# Fileset [07 Vol.14 No.1 9-19.pdf](https://mdr.nims.go.jp/filesets/a974a14a-1b70-40c2-9a89-6e5b34352258/download) ## Creator [田沼 繁夫](https://orcid.org/0000-0003-2628-9941) ## Rights [Creative Commons BY-NC Attribution-NonCommercial 4.0 International](https://creativecommons.org/licenses/by-nc/4.0/) ## Other metadata [オージェ電子分光法における背面散乱補正　I．広い分析条件で使用可能な電子の背面散乱補正式の開発](https://mdr.nims.go.jp/datasets/a545030f-8129-4428-a471-29b3a709464c) ## Fulltext Ł\ŒÊŁª’Í„¤‰ƒ›ï-’ÓŠ¹.inddJournal of Surface Analysis Vol.14, No. 1 (2007) pp. 9-19 I9I* 305-0047 1-2-1 *tanuma.shigeo@nims.go.jp 2007 4 6 ; 2007 5 22AES(MC)Be, B, C, Al, Si, Cu, Zr, Ag, La, Au 1010-30 keV5 keV3-30 keV 0-6010-30 keV MCRMS 10 over-voltage ratio U=1.5-100=0 -60 3% 10 keVIchimura-Shimizu [Surf. Sci. 112, 386 (1981)] MCBackscattering Correction for Auger Electron Spectroscopy I. Development of an Improved Backscattering Correction Equation for Wide Analytical Conditions S. Tanuma*Material analysis station & Advanced nano characterization center, National Institute for Material Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan *Tanuma.Shigeo@nims.go.jp (Received: April 6, 2007; Accepted: May 22, 2007) This paper describes the backscattering correction for Auger quantitative surface analysis. The energy and electron incident angle dependence of backscattering coefficient for 10 elemental solids (Be, B, C, Al, Si, Cu, Zr, Ag, La, Au) were investigated using Monte Carlo (MC) simulations. In conclusions, the back-scattering coefficient at incident angle could be described as cos1.1001.10 84.001.084.001.0where 0 is the backscattering coefficient at incident angle 0 . The Love-Scott equation [J. Phys. D 11, 106 Copyright (c) 2007 by The Surface Analysis Society of Japan 9Journal of Surface Analysis Vol.14, No. 1 (2007) pp. 9-19 I10(1978)] for 0 was superior to the others in wide incident energy range. Using these backscattering coeffi-cient equations, we have proposed an improved equation for backscattering correction in Auger electron spectroscopy, which can be used for wide incident energy range (3-30 keV) and incident angles (0-60 ).The parameters in the equation were determined from the curve fit to the backscattering factors at normal incident angle in the 3, 5, 7.5 and 10 keV electron incident energy calculated by Ichimura-Shizimu [Surf. Sci. 112, 386 (1981)] with MC method. The root mean square (RMS) differences for backscattering factors for 10 elemental solids calculated by Monte Carlo method using continuous slowing down approximation and those from proposed equation were less 3% in the 10-30 keV (over-voltage ratio U=1.5-100 and inci-dent angle =0-60 ). In the 3-10 keV energy range, we have also compared the proposed equation to the calculated values at incident angle 30 and 45 by Ichimura-Shimizu with MC method. We found that they coincide well each other. Then, the proposed equation for backscattering correction could be applied to the quantitative Auger analysis in wide analytical conditions. 1.Auger Electron SpectroscopyIchimura-Shimizu [1]ISO18118 [2]3 10 keV0, 30, 4520-25 keV[3]I 10 keV060 3 keV 30 keVIchimura-Shimizu [4] II 2. R[5]EPMAEPMA 10-30 keV[5].EPMA 0MC2.1. Be, B, C, Al, Si, Cu, Zr, Ag, La, Au 1030, 20, 10 kV0 10 70[6,7]4000[8]22242cos11jjjjvpZZedd (1) p, v, eZj jj Thomas-Fermi Potential Nigam [9]1 j (1)22411vpZZejjjjj (2) Bethe [10]j jjjjJEAZcEsddE 166.1ln1085.7 4gcmkeV 2 (3) 10Journal of Surface Analysis Vol.14, No. 1 (2007) pp. 9-19 I11Jj Z 12 Berger[11] Z<10 Reed [12]cj j Aj (3)E0.25 0<0.2 A 0A=a 0b+c a, b, c84.001.0 1.10A (9) Table 1 Comparison of backscattering coefficient. Incident energy(keV) 25.2 17.3 11 Element MC* EXP** MC* EXP** MC* EXP** Al 0.158 0.151 0.160 0.159 0.176 0.171 Cu 0.310 0.307 0.326 0.310 0.331 0.310 *Monte Carlo method **Experimental value [15] 11Journal of Surface Analysis Vol.14, No. 1 (2007) pp. 9-19 I12Fig. 4(9)0 0.3 A=0.86~0.88Darlington0 00cos1.1001.10 84.001.084.001.0 (10) 10 keV3 keV 30 keVEPMA 10 keVReuter [17], Love-Scott [18], Tomlin[19] 010 keV Fitting [20], Reimer [21]Murata [22,23] Au, Cu, Al. 1-10 keVLove-Scott1-10 keV0Love-ScottFig. 1. Electron backscattering coefficient at 10 keV elec-trons for 10 elemental solids (B, C, Al, Si, Ti, Cu, Zr, Ag, La, and Au) as functions of electron incident angle. The values were calculated from Monte Carlo simulation using continuous slowing down approximation. Fig. 2. Electron backscattering coefficient at 20 keV elec-trons for 10 elemental solids as functions of electron incident angle. See caption to Fig. 1. Fig. 3. Electron backscattering coefficient at 30 keV elec-trons for 10 elemental solids as functions of electron incident angle. See caption to Fig. 1. Fig. 4. Curve fit results of A values in =A( 0/A)cos [equation (8)] from the data in Figs. 1-3 as a function of backscattering coefficient 0 at normal incident angle. means the incident angle from surface normal. Solid line shows A=0.01 0-1.1+0.84 [equation (9)]. 12Journal of Surface Analysis Vol.14, No. 1 (2007) pp. 9-19 I1320ln1 020200EZG (11) 432201000716.067373.148371.1503791.52ZZZ (11a) 42201015498.0289.308.1112)(ZZZG (11b) Z3.3. E ,EmE Em10, 20, 30 keV Fig. 50E /E0, Em /E0 0.1000 153.0EE (12) 00m 27.1152.0EE (13) 0.994, 0.9920.530.5-4 keV Fitting [20]0.52 1 keV 30 keV3.4. RR(0)[24]. PBPBIIR 11 (14) QQQGreen-Cosslett [24]UUQEnl ln2 (15) Enl nlEnl over-voltage ratio UBU0 ,(12), (13)10B kUU (16) k P B00 111UkUlnkUUln BBBBP00UUlnPBP, B(14) .Fig. 5. Mean and median values of backscattered electron for 10 elemental solids at 10, 20, and 30 keV incident electron energy versus backscattering coefficient . Open squares and circles show the ratios of mean value of backscattered electron to incident energy and the ratios of median value of backscat-tered electron to incident energy Em /E0, respectively. The solid line shows the curve fit results [eqs. (12) and (13)]. 13Journal of Surface Analysis Vol.14, No. 1 (2007) pp. 9-19 I142001001111111lnUbUaUlnkUlnkRPBpB (17) a(U0), b(U0) U01,2 UB3-10 keV[2] RBetheIchimura-Shimizu [4]Thomas-Fermi-Dirac 0R a, b1=1 2 =1.27 Fig. 63, 5, 7.5, 10 keVa, bover-voltage ratio U1/U, 1/lnU, ln(1/U) Fig. 6. Curve fit results of equations (17), (18a), and (18b) to the backscattering factors at normal incident angle calculated from MC method by Ichimura-Shimizu [4]. The parameter a and b are described by 2000 1606.21028.6727.2 UUUa ,40302000 1ln109.01ln007.11ln688.21ln816.1933.2 UUUUUbwhere U is the over-voltage ratio. The constants in the above equations were determined from the curve fits. The solid line shows the curve fit results. Solid marks were cited from Ichimura-Shimizu [4]; : Eb=0.1 keV, : Eb=0.5 keV, : Eb=1.0 keV, : Eb=2.0 keV. 14Journal of Surface Analysis Vol.14, No. 1 (2007) pp. 9-19 I152000 1606.21028.6727.2 UUUa (18a) 403020001ln109.01ln007.11ln688.21ln816.1933.2UUUUUb (18b) 3.5. R0= 0/cosR( ) (14)cosUQUQRPBBPB011 (19) (12), (13)UB=kU0(1+ )(17)27.11lncos1100 UbUaR (20) 2000 1606.21028.6727.2 UUUa (20a) 403020001ln109.01ln007.11ln688.21ln816.1933.2UUUUUb (20b) cos1.1001.10 84.001.084.001.0 (20c) 20ln1 020200EZG (20d) Fig. 7. Comparison of calculated backscattering factors at 30 incident angle with MC method by Ichimura-Shimizu [4] and those from the proposed equations for R [Eqs. (20)-(20g)]. The data of : Eb=0.1 keV, :Eb= 0.5 keV, : Eb=1.0 keV, and : Eb=2.0 keV are cited from Ichimura-Shimizu [4]. Solid line shows the calculated values from equations (20) and (20a-g). 15Journal of Surface Analysis Vol.14, No. 1 (2007) pp. 9-19 I16432201000716.067373.148371.1503791.52ZZZ (20e) 42201015498.0289.308.1112)(ZZZG (20f) U0E0Enl (20g) Enl nlE0 Z(20)(20)-(20g)10, 20, 30 keVBe, B, C, Al, Si, Cu, Zr, Ag, La, AuRMS0-60 , over-voltage ratio U=1.5-100RMS 3 (20)0-60 10-30 keV3-10 keVIchimura 30 , 45MC [4]Fig. 7 30 Fig. 8 45(20) Ichimuraover-voltage ratio, 10 keV30 , 45AES [25]4.AESBe, B, C, Al, Si, Cu, Zr, Ag, La, Au 10 Fig. 8. Comparison of calculated backscattering factors at 45 incident angle with MC method by Ichimura-Shimizu [4] and those from the proposed equations for R [Eqs. (20)-(20g)]. The data of : Eb=0.1 keV, :Eb= 0.5 keV, : Eb=1.0 keV, and : Eb=2.0 keV are cited from Ichimura-Shimizu [4]. Solid line shows the calculated values from equations (20) and (20a-g). 16Journal of Surface Analysis Vol.14, No. 1 (2007) pp. 9-19 I170 0cos1.1001.10 84.001.084.001.00 Love-Scott10-30 keV0(12), (13)5 keV3-30 keV 0-60R 10-30 keVMC RMS10 over-voltage ratio U=1.5-100 , 0-60 3%10 keVIchimura-Shimizu MCR (20)5.25MC 4000AES 20 keVTIFNIMSNIMS6.[1] S.Ichimura, R. Shimizu, and J. P. Langeron, Surf. Sci.124, L49 (1983). [2] ISO 18118:2004 -Surface chemical analysis - Auger electron spectroscopy and X-ray photoelectron spectroscopy - Guide to the use of experimentally determined relative sensitivity factors for the quan-titative analysis of homogeneous materials.[3] Scanning Auger Electron Microscopy, ed. by M. Prutton and M, El Gomati, pp. 329-330, John Wiely & Sons, Chichester (2006). [4] S. Ichimura and R. Shimizu, Surf. Sci. 112, 386 (1981). [5] S. J. B. Reed, in Electron Microprobe Analysis, p. 205, Cambridge University Press (1975). [6] A. Jablonski, Prog. Surf. Sci. 79, 3 (2005). [7] L. Reimer, H. Gilde, and K. H. Sommer, Optik 27, 86 (1968). [8] , 87 (1981 .[9] B. P. Nigam, M. K. Sandaresan, and Ta-You Wu, Phys. Rev. 115, 491 (1959). [10] H. E. Bishop, NBS Special Publication 460, 5 (1976). [11] M. J. Berger and S. M. Seltzer, Natl. Acad. Sci. Natl. Res. Council Pub. 113, 205 (1964). [12] S. J. B. Reed, in Electron Microprobe Analysis, p. 221, Cambridge Univ. Press (1975). [13] T. Rao-Sahib and D. B. Wittry, J. Appl. Phys. 45,5060 (1974). [14] M. Gryzinski, Phys. Rev. A 138, 336 (1965). [15] H. Drescher, L. Reimer, and H. Seidel, Z. Angew. Phys. 29, 331 (1970). [16] E. H. Darlington, J. Phys. D 8, 85 (1975). [17] W. Reuter, in Proc. 6th Intern Cnf. on X-ray Optics and Microanalysis, ed. by G. Shinoda, K. Kohra and T. Ichiokawa, p. 121, Univ. of Tokyo Press, Tokyo (1972). [18] G. Love and V. E. Scott, J. Phys. D 11, 106 (1978). [19] S. G. Tomlin, Proc. Phys. Soc. London 92, 465 (1963). [20] H. J. Fitting, J. Phys. D 8, 1480 (1975). [21] L. Reimer, in Scanning Electron Microscopy: Sys-tems and Applications, p. 120, The Institute of Physics, London (1973). [22] M. Kotera, K. Murata, and K. Nagami, J. Appl. Phys.52, 997 (1981). 17Journal of Surface Analysis Vol.14, No. 1 (2007) pp. 9-19 I18[23] M. Kotera, K. Murata, and K. Nagami, J. Appl. Phys.52, 7403 (1981). [24] M. Green and V. E. Cosslett, Proc. Phys. Soc. Lon-don 78, 1206 (1961). [25] J. Surf. Anal. (to be submitted).130 kVJSA1-1i (17)(19) (20){ i}2AESJSA2-1(16), (17) (12) (13)0 0(20) 060 0RMS ~3%(12), (13)0(17) a, b(12), (13)2-2(17)(17)a b2-2-1(14)(17)a b2-2-2a b 1/lnU (16)1/lnU1/lnU ab 1/lnUa b (1/U)nlnU Taylar18Journal of Surface Analysis Vol.14, No. 1 (2007) pp. 9-19 I19(17) a, b0ln1UkkaPB0ln1UkbPBa, b 1/U, ln(1/U), 1/lnU 14AIC42-314 4-7UB(17)(12) (13) 0 2(18) a b2519