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On the energy dependence of the escape depth for electrons
Surface Science 0 North-Holland
65 (1977) 345-348 Publishing Company
LETTERS TO THE EDITOR ON THE ENERGY DEPENDENCE OF THE ESCAPE DEPTH FOR ELECTRONS Received
2 December
1976; manuscript
received
in final form 4 March 1977
Using synchrotron radiation, Pianetta et al. have demonstrated that the ratio of surface-to-bulk photoemission intensities depends strongly on photon energies [ 11. It is convincing that they concentrated on the ratio of intensities of the surface oxide peak to the non-oxidized peak of the same element because the effects due to cross-section changes for different photon energies are minimized [ 11. From their experimental results we intend to get the information on the escape depth for electron. Pianetta et al. have presented photoemission spectra of heavily oxidized GaAs (110) as a function of photon energy [ 11. They estimated that the oxygen coverage of that surface was about 0.5 monolayer. The ratio of surface-to-bulk emission intensities of that system is given by the ratio of the As 3d oxide peak area to the non-oxidized As 3d peak area, I(As ox/As)sd. The peak areas are obtained as follows. At first each spectrum of Pianetta et al. is magnified by projection. Then, subtracted is the background from inelastically scattered electrons which is proportional to the spectrum intensity integrated from the starting point where the background is zero to the considered point. Finally, the spectrum is decomposed into skew Gaussian functions, which represent oxidized and non-oxidized As 3d peaks, by the iterative least-squares procedure [2]. Fig. 1 shows I(As ox/As)sd, which is reproduced as mentioned above from fig. 2 of ref. [ 11, as a function of the kinetic energy, E,, of the electron inside the solid which is photoexcited from the 3d level of the oxidized As. The kinetic energy E, is given by Es = hv - EB(As ox)ad,
(1)
where hv is the incident X-ray energy and AB(As ox)ad is the binding energy of an electron in the 3d level of the oxidized As. The accuracy of each value of I(As ox/As)sd is represented by the vertical error bar in fig. 1. The schematic diagram inserted in fig. 1 shows the model of the surface partially covered by the oxide overlay of the thickness d and the coverage 8. It is assumed that the three step model of the photoemission [3,4] is applicable for such a thin surface layer. Then, the electrons which pass through the materials without any energy loss decay by the factor exp(-x/X), where x is the distance the electron travelled and h is the mean-free-path for inelastic scattering. The mean-free-path h is assumed to vary as X=CE”,
(2) 345
i’
0
50
100 KINETIC
I50 ENLRGY
200
250
ES ieVI
Fig. 1. The ratio of the peak areas. &As ox/As)~d as a function of the kinctic energy t:‘,. i-xpsricurve sho\vs rncntal results (A) are reproduced from fig. 2 of Pianetta et al. 111.The calculated the best fitted function I(s/b) to the exptxirnental results (see text). Inset shows the model of the surface partially covered by the overlay.
where C is a constant and E is the kinetic energy of the electron. As usual for the first order ap~roxii~latio~~ the values of C arc assun~ed to be equal fog-the bulk &LAS and the oxide layer. If it is further assumed that the photoioni/ation cross sections and the densities are the same for both chemical states of As, one gets the ratio of surface-tab-buIk emission illte~lsities I(q’b) as follows:
where k E d/C cos 0, if, represents the kinetic energy for an electron emitted from non-oxidized As, 8 is the ejection angle of a photoelectron from the surface nornlal and LW is the solid-angle aperture of the spectrometer. For the first order approximation. we assume that 0 does not depend ou E, or Et, for the energy range investigated (SOL200 eV). As the binding energy of the 3d level of the oxidized As is chemically shifted by 4.5 eV toward the higher energy side [ I] ( the following relation exists, Et, = Es + 4.5.
(4)
H. Iwasaki, S. Nakamura /Energy
dependence
of escape depth for electrons
347
Table 1 The least root-mean values
squares,
6, and the optimum
values of 0 and (h cos o/d)1 00 for a set of n
n
6(X 10-Z)
e
(A cos G/d) 1 OO
lb/b)
0.5
1.1 0.70 0.40 0.58 1.0 5.0
0.59 0.58 0.58 0.57 0.57 0.57
0.52 0.47 0.44 0.42 0.40 0.21
0.34 0.28 0.23 0.19 0.15 0.02
0.6 0.7 0.8 0.9 2.0 a Extrapolated
12 15a
values of Z(s/b) for Es = 1215 eV.
The function I(s/b) which contains the parameters 0 and k is fitted to the experimental results using an iterative least-squares procedure [S] for each value of n. The values of the root-mean square deviation between the calculated and observed values, F, and f3in the best fit condition for each value of n are summarized in table 1. Instead of the optimum values of k, the values of X cos g/d, which are equal to E”/k from eq. (2), are shown in table 1 for, e.g., E = 100 eV. Taking into account of the error in reading the spectra of Pianetta et al. of about 0.01, we may conclude that iz = 0.7 f 0.1.
(5)
The calculated profile of I(s/b) for n = 0.7 is shown in fig. 1 by the solid curve. Also the extrapolated values of [(s/b) for Es = 1215 eV are calculated using eq. (3) and shown in table 1. E,= 1215 eV corresponds to the kinetic energy of a photoelectron excited from the As 3d level by the Mg Ko radiation. From table 1 it may be seen that the ratio of surface-to-bulk emission intensities using Mg Kcu radiation from an about 0.6 monolayer covered GaAs surface is 0.23 * 0.05. The theoretical estimate by Penn [6] indicates that IZ= 0.8 for kinetic energies from about 300 to 2000 eV. Present results suggest that the X versus log E curve estimated by Penn may be expanded nearly straightly to lower kinetic energies about 50 eV. However, it needs more experimental and theoretical work to exclude the possibility that X varies as I?‘.‘, which was derived by Quinn [7] and Powell [8]. The optimum values of 0 and k are 0.58 and 56.8 respectively, for n = 0.7. The 10% changes of the 0 and k increase the value of 6 by a factor of about 30-50 and 5, respectively. The value of 8 of 0.57-0.58 is in good agreement with the estimation of the saturation coverage of 60% of a monolayer for the vacuum cleaved GaAs(110) [9]. It may be seen from table 1 that (X cos G/d),,, For,
e.g.,
d =
= 0.44 * 0.03.
(6)
5 A, X cos 0 = 2.2 A. Probably the value of d represents the effective
348
H. Iwasaki, S. Nakamura /Energy
dependence
of escape depth for electrons
thickness of the overlay rather than the geometrical thickness. In passing it might be noticed that the values 0 and (X cos 07/d)sO_200 vary rather slightly for the variation of n. This letter has shown that the experimental data of [(s/b) as a function 01’1~ may be useful for the rigorous understanding of the electron escape depth. The authors would like to express their appreciation to Mr. Nishitani and Dr. Mizokawa for fruitful discussions. This work was partially supported by the GrantAid for Special Research Programme of Surface Electronics from the Ministry of Education of Japan.
Institute
ofScitxtifTc
Hiroshi and Industrial
Research,
IWASAKI
and Shogo
NAKAMURA
Osaka Universit~~, Suita, Osaka 565,
Japan
References [l] P. Pianetta, I. Lindau, C. Garner and W.E. Spicer, Phys. Rev. Letters 35 (1975) 1356. [2] R.D.B. Fraser and E. Suzuki, in: Biological Applications, Spectral Analysis, Ed. J.A. Blackburn (Dekker, New York, 1970). [3] W.E. Spicer, Phys. Rev. 112 (1958) 114. [4] P.J. Feibelman and D.E. Eastman, Phys. Rev. BlO (1974) 4932. [5] J.M. McCormick and M.G. Salvadri, Numerical Methods in FORTRAN (Prentice-Hall, 1964). [6] D.R. Penn, J. Vacuum Sci. Technol. 13 (1976) 211. [7] J.J. Quinn, Phys. Rev. 126 (1962) 1453. (81 C.J. Powell, Surface Sci. 44 (1974) 29. [9] R. Dorn, H. Liith and G.J. Russell, Phys. Rev. BlO (1974) 5049.
65 (1977) 345-348 Publishing Company
LETTERS TO THE EDITOR ON THE ENERGY DEPENDENCE OF THE ESCAPE DEPTH FOR ELECTRONS Received
2 December
1976; manuscript
received
in final form 4 March 1977
Using synchrotron radiation, Pianetta et al. have demonstrated that the ratio of surface-to-bulk photoemission intensities depends strongly on photon energies [ 11. It is convincing that they concentrated on the ratio of intensities of the surface oxide peak to the non-oxidized peak of the same element because the effects due to cross-section changes for different photon energies are minimized [ 11. From their experimental results we intend to get the information on the escape depth for electron. Pianetta et al. have presented photoemission spectra of heavily oxidized GaAs (110) as a function of photon energy [ 11. They estimated that the oxygen coverage of that surface was about 0.5 monolayer. The ratio of surface-to-bulk emission intensities of that system is given by the ratio of the As 3d oxide peak area to the non-oxidized As 3d peak area, I(As ox/As)sd. The peak areas are obtained as follows. At first each spectrum of Pianetta et al. is magnified by projection. Then, subtracted is the background from inelastically scattered electrons which is proportional to the spectrum intensity integrated from the starting point where the background is zero to the considered point. Finally, the spectrum is decomposed into skew Gaussian functions, which represent oxidized and non-oxidized As 3d peaks, by the iterative least-squares procedure [2]. Fig. 1 shows I(As ox/As)sd, which is reproduced as mentioned above from fig. 2 of ref. [ 11, as a function of the kinetic energy, E,, of the electron inside the solid which is photoexcited from the 3d level of the oxidized As. The kinetic energy E, is given by Es = hv - EB(As ox)ad,
(1)
where hv is the incident X-ray energy and AB(As ox)ad is the binding energy of an electron in the 3d level of the oxidized As. The accuracy of each value of I(As ox/As)sd is represented by the vertical error bar in fig. 1. The schematic diagram inserted in fig. 1 shows the model of the surface partially covered by the oxide overlay of the thickness d and the coverage 8. It is assumed that the three step model of the photoemission [3,4] is applicable for such a thin surface layer. Then, the electrons which pass through the materials without any energy loss decay by the factor exp(-x/X), where x is the distance the electron travelled and h is the mean-free-path for inelastic scattering. The mean-free-path h is assumed to vary as X=CE”,
(2) 345
i’
0
50
100 KINETIC
I50 ENLRGY
200
250
ES ieVI
Fig. 1. The ratio of the peak areas. &As ox/As)~d as a function of the kinctic energy t:‘,. i-xpsricurve sho\vs rncntal results (A) are reproduced from fig. 2 of Pianetta et al. 111.The calculated the best fitted function I(s/b) to the exptxirnental results (see text). Inset shows the model of the surface partially covered by the overlay.
where C is a constant and E is the kinetic energy of the electron. As usual for the first order ap~roxii~latio~~ the values of C arc assun~ed to be equal fog-the bulk &LAS and the oxide layer. If it is further assumed that the photoioni/ation cross sections and the densities are the same for both chemical states of As, one gets the ratio of surface-tab-buIk emission illte~lsities I(q’b) as follows:
where k E d/C cos 0, if, represents the kinetic energy for an electron emitted from non-oxidized As, 8 is the ejection angle of a photoelectron from the surface nornlal and LW is the solid-angle aperture of the spectrometer. For the first order approximation. we assume that 0 does not depend ou E, or Et, for the energy range investigated (SOL200 eV). As the binding energy of the 3d level of the oxidized As is chemically shifted by 4.5 eV toward the higher energy side [ I] ( the following relation exists, Et, = Es + 4.5.
(4)
H. Iwasaki, S. Nakamura /Energy
dependence
of escape depth for electrons
347
Table 1 The least root-mean values
squares,
6, and the optimum
values of 0 and (h cos o/d)1 00 for a set of n
n
6(X 10-Z)
e
(A cos G/d) 1 OO
lb/b)
0.5
1.1 0.70 0.40 0.58 1.0 5.0
0.59 0.58 0.58 0.57 0.57 0.57
0.52 0.47 0.44 0.42 0.40 0.21
0.34 0.28 0.23 0.19 0.15 0.02
0.6 0.7 0.8 0.9 2.0 a Extrapolated
12 15a
values of Z(s/b) for Es = 1215 eV.
The function I(s/b) which contains the parameters 0 and k is fitted to the experimental results using an iterative least-squares procedure [S] for each value of n. The values of the root-mean square deviation between the calculated and observed values, F, and f3in the best fit condition for each value of n are summarized in table 1. Instead of the optimum values of k, the values of X cos g/d, which are equal to E”/k from eq. (2), are shown in table 1 for, e.g., E = 100 eV. Taking into account of the error in reading the spectra of Pianetta et al. of about 0.01, we may conclude that iz = 0.7 f 0.1.
(5)
The calculated profile of I(s/b) for n = 0.7 is shown in fig. 1 by the solid curve. Also the extrapolated values of [(s/b) for Es = 1215 eV are calculated using eq. (3) and shown in table 1. E,= 1215 eV corresponds to the kinetic energy of a photoelectron excited from the As 3d level by the Mg Ko radiation. From table 1 it may be seen that the ratio of surface-to-bulk emission intensities using Mg Kcu radiation from an about 0.6 monolayer covered GaAs surface is 0.23 * 0.05. The theoretical estimate by Penn [6] indicates that IZ= 0.8 for kinetic energies from about 300 to 2000 eV. Present results suggest that the X versus log E curve estimated by Penn may be expanded nearly straightly to lower kinetic energies about 50 eV. However, it needs more experimental and theoretical work to exclude the possibility that X varies as I?‘.‘, which was derived by Quinn [7] and Powell [8]. The optimum values of 0 and k are 0.58 and 56.8 respectively, for n = 0.7. The 10% changes of the 0 and k increase the value of 6 by a factor of about 30-50 and 5, respectively. The value of 8 of 0.57-0.58 is in good agreement with the estimation of the saturation coverage of 60% of a monolayer for the vacuum cleaved GaAs(110) [9]. It may be seen from table 1 that (X cos G/d),,, For,
e.g.,
d =
= 0.44 * 0.03.
(6)
5 A, X cos 0 = 2.2 A. Probably the value of d represents the effective
348
H. Iwasaki, S. Nakamura /Energy
dependence
of escape depth for electrons
thickness of the overlay rather than the geometrical thickness. In passing it might be noticed that the values 0 and (X cos 07/d)sO_200 vary rather slightly for the variation of n. This letter has shown that the experimental data of [(s/b) as a function 01’1~ may be useful for the rigorous understanding of the electron escape depth. The authors would like to express their appreciation to Mr. Nishitani and Dr. Mizokawa for fruitful discussions. This work was partially supported by the GrantAid for Special Research Programme of Surface Electronics from the Ministry of Education of Japan.
Institute
ofScitxtifTc
Hiroshi and Industrial
Research,
IWASAKI
and Shogo
NAKAMURA
Osaka Universit~~, Suita, Osaka 565,
Japan
References [l] P. Pianetta, I. Lindau, C. Garner and W.E. Spicer, Phys. Rev. Letters 35 (1975) 1356. [2] R.D.B. Fraser and E. Suzuki, in: Biological Applications, Spectral Analysis, Ed. J.A. Blackburn (Dekker, New York, 1970). [3] W.E. Spicer, Phys. Rev. 112 (1958) 114. [4] P.J. Feibelman and D.E. Eastman, Phys. Rev. BlO (1974) 4932. [5] J.M. McCormick and M.G. Salvadri, Numerical Methods in FORTRAN (Prentice-Hall, 1964). [6] D.R. Penn, J. Vacuum Sci. Technol. 13 (1976) 211. [7] J.J. Quinn, Phys. Rev. 126 (1962) 1453. (81 C.J. Powell, Surface Sci. 44 (1974) 29. [9] R. Dorn, H. Liith and G.J. Russell, Phys. Rev. BlO (1974) 5049.