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The inelastic mean free path and the inelastic scattering cross-section of electrons in GaAs determined from highly resolved electron energy spectra
Surface Science 402–404 (1998) 491–495
The inelastic mean free path and the inelastic scattering cross-section of electrons in GaAs determined from highly resolved electron energy spectra M. Krawczyk a,*, A. Jablonski a, S. Tougaard b, J. Toth c, D. Varga c, G. Gergely d a Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland b Physics Department, Odense University, DK 5230-Odense M, Denmark c Research Institute for Nuclear Physics, Hungarian Academy of Sciences, ATOMKI, P.O. Box 51, H-4001 Debrecen, Hungary d Research Institute for Technical Physics, Hungarian Academy of Sciences, P.O. Box 76, H-1325 Budapest, Hungary Received 30 July 1997; accepted for publication 29 September 1997
Abstract GaAs samples have been studied with a hemispherical analyser of high resolution (type ESA 31). The analyser covers the energy range 10–5000 eV with controlled energy resolution. Prior to measurements, sample surfaces have been exposed to Ar+ ions in order to amorphise the surface layer. This procedure resulted in Ga enrichment (70–85 at.% Ga as determined by XPS ). The elastic peak and EELS spectra were measured in the loss range E−E of 50 eV. The elastic peak intensity ratios of GaAs sample and the Ni l reference were used to determine the IMFP in GaAs. The relations between these ratios and the IMFP have been determined from Monte Carlo simulation of the elastic backscattering effect. The values of the IMFP resulting from this procedure are in reasonable agreement with the literature data. The inelastic scattering cross-sections have been determined using the Tougaard procedure. The energy loss distributions l K are presented in the 0.2–5.0 keV range. © 1998 Elsevier Science B.V. All rights reserved. i Keywords: Amorphous surfaces; Elastic peak electron spectroscopy; Electron energy loss spectroscopy; Electron inelastic mean free path; Gallium arsenide; Inelastic electron scattering cross-section; Monte Carlo simulation
1. Introduction Gallium arsenide is an important material for semiconductor devices and for material research. Generally, surface analysis of solids requires knowledge of two fundamental parameters: the inelastic mean free path of electrons (IMFP), l , i and the inelastic electron scattering cross-section K(E, E ). The IMFP data published by the NIST l * Corresponding author. Fax: (+48) 3912 0238; e-mail: [email protected] 0039-6028/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 97 ) 0 09 3 9 -4
[1,2] in the 50–2000 eV energy range are crucial for quantitative analysis of solid surfaces. Some other theoretical data of the IMFP in GaAs have also been reported for higher energy range of electrons [3–5]. The IMFP is determined by the sum of the electron energy loss processes. The electron energy loss ( EELS ) spectra for GaAs have been measured in the transmission mode at high electron energy [6 ]. However, experimental reflected electron energy loss (REELS ) spectra have been published mainly in the second derivative mode d2N(E )/dE2. They are strongly affected by surface
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M. Krawczyk et al. / Surface Science 402–404 (1998) 491–495
stoichiometry [7,8]. The REELS spectra contain the information on electronic transitions in solids but no data are available on the inelastic scattering probability of electrons K(E, E ). The goal of the l present paper is experimental determination of l i and the product l (E ) · K(E, E ) for GaAs in the i l electron energy range 0.2–5.0 keV. The IMFP values were determined by means of the elastic peak electron spectroscopy ( EPES ) [9–11] using Ni as the reference standard [12,13]. The l (E )K(E, E ) curves for GaAs were determined i l from experimental EELS spectra with background subtraction using the Tougaard procedure [14,15].
2. Experimental Commercially available GaAs(100) wafers have been studied in the present work. The surface was cleaned by Ar+ ion bombardment (2 keV, 10 mA, 5 min), amorphising the surface layer to eliminate the diffraction effects [16 ]. The procedure of ion bombardment was performed in a sample handling chamber. Due to selective sputtering, the surface composition was enriched in Ga [17,18] (70–85 at.%) as evidenced by quantitative XPS [19]. Preparation of the Ni reference sample was described elsewhere [20]. Highly resolved electron energy spectra of the elastic peak and of adjacent loss peaks were measured with a hemispherical analyser (HSA, type ESA 31) [21] operating in the 10–5000 eV range with an adjustable resolution DE between 50 and s 2700 meV. In the present study, resolution of DE =200 meV was used. The FWHM of the s electron gun was 400 meV. The beam current i =2 nA. The analyser was operating in the countp ing mode; the spectra were recorded in the step DE#450 meV, scanned 20 times and averaged. The angle of incidence was 50° and the normal angle of detection was used. The stability of the spectrometer system was 1% during the measurement. The values of intensity ratios I /I (s) at a selected E E electron energy, obtained from the EPES experiments for GaAs, were determined by comparing
the sample elastic peak intensity I with that of E the standard I (s). A possible contamination of the E surface from the residual gases was tested by XPS.
3. Monte Carlo (MC ) evaluation of the EPES experiments The l (E) IMFP values have been deduced from i experimental intensity ratios I /I (s) [9–13,22]. This E E function can be expressed in terms of energy, inelastic mean free path of electrons and Ga surface concentration (c ): Ga I /I (s) =F(E, l , c ). (1) E E i Ga In Eq. (1), l represents a free parameter of the i GaAs sample. The MC algorithm for calculating the backscattering intensities from elements I and E I (s) has been described earlier in detail [22]. In the E present work, this algorithm has been extended to two-component compounds. This procedure was also developed for simulating the electron trajectory in GaAs. The calibration curves have been calculated for the HSA geometry by generating 107 electron trajectories. They were calculated at selected electron energies in the 1–5 keV range and for Ga surface concentrations of 50 at.% and 80 at.%. Calculations were based on the NIST database of differential elastic scattering crosssections [23]. The values of l for the Ni standard i were taken from Tanuma et al. [1,2] for E<2 keV. Above 2 keV the Bethe equation [1,2,24] resulted in IMFP values close to those obtained by Ashley and Tung [3].
4. Results and discussion 4.1. Experimental IMFP values in GaAs Exemplary calibration curves are displayed in Fig. 1 for c of 50 at.% and 80 at.%. These curves Ga were used to determine the IMFP in GaAs from the experimental values of the intensity ratios I /I (Ni). Obtained values of l are plotted in Fig. 2 E E i as a function of energy. Additionally, these experimental data are compared in Fig. 2 with the theoretical data on IMFP published in the literature
M. Krawczyk et al. / Surface Science 402–404 (1998) 491–495
Fig. 1. Exemplary calibration curves resulting from the MC calculations for the GaAs sample surface with c =50 at.% Ga (open circles) and 80 at.% (solid circles). Solid lines represent the fit to the calculated data.
[1–5]. Values of the IMFP obtained in the present work for GaAs are located among four curves with the theoretical IMFP values [1–5]. In fact, the best agreement is observed with the G1 equation [5] and the results of Kwei and Chen [4] extended to 5 kV [24]. Experimental values of the IMFP refer to the GaAs sample with a thin surface layer enriched in Ga. Above 2 keV, the region of surface enrichment seems to Ga smaller than the sampling depth of EPES, and the resulting l i values can be considered within a reasonable approach as the bulk IMFP in GaAs. This assumption is also supported by l (E )K(E, E ) curves for i l GaAs determined from experimental EELS.
493
Fig. 2. Dependence of the IMFP in GaAs on electron energy. Circles: experimental HSA data of the present work; dashed line: Kwei and Chen [4]; dot-dashed line: Gries [5] (based on the G1 equation with fitting parameters k , k =0.0019, 1.30 1 2 and extended to 5 kV ); double dot-dashed line: Ashley and Tung [3]; solid line: Tanuma et al. [1,2] (based on optical data; above 2 kV the Bethe equation was used [24]).
4.2. Inelastic scattering cross-section of electrons in GaAs Fig. 3 shows the l (E )K(E, E ) curves for GaAs i l derived from EELS at various primary electron energies. They represent the inelastic scattering cross-sections of electrons in GaAs. Except for the 0.2 keV spectrum, the other spectra within the higher energy range 1–5 keV are quite similar to those recorded for GaAs in the transmission mode [6 ]. The spectra exhibit four characteristic features evidenced by REELS [8]: (i) the low energy valance-intraband transitions at 3 eV; (ii) the pres-
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M. Krawczyk et al. / Surface Science 402–404 (1998) 491–495
Fig. 3. Inelastic scattering cross-section l K determined for GaAs from the EELS spectra. i
ence of dominant bulk plasmon loss peak at 15.6 eV; (iii) the bulk plasmon loss peak is accompanied by the surface plasmon loss peak (~11 eV ) which is more pronounced in the direction of decreasing energy; (iiii) the 20 eV loss peak is produced by the M core levels of Ga. The 45 spectrum at primary electron energy of 0.2 keV is dominated by surface plasmon losses formed by overlapping both the peaks at 9.8 and ~11 eV. They can be produced partly by the surface enriched in Ga as deduced from the energy of Ga bulk plasmon [25].
5. Conclusions EPES proved to be a useful method for determination of the IMFP in the semiconducting III–V compound GaAs. Experimental l data are in i reasonable agreement with the theoretical values using the Gries model and the model of Kwei and
Chen extrapolated above 2 keV. The inelastic electron scattering cross-sections in GaAs will be useful for quantitative EELS, and also for nondestructive depth profiling and for the line shape analysis [26 ].
Acknowledgements This research program was supported by OTKA TO24133 and TO7274 ( Hungarian National Research Council ), KBN 2PO3B 009 10 (Polish Committee of Science Investigations) and INCO COPERNICUS ERBIC15CT960800 projects.
References [1] S. Tanuma, C.J. Powell, D.R. Penn, Surf. Interface Anal. 17 (1991) 911, 927.
M. Krawczyk et al. / Surface Science 402–404 (1998) 491–495 [2] S. Tanuma, C.J. Powell, D.R. Penn, Surf. Interface Anal. 21 (1994) 165. [3] J.C. Ashley, C.J. Tung, Surf. Interface Anal. 4 (1982) 52. [4] C.M. Kwei, L.W. Chen, Surf. Interface Anal. 11 (1988) 60. [5] W.H. Gries, Surf. Interface Anal. 24 (1996) 38. [6 ] C. v. Festenberg, Z. Physik 227 (1969) 455. [7] J. Massies, P. Etienne, F. Dezaly, N.T. Linh, Surf. Sci. 99 (1980) 121. [8] S.R. Ludeke, A. Koma, J. Vac. Sci. Technol. 13 (1976) 241. [9] A. Jablonski, P. Mrozek, G. Gergely, M. Menyhard, A. Sulyok, Surf. Interface Anal. 6 (1984) 291. [10] A. Jablonski, B. Lesiak, G. Gergely, Phys. Scripta 39 (1989) 363. [11] B. Lesiak, A. Jablonski, G. Gergely, Vacuum 40 (1990) 67. [12] G. Gergely, M. Menyhard, K. Pentek, A. Sulyok, A. Jablonski, B. Lesiak, Cs. Daroczi, Vacuum 46 (1995) 591. [13] G. Gergely, M. Menyhard, K. Pentek, A. Sulyok, A. Jablonski, B. Lesiak, Cs. Daroczi, Surf. Sci. 331 (1995) 1203. [14] S. Tougaard, J. Kraaer, Phys. Rev. B 43 (1991) 1651. [15] S. Tougaard, Surf. Interface Anal. 25 (1997) 137.
495
[16 ] T. Ishiguro, T. Suzuki, N. Suzuki, M. Ozawa, in: Proc XIth Int. Conf. on Electron Microscopy, Kyoto, 1986, p. 353. [17] J.B. Malherbe, Crit. Rev. Solid State Phys. Mater. Sci. 19 (1994) 55. [18] J.B. Malherbe, Crit. Rev. Solid State Phys. Mater. Sci. 19 (1994) 129. [19] A. Jablonski, B. Lesiak, L. Zommer, M.F. Ebel, H. Ebel, Y. Fukuda, Y. Suzuki, S. Tougaard, Surf. Interface Anal. 21 (1994) 724. [20] G. Gergely, M. Menyhard, A. Konkol, Cs.S. Daroczi, J. Loranth, B. Gruzza, A.D. Zeze, in: H.J. Mathieu et al. ( Eds.), Proc. 6th ECASIA, Wiley, Montreux, 1996, p. 663. [21] L. Kover, D. Varga, I. Cserny, J. Toth, K. Tokesi, Surf. Interface Anal. 19 (1992) 9. [22] A. Jablonski, Phys. Rev. B 43 (1991) 7546. [23] NIST Database 64, Nat. Inst. Standards and Techn., Gaithersburg, MD, 1996. [24] A. Jablonski, Surf. Interface Anal. 20 (1993) 317. [25] K. Zeppenfeld, Z. Physik 223 (1969) 32. [26 ] S. Tougaard, A. Jablonski, Surf Interface Anal. 25 (1997) 409.
The inelastic mean free path and the inelastic scattering cross-section of electrons in GaAs determined from highly resolved electron energy spectra M. Krawczyk a,*, A. Jablonski a, S. Tougaard b, J. Toth c, D. Varga c, G. Gergely d a Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland b Physics Department, Odense University, DK 5230-Odense M, Denmark c Research Institute for Nuclear Physics, Hungarian Academy of Sciences, ATOMKI, P.O. Box 51, H-4001 Debrecen, Hungary d Research Institute for Technical Physics, Hungarian Academy of Sciences, P.O. Box 76, H-1325 Budapest, Hungary Received 30 July 1997; accepted for publication 29 September 1997
Abstract GaAs samples have been studied with a hemispherical analyser of high resolution (type ESA 31). The analyser covers the energy range 10–5000 eV with controlled energy resolution. Prior to measurements, sample surfaces have been exposed to Ar+ ions in order to amorphise the surface layer. This procedure resulted in Ga enrichment (70–85 at.% Ga as determined by XPS ). The elastic peak and EELS spectra were measured in the loss range E−E of 50 eV. The elastic peak intensity ratios of GaAs sample and the Ni l reference were used to determine the IMFP in GaAs. The relations between these ratios and the IMFP have been determined from Monte Carlo simulation of the elastic backscattering effect. The values of the IMFP resulting from this procedure are in reasonable agreement with the literature data. The inelastic scattering cross-sections have been determined using the Tougaard procedure. The energy loss distributions l K are presented in the 0.2–5.0 keV range. © 1998 Elsevier Science B.V. All rights reserved. i Keywords: Amorphous surfaces; Elastic peak electron spectroscopy; Electron energy loss spectroscopy; Electron inelastic mean free path; Gallium arsenide; Inelastic electron scattering cross-section; Monte Carlo simulation
1. Introduction Gallium arsenide is an important material for semiconductor devices and for material research. Generally, surface analysis of solids requires knowledge of two fundamental parameters: the inelastic mean free path of electrons (IMFP), l , i and the inelastic electron scattering cross-section K(E, E ). The IMFP data published by the NIST l * Corresponding author. Fax: (+48) 3912 0238; e-mail: [email protected] 0039-6028/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 97 ) 0 09 3 9 -4
[1,2] in the 50–2000 eV energy range are crucial for quantitative analysis of solid surfaces. Some other theoretical data of the IMFP in GaAs have also been reported for higher energy range of electrons [3–5]. The IMFP is determined by the sum of the electron energy loss processes. The electron energy loss ( EELS ) spectra for GaAs have been measured in the transmission mode at high electron energy [6 ]. However, experimental reflected electron energy loss (REELS ) spectra have been published mainly in the second derivative mode d2N(E )/dE2. They are strongly affected by surface
492
M. Krawczyk et al. / Surface Science 402–404 (1998) 491–495
stoichiometry [7,8]. The REELS spectra contain the information on electronic transitions in solids but no data are available on the inelastic scattering probability of electrons K(E, E ). The goal of the l present paper is experimental determination of l i and the product l (E ) · K(E, E ) for GaAs in the i l electron energy range 0.2–5.0 keV. The IMFP values were determined by means of the elastic peak electron spectroscopy ( EPES ) [9–11] using Ni as the reference standard [12,13]. The l (E )K(E, E ) curves for GaAs were determined i l from experimental EELS spectra with background subtraction using the Tougaard procedure [14,15].
2. Experimental Commercially available GaAs(100) wafers have been studied in the present work. The surface was cleaned by Ar+ ion bombardment (2 keV, 10 mA, 5 min), amorphising the surface layer to eliminate the diffraction effects [16 ]. The procedure of ion bombardment was performed in a sample handling chamber. Due to selective sputtering, the surface composition was enriched in Ga [17,18] (70–85 at.%) as evidenced by quantitative XPS [19]. Preparation of the Ni reference sample was described elsewhere [20]. Highly resolved electron energy spectra of the elastic peak and of adjacent loss peaks were measured with a hemispherical analyser (HSA, type ESA 31) [21] operating in the 10–5000 eV range with an adjustable resolution DE between 50 and s 2700 meV. In the present study, resolution of DE =200 meV was used. The FWHM of the s electron gun was 400 meV. The beam current i =2 nA. The analyser was operating in the countp ing mode; the spectra were recorded in the step DE#450 meV, scanned 20 times and averaged. The angle of incidence was 50° and the normal angle of detection was used. The stability of the spectrometer system was 1% during the measurement. The values of intensity ratios I /I (s) at a selected E E electron energy, obtained from the EPES experiments for GaAs, were determined by comparing
the sample elastic peak intensity I with that of E the standard I (s). A possible contamination of the E surface from the residual gases was tested by XPS.
3. Monte Carlo (MC ) evaluation of the EPES experiments The l (E) IMFP values have been deduced from i experimental intensity ratios I /I (s) [9–13,22]. This E E function can be expressed in terms of energy, inelastic mean free path of electrons and Ga surface concentration (c ): Ga I /I (s) =F(E, l , c ). (1) E E i Ga In Eq. (1), l represents a free parameter of the i GaAs sample. The MC algorithm for calculating the backscattering intensities from elements I and E I (s) has been described earlier in detail [22]. In the E present work, this algorithm has been extended to two-component compounds. This procedure was also developed for simulating the electron trajectory in GaAs. The calibration curves have been calculated for the HSA geometry by generating 107 electron trajectories. They were calculated at selected electron energies in the 1–5 keV range and for Ga surface concentrations of 50 at.% and 80 at.%. Calculations were based on the NIST database of differential elastic scattering crosssections [23]. The values of l for the Ni standard i were taken from Tanuma et al. [1,2] for E<2 keV. Above 2 keV the Bethe equation [1,2,24] resulted in IMFP values close to those obtained by Ashley and Tung [3].
4. Results and discussion 4.1. Experimental IMFP values in GaAs Exemplary calibration curves are displayed in Fig. 1 for c of 50 at.% and 80 at.%. These curves Ga were used to determine the IMFP in GaAs from the experimental values of the intensity ratios I /I (Ni). Obtained values of l are plotted in Fig. 2 E E i as a function of energy. Additionally, these experimental data are compared in Fig. 2 with the theoretical data on IMFP published in the literature
M. Krawczyk et al. / Surface Science 402–404 (1998) 491–495
Fig. 1. Exemplary calibration curves resulting from the MC calculations for the GaAs sample surface with c =50 at.% Ga (open circles) and 80 at.% (solid circles). Solid lines represent the fit to the calculated data.
[1–5]. Values of the IMFP obtained in the present work for GaAs are located among four curves with the theoretical IMFP values [1–5]. In fact, the best agreement is observed with the G1 equation [5] and the results of Kwei and Chen [4] extended to 5 kV [24]. Experimental values of the IMFP refer to the GaAs sample with a thin surface layer enriched in Ga. Above 2 keV, the region of surface enrichment seems to Ga smaller than the sampling depth of EPES, and the resulting l i values can be considered within a reasonable approach as the bulk IMFP in GaAs. This assumption is also supported by l (E )K(E, E ) curves for i l GaAs determined from experimental EELS.
493
Fig. 2. Dependence of the IMFP in GaAs on electron energy. Circles: experimental HSA data of the present work; dashed line: Kwei and Chen [4]; dot-dashed line: Gries [5] (based on the G1 equation with fitting parameters k , k =0.0019, 1.30 1 2 and extended to 5 kV ); double dot-dashed line: Ashley and Tung [3]; solid line: Tanuma et al. [1,2] (based on optical data; above 2 kV the Bethe equation was used [24]).
4.2. Inelastic scattering cross-section of electrons in GaAs Fig. 3 shows the l (E )K(E, E ) curves for GaAs i l derived from EELS at various primary electron energies. They represent the inelastic scattering cross-sections of electrons in GaAs. Except for the 0.2 keV spectrum, the other spectra within the higher energy range 1–5 keV are quite similar to those recorded for GaAs in the transmission mode [6 ]. The spectra exhibit four characteristic features evidenced by REELS [8]: (i) the low energy valance-intraband transitions at 3 eV; (ii) the pres-
494
M. Krawczyk et al. / Surface Science 402–404 (1998) 491–495
Fig. 3. Inelastic scattering cross-section l K determined for GaAs from the EELS spectra. i
ence of dominant bulk plasmon loss peak at 15.6 eV; (iii) the bulk plasmon loss peak is accompanied by the surface plasmon loss peak (~11 eV ) which is more pronounced in the direction of decreasing energy; (iiii) the 20 eV loss peak is produced by the M core levels of Ga. The 45 spectrum at primary electron energy of 0.2 keV is dominated by surface plasmon losses formed by overlapping both the peaks at 9.8 and ~11 eV. They can be produced partly by the surface enriched in Ga as deduced from the energy of Ga bulk plasmon [25].
5. Conclusions EPES proved to be a useful method for determination of the IMFP in the semiconducting III–V compound GaAs. Experimental l data are in i reasonable agreement with the theoretical values using the Gries model and the model of Kwei and
Chen extrapolated above 2 keV. The inelastic electron scattering cross-sections in GaAs will be useful for quantitative EELS, and also for nondestructive depth profiling and for the line shape analysis [26 ].
Acknowledgements This research program was supported by OTKA TO24133 and TO7274 ( Hungarian National Research Council ), KBN 2PO3B 009 10 (Polish Committee of Science Investigations) and INCO COPERNICUS ERBIC15CT960800 projects.
References [1] S. Tanuma, C.J. Powell, D.R. Penn, Surf. Interface Anal. 17 (1991) 911, 927.
M. Krawczyk et al. / Surface Science 402–404 (1998) 491–495 [2] S. Tanuma, C.J. Powell, D.R. Penn, Surf. Interface Anal. 21 (1994) 165. [3] J.C. Ashley, C.J. Tung, Surf. Interface Anal. 4 (1982) 52. [4] C.M. Kwei, L.W. Chen, Surf. Interface Anal. 11 (1988) 60. [5] W.H. Gries, Surf. Interface Anal. 24 (1996) 38. [6 ] C. v. Festenberg, Z. Physik 227 (1969) 455. [7] J. Massies, P. Etienne, F. Dezaly, N.T. Linh, Surf. Sci. 99 (1980) 121. [8] S.R. Ludeke, A. Koma, J. Vac. Sci. Technol. 13 (1976) 241. [9] A. Jablonski, P. Mrozek, G. Gergely, M. Menyhard, A. Sulyok, Surf. Interface Anal. 6 (1984) 291. [10] A. Jablonski, B. Lesiak, G. Gergely, Phys. Scripta 39 (1989) 363. [11] B. Lesiak, A. Jablonski, G. Gergely, Vacuum 40 (1990) 67. [12] G. Gergely, M. Menyhard, K. Pentek, A. Sulyok, A. Jablonski, B. Lesiak, Cs. Daroczi, Vacuum 46 (1995) 591. [13] G. Gergely, M. Menyhard, K. Pentek, A. Sulyok, A. Jablonski, B. Lesiak, Cs. Daroczi, Surf. Sci. 331 (1995) 1203. [14] S. Tougaard, J. Kraaer, Phys. Rev. B 43 (1991) 1651. [15] S. Tougaard, Surf. Interface Anal. 25 (1997) 137.
495
[16 ] T. Ishiguro, T. Suzuki, N. Suzuki, M. Ozawa, in: Proc XIth Int. Conf. on Electron Microscopy, Kyoto, 1986, p. 353. [17] J.B. Malherbe, Crit. Rev. Solid State Phys. Mater. Sci. 19 (1994) 55. [18] J.B. Malherbe, Crit. Rev. Solid State Phys. Mater. Sci. 19 (1994) 129. [19] A. Jablonski, B. Lesiak, L. Zommer, M.F. Ebel, H. Ebel, Y. Fukuda, Y. Suzuki, S. Tougaard, Surf. Interface Anal. 21 (1994) 724. [20] G. Gergely, M. Menyhard, A. Konkol, Cs.S. Daroczi, J. Loranth, B. Gruzza, A.D. Zeze, in: H.J. Mathieu et al. ( Eds.), Proc. 6th ECASIA, Wiley, Montreux, 1996, p. 663. [21] L. Kover, D. Varga, I. Cserny, J. Toth, K. Tokesi, Surf. Interface Anal. 19 (1992) 9. [22] A. Jablonski, Phys. Rev. B 43 (1991) 7546. [23] NIST Database 64, Nat. Inst. Standards and Techn., Gaithersburg, MD, 1996. [24] A. Jablonski, Surf. Interface Anal. 20 (1993) 317. [25] K. Zeppenfeld, Z. Physik 223 (1969) 32. [26 ] S. Tougaard, A. Jablonski, Surf Interface Anal. 25 (1997) 409.