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Angular Distribution of Photoemission from Thin AL Foil
357
ANGULAR DISTRIBUTION OF PHOTOEJIISSION FROM THIN AL FOIL J. Zemek1 and A.Jablonski 2 1Institute of Physics, Czechoslovak Academy of Sciences Ha Slovance 2, 180 40 Prague 8, Czechoslovakia 2rnstitute of Physical Chemistry, Polish Academy of Sciences ul. Kasprzaka 44/52. 01-224 Warsaw. Poland Theory The signal intensity oorresponding to a given photoelectron line is given by [1] I=kH).,(dG'/dU). (1) where H is atomic density of analysed element, A is inelastic mean free path. and the parameter k includes the properties of the spectrometer. In general. k is a function of analysed energy. dsl dn decribes the angular distribution of emitted photoelectrons. For randomly oriented atoms or molecules the following expression was proposed [2-51 d ~ 1 dn. = (G 1 4 1i) [1 - t n1 4) (3 cos2 r - 1 )]) (2)
where G is the total photoelectric cross-section, ~ is the asymetry parameter, and r is the angle defined in Fig.1. A number of theoretical values of parameter ~ were published in the literature (6,7J. An attempt was made to de~ne the values of (}, experimentally [81. Only several experimental values were published. They were found to differ profoundly from the theoretical prediction. The purpose of the present paper is to establish the reason for observed discrepancy. The values of observed asymmetry parameter were found to be affected by elastic collisions of photoelectrons [1,9.10] • The elastic electron collisions randomize photoelectron trajectories in the solid. and thus decrease the angular anisotropy. It has been proposed to de~cribe the angular distribution of photoelectrons leaving the surface by the effective asymmetry parameter, f!>" which is smaller that parameter 1.3 • A number of reports were published on Monte Carlo simulation of photoelectron trajectories in the solid [1.10-12J. In the present work the Monte Carlo method was used in calculations of angular distribution of photoelectrons. All details of the oorresponding algorithm were recently pUblished [13]. Only the main
features of this algorithm are briefly sketched below. Creation of the photoelectron trajeotory requires generating the following parameters: photoeleotron emission angle, elastio scattering angles, and the length of the linear step between elastic collisions. The photoeleotron emission angles were ~~nerated according to eq. (2) using values of ~ published by ReiLman et al (5]. The scattering centres of the solid state were approximated by the Thomas-Fermi-Dirac potentials. The differential scattering cross-section describing the elastic scattering event were caloulated within the partial wave expansion method. The Calogero method [14] was used to de1J?i.mine the so-called phase shifts. Calculations were made for aluminium 2s and 2p photoelectron lines. Normal incidence of X-rays on the Al foil was assumed (Fig. 1 00 0 wi th 0( =0 ). The angle (analysis 'f , was varied in steps of'" 4.5 • To obtain reasonable aocuracy it was necessary to generate 200 000 oomplete photoelectron trajectories. Results Angular resolved experiments were carried out in VG ADES 400. The 2 pm thin foil of poly-AI was used as a sample after Xe ion sputtering of surface contaminations and the oxide layer. Al Ko.:. radiation passing through the foil excited photoelectrons near by surface region [91. Thus, it was possible to move the energy analyser in interesting angular interval. The ratio 1 2s/12p was measured for clean Al foil at different analyser angles,r. The geometry of measurement is shown in Fig.1. All the experimental values of the ratios 1 2s/1 2p are compiled in Fig.2. The obtained angular dependenoe is a direct experimental proof for anisotropy of photoeleotron emission. Let us oompare experimental results with the theory prediction. From eqs (1) and (2) we obtain for 12s/12p ratio 12s/12p ~ [1-(a 2s / 4 ) (3 oos2 ~ - 1)1 [1-(n 2p/ 4 ) (3c082 ~1~, where
L = A2s
g 28 I( A2p G 2p)·
0)
The kinetic energy of Al 28 and 2p photoelectrons is equal to 1369 eV and 1414 eV, respectively. The constant ko
359
hJ
X ray gun
Fig. 1.: Geometry of measurements.
20 0.
10
<,
~
•
N
H
•
•
• . . . . .0
lJ)
·
0<-=0
-formalism • • Monte Carlo • ° exper iment : . . . .
·0
~"oo ·7 0.0
.. flo
.°0 • 0
••CbCQ:PoQ·o
N
H
Ol--_--L_ _
-90 -60
L..----'~~___l _ __'____
-30
o
30
__'_
601ft 90
Fig. 2.: Angular dependences of the ratios 1 2s/12p resulting from experiment, Monte Carlo calculations, and the usual formalism of XPS.
:J(,()
The above formalism is neglecting the photoelectron elastic scattering. The intensity ratios I 2s/I2p can also be estimated using the desclbed Monte Carlo algorithm, which takes into aocount photoelectron trajectories. These calculations were made only for the angle c/... = 0, i. e. assuming normal incidence of X-rays. In such a case the studied system has axial symmetry which greatly facilitates calculations. As one can see from Fig.2, the anisotropy observed experimentally is much less pronounoed than anisotropy resulting from the fOrmalism (eq The experimental data are in much better agreement with Monte Carlo results. This fact indicates that main part of observed discrepancies is due to neglect of photoelectron elastic scattering. In effeot, the angular distribution of photoeleotrons is somewhat "nattened". The difference between experimental results and the Monte Carlo data may be due to other effects, which may further randomize the photoelectron trajectories e.g. surface roughness and an~ser aoceptance angle. The discrepancy may also be due to inaccuraoi es in published values of .\ and r:5 • Eq. (J) can be used for fitting procedure of experimental data. It was based on non-linear minimalization of the sum of squared deviations from eq (3) using Lot , (:/'2s and ~·2p as the fitted parameters. Results of minimalization are listed in Table 1 and compared wi th corresponding values published in the literature. The parameter L"tdetermined on the basis of experimental data differs noticeably from the theoretical va~ lue of L • This indicates that the published values of ~ and i may be subjects of systematic errors. The I~;s and (5'2p are smaller than the corresponding values resulting from the Monte Carlo calculations. This supports the observation that, exoept of elastic photoelectron collisions, the photoelectron angular anisotropy may deorease by other factors. Table 1. Comparison of the fitted parameter for eq.O) with the published data I 2s / I 2p L L~ /3 2s, ;'?;s 13 2p , /3"2 p
0».
I
Experiment Monte Carlo Formalism
1.1109 1•.3514 1• 3667 [15,1 6 ]
1.171 1.525 2.0 [5]
0.4.35 0.49.3 0.9.3
t5J
:1(;]
Conclusions The analyser response due to Al 2s and 2p photoelectrons was found to be practically independent of the aluminium foil position. It depends mainly on the angle Y;. The experimentally determined anisotropy is smaller than anisotropy predicted theoretically. It is shown by Monte Carlo calculation that the difference is due mainly to elastic photoelectron collisions. Aoknowledgement One of the authors (A. Jablonski) would like to acknowledge the support of the Research Project 12.2. References
[7J
[aJ
[9J
[1 OJ
[12] [13J
[14J
Jablonski A., Ebel M.F., Ebel H.: J. Electron Spectrosc. Relat. Phenom. 40 (1986) 125. Kennedy D.J. and Manson S.T.: Phys.Rev. A5 (1972) 227. Ellison F.O.: J.Chem.Phys. 61 (1974) 507. Huang J.-T.J., Rabalais J.W. and Ellison F.D.: J.Electron Spectrosc. Relat. Phenom. 6 (1975) 85. Reilman R.F., Msezane A. and Manson S.T.: J.Electron Spectrosc. Relat. Phenom. 8 (1976) 389. Ebel M.F., Ebel H. and Hirokawa K.: Spectrochimica Acta B37 (1982) 461. Hanke W., Ebel H., Ebel M.F., Jablonski A. and Hirokawa K.: J.Electron Spectrosc. Relat.Phenom. 40 (1986) 241. Vulli M.: Surface Interface Anal. 3 (1981) 67. Baschenko O.A., Machavariani G.V. and Nefedov V.I.: J. Electron Relat. Phenom. 34 (1984) 305. Ebel H., Ebel M.F. and Jablonski A.: J • Electron Spectrosc. Relat. Phenom. 35 (1985) 155. Baschenko O.A. and Nefedov V.I.: J. Electron Spectrosc. 17 (1979) 405; 21 (1980) 153; 27 (1982) 109. Jablonski A. and Ebel H.: Surface Interface Anal. 6 (1984) 21 Jablonski A.: Surface Sci., in press. Calogero F.: Variable Phase Approach to Potential Scattering, (Academic Press, New York, 1967). Ashley J.e. and Tung C.J.: Surface Interface Anal. 4 (1982) 52 Scofield J.H.: J.Electron Spectrosc.Relat.Phenom. 8 (1976) 129.
ANGULAR DISTRIBUTION OF PHOTOEJIISSION FROM THIN AL FOIL J. Zemek1 and A.Jablonski 2 1Institute of Physics, Czechoslovak Academy of Sciences Ha Slovance 2, 180 40 Prague 8, Czechoslovakia 2rnstitute of Physical Chemistry, Polish Academy of Sciences ul. Kasprzaka 44/52. 01-224 Warsaw. Poland Theory The signal intensity oorresponding to a given photoelectron line is given by [1] I=kH).,(dG'/dU). (1) where H is atomic density of analysed element, A is inelastic mean free path. and the parameter k includes the properties of the spectrometer. In general. k is a function of analysed energy. dsl dn decribes the angular distribution of emitted photoelectrons. For randomly oriented atoms or molecules the following expression was proposed [2-51 d ~ 1 dn. = (G 1 4 1i) [1 - t n1 4) (3 cos2 r - 1 )]) (2)
where G is the total photoelectric cross-section, ~ is the asymetry parameter, and r is the angle defined in Fig.1. A number of theoretical values of parameter ~ were published in the literature (6,7J. An attempt was made to de~ne the values of (}, experimentally [81. Only several experimental values were published. They were found to differ profoundly from the theoretical prediction. The purpose of the present paper is to establish the reason for observed discrepancy. The values of observed asymmetry parameter were found to be affected by elastic collisions of photoelectrons [1,9.10] • The elastic electron collisions randomize photoelectron trajectories in the solid. and thus decrease the angular anisotropy. It has been proposed to de~cribe the angular distribution of photoelectrons leaving the surface by the effective asymmetry parameter, f!>" which is smaller that parameter 1.3 • A number of reports were published on Monte Carlo simulation of photoelectron trajectories in the solid [1.10-12J. In the present work the Monte Carlo method was used in calculations of angular distribution of photoelectrons. All details of the oorresponding algorithm were recently pUblished [13]. Only the main
features of this algorithm are briefly sketched below. Creation of the photoelectron trajeotory requires generating the following parameters: photoeleotron emission angle, elastio scattering angles, and the length of the linear step between elastic collisions. The photoeleotron emission angles were ~~nerated according to eq. (2) using values of ~ published by ReiLman et al (5]. The scattering centres of the solid state were approximated by the Thomas-Fermi-Dirac potentials. The differential scattering cross-section describing the elastic scattering event were caloulated within the partial wave expansion method. The Calogero method [14] was used to de1J?i.mine the so-called phase shifts. Calculations were made for aluminium 2s and 2p photoelectron lines. Normal incidence of X-rays on the Al foil was assumed (Fig. 1 00 0 wi th 0( =0 ). The angle (analysis 'f , was varied in steps of'" 4.5 • To obtain reasonable aocuracy it was necessary to generate 200 000 oomplete photoelectron trajectories. Results Angular resolved experiments were carried out in VG ADES 400. The 2 pm thin foil of poly-AI was used as a sample after Xe ion sputtering of surface contaminations and the oxide layer. Al Ko.:. radiation passing through the foil excited photoelectrons near by surface region [91. Thus, it was possible to move the energy analyser in interesting angular interval. The ratio 1 2s/12p was measured for clean Al foil at different analyser angles,r. The geometry of measurement is shown in Fig.1. All the experimental values of the ratios 1 2s/1 2p are compiled in Fig.2. The obtained angular dependenoe is a direct experimental proof for anisotropy of photoeleotron emission. Let us oompare experimental results with the theory prediction. From eqs (1) and (2) we obtain for 12s/12p ratio 12s/12p ~ [1-(a 2s / 4 ) (3 oos2 ~ - 1)1 [1-(n 2p/ 4 ) (3c082 ~1~, where
L = A2s
g 28 I( A2p G 2p)·
0)
The kinetic energy of Al 28 and 2p photoelectrons is equal to 1369 eV and 1414 eV, respectively. The constant ko
359
hJ
X ray gun
Fig. 1.: Geometry of measurements.
20 0.
10
<,
~
•
N
H
•
•
• . . . . .0
lJ)
·
0<-=0
-formalism • • Monte Carlo • ° exper iment : . . . .
·0
~"oo ·7 0.0
.. flo
.°0 • 0
••CbCQ:PoQ·o
N
H
Ol--_--L_ _
-90 -60
L..----'~~___l _ __'____
-30
o
30
__'_
601ft 90
Fig. 2.: Angular dependences of the ratios 1 2s/12p resulting from experiment, Monte Carlo calculations, and the usual formalism of XPS.
:J(,()
The above formalism is neglecting the photoelectron elastic scattering. The intensity ratios I 2s/I2p can also be estimated using the desclbed Monte Carlo algorithm, which takes into aocount photoelectron trajectories. These calculations were made only for the angle c/... = 0, i. e. assuming normal incidence of X-rays. In such a case the studied system has axial symmetry which greatly facilitates calculations. As one can see from Fig.2, the anisotropy observed experimentally is much less pronounoed than anisotropy resulting from the fOrmalism (eq The experimental data are in much better agreement with Monte Carlo results. This fact indicates that main part of observed discrepancies is due to neglect of photoelectron elastic scattering. In effeot, the angular distribution of photoeleotrons is somewhat "nattened". The difference between experimental results and the Monte Carlo data may be due to other effects, which may further randomize the photoelectron trajectories e.g. surface roughness and an~ser aoceptance angle. The discrepancy may also be due to inaccuraoi es in published values of .\ and r:5 • Eq. (J) can be used for fitting procedure of experimental data. It was based on non-linear minimalization of the sum of squared deviations from eq (3) using Lot , (:/'2s and ~·2p as the fitted parameters. Results of minimalization are listed in Table 1 and compared wi th corresponding values published in the literature. The parameter L"tdetermined on the basis of experimental data differs noticeably from the theoretical va~ lue of L • This indicates that the published values of ~ and i may be subjects of systematic errors. The I~;s and (5'2p are smaller than the corresponding values resulting from the Monte Carlo calculations. This supports the observation that, exoept of elastic photoelectron collisions, the photoelectron angular anisotropy may deorease by other factors. Table 1. Comparison of the fitted parameter for eq.O) with the published data I 2s / I 2p L L~ /3 2s, ;'?;s 13 2p , /3"2 p
0».
I
Experiment Monte Carlo Formalism
1.1109 1•.3514 1• 3667 [15,1 6 ]
1.171 1.525 2.0 [5]
0.4.35 0.49.3 0.9.3
t5J
:1(;]
Conclusions The analyser response due to Al 2s and 2p photoelectrons was found to be practically independent of the aluminium foil position. It depends mainly on the angle Y;. The experimentally determined anisotropy is smaller than anisotropy predicted theoretically. It is shown by Monte Carlo calculation that the difference is due mainly to elastic photoelectron collisions. Aoknowledgement One of the authors (A. Jablonski) would like to acknowledge the support of the Research Project 12.2. References
[7J
[aJ
[9J
[1 OJ
[12] [13J
[14J
Jablonski A., Ebel M.F., Ebel H.: J. Electron Spectrosc. Relat. Phenom. 40 (1986) 125. Kennedy D.J. and Manson S.T.: Phys.Rev. A5 (1972) 227. Ellison F.O.: J.Chem.Phys. 61 (1974) 507. Huang J.-T.J., Rabalais J.W. and Ellison F.D.: J.Electron Spectrosc. Relat. Phenom. 6 (1975) 85. Reilman R.F., Msezane A. and Manson S.T.: J.Electron Spectrosc. Relat. Phenom. 8 (1976) 389. Ebel M.F., Ebel H. and Hirokawa K.: Spectrochimica Acta B37 (1982) 461. Hanke W., Ebel H., Ebel M.F., Jablonski A. and Hirokawa K.: J.Electron Spectrosc. Relat.Phenom. 40 (1986) 241. Vulli M.: Surface Interface Anal. 3 (1981) 67. Baschenko O.A., Machavariani G.V. and Nefedov V.I.: J. Electron Relat. Phenom. 34 (1984) 305. Ebel H., Ebel M.F. and Jablonski A.: J • Electron Spectrosc. Relat. Phenom. 35 (1985) 155. Baschenko O.A. and Nefedov V.I.: J. Electron Spectrosc. 17 (1979) 405; 21 (1980) 153; 27 (1982) 109. Jablonski A. and Ebel H.: Surface Interface Anal. 6 (1984) 21 Jablonski A.: Surface Sci., in press. Calogero F.: Variable Phase Approach to Potential Scattering, (Academic Press, New York, 1967). Ashley J.e. and Tung C.J.: Surface Interface Anal. 4 (1982) 52 Scofield J.H.: J.Electron Spectrosc.Relat.Phenom. 8 (1976) 129.