# Fileset [08 Tanuma_JSA_rev.pdf](https://mdr.nims.go.jp/filesets/3f392fb8-b1f1-4247-8b05-2dbc16ed3879/download) ## Creator [S. Tanuma](https://orcid.org/0000-0003-2628-9941), [H. Yoshikawa](https://orcid.org/0000-0002-7389-8865), N. Okamoto, K. Goto ## Rights [In Copyright](http://rightsstatements.org/vocab/InC/1.0/) ## Other metadata [Estimation of Inelastic Mean Free Paths in Au and Cu from Their Elastic Peak Intensity Ratios without IMFP Values of Reference Material in The 200 – 5000 eV Energy Range](https://mdr.nims.go.jp/datasets/730b852d-326c-4723-87c1-76235f7a2dbb) ## Fulltext Original paperJournal of Surface Analysis Vol.15, No. 2 (2008) pp. 195−199 S. Tanuma et al. Estimation of Inelastic Mean Free Paths in Au and Cu from Their Elastic Peak Intensity Ratios without IMFP Values of Reference Material in The 200 – 5000 eV Energy Range Letter Estimation of Inelastic Mean Free Paths in Au and Cu from Their Elastic Peak Intensity Ratios without IMFP Values of Reference Material in The 200 – 5000 eV Energy Range S. Tanuma,a,b,* H. Yoshikawa,b N. Okamoto,a and K. Gotoc aMaterials Analysis Station, National Institute of Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0043, Japan bNano Characterization Center, National Institute of Materials Science1-2-1 Sengen, Tsukuba, Ibaraki 305-0043, Japan cAIST-Chubu Center, Anagahora 2266, Moriyama-ku, Nagoya 463-8560, Japan *TANUMA.Shigeo@nims.go.jp (Received: November 6, 2008; Accepted: November 7, 2008) We have determined electron inelastic mean free paths (IMFPs) and surface-electronic excitation pa-rameters (SEPs) of Au and Cu in the 200 – 5000 eV from their elastic peak intensity ratios without refer-ence IMFP values. This proposed method does not require the IMFP values of the reference material. The measurements of elastic peak intensities of these elements were done with noble CMA system. The elastic peak intensities were also calculated from two parameter sets (IMFPs and SEPs for both elements) with Monte Carlo method. By comparison of these two EPI ratios as changing the parameter sets, we have es-timated their IMFPs and SEPs in the 200 – 5000 eV energy range. The resulting IMFPs of Au and Cu were in good agreement with optical IMFPs over 1000 eV energy range. The elastic and inelastic scatterings of electron in solid are very important for surface electron spectroscopies. Especially, it is essential to describe the attenuation rate of the electron signal due to inelastic scattering events in a solid. Therefore, the knowledge of the electron inelas-tic mean free paths (IMFPs) for low-energy electrons in solids is required for quantitative surface analysis by AES and XPS as well as for determining the surface sen-sitivity of other electron-spectroscopic methods of sur-face characterization. In a series of the papers Tanuma et al. calculated IMFPs for 50 - 2000 eV electrons in a group of 41elemental solids [1-3], a group of 15 inorganic com-pounds [4], and a group of 14 organic compounds [5] from their optical energy loss functions with Penn algo-rithm [7]. They fitted the calculated IMFPs for the groups of elements and organic compounds to a modified form of the Bethe equation for inelastic electron scatter-ing in matter and found that the four parameters in this equation could be related empirically to several material parameters [5]. The resulting general formula TPP-2M for IMFPs in solids could be used to estimate IMFPs for other materials in the 50 – 30,000 eV energy range. The evaluation of the accuracy of theoretical IMFPs for a given material is very difficult because it depends on the accuracy of the particular energy loss function (ELF) on which the calculation is based and of the ap-proximations used in Penn algorithm. It is valuable to compare calculated IMFPs and those obtained from ex-perimental method in order to assess the consistency of the IMFP values. Elastic peak electron spectroscopy (EPES) is a useful method for experimental determination of IMFPs [6]. In most EPES measurements it has been convenient to compare elastic peak intensities from a target material with those of a suitable reference material. With this method the instrumental factor such as mesh transmis-sion efficiency could be removed. However, it requires the IMFP values of the used reference material. Alterna-tively, the resulting IMFPs depend on the IMFPs of ref-erence material. On the other hand, IMFPs can be di-rectly determined from absolute measurement of elas- Copyright (c) 2008 by The Surface Analysis Society of Japan −195− Journal of Surface Analysis Vol.15, No. 2 (2008) pp. 195−199 S. Tanuma et al. Estimation of Inelastic Mean Free Paths in Au and Cu from Their Elastic Peak Intensity Ratios without IMFP Values of Reference Material in The 200 – 5000 eV Energy Range tic-backscattering coefficient of incident electrons. With this approach, it is necessary to make several corrections such as surface-electronic excitation, transmission effi-ciency etc. Generally it is very difficult to measure the transmission efficiency of the analyzer with high accu-racy. Then, we have developed a new method to deter-mine IMFPs of the target material from elastic peak in-tensity ratios without IMFPs of the reference. The energy dependence of elastically backscattered primary electrons were measured for Au and Cu with a novel cylindrical mirror analyzer (CMA) [8,9] in the 50 – 50 000 eV energy range. The details of the measure-ment were already published [10]. Figure 1 shows the measured peak intensity ratios of Au to Cu as a function of primary energy. 01234510 100 1000 104Ratio of measured EPI : I(Au)/I(Cu)Electron energy (eV) Fig. 1. Ratios of measured elastic peak intensities for Au to Cu as a function of primary electron energy. The intensity ratio of elastically backscattered primary electrons for Au and Cu, IAu/ICu, can be calculated from the following equation: ( ) ( )( ) ( )( )( )CuAuCusAuSCuCuCuAuAuAuCusAuSCuAuEHEHffdSSNdSddSSNdSdffIIλλληλη,,exp/exp/000 0=−−=⎟⎟⎠⎞⎜⎜⎝⎛∫∫∞∞ (1) where fs is a surface-electronic excitation (SEE) correc-tion factor, dη/dS is the path-length distribution of elas-tically backscattered electrons, N0 is the number of input electrons, S is total path length, and λ is the electron ine-lastic mean free path. The H(E,λ) is the reflection coeffi-cient of the incident electron at primary energy E and IMFP λ. The dη/dS were calculated with Monte Carlo (MC) method. In this calculation, we require the differ-ential elastic-scattering cross sections for their elements and energies at elastic peak intensities measured. The differential cross section dσ(E)/dq for elastic scattering used in the calculations were cited from the database of NIST [11]. In the calculation of dη/dS, MC calculation traces the input electrons until they are scattered back from the target specimen or until their total path length becomes larger than 10×λTPP-2M, where λTPP-2M denoted the IMFP values calculated from TPP-2M [5]. We collect the backscattered electron from the target within 42.3±6° to get the histogram dη/dS until at least over 10 000 electrons are detected. The dependence of reflection coefficient H(E,λ) on IMFPs for Au and Cu were calculated in the 50 – 5000 eV energy range. The calculated results at 200, 1000, and 5000 eV were shown in Fig. 2. From this figure, we see that the H(E,λ) values are monotonically increased ac-cording to the increase of IMFP. Then, we have fitted H(E,λ) with quintic equation. The results were already shown in Fig. 2 as solid lines. The root mean square (rms) differences for the fits were within 0.2% in the range of λ from 0.2λ to 3λ. Then, H(E,λ) can be ex-pressed by the quintic equation of λ at primary energy E with high accuracy. Over 200 eV, the energy dependence of IMFP can be expressed by the following simple Bethe equation [1] λ E( )=EE 2β ln γE( )p (2) where Ep is the bulk plasmon energy (in eV) of the mate-rial, and β and γ are the fitting parameters for the mate-rial. Then, the energy dependence the reflection coeffi-cient H(E,λ) can be expressed as a function of β and γ. The surface-electronic excitation correction factor fs for EPES can be described as fS = exp −PS α in,E( )[ ] [ ]exp −PS αout,E( ) (3) where Ps is the surface-excitation probabilities (SEP) for electrons entering or leaving the solid. αin is the electron incident angle to the surface normal and αout is the angle −196− Journal of Surface Analysis Vol.15, No. 2 (2008) pp. 195−199 S. Tanuma et al. Estimation of Inelastic Mean Free Paths in Au and Cu from Their Elastic Peak Intensity Ratios without IMFP Values of Reference Material in The 200 – 5000 eV Energy Range of detected electrons. In the present study, 0 and 42.3 degrees were used for αin and αin, respectively. Werner et al. [12] proposed the following formula for estimating the SEP in a material based on the Oswald equation [13]. PS =1a E cos α( )+1 (4) where α is the angle of electron incidence or emission with respect to the surface normal and a is a material parameter. From equations (1) to (4), then, the intensity ratio of elastically backscattered primary electrons for Au and Cu, IAu/ICu, can be expressed by the following equation using three parameters a, β and γ for the material over 200 eV energy region. ( )( )( ) ( )[ ]( ) ( )[ ]( ){ }( ){ }EEEHEEEHaEEaaEEaHHffIICuCuCupAuAuAupCuCuAuAuCuAuCusAuSCuAuγβγβλλlnln174.0111exp174.0111exp2,2,×+−+−+−+−≈=⎟⎟⎠⎞⎜⎜⎝⎛ (5) where H can be expressed by the quintic equation of λ or E/Ep2β ln(γE), and their coefficients at energy E were determined by the curve fits as stated above. Then, we optimized the two sets of three parameters (a, β and γ for Au and Cu) in the 200 – 5000 eV energy range so as to Σ{(IAu/ICu)cal/(IAu/ICu)obs−1}2→min with “solver” command in EXCEL. The calculated results were shown in Fig. 3 as a solid line. We see that the cal-culated values with Eq (5) are in excellent agreement with the measured value. Their rms difference was about 4.3%. The dotted line showed the EPIs without sur-face-electronic excitation contribution, and these are, of course, smaller than those of measured one. However over 2000 eV, their differences are small. 00.0050.010.0150.020.0250.030 0.5 1 1.5 2 2.5 3Au200eV500eV1000eV5000eVReflection coefficient H(λ)Normalized IMFP λ/λopt 00.0050.010.0150.020.0250.030.0350 0.5 1 1.5 2 2.5 3Cu200eV500eV1000eV5000eVReflection coefficient H(λ)Normalized IMFP λ/λopt Fig. 2. Dependence of the theoretical reflection coefficient H(l) on the normalized IMFPs for Au and Cu at several energies. Solid marks show the calculated reflection coefficient at sev-eral electron energies by MC method. The solid lines show the The resulting IMFPs of Au (β = 0.0159, γ = 0.456) and Cu (β = 0.0111, γ = 0.106) were shown in Fig. 4 together with optical IMFPs (solid line) which were calculated 012345100 1000 104mesauredoptimizedHAu/HCuElatsic peak intensity ratio I Au/I CuElectron energy (eV) Fig. 3. Calculated elastic peak intensity (EPI) ratios ,IAu/ICu, for Au to Cu with Monte Carlo calculations as a function of pri-mary electron energies. The solid line shows the results of optimization with the proposed method and solid circles show the measured peak intensity ratios. The dotted line indicates the EPIs without surface-electronic excitation correction factor. −197− Journal of Surface Analysis Vol.15, No. 2 (2008) pp. 195−199 S. Tanuma et al. Estimation of Inelastic Mean Free Paths in Au and Cu from Their Elastic Peak Intensity Ratios without IMFP Values of Reference Material in The 200 – 5000 eV Energy Range from their energy loss function with Penn algorithm. On both elements, the resulting IMFPs were in good agree-ment with optical IMFPs over 1000 eV. The resulting IMFPs for Cu were smaller than those of optical values especially under 1000 eV. Their rms relative differences between IMFPs in this study and those of optical were 12.5% for Au and 8.4% in the 200 – 5000 eV energy range. These values are slightly larger than the results of IMFP determination with EPES using Ni standard [13]. In this energy region, surface-electronic excitation ef-fect may play important roll. Then, Fig. 5 shows the re-sulting ratio of surface-electronic excitation factors fSAu/fSCu (aAu = 0.402, aCu = 0.191) together with that of Werner (aAu = 0.260, aCu = 0.346) [12]. Form this figure, we see that the SEE on present work was larger than the unity by 20 to 30% under 1000 eV energy range. On the other hand, its effect was smaller than unity over 200 to 5000 eV in Werner results. This is due to the difference of order of the magnitude of surface-electronic excitation effect of Au and Cu on both studies. The details will be discussed elsewhere [14]. 0.40.60.811.21.41.6fAu/fCufAufCufAu/fCu :WernerfAu wernerfCu werner10 3 10 4Surface excitation factor f s and the ratio f sAu/f sCuElectron energy (eV) 01020304050100 1000 104optical IMFPpresent workInelastic mean free paths (Å)Electron energy (eV)Au 0102030405060100 1000 104optical IMFPpresent workInelastic mean free paths (Å)Electron energy (eV)Cu Fig. 4. IMFP values (solid circles) for Au and Cu determined from elastic peak intensity ratios in Fig. 3 as a function of elec-tron energy. The solid line shows IMFPs calculated from Penn l i h i h i l l f i f dFig. 5. The energy dependence of the surface-electronic excita-tion factor fs for Au and Cu, and their ratios (fAu/fCu). The solid line shows the fAu/fCu in the present work. The dotted line shows the calculated fAu/fCu from Werner equation and his a values for Au and Cu. The solid circles and squares represent the fAu and fCu determined present study. The open circles and squares show the fAu and fCu calculated from Werner equation and his a values for Au and Cu. In summary we have determined electron IMFPs of Au and Cu in the 200 – 5000 eV from their elastic peak intensity ratios without reference IMFP values. This used method does not require the IMFP values of the refer-ence material. The resulting IMFPs of Au and Cu were in good agreement with their optical IMFPs(rms differences for Au was 12.5% and that for Cu was 8.4%). This method must be useful to measure the IMFPs of wide variety of materials with EPES in wide energy range. −198− Journal of Surface Analysis Vol.15, No. 2 (2008) pp. 195−199 S. Tanuma et al. Estimation of Inelastic Mean Free Paths in Au and Cu from Their Elastic Peak Intensity Ratios without IMFP Values of Reference Material in The 200 – 5000 eV Energy Range References [10] S. Tanuma, T. Shiratori, T. Kimura, K. Goto, S. Ichimura, and C. J. Powell, Surf. Interface Anal. 37, 833 (1994). [1] S. Tanuma, C. J. Powell, and D. R. Penn, Surf. Inter-face Anal. 11, 577 (1988). [11] A. Jablonski, F. Salvat, and C. J. Powell, NIST Elec-tron Elastic-Scattering Cross-Section Database, version 3.1, Standard Reference Database 64, U.S. Department of Commerce, National Standards and Technology, Gaithersburg, MD (2003). [2] S. Tanuma, C. J. Powell, and D. R. Penn, Surf. Inter-face Anal. 17, 911 (1991). [3] S. Tanuma, C. J. Powell, and D. R. Penn, Surf. Inter-face Anal. 36, 1 (2005). [4] S. Tanuma, C. J. Powell, and D. R. Penn, Surf. Inter-face Anal. 17, 929 (1991). [12] W. S. M. Werner, W Smekal, C Tomastik, and H Stori., Surf. Sci. 486, L461 (2001). [5] S. Tanuma, C. J. Powell, and D. R. Penn, Surf. Inter-face Anal. 21 165 (1994). [13] R. Oswald, Doctoral Dissertation, University of Tubingen, 1997. [6] G. Gergely, Prog. Surf. Sci. 71, 31 (2002). [7] D. R. Penn, Phys. Rev. B, 35, 482 (1987). [14] S. Tanuma, H. Yoshikawa, N. Okamoto, and K. Goto (to be published). [8] K. Goto, N. Sakakibara, and Y. Sakai, Microbeam Anal. 2, 123 (1993). [9] Y. Takeichi and K. Goto, Surf. Interface Anal. 25 17 (1997). −199− 10 Figure captions. Fig.1. Ratios of measured elastic peak intensities for Au to Cu as a function of primary electron energy. Fig.2. Dependence of the theoretical reflection coefficient H(λ) on the normalized IMFPs for Au and Cu at several energies. Solid marks show the calculated reflection coefficent at several electron energies by MC method. The solid lines show the curve ft results with the quintic equation of normalized λ. Fig.3. Calculated elastic peak intensity (EPI) ratios ,IAu/ICu , for Au to Cu with Monte Carlo calculations as a function of primary electron energies. The solid line shows the results of optimization with the proposed metho and solid circles show the measured peak intensity ratios. The dotted line indicates the EPIs without surface-electronic excitation correction factor. Fig.4. IMFP values (solid circles) for Au and Cu determined from elastic peak intensity ratios in Fig.3 as a function of electron energy. The solid line shows IMFPs calculated from Penn algorithm using the optical energy loss functions of Au and Cu. Fig.5. The energy dependence of the surface-electronic excitation factor fs for Au and Cu, and their ratios (fAu/fCu). The solid line shows the fAu/fCu in the present work. The 11 dotted line shows the calculated fAu/fCu from Werner equation and his a values for Au and Cu. The solid circles and squares represent the fAu and fCu determined present study. The open circles and squares show the fAu and fCu calculated from Werner equation and his a values for Au and Cu.<< /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Error /CompatibilityLevel 1.4 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJDFFile false /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /CMYK /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams false /MaxSubsetPct 100 /Optimize true /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments true /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 300 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /Description << /CHS /CHT /DAN /DEU /ESP /FRA /ITA /JPN /KOR /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. 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