of analyticalresults, including microscopic observation, density,elemental analysis, γ -ray analysis of radioactivenuclides originating from cosmic rays, the pieceswere concluded to be meteorite pieces.

560 X-RAY SPECTROMETRY IN FORENSIC RESEARCH50000Fe40000Intensity (counts)3000020000Fe(a)100000NiCr Ni0 2 4 6 8 10 12 14 16Energy (keV)2000FeFeNi1500MnCrIntensity (counts)1000500CaTiNi(b)00Al Si ArGe2 4 6 8 10 12 14 16Energy (keV)ThSrFigure 7.4.7 Grazing incidence XRF spectra of the Kobe meteorite (fragment D). Spectrum (b) is the magnified version ofspectrum (a)The meteorite was clarified to be a carbontypemeteorite, which was the first example inJapan. These fragments have magnetic propertiesand elemental mapping analysis of a fragmentusing SR-XRF at SPring-8 has been applied toexamine the magnetic structure in the meteorite. 38In addition, radioisotopes with very short life-time(Ni57, Mg28, Sc47 and K43) were detected inthis meteorite.This meteorite was named ‘Kobe’ and detailshave been presented elsewhere. 38 7.4.3 FORENSIC APPLICATIONSOF SYNCHROTRON RADIATION XRF7.4.3.1 FLUORESCENT TRACINGAGENTA plastic ball, called a ‘color ball’ in Japan,contains a fluorescent powder suspension, whichmay act as a tracing agent for criminals or carsinvolved in crimes. If a robbery happened in abank, this ball would be thrown at the criminal

FORENSIC APPLICATIONS OF SYNCHROTRON RADIATION XRF 561or a car leaving the crime scene to trace thecriminal or the car. The criminals or cars may betraced if some of the fluorescent powder remainedon the road and this might help to investigatethe criminal or the car. Synchrotron radiationXRF (SR-XRF) can be applied to forensic tracesamples.As an X-ray source, 10 keV X-rays fromundulator radiation at beam line 39XU of SPring-8was used and the X-rays were shaped to a smallbeam (100 µm × 100 µm) to analyse the ultratrace of fluorescent powder. The XRF spectrumwas measured by a Si(Li) semiconductor detectorfor 200 s. Each trace powder sample was keptin a small polypropylene bag (6 µm thickfilm)and was measured. Figure 7.4.8 shows SR-XRFspectra of three kinds of reddish color fluorescentpowders. Each spectral pattern is different. Peaksof S and Zn are characteristic in Figure 7.4.8(a),there is a large Ca peak in Figure 7.4.8(b), andpeaks of S, Fe and Zn are the main peaks inFigure 7.4.8(c).SR-XRF is a very useful technique to identifyultra traces of fluorescent powder. Recently thistechnique was applied successfully to solve abank robbery case. The SR-XRF spectrum of thefluorescent powder used in the case is shown inFigure 7.4.9.7.4.3.2 DRUGS OF ABUSE(COCAINE, HEROIN, MARIJUANAAND OPIUM)Using our laboratory TXRF system, it was verydifficult to detect pg amounts of trace elementsin drugs of abuse. Ultra trace analysis of seizeddrugs of abuse (cocaine, heroin, marijuana andopium) using synchrotron radiation total reflectionX-ray (SR-TXRF) analysis has been presentedelsewhere. 39Sample amounts of 1 µl solutions containing10 µg of drugs (cocaine and heroin) were spottedon Si wafers. A leaflet of marijuana was setdirectly on a Si wafer and opium in the formof a soft lump was smeared on another Siwafer. These samples were then measured by SR-TXRF. The X-ray source was 10 keV X-rays fromundulator radiation at Hyogo Prefecture beam line24XU (hutch B) of SPring-8 and X-rays wereincident onto the sample surface at 0.005 ◦ underatmospheric conditions. The TXRF spectrum wasmeasured by a Si (Li) semiconductor detectorfor 500 s. In these experiments, pg levels ofcontaminant elements in 1 µl sample could bedetected.Figure 7.4.10(a) and 7.4.10(b) show SR-TXRFspectra of cocaine and heroin, respectively. InFigure 7.4.10(a), a large peak of Cl at 2.6 keVis derived from the cocaine hydrochloride saltand Ca and Zn are supposed to be contaminantelements from the purification procedures ofcocaine. In Figure 7.4.10(b), characteristic peakswere observed at 3.9 keV (Lα), 4.2 keV (Lβ 1 ),4.5 keV (Lβ 2 ) and 4.8 keV (Lγ 1 ), attributed toiodine. Infante et al. referred to metal contaminationin illicit heroin samples using atomic absorptionspectrometry and also reported that calciumwas encountered in most of the samples. 37 However,they did not mention the existence of iodinein illicit heroin samples. The origin of iodine inthe sample shown in Figure 7.4.10(b) is underinvestigation.Marijuana and opium are derived from botanicaltissues and SR-TXRF spectra of them werecompared. A SR-TXRF spectrum of a chip ofmarijuana leaflet is shown in Figure 7.4.10(c) anda SR-TXRF spectrum of a smear of black opiumis shown in Figure 7.4.10(d). In Figure 7.4.10(c),peaks of Ca at 3.7 keV (Kα) and 4.0 keV (Kβ),a peak of Fe Kα at 6.4 keV, a peak of Zn Kαat 8.6 keV, a peak of Ti Kα at 4.5 keV, a peakof Cl Kα at 2.6 keV and a small peak of S Kα at2.3 keV were observed. In Figure 7.4.10(d), a peakof K Kα at 3.3 keV and a moderately large peakof S Kα at 2.3 keV were observed. No peaks of Ti,Fe or Zn were observed.From the above results, ultra trace drugs ofabuse samples could be differentiated from oneanother by SR-TXRF, while, in general, blackresin-like compounds could hardly be discriminatedby microscopic observation. This method canalso be applied to other botanical samples.

562 X-RAY SPECTROMETRY IN FORENSIC RESEARCH5000040000SIntensity (counts)3000020000Zn100000(a)02 4 6 8 10Energy (keV)400000CaIntensity (counts)300000200000100000(b)00SZn2 4 6 8 10Energy (keV)20000SIntensity (counts)15000100005000FeZn(c)00Cr Fe2 4 6 8 10Energy (keV)Figure 7.4.8 SR-XRF spectra of reddish fluorescent powders: (a) powder A; (b) powder B; (c) powder C

FORENSIC APPLICATIONS OF SYNCHROTRON RADIATION XRF 56320000Intensity (counts)1500010000500000ZnClCuKZnS CaFe2 4 6 8 10Energy (keV)Figure 7.4.9 SR-XRF spectrum of the reddish fluorescent powder DIntensity (counts)1000800600400200ClCaZnIntensity (counts)1000800600400200ClIZn(a)00 2 4 6 8 10Energy (keV)(b)00 2 4 6 8 10Energy (keV)3000KCa3000Intensity (counts)20001000SClTiFeZnIntensity (counts)20001000SK(c)00 2 4 6 8 10Energy (keV)(d)00 2 4 6 8 10Energy (keV)Figure 7.4.10 TXRF spectra of drugs of abuse: (a) seized cocaine A; (b) seized heroin B; (c) seized marijuana C; (d) seizedopium D

564 X-RAY SPECTROMETRY IN FORENSIC RESEARCH7.4.4 FORENSIC APPLICATIONSOF HIGH ENERGY SYNCHROTRONRADIATION XRF7.4.4.1 GUNSHOT RESIDUEIt is known that trace gunshot residue (GSR)remains in an empty cartridge case or on thesurface of the hand which held the handgun.Usually, electron probe microanalysis (EPMA) hasbeen utilized to examine GSR particles. However,electron beam excitation is far less sensitive thanX-ray excitation on X-ray elemental analysis. Also,EPMA needs high vacuum analytical conditions,70000S & W 45-caliber60000Intensity (counts)50000400003000020000SbBaPbPb1000000 20 40 60 80 100Energy (keV)Figure 7.4.11 High energy SR-XRF spectrum of GSR sample A12000TokarevIntensity (counts)100008000600040002000HgSbSnSnSbHgHg00 20 40 60 80 100Energy (keV)Figure 7.4.12 High energy SR-XRF spectrum of GSR sample B

FORENSIC APPLICATIONS OF HIGH ENERGY SYNCHROTRON RADIATION XRF 56550004000PbPbIntensity (counts)30002000Ba(a)1000 MoPbBaSbW00 20 40 60 80 100Energy (keV)25002000PbPbIntensity (counts)15001000MoBaPb500BaWSb(b)00 20 40 60 80 100Energy (keV)Figure 7.4.13 High energy SR-XRF spectra of paint chips: (a) a trace of paint chip from the scene of the crime; (b) a paint chipof the car concernedwhich interrupts detection of a volatile element,for example, mercury from GSR.High energy SR-XRF at SPring-8 was appliedto detect trace elements in GSR under atmosphericconditions. The X-ray source was highenergy X-rays (116.4 keV) through a Si (400)monochromator from an elliptic multipole wigglerat beam line 08 W of SPring-8. Traces oftwo kinds of GSR collected from the empty cartridgecases of guns A and B were mountedon surfaces of Scotch mending tape (No. 810).The SR-XRF spectrum was measured by using aGe semiconductor detector for 600 s. The resultsare shown in Figures 7.4.11 and 7.4.12. Eachspectral pattern gave a distinct profile: Ba, Sband Pb were detected in the GSR sample A,while Hg, Sb and Sn were detected in that ofGSR sample B. Also, GSR analysis on a handhaving shot a gun can be applied using thistechnique. 40

566 X-RAY SPECTROMETRY IN FORENSIC RESEARCH7.4.4.2 PAINT CHIPIn hit-and-run cases, it is very important toexamine traces of evidential samples obtainedat crime scenes. High energy SR-XRF analysisat SPring-8 was applied to analyse traces ofpaint chips from a hit-and-run case. 41 The X-raymeasurement system was the same as for the aboveGSR case.Figure 7.4.13(a) shows a high energy SR-XRFspectrum of a trace of a paint chip, which wasdiscovered at a hit-and-run scene. The high energySR-XRF spectrum of the paint chip from thecar concerned is shown in Figure 7.4.13(b). Bothspectra resemble each other closely. Microscopiccolor observation and Fourier transform infraredspectra of the two paint chips confirmed that thetrace of paint chip at the scene was of the samequality of the car concerned.As shown in the above cases, K-series XRFsignals of Sn, Sb, Ba, W, Hg and Pb, which areimpossible to detect using conventional laboratoryXRF instruments, can be detected by high energySR-XRF at SPring-8.ACKNOWLEDGEMENTSThe author expresses thanks to all of his coworkersfor their contributions and also expresses thanks toDr S. Hayakawa for helping with small beam SR-XRF experiments and to Dr I. Nakai for helpingwith high energy SR-XRF experiments. The synchrotronradiation experiments were performed atthe SPring-8 with the approval of the Japan SynchrotronRadiation Research Institute (JASRI).REFERENCES1. Yoneda, Y. and Horiuchi, T. Optical flats for use in X-ray spectrochemical microanalysis. Rev. Sci. Instrum., 42,1069–1070 (1971).2. Klockenkämper, R. Total-Reflection X-ray FluorescenceAnalysis. John Wiley & Sons, New York, 1997.3. Prange, A., Reus, U., Boddeker, H., Fischer, R. and Adolf,F. P. Microanalysis in forensic science–characterization ofsingle textile fibers by total reflection X-ray fluorescence.Anal. Sci., 11, 483–487 (1995).4. Duwel, F., Fischer, R., Schonberger, T., Simmross, U. andWeis, D. Quantitative elemental microanalysis of thermoplasticremains using total reflection X-ray fluorescence(TXRF) spectrometry. Proc. Meet. Int. Assoc. Forensic Sci.14, 1–4 (1996).5. Ninomiya, T., Nomura, S. and Taniguchi, K. Applicationof total reflection X-ray fluorescence analysis to forensicsamples: chromium detection in fibers. Memoirs OsakaElectro-Commun. Univ. 22, 51–57 (1986).6. Nomura, S., Ninomiya, T. and Taniguchi, K. Elementalanalysis of micro water samples using total reflection X-ray fluorescence spectrometry. Memoirs Osaka Electro-Commun. Univ. 24, 127–138 (1989).7. Nomura, S., Ninomiya, T. and Taniguchi, K. Trace elementalanalysis of titanium oxide pigments using totalreflection X-ray fluorescence analysis. Adv. X-ray Chem.Anal. Jpn. 19, 217–226 (1988).8. Ninomiya, T., Nomura, S. and Taniguchi, K. Elementalanalysis of trace plastic residuals using total reflection X-ray fluorescence analysis. Adv. X-ray Chem. Anal. Jpn. 19,227–235 (1988).9. Ninomiya, T., Nomura, S., Taniguchi, K. and Ikeda, S.Quantitative analysis of arsenic element in a trace of waterusing total reflection X-ray fluorescence spectrometry. Adv.X-ray Anal. 32, 197–204 (1989).10. Ninomiya, T., Nomura, S. and Taniguchi, K. Probing intoresidual forensic evidences–application of total reflectionX-ray fluorescence spectrometry. J. Surface Sci. Soc. Jpn.11, 189–194 (1990).11. Ninomiya, T., Nomura, S. and Taniguchi, K. Applicationof total-reflection X-ray fluorescence spectrometry toelemental toner analysis. J. Jpn. Soc. Color Mater. 65,176–181 (1992).12. Nomura, S., Ninomiya, T., Taniguchi, K. and Ikeda, S.Application of total reflection X-ray fluorescence spectrometryto drug analysis. Adv. X-ray Anal. 35, 969–974(1992).13. Nomura, S., Ninomiya, T. and Taniguchi, K. Indirect druganalysis using total reflection X-ray fluorescence spectrometry.Adv. X-ray Chem. Anal. Jpn. 24, 113–119 (1993).14. Ninomiya, T., Nomura, S., Taniguchi, K. and Ikeda, S.Application of GIXF to forensic samples. Proceedings ofthe 5th workshop on total reflection X-ray fluorescencespectroscopy and related spectroscopical methods held inTukuba, Japan. Adv. X-ray Chem. Anal. Jpn. 26s, 9–18(1994).15. Ninomiya, T., Nomura, S., Taniguchi, K. and Ikeda, S.Application of grazing incidence X-ray fluorescence analysisto forensic samples. Anal. Sci., 11, 489–494 (1995).16. Nomura, S., Taniguchi, K. and Ninomiya, T. Applicationof total reflection X-ray fluorescence analysis to soils andliquors. Memoirs Osaka Electro-Commun. Univ. 31, 45–49(1996).17. Shimoyama, M., Nakanishi, T., Hamanaga, Y., Ninomiya,T. and Ozaki, Y. Non-destructive discriminationbetween elephant ivory products and mammoth tusk

REFERENCES 567products by glancing incidence X-ray fluorescence spectroscopy.J. Trace Microprobe Tech. 16, 175–181 (1998).18. Muratsu, S., Fukui, S., Maeda, T., Matsushita, T.,Kaizaki, S. and Ninomiya, T. Trace elemental analysis ofillicit methamphetamines using total reflection X-ray fluorescencespectroscopy. J. Health Sci. 45, 166–171 (1999).19. Ninomiya, T. Japanese Patent Application No. 194381(1993).20. Nomura, S., Ninomiya, T. and Taniguchi, K. Applicationsof total reflection X-ray fluorescence spectrometry to traceevidential materials. Abstract of 42nd Annual DenverConference on Applications of X-ray Analysis, Denver,Colorado, p. 28 (1993).21. Ninomiya, T., Nomura, S., Nakai, I., Hayakawa, S. andTaniguchi, K. XRF imaging of a fingerprint using synchrotronradiation. Photon Factory Activ. Rep. 11, 43(1993).22. Ninomiya, T. Analytical chemistry in human life-criminalinvestigation and chemical analysis. Bunseki 325(10),578–585 (2000).23. Verweij, A. M. A. Impurities in illicit drug preparations:amphetamine and methamphetamine. Forensic Sci. Rev. 1,1–11 (1989).24. Inoue, T. Discrimination of abused drug samples byimpurity profiling analysis (chemical fingerprint). Jpn. J.Forensic Toxicol. 10, 204–217 (1992).25. Kobayashi, K., Iwata, Y., Kanamori, T., Inoue, H. andKishi, T. Analysis of impurities in methamphetamine andimpurity profiling. Rep. Nat. Res. Inst. Police Sci. Res.Forensic Sci. 53, 1–9 (2000).26. Inoue, T., Tanaka, K., Ohmori, T., Togawa, Y. and Seta, S.Impurity profiling analysis of methamphetamine seized inJapan. Forensic Sci. Int. 69, 97–102 (1994).27. Tanaka, K., Ohmori, T., Inoue, T. and Seta, S. Impurityprofiling analysis of illicit methamphetamine by capillarygas chromatography. J. Forensic Sci. 39, 500–511(1994).28. Perkal, M., Ng, Y. L. and Pearson, J. R. Impurity profilingof methylamphetamine in Australia and the developmentof a national drugs database. Forensic Sci. Int. 69, 77–87(1994).29. King, L. A., Clarke, K. and Orpet, A. J. Amphetamineprofiling in the U.K. Forensic Sci. Int. 69, 65–75 (1994).30. Jonson, C. S. L. Amphetamine profiling–improvements ofdata processing. Forensic Sci. Int. 69, 45–54 (1994).31. Kishi, T., Inoue, T., Suzuki, S., Yasuda, T., Oikawa, T.and Niwaguchi, T. Analysis of impurities in methamphetamine.Eisei Kagaku 29, 400–406 (1983).32. Kishi, T. Application of neutron activation analysis toforensic chemistry. Eisei Kagaku 32, 335–343 (1986).33. Kishi, T. Forensic neutron activation analysis–the Japanesescene. J. Radioanal. Nucl. Chem. 114, 275–280 (1987).34. Kishi, T. Determination of sodium, bromine, palladium,iodine and barium in authentic methamphetamine hydrochlorideby inductively coupled plasma-mass spectrometry.Rep. Nat. Res. Inst. Police Sci. Res. Forensic Sci. 41,256–259 (1988).35. Suzuki, S., Tsuchihashi, H., Nakajima, K., Matsushita, A.and Nagao, T. Analyses of impurities in methamphetamineby inductively coupled plasma mass spectrometry and ionchromatography. J. Chromatogr. 437, 322–327 (1988).36. Marumo, Y., Inoue, T. and Seta, S. Analysis of inorganicimpurities in seized methamphetamine samples. ForensicSci. Int. 69, 89–95 (1994).37. Infante, F., Domiguez, E., Trujillo, D. and Luna, A. Metalcontamination in illicit samples of heroin. J. Forensic Sci.44, 110–113 (1999).38. Maeda, T., Shimoda, O., Muratsu, S., Shimoyama, M.,Misaki, K., Nakanishi, T., Ninomiya, T., Kagoshima, Y.,Takai, K., Ibuki, T., Yokoyama, K., Takeda, S., Tsusaka, Y.and Matsui, J. An identification of a Meteorite. Rep.Nat. Res. Inst. Police Sci. Res. Forensic Sci. 54, 11–18(2001).39. Muratsu, S., Ninomiya, T., Kagoshima, Y. and Matsui, J.Trace elemental analysis of drugs of abuse using synchrotronradiation total reflection X-ray fluorescenceanalysis (SR-TXRF). J. Forensic Sci. 47, 944–949(2002).40. Ninomiya, T., Muratsu, S., Maeda, T., Shimoda, O.,Nakanishi, T., Hashimoto, T., Saitoh, Y., Nakai, I., Terada,Y., Nishiwaki, Y., Marumo, Y., Suzuki, S., Suzuki,Y. and Kasamatsu, M. Trace element characterization ofgunshot residues using SR-XRF technique. SPring-8 UserExperiment Report (JASRI), No. 5 (2000A), 129 (2000).41. Ninomiya, T., Nakanishi, T., Muratsu, S., Saitoh, Y., Shimoda,O., Watanabe, S., Nishiwaki, Y., Matsushita, T.,Suzuki, S., Suzuki, Y., Ohta, H., Kasamatsu, M., Nakai, I.and Terada, S. Elemental analysis of a trace of paint chipusing SR-XRF. SPring-8 User Experiment Report (JASRI),No. 7 (2001A), 67 (2001).

7.5 Speciation and Surface Analysis of SingleParticles Using Electron-excited X-ray EmissionSpectrometryI. SZALÓKI 1 , C.-U. RO 2 ,J.OSÁN 3 , J. DE HOOG 4 and R. VAN GRIEKEN 41 University of Debrecen, Debrecen, Hungary, 2 Hallym University, Chun Cheon, Korea, 3 KFKI AtomicEnergy Research Institute, Budapest, Hungary and 4 University of Antwerp, Antwerp, Belgium7.5.1 INTRODUCTIONIn the last decade, both the technological backgroundand the data evaluation methods, i.e.X-ray spectra analysis and quantitative determinationof sample composition, have beensignificantly improved for electron probe microanalysis(EPMA). One of the most essential breakthroughsin this field was the appearance of newlydesigned high-resolution energy-dispersive detectorssuch as microcalorimeters, as well as commercialsilicon-based spectrometers equipped withthin polymer window having weak attenuation forlow-energy X-rays. Another important improvementcan be found in the recently developed evaluationmodels for quantitative analysis, which arecapable of handling a wide variety of target sampletypes. The ultimate goal of this scientific efforthas been to increase the X-ray detection efficiency,to broaden the energy range of the X-rays to beanalysed, to extremely decrease the irradiated andexcited volume (Watanabe and Williams, 1999) inthe specimen and to obtain maximum informationabout sample composition and structure by applicationof adequate quantitative model for fast calculation.The recent development trend in the fieldof calculation models shows two main directionsin quantitative EPMA i.e. conventional φ(ρz)-based methods and Monte Carlo (MC) simulationof basic elementary interactions between electrons–atomsand photons–atoms.EPMA equipped with an energy-dispersivedetector qualifies to detect simultaneously all themorphology and the constitution elements (withina microscopic size volume) of a sample. Thisadvantageous analytical capability of the EPMAhas been successfully utilized in atmosphericaerosol research, where two new techniques haveappeared resulting in a significant improvement ofthe applicability of EPMA in single-particle analysis:(i) grazing-exit EPMA (Tsuji et al., 1999a);and (ii) low-Z EPMA described in this subchapter(Scott and Love, 1999).One of the principal aspects that limit theefficient application of energy-dispersive X-ray(EDX) detectors lies in the fact that the detectionof low-Z elements is hindered by theabsorption of characteristic X-rays by the berylliumwindow of the detectors. This technicaldifficulty can be avoided by using thin polymerwindows instead; their thickness is approximately200 nm, they are commercially availableand have been introduced in routine analysis forseveral years. The characteristic X-ray lines ofthe main components, which are mostly low-Z elements (Z

570 SPECIATION AND SURFACE ANALYSIS OF SINGLE PARTICLESmatrix effect is important. Quantitative determinationof low-Z elements is a necessarydevelopment for further research of individual particles,firstly because these elements (C, N, O)are abundantly present e.g. in atmospheric particles,and secondly because quantitative informationis necessary for speciation of individualmicroscopic particles; indeed, many environmentalparticles contain low-Z elements in the formof nitrates, sulfates, oxides or mixtures includinga carbon matrix.7.5.2 EXPERIMENTAL CONDITIONSFOR PARTICLE ANALYSIS7.5.2.1 TECHNOLOGICALDEVELOPMENTS IN EPMA FORPARTICLE ANALYSISElectron microscopy has always had to cope withsome limitations, not only for particle analysis.Since the development of the first electron microscopes(either called electron probe microanalysersor electron microscopes), researchers have beenimproving the technology within their instruments.Most of the useful developments were commercializedand put into use for different applications.During the last decades, particle analysis hasbenefited from the technological improvements inthe different components of the electron microscope.However, for practical and financial reasons,new technology has not always been acceptedor applied very fast in the whole of the particleanalysis community (like in many other fields).In environmental particle analysis, for instance,one could say that most of the research goesinto the study of the environmental effects ofthe particles themselves, and that less time andmoney is spent on applying the new availabletechniques. Environmental institutes are, therefore,expected to spend money on new technologywhen the costs are acceptable, or when theneed for better, rapidly available data is high.A contrary example is the semiconductor industry,which has always supported the developersof electron microscopes by offering its semiconductortechnology, getting better analytical instrumentsin return and resulting in mutual, stimulatingbenefits.One of the basic parts of an electron microscopeis the electron gun. A short discussion aboutthe evolution in the electron gun technology isappropriate in the context of X-ray spectrometry,since electron beam optics not only play animportant role in image formation, but also inX-ray analysis. For example, the size of the electronbeam determines the resolution of the electronimages, as well as the size of the interaction volumein which the X-rays for microanalysis aregenerated. A detailed discussion on the principlesof electron guns and electron beam opticsis beyond the scope of this subchapter, but canbe found in literature on the basics of electronmicroscopy. Numerous electron microscopes ‘inthe field’ are still equipped with conventional electronguns based on thermionic emission, requiringa tungsten filament or a lanthanum hexaborideemitter, but much recent research has been doneon field-emission sources. Although field-emissionguns (FEGs) were developed several decades ago,they are still in the process of gaining more andmore acceptance in the particle analysis community.This type of electron gun uses a verysmall source (e.g. a tungsten hairpin) and requiresonly simple optics to obtain much narrower andbrighter beams (nanometer sizes) than with thethermionic guns (micrometer sizes). This advantageis very useful for high-resolution imaging atlow voltages, since thermionic guns show insufficientbeam currents and degraded probe sizesunder low-voltage conditions, whereas FEGs providenanometer probes with nanoampere beam currents.The main practical disadvantage, however,lies in the vulnerability of the hairpin emitter toresidual gas traces in the vacuum of the specimenchamber. The vacuum should be at leastbetter than 10 −8 Pa in order to obtain reasonablystable emission, since monolayers or thicker coatingsof foreign gas molecules on the tip’s surfacereduce the electron emission. So, the quality ofthe vacuum determines the stability of the electrongun and the electron beam. Some methods

EXPERIMENTAL CONDITIONS FOR PARTICLE ANALYSIS 571(e.g. ‘flashing’) can be used to restore stable emission,but repeated use of these methods tends toblunt the sharp tip of the hairpin, which should,therefore, be replaced after many months of operation.Short-term beam instabilities causing streaksin scanned images may be reduced using feedbackcircuits for compensation. The quality of theimages made with field-emission electron guns isvery high, and, therefore, more and more authorsmention the application of this type of source formaking images of single particles in their publications(Ortner et al., 1998; Ortner, 1999; Höflichet al., 2000; Jones et al., 2000; Laskin and Cowin,2001). The very narrow probe size could alsobe very advantageous for the X-ray analysis ofsmall particles, since the electron interaction volumeis also considerably smaller. Many authors,however, use field-emission gun scanning electronmicroscopy (FEG-SEM) mostly for imagingor for qualitative analysis only. One reason mightbe that the long-term or short-term instabilitiesof field emission are expected to hamper quantitativeX-ray analysis. Other authors, however,have already used FEGs for quantitative particleanalysis (Laskin and Cowin, 2001) or to comparethe quality of different X-ray detectors for particleanalysis (Newbury et al., 1999; Wollman et al.,2000a). FEG-SEM is sometimes referred to as lowvoltagescanning electron microscopy (LV-SEM),since it can be used for X-ray analysis at low voltages(still offering small enough probe sizes andhigh enough beam currents), however, this techniqueis not used very often. One reason is that theanalysts should be able to select beam-acceleratingvoltages that are sufficiently adequate to excitethe characteristic peaks of the elements of interest,which is not evident. First of all, the efficiency ofcharacteristic X-ray generation, and evidently alsothe analytical range, are strongly dependent on theovervoltage U, which is inevitably low for lowvoltageanalysis. Secondly, the very unpredictableeffect of charging becomes also very important atlower voltages, since its influence on the overvoltageis very critical for X-ray generation (Newbury,2000). A second reason is that low-voltage X-ray analysis also requires the capability to performlight-element detection, which was and isnot always straightforward in all applications (aswill be discussed further below). The fact thatearlier simulation models for quantitative analysisalso did not take into account the different physicalbehavior of electrons at low voltages, couldhave been a third reason for many researchersnot to use FEG-SEM or LV-SEM for quantitativeanalysis. However, many changes in the availablesoftware are being made, and, for example, theCASINO Monte Carlo program (Hovington et al.,1997), which was adapted for quantitative particleanalysis in the presented research, was originallydeveloped for this reason, implementing improvedfunctions for better simulating the electron interactionsat low voltages. The interest in low-voltageanalysis is growing, so further studies using FEGsfor quantitative analysis are to be expected inthe future.The most spectacular technological evolutionscan probably be found in the development of X-ray detectors (explained more in detail in othersubchapters of this book). Although wavelengthdispersivespectrometers (WDS) are able to recordspectra with very high resolution, their applicationsfor particle analysis are rather limited. Due to itslow quantum and geometry efficiency, a higherbeam current has to be set in order to cause enoughelectron interactions which result in a suitableamount of detected X-ray signals. Since WDS alsorequires long measuring times, the exposure ofsmall or volatile particles could cause damage oreven total evaporation (Szalóki et al., 2001a). Thelong measuring times also limit the applicabilityof WDS, because particle studies mostly involvethe analysis of huge amounts of particles, whichwould require too much time. These disadvantageslimit WDS to the analysis of more stable particles,e.g. metal oxides or silicates (Ortner et al., 1998;Ortner, 1999; Höflich et al., 2000).The improved energy-dispersive (semiconductor)spectrometers (EDS), which can now alsodetect the X-rays from light elements (with atomicnumber Z

572 SPECIATION AND SURFACE ANALYSIS OF SINGLE PARTICLESdetector window set-up for particle analysis weredone either by just removing the beryllium window(windowless mode) or by replacing it withthe first versions of thin windows, consisting ofa thin foil. The latest thin windows mostly consistof a silicon grid supporting a thin polymerfoil, coated with a metal film for opacity. Thisimproved kind of energy-dispersive Si(Li) detectorshave been fully commercialized and somerecent examples of thin-window electron probemicroanalysis (TW-EPMA) can be found in theliterature (Diebold et al., 1998; Roth and Okada,1998; Paoletti et al., 1999; Ro et al., 1999; Szalókiet al., 1999; Newbury, 2000; Osán et al., 2000;Laskin and Cowin, 2001). The advantages of semiconductorEDS over WDS are its better geometryand quantum efficiency, but it always had tocope with many spectral problems (which will bediscussed in detail below) due its poorer energyresolution. The fact that many of these problemsoccur in the low-energy part of the spectra, mightseem a drawback to use this technique for quantitativeanalysis in some applications. However,despite these remaining, but improved, spectrallimitations, TW-EPMA currently appears to bethe best, commercially available option to performparticle analysis over a broad range of elements(from low-Z to high-Z) in a straightforward,fast way.Another very recent kind of energy-dispersivedetector is the microcalorimeter (sometimes calledbolometer), which could hardly have been unnoticedby particle analysts (Wollman et al., 1997;Diebold et al., 1999). These detectors are discussedin detail in subchapter 4.4 of this volume.Microcalorimeters combine the advantages of bothWDS and conventional EDS, since their excellentenergy resolution (comparable with WDS)allows straightforward identification of closelyspaced X-ray peaks in complicated spectra at fastoperation times (comparable with EDS). Wollmanet al. (1998) used a microcalorimeter detector forthe analysis of sub-micrometer particles down to0.1 µm on silicon wafers. Besides proving thatmicrocalorimeter EDS is suitable for this kindof analysis (even in non-optimal cases where theelectron beam diameter is larger than the analyzedparticle), they also performed chemical shiftanalysis on particles. Changes in electron bindingenergies with the chemical environment ofatoms result in ‘chemical’ shifts of peaks in theacquired spectra, providing information on oxidationstates. With the X-ray information on chemicalbonding, the analysts were able to differentiatebetween chemical species present in investigatedparticles. Chemical shift analysis is alsopossible with WDS, but this was never routinelyperformed because of the long scanning timesinvolved. Therefore, when the much faster, highresolution microcalorimeters are further improvedand commercialized, they would undoubtedly providesignificant benefits for particle analysis, certainlyif they were combined with FEG-SEM inorder to analyze small particles. In order to performX-ray analysis with FEG-SEM, Newbury et al.(1999) equipped a microcalorimeter detector witha polycapillary X-ray optic to increase the solidangle of the instrument by a factor of 300 (dependenton photon energy), since the standard solidangle of the detector was too small to obtain statisticallyuseful spectra with a nanoampere beamwithin 100–1000 s. The developers often publishthe status of the performance of the microcalorimeter(Wollman et al., 2000b), and in the future,efforts to improve the detector resolution, countingrates, low-photon cut-off and the solid angleare to be expected.A technique, which has been reported touse a different X-ray detector geometry, ratherthan new detector technology, is grazing exitEPMA (GE-EPMA). In this technique, the X-raydetector (WDS or EDS) is positioned at low takeoffor exit angles in order to minimize the effectof the substrate on the acquired spectra, whetherby tilting the sample or by moving the detectorwith a step-motor. Tsuji et al. (1999a–c, 2001)have discussed this technique and its advantages inthis book, but, in short, it offers a better detectionof X-rays coming from very small particles orthin layers. An additional aspect regarding particleanalysis is the specific detection of signals comingfrom the top layers of a particle only. Coatedparticles or particles with a core-shell structure

QUANTIFICATION MODELS IN EPMA 573could be analysed using GE-EPMA at negativeexit-angles, if the particles are positioned at theedge of a tilted specimen substrate. By increasingthe exit angle in small steps, the particle structureis then revealed layer by layer. Another optionfor the analysis of structured particles is dualvoltageEPMA (DV-EPMA) in which particles areanalysed at two or more different voltages (e.g.5 and 15 kV), using the change in informationdepth to study particle layers (Ro et al., 2001a).This technique will be further discussed below inSection 7.5.4.Regarding sample treatment during analysis,developments have been reported on the use oflow-vacuum, environmental or variable pressureSEM (VP-SEM). The difference with SEM can befound in the specimen chamber, which is not undervacuum conditions, but contains a gas mixture inorder to perform electron microscopy at higherpressure (Danilatos, 1994). The technology behindVP-SEM depends on a combination of differentialpumping and an electron beam transfer system,allowing an electron beam to be formed in vacuumand being transferred to the specimen in the gasmedium. The advantage of this technique lies inits possibility to study wet, volatile and evennon-conducting samples, since the gas mediumpreserves the samples from evaporation, and itacts as a charge dissipating means which freesthe sample from conductive coatings or chemicaltreatments. Since these advantages would be ableto broaden the range of applications for X-rayanalysis in electron microscopy, this techniqueappears to be very promising. However, most ofthe applications reported concern visual analysisin morphology studies (using special imagingdetectors adapted to the gas medium), since X-ray analysis is still rather difficult. One reason iselectron ‘skirting’, a process in which electronstransfer energy to the gas medium. The energy loss,which is difficult to predict or to quantify, affectsall the electron interactions with the specimen. Thelack of suitable standards is also reported to be adrawback for X-ray analysis in VP-SEM (Griffinet al., 2000), and, therefore, one can only findexamples of particle imaging in the literature.However, VP-SEMs now account for 50 % ofthe market for non-field emission SEMs, so moreis to be expected from this technique (Mohanet al., 1998). A recent development, for example,is the combination with FEG-SEM by Kim andLee (2001).Another example of enhanced sample treatmentcan be found in cryogenic SEM (Cryo-SEM) inwhich the samples are cooled down to low temperaturesusing special sample stages (Gregory et al.,1998). A stream of nitrogen gas flows throughthe stage, after it has been cooled down withliquid nitrogen (−193 ◦ C). This technique offersthe possibility to study more volatile species, likeammonium sulfate and nitrate. In environmentalanalysis, these compounds are very important sincetheir abundance in atmospheric particles is veryhigh (Osán et al., 2000; Szalóki et al., 2001a). Thereduction of the beam damage effects is reportedto be very spectacular, since very small particles(downto0.3µm) can still be analysed. Quantificationis still a problem, because it is almost impossibleto prevent all particles from evaporating, andsince this process is very difficult to predict. Theresults for several compounds have proven to bequite spectacular, and they will be discussed morein detail below.Considering the developments mentioned above,one could conclude that different techniques arelooking very promising. However, since they aremostly still under development, TW-EPMA with athermionic electron source and the possibility forcryogenic cooling, offers the most stable, easilyavailable technology for particle analysis over abroad range of sample types. For this reason, thework discussed in this subchapter, has been doneusing this combination.7.5.3 QUANTIFICATION MODELSIN EPMA7.5.3.1 ANALYTICAL MODELSThe ultimate goal in the development of modelsfor quantitative EPMA is to provide an adequatemacroscopic description of the basic interactionsbetween the electron beam and the atoms in solid

574 SPECIATION AND SURFACE ANALYSIS OF SINGLE PARTICLESmatter in order to solve micro-analytical tasks onvarious type of target samples: solid bulk materialshaving rough or flat polished surface, layeredthin films, and micro-sized particles. Thebasic event taking place in the specimen caneasily be described: the focused electron beambombards the sample and the electrons lose aportion of their energy by means of an inelasticscattering process, which yields X-ray emissionby de-excited atoms. Through elastic scatteringthe electrons change their original traveling directionsand finally they lose their energy in inelasticevents or they leave the sample volume. Thecharacteristic and Bremsstrahlung radiations arepartly absorbed by the sample mass, but a certainportion can propagate into the X-ray detector(ED or WD) after they leave the sample volume.The detected intensity of the characteristicX-rays depends on the excitation conditions i.e.the beam current and the electron energy, thesample size and the quantitative composition ofthe irradiated material. The geometrical shape andsizes of the sample also influence the X-ray fluxeffectively through absorption and secondary fluorescenceexcitation effects generated by primarycharacteristic and Bremsstrahlung radiation. Correspondingto this depiction, the physical kernelof the mathematical models consists of the calculationof: (i) the excitation conditions i.e. theionization cross sections, the linear energy loss andthe backscattering factor of the electrons; (ii) thefluorescence yield or the transition probability ofthe X-ray lines; and (iii) the absorption and fluorescencecorrection factors and the spectrometerefficiency function, which allow approximation ofthe theoretical value of the detected intensities.Based on the calculation mode of the X-ray intensities,the models can be classified into three maingroups (Newbury, 1999): (i) classical ZAF correctionprocedures, where additional X-ray spectraoriginating from standard samples are required;(ii) standardless calculation procedures that needknowledge of the depth-distribution of the generatedX-ray photons [φ(ρz) function] for theanalysed bulk sample; and (iii) MC simulations.The principal difficulty for empirical or semiempiricalquantitative EPMA is to correctly modelthe depth-dependence of this X-ray generationfunction (Brown, 1999). They are constructed onthe basis of: (i) theoretical considerations (Pfeifferet al., 1996); (ii) empirical models (Bastin et al.,1998; Staub, 1998; Bastin et al., 2001) usingmacroscopic physical parameters; or (iii) directmeasurement of the φ(ρz) function. Since EPMAis applied to a great variety of material types,sometimes the so-called second order effects (e.g.excitation by Bremsstrahlung) can become importantin the numerical calculations of the samplecomposition (Cazaux, 1996; Pfeiffer et al., 1996).The computer codes written for iterative EPMAquantification sometimes allow the use of differentmatrix-correction and model parameters suitablefor special experimental and sample conditions(Trincavelli et al., 1998; Trincavelli andCastellano, 1999).7.5.3.2 MC SIMULATION MODELSThe main disadvantage of the conventional analyticalmodels is that they are not flexible enoughfor various experimental and sample conditions,such as the analysis of microparticles having irregularshapes and heterogeneous compositions. MCsimulation-based models are capable of handlingany arbitrary geometry conditions (Hu and Pan,2001) e.g. sample porosity (Sorbier et al., 2000)or rough surfaces (Gauvin and Lifshin, 2000) thatinfluence the X-ray characteristic flux. Therefore,MC simulation can be applied for the analysisof both particles and flat bulk samples or layeredfilms. Other secondary effects such as photon–atominteractions, i.e. photoelectric effect andcontinuum background generation, can also beinvolved in the model (Jbara et al., 1997). Usingsimulation models, unknown parameters such asthe φ(ρz) function at different X-ray energies,the k-ratio between films and bulk samples, thebackscattering factor, etc. can be estimated fordifferent compositions and elementary distributions.In single scattering models all elementaryelectron–atom collisions are calculated, while inmultiple scattering models a great number ofevents are condensed into one occurrence requiringmuch shorter computer calculation times (Chan

QUANTIFICATION MODELS IN EPMA 575and Brown, 1997a, b). Considering all the possibleinteraction types, a more reliable assessment forcomplete detected X-ray spectra can be obtainedif angle-dependent Bremsstrahlung simulations areincluded (Acosta et al., 1999). Such a complexsimulation procedure allows the structure of differentsamples and the reliability of the theoreticalmodel of elementary events used in the MC codeto be studied. The fact that classical ZAF or φ(ρz)procedures are not suitable for quantitative EPMAof inclusions embedded in a bulk matrix, motivatedHovington et al. (1997) to develop a complexsimulation code, called CASINO, speciallydesigned to describe the electron–solid interactionsand to generate all the possible recordedelectron and X-ray signals in the low energy rangeof electrons 0.1

576 SPECIATION AND SURFACE ANALYSIS OF SINGLE PARTICLESfor a general case, which can be obtained by successiveapproximation:C (k+1)i=I (k)i,simC (k)iI i,measn∑j=1C (k)jI j,meas /I (k)j,sim(7.5.2)where C (k+1)iis the (k + 1)th approximation ofthe ith concentration value. This form contains thenormalization of the concentration values based onthe assumption that (practically) all the constituentelements are observed. The convergence speed ofthe numerical approximation depends strongly onthe number of simulated electrons and the numberof particle elements and the computer performance.Typical convergence of the calculationalgorithm is demonstrated by a simple exampleof a CaSO 4 particle for the Ca concentration inFigure 7.5.1. The shape and size of the particlecan be determined by means of SEM images, butthese estimated parameters sometimes have largeuncertainty (Osán et al., 2000). For the estimationof the unknown particle density, the only availablepossibility is to approximate it by the intensities,to predetermine the type of the particle.In order to avoid the large uncertainties causedby the improper information of the density, theshape and sizes, the influence of the variation ofthese parameters on the final results of the successiveapproximations was investigated. Testingthe present simulation on the analysis of standardparticles showed that the concentration of the particleelements varies only in a relatively narrowrange due to the average diameter of the particleas illustrated by Figure 7.5.1, which shows 5–10 %variation of the elements in CaSO 4 over the diameterrange 400–2000 nm with 10 keV excitationelectron energy. The detected X-ray flux is emittedmostly from the volume located directly under theparticle surface because of the strong attenuation ofthe low-energy X-ray lines. An opposite relationshipis expected between the particle diameter andthe intensity of the substrate lines, because of the1.31.0Ratio of simulated/nominal concentrations1.21.11.00.9OSCalculated diameter of CaSO 4 particle = 814 nmCa0.80.60.40.2Relative Kα intensity of the Al substrate0.80 200 400 600 800 1000 1200 1400Particle diameter (nm)Al0.0Figure 7.5.1 Result of successive approximation for a CaSO 4 standard particle. The left axis is the ratio of simulated and nominalconcentration values as a function of the particle diameter; the particle density was chosen to be 2.71 g/cm 3 . The right axis isthe relative intensity of the Kα radiation emitted by the Al substrate

QUANTIFICATION MODELS IN EPMA 577attenuation effect in the particle volume. Increasingthe particle diameter results in a lower numberof electrons in the substrate volume; therefore theemitted number of X-ray quanta of the substratelines is decreased. Because a similar dependenceof the intensities on the sample density was alsorecognized, the measured and simulated substrateintensities were introduced into the iterative algorithmin order to compensate for the improperdetermination and the uncertainty of the particlediameter and density. Because of the general insensitivebehavior of these parameters, the diameter orthe density can be varied during the iteration processin order to fit the calculated substrate intensityto the measured one yielding a more realistic result.In practice, after every iteration step of the concentrationcalculation, an optimization procedure forthe diameter is performed based on the minimizationof difference between calculated and measuredsubstrate intensities.7.5.3.4 DETECTION, SAMPLEHOLDER, BEAM DAMAGE EFFECTStandardless quantitative X-ray spectrometry needsaccurate knowledge of the detector efficiency functionin the analysed range of X-ray energy. For theconventional semiconductor detectors one can givea simple mathematical expression:⎛⎜ε(E) = exp ⎝−⎞µ W d W + µ Si d inSi+ µ con d con + µ ice d ice ⎟⎠sin φ[ (× 1 − exp − µ )]Sid acSisin φ(7.5.3)where µ W , µ Si , µ con , µ ice and d W , d inSi , d con ,d ice , d acSi are the attenuation function and thethickness of different absorbing layers: windowmaterial (W), dead (inSi) and active layer (acSi)of the Si crystal and the conductive layer (con),respectively, and φ is the angle between theplane of the detector window and impinging X-ray beam (Szalóki et al., 2001b). For low-energyX-ray detection (E

578 SPECIATION AND SURFACE ANALYSIS OF SINGLE PARTICLES1.00.8Transmission0.60.40.2factory datamodel data0.04 5 6 7 8 9 10Atomic numberFigure 7.5.2 Fitted transmission model for super atmospheric thin-window of Si(Li) detector. Reproduced from Osán et al.(2001a) by permission of John Wiley & Sons Ltdand oxygen. They also require conductive coatingin order to avoid charging effects induced byelectron beam, which is not desirable for low-Zelement detection because of the intensive attenuationfor low-energy X-rays in the coated layerlocated on the particle surface and because of theX-ray line interference with lines of the light elementsin the particle. In order to minimize theinterference from the substrate and the chargingeffect, metallic substrates are used for aerosol collectionand EPMA measurement. Several metallicsubstrates were investigated, such as Be, Al, Si,and Ag (Szalóki et al., 2001a). If the particlescontain the same chemical element as the substrate,the quantification of the chemical elementbecomes difficult. Sometimes the X-ray peaks fromthe substrate overlap with those of the chemicalelements present in the particles. In that case, thequantitative analysis of the elements shows moreuncertainty.BasedontheresultsreportedbySzalóki et al.(2001a), the best substrate for TW-EPMA ofindividual particles was found to be Be, using lowexcitation electron accelerate voltages (5–10 keV)and beam currents of 0.5–1 nA. However, othersubstrate materials (Ag, Al, Si) provide moreadvantageous analytical conditions for automatedanalysis in some other aspects. Because the carboncoating on the particle surface disturbs the low-Z detection, the electrical conductivity of thesubstrate should be high. Better quality of contrastthan for the inverse Be image was obtained withAg substrate for low-Z elements, which resultedin a more reliable estimation of the particle shapeand size. The intensive fluorescence peaks ofthe substrate often disturb the particle spectra,especially in case of the Ag L and M lines.However, in case of the Al K peaks additionalinformation is provided for the iterative correctionof the particle size.The beam damage effect is a considerable difficultyin the electron bombardment of light elementcompounds, since many of them are very sensitivefor the energy impact transferred by electron–atomcollisions. In Figure 7.5.3, the beam sensitivityeffect is visually illustrated by two secondary

QUANTIFICATION MODELS IN EPMA 579Figure 7.5.3 Visualization of beam damage effect in ammonium nitrate-type particle. Reproduced from Szalóki et al. (2001a) bypermission of John Wiley & Sons Ltd. The pictures were recorded as SE images after EPMA at room temperature (≈295 K).The measuring time was 10 s, accelerating voltage 10 keV and beam current 0.5 nA1.01.0Normalized Kα intensity0.80.60.40.2KSOCAl0.80.60.40.20.0N0 100 200 300 400 500 600 700 800 900Irradiation time (s)0.0Figure 7.5.4 Experimental evidence is shown for selective beam sensitivity for different species in thin-window EPMA.Reproduced from Szalóki et al. (2001a) by permission of John Wiley & Sons Ltd. The O, N and S elements disappear after250–300 s while K Kα intensity decreases only at 800 s. The higher carbon background intensity between 0.4 and 0.6 may becaused by external contamination originating from the vacuum system of the EPMA device. The scale of the vertical axis isthe relative intensity of Kα lines emitted by elements of a volatile aerosol particle located on Al substrate versus irradiationtime. The particle diameter is 1.5 µm. The series of individual measurements were carried out sequentially with 30 s recordingtime for each measurement at ca. ≈81 K sample temperature with 10 kV accelerating voltage and 1 nA beam current. Each setof intensities was normalized to their maximum valueselectron (SE) images of an environmental typeparticle, successively recorded after 10 s irradiationduration at room temperature (∼295 K). Thisvolatilization effect must be considered in quantitativeTW-EPMA analysis, because the great variationin detected fluorescence intensity stronglyinfluences the result of the iterative solution ofEquation (7.5.1), as demonstrated in Figure 7.5.4.The required reduction of these effects can beachieved by optimizing the measuring conditions(Szalóki et al. 2001a), such as choosingthe best substrate material, using liquid nitrogen

580 SPECIATION AND SURFACE ANALYSIS OF SINGLE PARTICLEStemperature to cool down the sample, minimizingthe energy impact on the particle by using lowbeam currents (0.5–1.0 nA) and as short as possiblemeasuring times 10–50 s.7.5.3.5 SPECTRUM AND DATAANALYSIS, AUTOMATED EVALUATIONThe main goal of particle analysis is to obtain asmuch information as possible on the abundance ofdifferent types of particles in the analysed sample.For this reason, huge numbers of individualparticles must be measured and thus the spectralacquisition time devoted to each individual particleshould be minimized. The most importantcharacteristics of spectra collected from individualmicroparticles using TW-EPMA are the lowcounting statistics and the strong spectral overlapsunder 1 keV. The so-called ‘top-hat’ filtermethod has been proven to be very useful inconventional computer-controlled EPMA for theon-line evaluation of spectra, usually having verypoor counting statistics (Small, 1998). Becauseof the strong overlap of the characteristic lines,this method cannot be applied for TW-EPMAspectra under 1 keV. Also the curvature of thebackground at low energies may cause significanterrors. A possible solution for the accurate determinationof the characteristic X-ray intensities isthe nonlinear least-squares fitting of the spectra.As the elements present in the particle must beincluded in the fitting model, an automatic evaluationcan only be done if supervised by the operator.As peak distortion due to incomplete chargecollection is most pronounced for low-energy X-ray lines, the usual Gaussian peak-shape modeldoes not work well, and a tailing and step functionmust be included (Van Espen and Lemberge,2000). The nonlinear least-squares fitting procedure(AXIL) was optimized for accurate modelingof the characteristic X-ray peaks and theBremsstrahlung background below 1 keV (Osánet al., 2001a). The appropriate mass absorptioncoefficients were taken into account, and the accurateparameters of the detector window were usedfor modeling the continuum background and therelative abundance of the characteristic lines in thesame line group. The spectral distortions caused byincomplete charge collection in the detector crystalwere also modeled in the peak functions as tail andstep functions. The incomplete charge collectionis most pronounced at low energies, and can alsocause the energy calibration to become nonlinear inthe low-energy range (Joy et al., 1996). Therefore,small deviations from the assumed linear energycalibration were allowed during the fitting procedure.Figure 7.5.5 shows the fitting of a typicalorganic particle spectrum (algae) collected by TW-EPMA. The contribution of the tailing effect wasfound to be around 10 % of the total area of thecharacteristic peaks. The agreement between thefitted functions and the experimental data is good,yielding a quite low χ 2 value. Due to the relativelypoor energy resolution of semiconductorenergy-dispersive detectors, characteristic L linesof heavier elements can completely overlap withK lines of C, N and O. A possible method forhandling strong spectral overlaps is the correctionof K X-ray intensities of low-Z element using MCsimulated L/K ratios for the overlapping L lines.The correction procedure is described in detailelsewhere (Osán et al., 2001a). The future applicationof the recently developed tunnel-junction ormicrocalorimeter detectors could simplify the handlingof the ED X-ray spectra in the low-energyrange, since their energy resolution is comparableto that of WD systems.Another possibility for processing X-ray spectrawith low energy resolution and poor countingstatistics is the application of the partialleast-squares (PLS) regression method that provideselemental concentration values without theneed of determining the characteristic intensities(Lemberge et al., 2000). The PLS methodbasically consists of a multivariate linear relationbetween the concentrations of the constituentsand the measured spectral data. An explicit evaluationof the spectrum is not required. The disadvantageof the method is that it requires alarge number of standards covering all possiblecompositions expected in the unknowns. Byusing MC simulated spectra as standards, major

QUANTIFICATION MODELS IN EPMA 581C10 5OTotal fitχ 2 = 1.86Intensity (arbitrary unit)10 410 3Fe10 5 10 2PSPbCa10 410 310 2Tailing fitBackground fit0 1 2 3 4 5Energy (keV)Figure 7.5.5 Least-squares fit of a low-energy X-ray spectrum collected from a typical organic particle (algae, IAEA-413).Reproduced from Osán et al. (2001a) by permission of John Wiley & Sons Ltdelements in brass could be determined with a relativeerror below 10 % (Van Espen and Lemberge,2000). After further optimization, the method canbe advantageous for thin-window EPMA of individualparticles, but the set-up of the simulatedstandard set requires a priori knowledge aboutthe composition of the particles in the sample tobe measured.The automatic TW-EPMA measurement of alarge number of particles in a sample producesa huge amount of spectral and morphologicaldata. For appropriate interpretation of the measureddata, quantitative chemical information should bederived from each particle individually. For thisreason, the overall procedure for converting thespectral information to concentration values shouldwork automatically if possible. Based on earlierresults (Osán et al., 2001a,b; Szalóki et al., 2001a)the most workable procedure for automatic evaluationconsists of the determination of the characteristicX-ray intensities by supervised least-squaresspectral processing and unsupervised concentrationcalculation using the reverse MC method. Theoutline of the automatic evaluation is shown inFigure 7.5.6. Based on the calculated concentrationdata, chemometric methods should be appliedfor deriving the most important particle types in theAutomatic TW-EPMA measurementusing normal or inverse backscattering contrastX-ray spectraSupervised leastsquaresdeconvolutionof the X-ray spectraX-ray intensitiesUnsupervised, iterative reverseMonte Carlo quantification procedureUnsupervised classification of particles with clusterand principal component analysisInterpretation of the resultsMorphology(size and shape)Elemental concentrationsfor each particleAbundance of differentparticle typesFigure 7.5.6 Outline of the automatic evaluation of thesingle-particle TW-EPMA datasample. A detailed discussion of the applicabilityof cluster and principal component analysis for

582 SPECIATION AND SURFACE ANALYSIS OF SINGLE PARTICLESlow-Z EPMA data has been published (Osán et al.,2001b). The combination of TW-EPMA with areverse MC quantification procedure yields environmentallymore relevant particle classes thancould be obtained using conventional computercontrolledEPMA. For example, ammonium sulfateand sulfur-containing organic particles can be distinguished,earlier they were classified together as‘sulfur-rich’ particles (Osán et al., 2000). Also, thequantitative knowledge of the oxygen concentrationmakes it possible to distinguish sulfides andsulfates in sediment particles (Osán et al., 2002).7.5.3.6 ANALYSIS OF STANDARDPARTICLESSuitable validity for the complete quantitativeanalytical procedure developed for TW-EPMA isoffered by analysis of standard particles of severalchemical compounds prepared from pro analysisgrade solid chemical compounds. In this test analysisthe particles were suspended in n-hexane anddropped by micropipette onto the surface of themetallic foils and dried in air. The quantificationmethod based on MC simulation combined withsuccessive approximation was evaluated by comparingthe weight concentrations obtained fromEPMA measurements with their nominal weightconcentrations. At least 10 independent analyseswere performed for each type of standard particleswith their diameters varying between 0.5 and5 µm. The results are summarized as a histogramof relative errors, = (C c − C n )/C n , based onthe comparison of the nominal (C n ) and calculated(C c ) concentrations for CaCO 3 , KNO 3 ,SiO 2 ,NaCl, CaSO 4 · 2H 2 O, BaSO 4 ,Fe 2 O 3 ,(NH 4 ) 2 SO 4and NH 4 NO 3 . Figure 7.5.7 shows the comparisonof the error distributions obtained for thereverse MC of particles including light elementsand a first-principles standardless method of bulksamples (NIST DTSA X-ray microanalysis softwareengine; Newbury, 1999). In first-principlesstandardless analysis, the physical equations forelectron-excited X-ray generation in the target,and X-ray absorption in the target and in othercomponents of the spectrometer are used to predictthe intensity from a pure element standardfor each constituent under the analytical conditionsin use (beam energy, beam incidence andX-ray take-off angles and detector solid angles).The sources of the relatively large relative error(95 % of the analyses are in the ±50 % interval)are the uncertainties in the physical parameters(ionization cross-section, mass absorption coefficients,fluorescence yield, detector parameters) andthe fact that the sum of the concentrations must beforced to 100 %. When light elements are not analyseddirectly, i.e. they are not ‘visible’ and theyare only taken into account based on stoichiometry,this normalization can introduce large errors.The distribution of errors for the reverse MC quantificationfor particle analysis (see Figure 7.5.7)shows that semi-quantitative analysis is possiblefor a wide range of chemicals. The analytical accuracyof the method is within 5 % relative, whichis due to systematic errors for some of the compoundsincluded (crystal water content can be differentfrom the nominal value for hygroscopicparticles, uncertainties of the physical parameters,etc.). More details of this study especially for Agsubstrate were published (Ro et al., 2001b). Theprecision, or the statistical uncertainty, of the analyticalresults (95 % of the analyses fall in the intervalof ±30 % relative error) is mainly due to thestatistical error of the X-ray intensity determinationoriginated from spectrum fitting procedure and thefluctuations in the shape and size parameters fromthe idealized models included in the simulation. Asall the elements except hydrogen can be detected,the normalization of the concentrations to 100 % issupported. As can be seen in Figure 7.5.7, the performanceof the reverse MC method is superior tothat of other first-principles standardless methods,even though particles are analysed using a muchworse counting statistics (10–20 s counting timevs 100–500 s).7.5.3.7 CHEMICAL SPECIATION OFSINGLE PARTICLES, HETEROGENEITYSince the technique can provide quantitative elementalconcentrations, except hydrogen, of individualparticles, the determination of chemical

QUANTIFICATION MODELS IN EPMA 5830.70.60.5Frequency0.40.30.20.1(a)0.0−80 −60 −40 −20 0 20 40 60 80Deviation to nominal value (%)0.300.25Frequency0.200.150.100.050.00−150 −100 −50 0 50 100 150(b)Deviation to nominal value (%)Figure 7.5.7 Distribution of errors with standardless analysis of a broad database of EDS spectra. (a) Reverse MC of particlesincluding light elements (EPPROC/CASINO). (b) First-principles method of bulk samples. (NIST DTSA X-ray microanalysissoftware engine. Reproduced from Newbury (1999) by permission of Springer-Verlagspecies in single particles is possible. This includes‘pure’ particles containing only one major chemicalspecies, and internally mixed particles containingtwo or more chemical species. Furthermore,in optimal cases even ‘molar’ concentrations ofthe different chemical species in internally mixedparticles can be determined. Because many atmosphericparticles contain only one or two chemicalspecies, low-Z EPMA could provide more detailsabout airborne particles of environmental interest.

584 SPECIATION AND SURFACE ANALYSIS OF SINGLE PARTICLESSome examples and detailed description for thisspeciation method are presented elsewhere (Roet al., 2000).In addition, it is of primary importance to havean analytical tool to distinguish chemical speciesin the surface region from that of the core regionin individual microparticles, because the analysiswould allow the direct and more conclusive investigationof the nature of atmospheric reactions,which some airborne particles may experience. Forexample, sea salt can react with NO x to producesodium nitrate particles in the air. Also, the atmosphericreaction between soil particles and SO xreceives considerable attention in the atmosphericenvironment society. And thus, if gaseous or aqueousNO x or SO x species react with solid sea-salt ordust particles in air and if the atmospheric reactionsare not completely finished, then it is expectedthat the product of the reactions would exist inthe surface layer and the original solid speciesin the core region. Therefore, the existence ofdifferent atmospheric reactions would be directlyproven if we could characterize both regions inindividual particles. However, since the analysisvolume of individual microparticles is quite small(pg range in mass), quantitative analysis of surfaceand core regions in individual particles has been areal challenge.Recently, a methodology based on EDX-EPMAwas developed that can analyse chemical speciesboth in surface and core regions of individual particles(Ro et al., 2001a). The idea was to investigateheterogeneous individual particles with differentprimary electron beam energies, i.e. X-rayphotons obtained with different primary electronbeam energies carry information on the chemicalcompositions for different regions in the particles,mainly because of the different excitation volumesaccording to the energies of the primary electronbeam. The excitation volume of the elements isdecreased with the decrease of the primary electronbeam energy. Figure 7.5.8 shows an exampleof electron trajectories for different primary electronbeam energies. The model particle is a heterogeneousCaCO 3 –CaSO 4 particle with 2 µm grossdiameter, while the thickness of the CaSO 4 surfacelayer is 0.25 µm. It is clear that primary(a)(b)(c)Figure 7.5.8 Simulation of electron trajectories in a heterogeneousCaCO 3 –CaSO 4 spherical particle at (a) 5 kV, (b) 10 kVand (c) 20 kV accelerating voltages. Reproduced from Ro et al.(2001a) by permission of American Chemical Societyelectron beams with different energies provide differentelectron probing regions. At 5 kV electronaccelerating energy, the CaSO 4 surface region ismostly probed, whereas at 20 kV, many electronsget through the particle and the signal from thesurface region is relatively suppressed.Artificial heterogeneous CaCO 3 –CaSO 4 particleswere synthesized, i.e. particles with CaSO 4in the surface region and CaCO 3 in the core.X-ray spectra, obtained at 5, 10, 15, and 20 kVelectron-accelerating voltages for a heterogeneousCaCO 3 –CaSO 4 spherical particle of 1.5 µm diameter,are shown in Figure 7.5.9. The measuredcharacteristic X-ray intensities for the elements inthe particle vary differently with the variation ofprimary electron beam energies. From the observationof different trends, for different elements, of

QUANTIFICATION MODELS IN EPMA 58510 5 10 010 5SiIntensity (arbitrary unit)10 410 310 210 110 0CO5 keV10 keVPrimary electron energy = 20 keVS15 keV0 1 2 3 4 5Energy (keV)Ca10 410 310 210 1Figure 7.5.9 X-ray spectra obtained from an artificially generated heterogeneous CaSO 4 –CaSO 3 particle at 5, 10, 15, and 20 kVaccelerating voltages. Reproduced from Ro et al. (2001a) by permission of American Chemical Societythe characteristic X-ray intensity variation accordingto the variation of electron beam energies,these X-ray spectra certainly contain informationon chemical species and heterogeneity of the particle.In Figure 7.5.10, simulated spectra calculatedby our modified MC program are shown. Thesimilarity between the simulated and experimentalspectra is remarkably obvious. The MC calculationalmost perfectly simulates the X-ray intensity variationsfor the elements according to the variationof the primary electron beam energies.By the application of the MC calculation, eventhe thickness of the CaSO 4 surface region ofthe artificially generated CaCO 3 –CaSO 4 particlescan be determined. In Figure 7.5.11, ratios ofsimulated-to-measured intensities with the variationof the CaSO 4 surface thickness for a sphericalCaCO 3 –CaSO 4 particle of 1.5 µm diameter areshown for a 15 kV primary electron beam energy.For oxygen, the ratios of simulated-to-measuredintensities are relatively constant with the variationof the CaSO 4 thickness, mainly because of theirsmall compositional differences between the twochemical species. However, the ratios for carbonand sulfur between the simulated and measuredintensities are strongly dependent on the thicknessof the surface CaSO 4 region. Furthermore,the ratios for sulfur decrease as the thickness ofCaSO 4 region decreases, whereas the ratios for carbonincreases as the thickness of the CaSO 4 regiondecreases. For the heterogeneous CaCO 3 –CaSO 4particles, the sulfur species is in the surface regionand carbon is in the core region. Therefore, ifthe assumed CaSO 4 surface thickness for the MCcalculation is thicker than the real one, then thecalculated intensities are larger than the measuredones for sulfur, whereas they are smaller for carbon.From the result in Figure 7.5.11, the goodmatch between the simulated and measured datais in the range of 160–200 nm thickness of thesurface region.The validity of this technique is investigatedmore systemically using a more controlled system,i.e. soda-lime glass particles (SPI #2716)coated with carbon by evaporation. The particleswere coated with carbon layers consecutivelyfour times, using the standard process for scanningelectron microscopes. The estimated carbonthickness for different numbers of carbon layersobtained by the proposed method is tabulatedin Table 7.5.1. The obtained results show goodagreement between the values obtained at differentaccelerating voltages, supporting the applicabilityof the proposed method. Further research is needed

586 SPECIATION AND SURFACE ANALYSIS OF SINGLE PARTICLESSi10 3OCa-KαIntensity (arbitrary unit)10 210 1CS10 3 10 -120 keV10 keVCa-Kβ10 210 110 05 keV10 010 -10 1 23 45Energy (keV)Figure 7.5.10 Simulated X-ray spectra using MC approach for a spherical, heterogeneous CaCO 3 –CaSO 4 particle at differentaccelerating voltages. Overall size of the particle is ≈1.5 µm in diameter and surface thickness is 0.18 µm. Reproduced from Roet al. (2001a) by permission of American Chemical SocietySimulated/measured intensity ratio1.61.41.21.00.80.60.4CaOCS1.61.41.21.00.80.60.40.250 100 150 200 250 300Thickness of CaSO 4 (nm)0.2Figure 7.5.11 Dependence of simulated/measured X-ray intensity ratios on CaSO 4 surface thickness, at 15 kV accelerationvoltages, for a heterogeneous CaCO 3 –CaSO 4 particle. Reproduced from Ro et al. (2001a) by permission of American ChemicalSocietyto evaluate the accuracy and reproducibility of thisapproach using well-defined heterogeneous particlesand also to optimize the iteration procedurefor automatic evaluation of the surface layer thicknessof heterogeneous particles. Furthermore, forreal atmospheric particles, another complexity isinvolved in the analysis; the elemental concentrationsof chemical compositions as well as the structureof the heterogeneity are not known a priori. Itis necessary to find a way to extract information

APPLICATIONS 587Table 7.5.1 Estimated carbon thickness for carbon-coated glassparticlesAcceleratingvoltage(kV)Number of carbon layer depositions1 2 3 4Estimated carbon thickness (nm)5 35 65 105 13510 35 70 95 14515 30 65 95 15020 25 55 85 140both on chemical compositions and the heterogeneityof the atmospheric particles from their X-rayspectral data.7.5.4 APPLICATIONS7.5.4.1 ENVIRONMENTAL PARTICLES,EXAMPLESCharacterization of Water-insolubleComponents of Asian DustLow-Z EPMA has been applied to characterizethe water-insoluble part of ‘Asian Dust’ depositedby washout in the form of rainwater during anAsian Dust storm event and collected in Seoul,Korea (Ro et al., 2001b). In addition to the AsianDust sample, China Loess particles collected in theloess layer in Gansu Province of China and a localsoil particle sample collected in the backyard ofthe Korea Meteorological Administration in Seoulwere analysed. In Figure 7.5.12, the observed frequenciesof four major water-insoluble chemicalspecies, e.g. aluminosilicates, carbonaceous,CaCO 3 ,andSiO 2 species, in the three samples,are shown. The frequencies are calculated for particles,which contain those species either as singlespecies or mixtures. Particles containing aluminosilicatespecies are the most abundant, andcarbonaceous species the next. The abundance ofSiO 2 containing particles is similar between thesamples. However, it is quite different for CaCO 3species; the local soil does not have the CaCO 3species, but the Asian Dust and China Loess do.Even though the abundance of particles containingaluminosilicate species is similar between thesamples, there are some differences in chemicalcomposition between particle samples originatingfrom China (the Asian Dust and China Loesssamples) and the local soil sample. Figure 7.5.13shows the frequencies of the elements most frequentlyencountered in aluminosilicate-containingparticles. In Asian Dust and China Loess samples,0.80.70.6Asian dustChina loesslocal soilFrequency0.50.40.30.20.10.0AluminosilicatecontainingCarbonaceousspecies-containingCaCO 3 -containingSiO 2 -containingFigure 7.5.12 Frequencies of four major chemical species observed in Asian Dust, China Loess and local soil particle samples

588 SPECIATION AND SURFACE ANALYSIS OF SINGLE PARTICLES1.00.90.80.7Asian dustChina loesslocal soilFrequency0.60.50.40.30.20.10.0Na Mg K Ca FeElementsFigure 7.5.13 Frequencies of major elements observed in aluminosilicate-containing particles of Asian Dust, China Loess andlocal soil particle samplesthose aluminosilicate-containing particles also containalmost always Mg. In contrast, K is the mostfrequently encountered element in aluminosilicatecontainingparticles of the local soil sample. Itimplies that the Asian Dust and China Loess samplescontain mostly Mg-enriched aluminosilicateminerals, whereas the local soil sample contains K-enriched minerals. Another difference in chemicalcomposition of those aluminosilicate-containingparticles is the absence of Ca in the local soilsample. This example demonstrates that the singleparticle analysis using the low-Z EPMA canprovide detailed information on various types ofchemical species in the samples and clearly distinguishthe particle samples with different sourcesbased on their chemical compositions.Direct Proof of Nitrate Formation fromSea-saltsThe low-Z EPMA was applied for the analysisof aerosol particles collected on 19 June, 1999at Cheju Island, Korea (Ro et al., 2001c). ChejuIsland is an ideal place to study continentaland marine influences on aerosols, because it issurrounded by the Korean peninsula, mainlandChina, Japan and the Yellow Sea and it is alsoone of the cleanest areas in Korea. Overall, 2888particles were analysed and one of the mostabundant particle types is marine-originated. Usinglow-Z EPMA, several different types of marineoriginatedparticles were identified, i.e. ‘genuine’sea salt particles such as NaCl-containing onesand ‘reacted sea salt’ particles such as NaNO 3 -and Na 2 SO 4 -containing ones. Since low-Z EPMAprovides quantitative elemental concentration datafor single particles, we could distinguish twodifferent ‘genuine’ sea-salts (i.e. NaCl particlesand particles with NaCl and MgCl 2 ) and also twodifferent nitrate particles (i.e. NaNO 3 particles andparticles with NaNO 3 and Mg(NO 3 ) 2 ).Thereisa good possibility that those nitrate and chlorideparticles which contain only Na, also contain Mgat trace level, because detection limits of ED-EPMA are in the range of 0.1–1 % by weight.However, the average atomic concentrations of Naand Mg elements in all 338 particles containingboth NaNO 3 and Mg(NO 3 ) 2 species are 14.8 % and1.9 %, respectively. In contrast, those of Na and

APPLICATIONS 589Mg elements in all the NaNO 3 particles are 19.8 %and 0.3 %, respectively. No particle identified asNaNO 3 and NaCl species contains a Mg contentlarger than 1 % in atomic fraction. In other words,two types of sea salts were indeed observed;with and without Mg. We do not know exactlywhy two different types of nitrate and chlorideparticles were observed, and yet this result showsthe powerful applicability of the low-Z EPMAtechnique for the elucidation of chemical speciesof aerosol particles.There are some strong implications that seasalts had reacted with other chemical speciesbefore the sampling. For example, the chance toobserve ‘genuine’ sea salt particles is relativelyvery small (3.1 %), compared to ‘reacted sea salt’particles, e.g. NaNO 3 - and Na 2 SO 4 -containingones (30.2 %). Also, internally mixed particleswith NaNO 3 and Mg(NO 3 ) 2 are abundant (11.9 %).In addition, particles containing Na 2 SO 4 and/orMgSO 4 species are also observed (4.6 %). Wealso observed a significant number of Na- andMg-containing particles with Cl as well as otherchemical species, e.g. (Na, Mg)(NO 3 , Cl), (Na,Mg)(SO 4 , Cl) and (Na, Mg)(NO 3 ,SO 4 , Cl) types,implying that the reactions between sea salts andthe other species were not complete so that theparticles still have some remnant Cl in them.Most importantly, we calculated the ratio ofatomic concentrations between Na and Mg inall the mixture particles containing NaNO 3 andMg(NO 3 ) 2 , i.e. 338 particles. The ratio is 0.128with a standard deviation of 0.047, which isremarkably similar to that of seawater (0.122). Thisresult provides strong evidence for the originalsource of those particles; they were from the seaand reacted with HNO 3 in air. The result based onquantitative analysis on Na and Mg concentrationin nitrate particles might be the most direct proofon nitrate formation from sea-salt up to now.Identification of Mine Pollution Particles inRiver SedimentNatural water ecosystems are very vulnerableto sedimentary heavy metal pollution. Especiallythe Tisza and Szamos rivers located in easternHungary are frequently polluted mostly due tomining activities in the catchment area. The speciationof heavy metals is necessary for estimating theenvironmental mobility and bioavailability of theseelements. Below, the capability of TW-EPMA forthe heavy metal speciation in sediment particles isdemonstrated. In March 2000, just a month afterthe world-widely discussed catastrophic cyanidepollution event, a thousand tons of heavy-metalcontaining sludge reached the surviving part of theTisza River due to a tailings dam failure at BaiaBorsa, Romania. Sediment samples were collectedfrom the main riverbed of the Hungarian sectionof Tisza at six sites, a week after the pollutionevent. All of the collected samples were subjectedto bulk XRF prior to the TW-EPMA measurements,and this technique showed that some ofthe samples collected at the river section between200–220 km from the pollution site, contained Cu,Zn and Pb at elevated concentrations. The observedconcentrations were an order of magnitude higherthan the background level for river and lake sedimentsin Hungary (Szalóki et al., 1999; Weiszet al., 2000). The average population of particlesin the sediment samples was investigated usingsingle-particle TW-EPMA, on samples preparedon silver foil using the inverse BSE contrast. Asthe determination of carbon and oxygen is feasiblewith this method, the most abundant particletype connected with the mine pollution could beclearly identified as pyrite. Internally mixed particlesconsisting of aluminosilicates (natural constituentsof sediment) and pyrite, zinc sulfide andlead oxide were also detected. The abundance ofthe pollution particles was below 10 % by numberfor the most polluted samples. In order toexclusively investigate the heavy-metal containingparticles, one sediment sample showing the highestpollution was prepared on silicon wafer for furtheranalysis. Using the normal BSE contrast, only particleshaving significantly higher average atomicnumber than that of silicon were selected for automaticmeasurement. Although a 10 keV electronexcitation energy was used, heavy metals could beidentified and determined using L and M X-raylines. Using this measurement setup, pyrite, zinc

590 SPECIATION AND SURFACE ANALYSIS OF SINGLE PARTICLESsulfide, iron–copper sulfide, lead oxide and leadsulfide as well as rare earth (La, Ce, Sn) oxideparticle types could be distinguished. Heavy metalswere also found to be connected to the aluminosilicatephase in some of the particles. The smallsize (

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592 SPECIATION AND SURFACE ANALYSIS OF SINGLE PARTICLESTsuji, K., Murakami, Y., Wagatsuma, K. and Love, G. Surfacestudies by grazin-exit electron probe microanalysis (GE-EPMA). X-Ray Spectrom., 30, 123–126 (2001).Van Espen, P. and Lemberge, P. ED-XRF spectrum evaluationand quantitative analysis using multivariate and nonlineartechniques. Adv. X-Ray Anal., 43, 560–569 (2000).Wagner, H. W., Werner, W. S. M., Störi, H. and Richardson,L. M. Electron probe microanalysis inverse modeling. Nucl.Instrum. Methods, B184, 450–457 (2001).Watanabe, M. and Williams, D. B. Atomic level detection byX-ray microanalysis in the analytical electron microscope.Ultramicroscopy, 78, 89–101 (1999).Weisz, M., Polyák, K. and Hlavay, J. Fractionation of elementsin sediment samples collected in rivers and harbors at LakeBalaton and its catchment area. Microchem. J., 67, 207–217(2000).Wollman, D. A., Irwin, K. D., Hilton, G. C., Dulce, L. L.,Newbury, D. E. and Martinis, J. M. High-resolution, energydispersivemicrocalorimeter spectrometer for X-ray analysis.J. Microscopy, 188, 196–223 (1997).Wollman, D. A., Hilton, G. C., Irwin, K. D., Dulcie, L. L.,Bergren, N. F., Newbury, D. E., Woo, K.-S., Liu, B. Y. H.,Diebold, A. C. and Martinis, J. M. High-resolution microcalorimeterenergy-dispersive spectrometer for X-raymicroanalysis and particle analysis, in Characterizationand Metrology for ULSI Technology (Eds D. G. Seiter,A. C. Diebold, W. M. Bullis, T. J. Shaffner, R. McDonaldand E. J. Walters), pp. 799–804 (1998).Wollman, D. A., Nam, S. W., Hilton, G. C., Irwin, K. D.,Bergren, N. F., Rudman, D. A., Martinis, J. M. and Newbury,D. E. Microcalorimeter energy-dispersive spectrometryusing a low voltage scanning electron microscope. J.Microscopy, 19, 37–44 (2000a).Wollman, D. A., Nam, S. W., Newbury, D. E., Hilton, G. C.,Irwin, K. D., Bergren, N. F., Deiker, S., Rudman, D. A. andMartinis, J. M. Superconducting transition-edge microcalorimeterX-ray spectrometer with 2 eV energy resolutionat 1.5 keV. Nucl. Instrum. Methods, A444, 145–150(2000b).

IndexActive pixel sensors (APS), 7, 181–190and DEPFET detector system, 183sideward depletion, 149XEUS mission, 181–182see also pixel detectorsADF imaging, 390Algebraic reconstruction technique (ART), 124–125Annular dark field (ADF) imaging, 390APS see Active pixel sensorsAPXS technique, 338–339Archaeometry, 11, 157–158, 533–552analytical techniques overview, 533EDXRF analysis, 329–334PIXE and micro-PIXE applications, 547–548terracotta sculptures, 547–548portable equipment, 329–334, 534–536detectors, 535–536energy dispersive spectrometers, 535radiation damage, 544–545glazes, 545–546safe limits, 546with X-ray primary beams, 546–547synchrotron radiation, 536–538, 548–549Egyptian cosmetic analysis, 548–549glass corrosion, 549micro-mapping, 549SR-XRD, 538, 548SR-XRF microprobe, 536–538texture analysis, 538–539beam energies, 540–542external microbeams, 542–543gold alloys (tumbaga), 540–542micro-mapping, 543–544paint layers, 539–540, 541PIXE depth profiling, 539–540proton penetration, 539–540ART see Algebraic reconstruction techniqueAtomic scattering factor, 64Auger electron, 391–392, 414, 415Bolometer see Cryogenic microcalorimetersCadmiumin fly ashes, 126–129concentration levels, 127, 128‘hot spots’, 127, 128micro-XAS spectra, 128micro-XRF maps, 128medical detection, 502, 503, 505, 508, 509CCDs see Charge-coupled detectorsCDDs see Controlled drift detectorsCFEG see Cold field emission gunCharge-coupled detectors (CCDs), 133, 137, 140–142CAST experiment, 180charge transfer efficiency (CTE), 172electron emission channelling spectroscopy, 179noise, 170–171performance, 169–175plasma diagnostics, 178–179quantum efficiency, 172–173quantum optics, 179sideward depletion, 141–142, 149three-phase MOS, 140–141transition radiation, 180X-ray microscopy, 178XMM satellite, 145–146, 172, 173, 174–175see also pn-CCDChemical analysis, 2–6Chemical mapping, 398CMT, 350–351Cold field emission gun (CFEG), 389Collimating optics, 97–98divergent angle, 97–98, 99intensity gain, 97Compound refractive lenses see Refractive X-ray lensesCompton scattering, 10, 254, 441, 443Computerisation methods, 435–485Monte Carlo simulation, 435–461spectrum evaluation, 463–485Computerised microtomography (CMT), 350–351Controlled drift detectors (CDDs), 7, 137, 163–166applications, 164–166trigger signal, 163–164see also Drift detectorsCryogenic microcalorimeters, 8, 229–245, 572absorber, 230–231metals, 230–231semiconductors, 231superconductors, 231X-Ray Spectrometry: Recent Technological Advances. Edited by K. Tsuji, J. Injuk and R. Van Grieken© 2004 John Wiley & Sons, Ltd ISBN: 0-471-48640-X

594 INDEXCryogenic microcalorimeters (continued)collecting area, 235–236arrays, 235–236, 239count rate, 233–235time constant, 234, 235detector microfabrication, 237–238electrothermal feedback, 234–235, 242energy resolution, 232–233determining factors, 233future trends, 241–242imaging detectors, 239–240lithography, 238multiplexers, 238–239noise, 232–233, 237, 241–242non-ideal effects, 236–237, 240absorber decoupling, 236compensating mechanisms, 240hot-electron effect, 236, 242non-ohmic behavior, 236–237operating principles, 230position sensitive detectors, 239–240quantum efficiency, 235sensor, 231–232, 240–241magnetic, 232, 240, 241non-resistive, 232, 240thermistor, 231–232transistor edge sensors (TES), 231, 232, 236–237‘Cumulative Centre’ line, 18, 19DAFS, 422Dentistry, 489, 492–493DEPFET see Depleted p-channel field effect transistorDepleted p-channel field effect transistor (DEPFET), 137,182–189advantages, 183clear procedure, 185, 186detector system and APS, 183detector-amplifier, 142–143, 184–185energy resolution, 187, 189noise, 187, 189performance figures, 185–187, 188position resolution, 187–188quantum efficiency, 188radiation background, 188repetitive nondestructive readout (RNDR), 189sideward depletion, 184system concept, 182–183and XEUS mission, 183Detectors see X-ray detectorsDiffraction anomalous fine structure (DAFS), 422Diodes, 135, 136Divergent angle, 97–98, 99Double-multilayer monochromator, 76–77Drift detectors, 137, 140, 141, 148–161controlled drift detector (CDD), 7, 137, 163–166energy measurement, 150–152energy resolution, 151, 152for high-energy XRF, 356leakage current, 151–152noise reduction, 150, 151, 152pn-CCDs, 166–180position resolution, 152–153principles, 148, 149–150sideward depletion, 140, 141for X-ray detection, 153–163X-ray holography, 161–162see also Controlled drift detectors; Silicon drift detectorsDuMond arrangement, 23EDS, 387, 388see also Energy-dispersive X-ray microanalysis (EDX)EDX see Energy-dispersive X-ray microanalysisEDXRF systems, 2–3, 8–9, 307–341applications, 307–308, 321, 328–339alloy analysis, 335, 336archaeometry, 329–334chlorine, 329, 331copper, 333, 334gold, 329, 331, 333, 334lead, 333, 334pigments, 329, 330sulfur, 329, 330, 331, 333titanium, 331environmental analysis, 334–335lead in paints, 334–335Martian soil analysis, 338–339soil and rock analysis, 335–337air gap correction, 335–336grain size, 336lead, 336–337trace element analysis, 337defined, 307element identification, 317instrumentation, 308–328Monte Carlo simulation, 458–459portable equipment, 319–3289000 XRF Field Analyser, 324–325AMPTEK, 321–323EDAX, 323–324, 325EIS, 319, 321, 322Horizon 600 Alloy Sorter, 326, 327ICS-4000, 327, 328Metallurgist Pro, 326Metorex, 327–328, 335NITON, 319–321, 323Oxford, 326, 327Roentec ArtAX, 323, 324summarized, 320Thermo Measure Tech, 324–326Warrington (Lead Star and µ-Lead), 328, 329X-MET 880, 970, or 2000, 327–328, 335XRF Corporation, 327software, 315–319‘fundamental parameter determination’ (FP), 317peak area analysis, 317spectral lines, 355and spectrum evaluation, 463, 483X-ray detectors, 313–315compared, 317cooling, 313, 316, 318efficiency, 316energy resolution, 313, 314, 315features, 313types, 313–314

INDEX 595X-ray sourcesradioactive sources, 308–309, 310X-ray optics, 310–313X-ray tubes, 309–310, 312, 313EELS see Electron energy loss spectroscopyElectron energy loss spectroscopy (EELS), 388, 419–420applications, 394background subtraction, 393detection rate and geometry, 392, 393–394and EDX compared, 392–395‘energy loss near edge structure’ (ELNES), 394, 419energy resolution, 392–393extended energy loss fine structure (EXELFS), 419multiple scattering, 393spectrum image, 394–395Electron guns, 570–571field-emission gun, 376–377, 382, 385, 387–388,570–571thermionic guns, 570Electron probe microanalysis (EPMA), 9, 103–104, 373–386,569BNC coatings, 377–380chemical mapping, 398detectors, 572–573dual voltage, 573grazing exit, 297–302, 572–573gunshot residue, 564–565particle analysis, 570–590polycapillary optics, 103–104setup, 379Electron-excited X-ray emission spectrometry, 569–592Element imaging, 158–160Ellipsoidal mirrors, 19–22magnification, 21performance, 21production, 20in protein crystallography, 21–22ENC, 266–267Energy recovery linac (ERL), 45–46brilliance, 46Energy-dispersive spectroscopy (EDS), 387, 388see also Energy-dispersive X-ray microanalysis (EDX)Energy-dispersive X-ray fluorescence systems see EDXRFsystemsEnergy-dispersive X-ray microanalysis (EDX), 387–404detection rate and geometry, 392, 393–394detectors, 569–570, 571–572and EELS compared, 392–395quantitative analysis, 395–402absorption correction, 396, 397, 398, 400boundary segregation, 399chemical mapping, 398–400Cliff-Lorimer Equation, 395–396, 397diffusion profiles, 401, 402, 403extrapolation method, 396–397fluorescence correction, 396, 397, 398ionic compounds, 400–401line profile, 399–400mass-thickness calibration, 397–398‘mean mass-absorption length’, 400–401parameterless correction method, 396–397thickness profile (garnet/OPX interface), 403, 404zeta-factor method, 397–398and STEM, 389see also Energy-dispersive X-ray spectroscopy;Transmission electron microscopyEnergy-dispersive X-ray spectroscopy (EDS), 103–104,387–404historical overview, 387–388Energy-dispersive X-ray spectroscopy (EDS)see also Energy-dispersive X-ray microanalysis;Transmission electron microscopyEnvironmental applications, 5EDXRF, 334–335high-energy XRF, 364–366EPMA see Electron probe microanalysisEpsilon 5, 359Equivalent Noise Charge (ENC), 266–267ERL see Energy recovery linacEXAFS (Extended X-ray absorption fine structure), 405–406,422–426data analysis, 425spectra, 422–423standardization, 423–426and X-ray fluorescence, 422EXEFS, 420–422Extended X-ray absorption fine structure see EXAFSFEG, 376–377, 382, 385, 387–388, 399FEG-SEM, 571FEL see Free electron laserField-emission gun (FEG), 376–377, 382, 385, 387–388, 399Field-emission gun scanning electron microscopy(FEG-SEM), 571Film analysis see Thin-film analysisForensic research, 11, 368–369, 553–567high-energy synchrotron radiation XRF, 564–566gunshot residue, 564–565paint chip, 565, 566synchrotron radiation XRF, 560–563drugs of abuse, 561, 563fluorescence tracing, 560–561, 562, 563TXRF studies, 553–560brandy, 555–556liquors, 554–555meteorite pieces, 559–560methamphetamine, 557–559poisoned food, 553, 554seal ink, 556–557, 558terrorism weapons, 554waste water, 556, 557FP, 317Free electron laser (FEL), 30, 41–44and light power, 42and radiation intensity, 41Front-end electronics, 266–269count rate performance, 267Equivalent Noise Charge (ENC), 266–267feedback capacitance discharge, 267–268noise, 266, 267, 268–269‘Fundamental parameter determination’ (FP), 317Gas proportional ionization counter (PC), 195, 196, 197Gas proportional scintillation counter (GPSC) seeScintillation counter

596 INDEX‘Gaussian equivalent FWHM’, 18GIIXD see Grazing-incidence in-plane X-ray diffractionGPSC see Scintillation counterGrazing-exit XRS, 8, 293–305apparatus, 295detector, 304electron probe microanalysis (GE-EPMA), 297–302particle analysis, 299–301setup, 297–298surface analysis, 298, 299thin-film analysis, 301–302exit angle control, 295, 297–298fluorescence (GE-XRF), 295–296future developments, 303–305grazing emission XEF (GE-XEF), 296grazing-incidence XRS compared, 293light element analysis, 296, 297localized surface analysis, 303–304particle induced X-ray emission (GE-PIXE), 302–303, 304particle analysis, 303setup, 302–303surface and thin-film analysis, 303principles, 293–295critical angle, 294emission intensities of X-rays, 293–294information depth, 294, 295refraction of X-rays, 293, 294TXRF compared, 293Grazing-incidence in-plane X-ray diffraction (GIIXD), 25–26Goorsky–Tanner technique, 25–26in-plane mosaic determination, 26Grazing-incidence XRS, 8, 277–291critical angle, 277future developments, 288–290impurity analysis, 285intensity distribution, 284interface analysis, 283–287internal X-ray electric field, 284microscopic imaging, 287–288, 289penetration depth (of X-rays), 277standing wave technique, 283, 285, 286, 287surface analysis, 283–287total reflection XRF, 278–283X-ray fluorescence, 278–290X-ray reflectometry, 285–287laser pulse intensity, 57, 58–59polarization, 57, 58pulse duration, 56, 57–58spectral range, 56–57, 58High-energy XRF, 9, 355–372applications, 363–371archaeology, 366–368environment, 364–366forensic, 368–369geology and geochemistry, 369–371garnet analysis, 370, 371heavy element analysis, 369–371Old Kutani chinaware, 366–368rare earth elements analysis, 364, 365soil analysis, 366experimental setup, 356–357, 358historical review, 355–356laboratory X-ray sources, 355–356synchrotron radiation light sources, 356instruments, 356–357detectors, 356, 357monochromatic X-rays, 357optics, 357, 359performance, 357–363absorption coefficients, 362–363analytical performance, 360–362detection limit, 363lower limit (LLD), 359–360minimum (MDL), 360–362excitation techniques, 357–359penetration depths, 362–363transmission power, 362–363spectral lines, 355High-resolution X-ray diffraction (HRXRD), 22–25configuration, 23rocking curve, 23, 24semiconductor characterization, 22–23spot size, 23, 24HRXRD see High-resolution X-ray diffractionIntensity gain, 97Kirkpatrick–Baez objective, 73, 74HAADF, 391‘Halo effect’, 108Hard X-ray multilayers, 72–77double-multilayer monochromator, 76–77microbeams and microscopy, 72–73multilayer-coated grating, 75–76reflectivity curves, 72, 73structure and composition, 72telescopes, 73–75Hard X-rays, 52–55HHG see High harmonic generationHigh angle annular dark field (HAADF) imaging, 391High harmonic generation (HHG), 49, 55–59short wavelength generation, 55–56X-ray source parametersconversion efficiency, 57, 58Laser-driven X-ray sources, 6, 49–62advances, 49–50applications, 50, 52–53, 54–55brilliance, 51compact coherent, 49–50generation mechanism, 53hard X-rays, 52–55high harmonic generation (HHG), 55–59laser technology, 50–52parameters, 52pulse speed and duration, 50–51, 52, 53, 54repetition rates, 51–52time-resolved X-ray diffraction, 54–55X-ray lasers, 55Least moduli method, spectrum evaluation, 499Lenses see Refractive X-ray lenses

INDEX 597Light element analysisby TXRF, 281, 282, 283, 518–519vapor phase decomposition (VPD-TXRF), 524Light emission, in FEL, 42Literature survey, 2–6country of origin, 5–6language of publication, 5Lithium drifted silicon (Si(Li)) detectors, 258, 387, 388Low-energy electron probe microanalysis see Electron probemicroanalysis (EPMA)Low-energy SEM see Scanning electron microscopy (SEM)Low-voltage scanning electron microscopy (LV-SEM), 571LV-SEM, 571Magnetic circular dichroism (MCD), 69–71MC simulation see Monte Carlo simulationMCD, 69–71Medical applications of XRF, 487–515element concentration, 487–489bromine, 493cadmium, 502, 503, 505, 508, 509calcium, 492, 508chromium, 489gold, 493, 508iodine, 490–491, 508iron, 506–508lead, 489–490, 501–502, 503, 509accumulation, 503–504childhood development, 505exposure, 502–503in pregnancy and lactation, 504mercury, 489, 490, 502, 503, 505–506, 507, 509multielement studies, 493nickel, 492–493palladium, 493, 508platinum, 491–492, 508thorium, 491trace elements, 490uranium, 508glomerular filtration rate (GFR), 491in vitro analysis, 487–488, 489PIXE method, 487in vivo analysis, 10, 488–489, 493–508accuracy, 501–502calibration, 499–500phantoms, 499, 500detectors and detection limit, 495–496, 500–501Monte Carlo simulation, 496–497neutron activation analysis (NAA), 488photonsfrom radionuclides, 493, 494–495from X-ray tube, 494, 495LXRF and KXRF, 495polarised, 494scattering, 494precision, 501–502uncertainty, 501–502spectrum analysis, 499thyroid activity, 490–491Micro-SRXAS, 126–129Micro-X-ray analysis, 296Micro-X-ray diffraction, 351Micro-X-ray fluorescence computed microtomography(XFCMT), 121–126experimental setup, 121future developments, 125–126ion transport in plants, 121–123micrometeorite studies, 123–126ART, 124–125biological, 124Micro-X-ray fluorescence computed tomography (XFCT),453–455Micro-X-ray sources, 6, 13–27applicationGIIXD, 25–26HRXRD, 22–25focusing opticsellipsoidal mirrors, 19–22polycapillary optics, 22and heat conduction, 13–14magnetic focusing, 15–17measurement, 17–18‘pinhole camera’, 17shadow technique, 17–18microfocus generator, 15–17and optics, 14–15phase contrast imaging, 18–19, 20photon collection, 14–15spot control, 15–17, 23target material, 14Wavefront distortion, 19Micro-XRF, 100–103, 117applications, 5beam confinement, 343and cell analysis, 118–121imaging, 287–288laboratory, 100, 101portable, 100–101, 102synchrotron radiation, 102–103Microbeams see X-ray microbeamsMicrocalorimeters see Cryogenic microcalorimetersMicroscopic X-ray fluorescence analysis see Synchrotronradiation micro-XRFMicrotomographyX-ray absorption techniques, 418, 419, 420, 421X-ray fluorescence, 121–126Monte Carlo (MC) simulation, 10, 435–461applications, 436Compton scattering, 10, 441, 443electrons in scintillation counters, 200, 204, 206experimental validation, 445–453detection geometry, 447, 450detection limits for rare earths, 451–453linear polarization, 451scatter distributions, 447, 448, 449, 450setup, 445future trends, 458–459general principles, 437–445atom type selection, 439detector response function, 445interaction type selection, 439–440photoelectric effect simulation, 440photon absorption, 440photon trajectory, 437–438scattering interactions simulations, 441–444

598 INDEXMonte Carlo (MC) simulation (continued)azimuth angle, 443inverse cumulative distribution function, 442scattering angle, 442–443scattering event modeling, 443–444simulation code, 437step length selection, 438–439variance reduction, 444–445historical summary, 435in vivo medical readings, 10, 496–497Rayleigh scattering, 10, 441spectrum evaluation, 474–476trace-element analysis, 455–458fly ash particles, 456, 457–458quantification algorithm, 455–457XRF tomography, 453–455Multilayer coatings, 7, 63–78applications, 63–64boundary of total reflection, 65–66design, 64–67fabrication, 63gratings, 75–76hard X-ray multilayers, 72–77‘layer-by-layer’ method, 66–67material selection, 67reflectivity, 64–65soft X-ray multilayers, 67–72Near edge X-ray absorption fine structure see XANESNEET (nuclear excitation by electron transition), 428NEXAFS (near edge X-ray absorption fine structure) seeXANESNoiselimits CCD performance, 169–171in semiconductor detectors, 135–137NRA, 378–379Nuclear excitation by electron transition (NEET), 428Nuclear reaction analysis (NRA), 378–379Pad detectors, 247Parabolic compound refractive X-ray lenses see RefractiveX-ray lensesParticle analysis, 569–592applications, 587–590heavy metals, 589–590nitrate formation, 588–589soil and dust analysis, 587–588by EPMA, 299–301, 573–590experimental conditions, 570–573detectors, 571–573electron gun, 570–571priorities, 570sample treatment, 573cryogenic SEM, 573variable pressure (VP) SEM, 573inclusions in stainless steel, 300–301quantification models, 573–587analytical models, 573–574automatic evaluation, 581beam damage effect, 578–580beam sensitivity, 579CASINO software, 575chemical species analysis, 582–584surface and core region, 584data analysis, 580–582detector efficiency, 577error distribution, 582, 583heterogeneity, 584–587iterative approach, 575–577MC simulation models, 574–575particle diameter calculation, 576–577reverse MC procedure, 11, 575–577spectrum analysis, 580–582substrate material, 577–578window parameters, 577on silicon wafers, 299–300Particle/proton-induced X-ray emission (PIXE) analysis, 1,3–4archaeometry, 539–544, 547–548grazing-exit, 302–303, 304in vitro analysis, 487literature survey, 3–4PC, 195, 196, 197Phase contrast imaging, 18–19, 20Photonsabsorption, 143–144collection, 14–15detection, 146–147, 148increase temperature, 229PIXE see Particle-induced X-ray emission analysisPixel detectors, 181–190, 247–248pn-CCD, 141–142, 166–180detector quality, 167development, 166frame store format, 175–176, 178, 180low energy response, 167p+ strips (shift registers), 167–168, 169, 170pixel size, 175–177position precision, 176readout speed, 175–177for ROSITA mission, 175, 178, 179, 180XEUS mission, 175, 177, 180see also charge-coupled detectorsPolarization, 69–71, 278Polycapillary optics, 7, 22, 89–110applications, 98–108electron probe X-ray microanalysis, 103–104micro-XRF, 100–103wavelength dispersion of X-rays, 104collimating optics, 97–98, 106, 108, 311, 314divergent angle, 97–98, 99intensity gain, 97in EDXRF systems, 310–313elemental analysis, 98–104fabrication, 92focusing optics, 90, 93–97beam size measurement, 95flux density gain, 95–97focal distance, 93–95focal spot size, 93–95, 108–109future trends, 108–109micro-XANES, 105–106for micro-XRF, 345monolithic polycapillary optics, 90, 91

INDEX 599photon trajectory, 92–93principles, 89–92simulation tools, 92–93structural analysis, 104–108transmission efficiency, 91–92wavelength dispersion, 104X-ray diffraction, 106–108XAFS, 106Portable EDXRF systems see EDXRF systemsPortable equipment for X-ray fluorescence analysis seeEDXRF systemsPosition sensitive semiconductor strip detectors see Stripdetectorsα-proton X-ray spectrometer 338–339Proton-induced X-ray emission (PIXE) analysis seeParticle/proton induced X-ray emission (PIXE) analysisQuantitative analysis, using EDX, 395–402Radiative Auger satellites, 420Radioisotope XRF, 3γ -ray camera, 162–163Rayleigh scattering, 10, 254, 441Readout electronics, 265–273analogue scheme, 270, 271, 272–273architectures, 269–273binary architecture, 269–271front-end electronics, 266–269multiplexing, 269, 270threshold discriminator, 271time-over-threshold principle, 270, 271–272Reciprocity theorem, 294Refractive X-ray lenses, 7, 111–131applications, 117–129cell analysis, 118–121experimental setup, 117–118µ-SRXAS, 126–129µ-SRXRF, 126–129XFCMT, 121–126attenuation, 112, 114design, 111, 112–113spherical aberration, 113imaging, 114–115material, 112–113microbeamsbackground, 116knife-edge technique, 116–117and nanofocusing lenses, 117production, 115–117properties, 116–117physics, 112–117absorption, 112refraction, 112PINK beam mode, 118, 119, 120properties, 113–114ROSITA mission, 175, 178, 179, 180Rotating anode generator, 13, 14and microfocus sources compared, 21–22Rotation analyzer, 71Rotational trapezoidal readout (ROTOR), 163ROTOR, 163SASE see Self-amplified spontaneous emission systemScanning electron microscopes, 158–160Scanning electron microscopy (SEM) (low energy),373–386advantages and disadvantages, 376applicationsanodised aluminium, 379BNC coatings, 377–380composition, 377–380fouled membranes, 382, 383meat casings, 382–385polymer membranes, 380–382experimental setup, 381feasibility tests, 380–381surface morphology, 381–382beam energy selection, 376high-resolution capabilities, 376, 379high-resolution imaging, 375–377Jeol JSM-6340F, 376, 377metal oxide images, 376–377, 378objective lens, 376, 377specimen chamber, 376, 377Scanning transmission electron microscope/microscopy(STEM) see Transmission electron microscopySchwarzchild optics, 68–69Scintillation counter (GPSC), 7, 195–214electron drift, 202–205, 206energy change, 202–205, 206velocity, 207, 208energy resolution, 209, 213Fano factor (F), 201material analysis applications, 211–213nonlinearity, 198–200, 213photodiodes, 211photosensors, 210–211compact implementation, 210–211photomultipliers, 210primary electron production, 198–200, 201, 202distribution function, 200–201, 203secondary scintillation, 206–207detection, 207–208solid angle compensation, 209curved grid technique, 209, 210masked photosensor technique, 209, 210statistical fluctuations, 200–201structure, 195–197, 207–209cylindrical geometry, 208spherical anode, 208uniform electric field, 195–197, 208–209tailing effects, 201–202, 203transport of electrons, 202–206Xe as filling medium, 197–198electron cascade, 197–198, 199Scintillation detectors, 162–163SDDs see Silicon drift detectorsSelf-amplified spontaneous emission (SASE) system, 30,41–45brilliance, 44electron beam, 42–43power production, 42–44wavelength region, 44SEM see Scanning electron microscopy

600 INDEXSemiconductor detectors, 133–193charge-coupled detectors (CCDs), 137, 140–142DEPFET detector-amplifier, 142–143diodes, 135, 136drift detectors, 137, 140, 141, 148–161future developments, 189–190gas detectors compared, 134germanium and silicon, 134–135materials see Semiconductor materialsproperties, 134–135sideward depletion, 140, 141–142, 149signal charge measurement, 135–137noise, 135–137X-ray detection, 148see also Strip detectorsSemiconductor materials, 247, 248, 250–251, 517absorption length, 250–251total reflection XRF, 517–532Semiconductor-radiation interaction, 143–144photon absorption, 143–144radiation entrance window, 144–145Sideward depletion, 140, 141–142, 149, 184Silicon drift detectors (SDDs), 7art investigation, 157–158drift detector drop (SD 3 ), 155–157in EDXRF systems, 314element imaging, 158–160energy resolution, 156entrance window, 153, 154γ -ray camera, 162–163and grazing-exit XRS, 304integrated JFET, 150–151layout, 160, 161low energy background, 153–155portable instrumentation, 158potential energy distribution, 154, 155properties, 155and X-ray fluorescence (XRF) spectrometer, 161see also Drift detectorsSilicon microsystems, 148Silicon strip detectors see strip detectorsSingle capillary X-ray optics, 7, 79–87analytical microscope, 81–86aluminum crystal growth, 84–85, 86pearl structure, 83microbeams, 79–80multidimensional analysis, 86–87production, 80–81, 82Soft X-ray multilayers, 67–72applications, 68focusing, 68–69materials selection, 67–68microscopy, 68–69polarimetry, 69–71Soft X-rays, 374–375applications, 55–56coatings analysis, 375lasers, 55problems and precautions, 374reasons for use, 374Speckle patterns, 39Spectrum evaluation, 463–485detectors, 467, 468response function, 474–476energy calibration, 467–468future applications, 483–484Gaussian peak, 467modified, 470–472Gaussian shape deviation, 468group fitting, 468least moduli method, 499least-squares fitting, 464–465, 468, 497, 499, 580filter-fit method, 465using analytical functions, 465continuum, 466linear and non-linear, 465–466using reference spectra, 464–465Lorentzian distribution, 472–473, 474Monte Carlo simulation, 474–476partial least-squares regression (PLS), 476–483, 580applicationcement analysis, 479–483other analyses, 483theory, 477–479collinearity (correlation) problem, 477–478model, 479root mean squared error (RMSE), 478–479validation method, 478–479peak area determination, 464peak shapedeviates from ideal, 468modified Gaussian, 470–472numerical correction, 468–469polynomials, 466–467, 468fluorescence lines, 467resolution calibration, 467–468Voigt profile, 472–474, 475SPIX, 303Spot size, 23, 24, 93–95, 108–109SR see Synchrotron radiationSRXRF see Synchrotron radiation induced X-ray fluorescenceSRXRS, 1, 4STEM see Transmission electron microscopySTJ see Superconducting tunnel junctionsStorage rings, 29, 30, 32, 33, 45in SR-based micro-SRF, 345Strip detectors, 8, 137–140, 247–275absorption length, 250–251, 253basic concept, 248biasing methods, 139–140diffusion, 250, 251–254charge distribution, 252–253full width at half maximum (FWHM), 252–253double-sided, 138–139front-end electronics, 266–269lithium drifted silicon Si(Li), 258manufacturing technology, 247, 248materials, 247, 248, 250–251absorption length, 250–251, 253non-silicon, 248, 255, 258, 264–265coplanar strip structure, 265germanium, 264–265photon scattering, 254–255, 263–264

INDEX 601readout electronics, 138, 139–140, 265–273architectures, 269–273silicon, 255, 258–264breakdown voltage, 258–259coupling capacitors, 260dead layer, 263double-sided, 261–262edge-on, 262–264guard ring structure, 263layout optimization, 259lithium contact layer, 261noise, 260readout strips, 259, 260, 261scattering effects, 263–264single-sided, 259–261strip isolation techniques, 260, 261strip structure, 259–260single-sided and double-sided, 248–249spatial resolution, 249–258diffusion, 250, 251–254energy deposition, 255–256, 257intrinsic, 250–258parallax effects, 256–258scattering, 254–256strip pitch, 249, 250, 253–254structures, 258–265Superconducting tunnel junctions (STJ), 8, 217–227applications, 224–226basic functioning, 217–218cascade excitation process, 218–220cooling systems, 226energy resolution, 218–221, 222, 223noise performance, 220–221one-dimensional-imaging detectors, 218, 223quasiparticle excitation, 218–220series-junction detectors, 218, 223–224absorption efficiencies, 224single-junction detectors, 221–223statistical fluctuation, 221structure, 217–218Surface analysisGE-EPMA, 298, 299GE-PIXE, 303grazing incidence XRS, 283–287Surface sensitive particle-induced X-ray analysis (SPIX), 303Synchrotron radiationapplicationsin archaeometry, 536–538in medicine, 492characteristics, 34–40beamline performance, 40, 41, 279brilliance, 34, 36–37, 38, 44, 45, 46coherence, 38–39electron beam, 34flux and flux spectra, 34–35, 37, 38intensity, 34light rejection, 39photon energy, 35polarization, 39, 40source degeneracy, 39time structure (short pulse production), 39–40history, 1, 4–5sources, 6, 29–47energy recovery linac (ERL), 45–46first generation, 29fourth generation, 30–32, 40–46energy recovery linacs, 45–46SASE-FEL, 41–44storage rings, 45listed, 31–32for micro-XRF, 346second generation, 29, 35storage rings, 29, 30, 33, 45third generation, 29–30, 32–33characteristics, 34–40classification, 33energy range, 37–38undulators, 32–33in TXRF spectrometry, 278–279Synchrotron radiation induced micro-X-ray absorptionspectroscopy (micro-SRXAS), 126–129Synchrotron radiation induced X-ray fluorescence (SRXRF),126–129Monte Carlo simulation, 436–445Synchrotron radiation micro-XRF, 9, 102–103, 343–353accuracy, 347–350background effects, 347electron Bremsstrahlung, 347modeling methodologies, 347standards compared, 349–350advantages, 344applications, 351–352beam confinement, 343–344computerised microtomography (CMT), 350–351imaging, 351instrumentation, 344–347detection limits, 347, 348, 349detectors, 345–346optics, 345polychromatic v. monochromatic excitation, 344–345SR sources, 346storage rings, 345‘Micro-XRF’ project, 350X-ray absorption methods, 350Synchrotron radiation X-ray spectrometry (SRXRS), 1, 4TEM see Transmission electron microscopyTEY method, 414, 415Thin-film analysisby GE-EPMA, 301–302by GE-PIXE, 303total reflection X-ray fluorescence (TXRF), 10–11,529–531two-angle grazing incidence XRF (GIXRF), 529–531X-ray reflectivity, 530Thin-window electron probe microanalysis (TW-EPMA), 572see also Electron probe microanalysisTotal reflection X-ray fluorescence (TXRF), 1, 4–5, 10–11,278–283, 517–532beam confinement, 343with chemical preconcentration, 521–524cleanliness, 279, 280detection, 518, 519–520, 521, 522forensic applications, 553–560

602 INDEXTotal reflection X-ray fluorescence (TXRF) (continued)instrumentation, 517–520background optics, 519–520continuous X-rays, 518, 519detection limit, 518elements analysed, 517–519light element analysis, 281, 282, 283, 518–519, 524monochromator, 278parasitic X-rays, 279, 280polarized radiation, 278semiconductor analysis, 517–532standard samples, 525–529standardization, 524–529angle scan profiles, 526, 528cross-check activities, 524–525depth profile of analyte, 525–528‘Immersion in Alkaline Hydrogen Peroxide Solution’(IAP) method, 526–528ISO standards, 524, 525synchrotron radiation (SR), 278–279thin-film analysis, 529–531vapor phase decomposition (VPD-TXRF), 521–524automation, 521–524wavelength-dispersive spectrometer, 281, 282Transmission electron microscopy (TEM), 9, 387–404beam diameters, 388–389and electron energy loss spectroscopy (EELS), 388generated signals, 389–392Bragg scattering, 389–390Rutherford scattering, 390–391historical developments, 387–389inelastic scattering, 391–392Si(Li) detectors, 387, 388and WDX, 388see also Energy dispersive spectroscopy (EDS); Energydispersive X-ray microanalysis (EDX)TW-EPMA see Thin-window electron probe microanalysisTXRF see Total reflection X-ray fluorescenceUndulators, 32–33, 35–37Vapor phase decomposition (VPD-TXRF), light elementanalysis, 524Wavelength-dispersion of X-rays, 104, 105Wavelength-dispersive spectrometry (WDS), 281, 373Wavelength-dispersive X-ray fluorescence (WDXRF), 2–3,104and spectrum evaluation, 463Wavelength-dispersive X-ray microanalysis (WDX), 388WDS, 373WDX, 388WDXRF see Wavelength-dispersive X-ray fluorescenceWFI, 182Wide field imager (WFI), 182Windows (detectors), 144–145, 153, 154, 571–572, 577X-ray absorption fine structure spectrometry see X-rayabsorption techniquesX-ray absorption near edge structures see XANESX-ray absorption techniques, 9–10, 405–433applications, 350, 351, 428‘atomic XAFS’, 422–423beamline, 426and DAFS, 422data analysis, 425and EELS, 419–420and EXEFS, 420–422extreme conditions, 407–408history, 406–407instrumentation, 426, 427liquid surface characterization, 414magnetic property determination, 416–418measurements, 106microscopy and microtomography, 418, 419, 420, 421with optical luminescence, 409–410photoconductive and electrochemical measurements,411–412polarized X-rays, 413, 415with scanning tunneling microscopes, 408–409secondary yield methods, 414–415, 417self-absorption effect, 414spectra, 128, 129standardization, 423–426theory and interpretation, 422–423, 424, 425spectrometer, 426, 428strong field effects, 415–418TEY method, 414, 415total reflection, 412–414, 416with X-ray fluorescence, 410–411X-ray reflectivity intensity, 414X-ray analytical microscope, 81–86applications, 82–86structure, 81–82X-ray detectors, 7, 133–275, 467, 468, 571–573classified, 229compared, 313count rates, 463for EDXRF systems, 313–315, 317energy-dispersive spectrometers (EDS), 571–572EPMA, 572–573gas proportional scintillation counters, 195–214microcalorimeter, 229–245, 572semiconductor detectors, 133–193, 247–275silicon microsystems, 148solid state detectors (parameters), 536spectrum evaluation, 463strip detectors, 247–275superconducting tunnel junctions, 217–227wavelength-dispersive spectrometers (WDS), 571X-ray diffraction, 106–108GIIXD, 25–26high resolution (HRXRD), 22–25lyzozyme diffraction patterns, 107–108micro X-ray diffraction, 351X-ray excited optical luminescence (XEOL), 409X-ray fluorescence (XRF), 1, 2applications, 5and EXEFS, 420–422and gas proportional scintillation counters (GPSC),211–213high energy, 355–372

INDEX 603and interface roughness, 286–287, 288in medicine see Medical applications of XRFMonte Carlo simulation, 435–461detection limits for rare earth elements, 451–453experimental validation, 445–453tomography, 453–455trace-element analysis, 455–458and silicon drift detectors, 161, 162trace element in vivo analysis, 337and X-ray absorption techniques, 410–411and X-ray reflectometry, 285–287X-ray fluorescence (XRF)see also EDXRF systems; Total reflection X-rayfluorescence (TXRF)X-ray holography, 161–162X-ray lenses see Refractive X-ray lensesX-ray microanalysis, 9, 387–404X-ray microbeamsformation, 79–80, 115–117multidimensional analysis, 86–87and refractive lenses, 115–117single capillary, 80–81X-ray optics, 7, 63–131micro-XRF, 345multilayer coatings, 63–78polycapillary, 89–110, 310–313refractive X-ray lenses, 111–131single capillaries, 79–87X-ray sources, 13–62laser-driven, 49–62micro X-ray sources, 13–27synchrotron radiation, 29–47X-ray spectrometry (XRS)chemical analysis, 26historical aspects, 1–2literature survey, 2, 3progress in sub-fields, 2X-ray telescope, 73–75XAFS (X-ray absorption fine structure spectroscopy) seeX-ray absorption techniquesXANES (X-ray absorption near edge structures), 405–406,407experiments, 105–106microscopes, 419spectral analysis, 425SR-based micro-SRF, 350see also X-ray absorption techniquesXAS see X-ray absorption techniquesXenon, X-ray absorption, 197–198XEOL, 409XEUS mission, 175, 177, 180, 188and active pixel sensors, 181–182and DEPFET, 183wide field imager, 182XFCMT see Micro-X-ray fluorescence computedmicrotomographyXFCT, 453–455XMM satellite, 145–146, 172, 173, 174–175XRF see X-ray fluorescenceXRS see X-ray spectrometryWith kind thanks to A. Griffiths for creation of this index.

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