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Photoelectron escape depth
Journal of Electron Spectroscopyand Related Phenomena76 (1995) 443-447
Photoelectron escape depth J. Zemek", S. Hucek ~, A. Jablonski b and I.S. Tilinin" ~Institute of Physics, Academy of Sciences, Cukrovarnickd 10, Prague 6, Czech Republic "Institute of Physical Chemistry, Polish Academy of Sciences, ul. Kasprzaka 44/52, 01-224 Warsaw, Poland
The average escape depth of AI 2s and O ls photoelectrons is determined for the A1/Al(oxide) system experimentally and theoretically (Monte Carlo simulations [ 1], analytical solution of the kinetic equation in the transport approximation [2]). Special attention is paid to a particular experimental geometry where pronounced effects of elastic scattering are expected [ 1]. The first results show that for the asymmetry parameter being equal to 2 and the emission directions close to that of x-ray propagation, the mean escape depth of electrons may differ noticeably from the value predicted by the usual XPS formalism (when elastic scattering is neglected). The results obtained may be of special practical interest in quantitative XPS analysis and transmission photoelectron microscopy.
I. Introduction In the usual XPS formalism widely used in practical surface analysis, the basic quantity characterizing the surface sensitivity is the product of the inelastic mean free path and the cosine of the emission angle measured from the normal. In particular, it is believed that at grazing emission, when the cosine of emission angle is small compared with unity, the thickness of the top surface layer contributing mostly to the recorded photoelectron intensity can be made as small as desired. This result follows from the assumption that elastic scattering of photoelectrons on their way out of the target can be neglected. Recent studies [1, 2] indicate, however, that disregard for elastic scattering may lead to over- or underestimating the probed volume in the near surface region. To account for the influence of elastic collisions they proposed to use the so-called attenuation length [3]. The concept of the attenuation length is based on the hypothesis about exponential behaviour of the escape probability as a function of the depth of origin. Unfortunately, in many cases the escape probability does not obey the exponential law and therefore the term "attenuation length" becomes questionable. In this connection making use of the mean escape depth of signal photoelectrons as a 0368-2048/95 $09.50 © 1995 ElsevierScience B.V. All rights reserved SSDI 0368- 2048 (95) 02507-3
measure of the analysed volume seems to be much more appropriate. The mean escape depth D is defined as the average value with respect to the depth distribution function [ 1, 2]:
t) = Iz,V(z)~/ I 'V(z)~
(1)
Here qb(z) is the depth distribution function characterizing the probability for an electron generated at a certain depth to leave the target in a particular direction and the integration is performed over all emission depths. The main advantage of the mean escape depth is that it is a strictly defined quantity and may be evaluated rapidly as soon as the function • is available. In a number of works [1, 2, 4] the mean escape depth was determined theoretically by means of the Monte Carlo approach and by solving analytically a kinetic equation with the corresponding boundary condition. Meanwhile, until recently no attempt has been made to determine the mean escape depth experimentally. This is primarily due to difficulties in measuring the depth distribution function. In this report a new experimental method is proposed to evaluate the mean escape depth of photoelectrons leaving the target without a considerable energy loss. The experimental values of the mean escape depth are compared with the corresponding theoretical predictions.
444
2. Theory First, we assume, for simplicity, that a broad beam of x-rays is incident at the angle 0 on a semiinfinite homogeneous sample. To find the depth distribution function and the mean escape depth of signal electrons it is necessary to solve a kinetic equation satisfying the corresponding boundary condition. In the medium energy range, when typical kinetic energies of photoelectrons are comparable with the average binding energy of atomic electrons, the electron transport can be described by a classical Boltzmann type kinetic equation [2, 5]. This refers to both amorphous and polycrystalline targets. The possibility of neglecting dynamical diffraction effects in the case of polycrystalline solids is substantiated by the fact that coherent scattering influences the electron motion far away from the directions of crystallographic axes insignificantly [6] and the electron momentum and energy relaxation processes are governed by incoherent scattering at least for temperatures exceeding several tens of Kelvins. On the other hand, the initial angular distribution of photoelectrons is characterized usually by a smoothly varying function and correlation of the initial emission direction and that of crystallographic axes is generally weak due to a random orientation of microcrystalline domains. The approach employing the transport equation usually encounters mathematical difficulties associated with a complex behaviour of the differential elastic scattering cross section. It turned out, however, that a highly accurate analytical solution to the boundary value problem may be obtained on the basis of the so-called generalized radiative field similarity principle [5]. According to this principle, the exact differential elastic scattering cross section may be replaced by an approximate one provided the typical angular distribution is not highly anisotropic and the approximate cross section yields the radiative field distribution similar to the exact one in the limiting cases of weak (~,i >> ~,r) and strong (~,i << ~,tr) absorption, where ~,i and ~,tr are the inelastic and the transport mean free paths of electrons in a solid. It can be shown that the transport approximation [2, 5] satisfies the requirements imposed by the radiative field similarity principle. In this approach the approximate scattering cross section is isotropic and
equal to the corresponding value of the momentum transfer cross section. Making use of the transport approximation allows us to obtain a relatively simple analytical expression for the mean escape depth [2] D = ~k,~,tr(~,i + ~Ltr)-u (cos 0t + S)
(2)
where cz is the polar emission angle with respect to the surface normal, while the quantity S is determined by the ratio (3)
S = $1/$2
of the two functions depending on a specific geometry and the asymmetry parameter lB. Within an accuracy of a few percent the functions Sn and $2 can be evaluated by means of the formulas 1
$1 = [o)/2(1 - to)] f0/.tH(I,t, to)dla
(4)
$2 = (1 - to)-l/2_ (lB/4)(3 cos20 - l)/H(cos tx, to) (5) Here to = ~,i(~,i + ~tr) -j is the single scattering albedo, O is the angle between the photoelectron emission direction and that of x-ray propagation and H(la, to) is the H-function of Chandrasekhar [7]. The mean escape depth can be also calculated employing the Monte Carlo method. The major assumptions underlying this approach are discussed in detail elsewhere [1]. In Table 1 we present the comparison of the analytical (AT) and Monte Carlo (MC) results for the mean escape depth of Cu 3p (Ek = 1180 eV, lB= 1.04) photoelectrons from different targets. The electrons are collected in the solid angle of +4.1 degrees along the surface normal (ct=0) while the x-ray angle of incidence 0 is varied from 0 to 80 degrees. It is seen that the Monte Carlo data are in close agreement with the analytical predictions. In contrast to this the corresponding D-values found in the straight line approximation are 5-30% larger than those presented in the table. An analytical solution of the secondary emission problem is also possible in the case of an overlayer/substrate target under the condition that the ratios of the inelastic to the transport mean free paths for the overlayer and the substrate are identical or differ little from each other. In the latter
445 Table 1. Comparison of the Monte Carlo (MC) and analytical (AT) results for the mean escape depth of Cu 3p photoelectrons, excited by Mg Ktz x-rays. 0, deg
Mean escape depth D,/~ AI
Cu
Ag
W
Pt
MC
AT
MC
AT
MC
AT
MC
AT
MC
AT
0.0
21.0
21.1
15.2
15.2
13.4
13.1
11.7
!1.6
11.2
11.2
20.0
20.9
20.9
15.2
15.0
13.1
13.0
11.5
11.4
11.2
11.0
40.0
20.9
20.6
14.2
14.6
12.9
12.7
11.1
11.1
10.7
10.6
60.0
19.9
20.5
14.1
14.4
12.3
12.4
10.7
10.8
10.5
10.4
80.0
19.6
20.4
13.8
14.2
12.4
12.3
10.6
10.7
10.3
10.3
case the mean escape depths from the overlayer (o) and substrate (s) materials can be found by simple formulas
D~ = ~o l,.(t)dt
(6)
D,, = ~o[1 - l,,(t)ldt
(7)
where lo(t) and l,.(t) are the photoelectron line intensities of the overlayer and the substrate respectively as functions of the overlayer thickness t. The functions Io and I,. are normalized in such a way that /o(oo) = / A 0 ) = 1
(8)
The accuracy of expressions (6) and (7) is about 8-Aco= Ico,,-co.,.I, where coo and co,. are the single scattering albedos for the overlayer and the substrate. Hence the mean escape depth can be determined by measuring the overlayer or the substrate signals in overlayer experiments.
3. Experimental X-ray photoelectron spectra were measured by the ADES-400 (V. G. Scientific) angle-resolved photoelectron spectrometer at room temperature using AI K(~ radiation (1486 eV, 200 W) at normal
incidence angle. The hemispherical energy analyzer was operated in the constant energy mode at a pass energy of 50 eV. The acceptance angle of the analyzer was set to _+ 4.1 degrees. Spectra were recorded in regions of AI 2s and O Is lines at fixed position of the sample at emission angles, ct, equal to 0, 5, 10 and 60 degrees with respect to the surface normal. Areas of the peaks were determined by applying the non-linear inelastic background subtraction procedure [8]. The target consisting of a 2 larn thick polycrystaline AI foil was carefully adjusted to the axis of analyzer rotation by a laser beam technique in order to keep the uncertainty in take-off angles below 1 degree. Unrestricted analyzer rotation at emission angles close to the x-ray propagation direction was ensured by the x-ray source positioning at the opposite side of the AI foil with respect to the analyzer. The AI foil was sputter-cleaned by means of a 4000 eV Ar ÷ ion beam incident at an angle 60 degrees relative to the surface normal. The beam current was 2x105 A into a spot of diameter 1 cm at the target. Then the surface was exposed to molecular oxygen of spectroscopic purity first at room temperature and later (to obtain higher values of the oxide thickness) at temperatures up to 400°C and pressures in the range of l x l 0 7 tO 10 Torr. After each consecutive oxygen exposure the target was cooled down to room temperature, the AI 2s and O ls spectra were recorded and the overlayer thickness was determined.
446 Table 2. The values of the inelastic (~i) and the transport (X~r) mean free paths used for estimation of the AI203 overlayer thickness. Photoelectron line
E k, eV
~,~, A
Z~r, A
)~e,f,/~
AI 2s
1368.0
27.4
142.6
23.0
O ls
956.0
20.9
82.5
16.7
up to about 3~,i. The behaviour of the escape probability as a function of the depth of origin at larger depths has little influence on the recorded intensity since the contribution of photoelectrons generated at depths exceeding 3Xi to the photoelectron current is negligible. It should be stressed that the AI 2s spectrum consists of the two overlapping peaks corresponding to the photoelectrons originating in the overlayer and the substrate. These peaks are located at (1367.0- 1366.5) eV and 1369.0 eV on the kinetic energy scale (Ek) respectively. The chemical shift has been found to be overlayer-thickness dependent and to vary from 2.0 eV for very small thicknesses to 2.5 eV for a semiinfinite overlayer. The lower kinetic energy of AI 2s photoelectrons from AI203 is associated with a higher binding energy of the AI 2s core shell in the oxide. To obtain true Ai 2s line intensities from the overlayer and the substrate the total spectrum was decomposed by the standard curve synthesis procedure of the program SPECTRA (VG).
4. Results and discussion The aluminum oxide thickness was estimated on the basis of the ratio of oxide and substrate AI 2s peak intensities recorded for 60 degrees emission angle assuming a simple overlayer/substrate model [9] corrected for electron elastic scattering. This correction consists in replacing the inelastic mean free path by the effective mean free path )~eff:
eff--"i
+ ~,;1
(9)
where )~i is the inelastic mean free path [10] and ~,tr is the transport mean free path [11]. The values of ~,i, )~tr, )~eg used for the oxide thickness determination are shown in Table2. Such a procedure to determine the overlayer thickness is justified by the Monte Carlo simulation data for the A! 2s line in aluminum [4]. From them it follows, in particular, that the depth distribution function obeys approximately the exponential law for the emission angle ot = 60 degree [4] in the emission depth range Table 3.
The mean escape depth D of O ls and AI 2s photoelectrons excited by AI Kcx radiation in AI203 , for different polar emission angles or. The x-rays are normally incident on the target. The notation Exp, SLA, AT and MC refers to the D-values found experimentally, in the straight line approximation, analytically by formula (2) and by the Monte Carlo method, respectively. Ct, deg
Mean escape depth D, ]k O 1s
AI 2s
Exp
SLA
AT
MC
Exp
SLA
AT
MC
0.0
24.2
20.9
21.2
24.1
30.7
27.4
29.0
34.7
5.0
23.2
20.8
21.0
23.8
30.3
27.3
28.6
33.2
10.0
20.7
20.6
20.2
22.9
29.8
27.0
27.4
31.9
60.0
9.1
10.5
9.1
8.5
11.5
13.7
12.3
11.6
447 The mean escape depth D for the O Is and AI 2s photoelectrons was calculated from the experimentally obtained dependence lo(t) by making use of Eq.(7). In addition, the corresponding D-values were evaluated by the Monte Carlo technique and analytically from Eq.(2). Experimental and theoretical results are summarized in Table 3. From Table 3 it follows that the values of the mean escape depth measured experimentally and calculated theoretically compare quite well. The deviations of the theoretical results obtained when accounting for elastic scattering effect (AT and MC) do not differ too much from those found in the straight line approximation (SLA) disregarding elastic collisions. This is mainly due to weak scattering properties of A1203. However, the SLA predicts a twofold decrease in the quantity D with increasing the emission angle from 0 to 60 degrees. Meanwhile the experimental, analytical and MC results clearly indicate that the mean escape depth for the normal emission is by a factor of 2.3 - 2.6 larger than the corresponding value at a = 6 0 degrees. Thus we conclude that elastic scattering influences the average depth of analysis even for elements with relatively low atomic numbers. This effect is expected to be much more strongly pronounced for heavy elements. In this connection further experimental studies of the mean escape depth from elements with higher Z-values are desirable.
Acknowledgements This work was partially supported by grant of 202/95/0032 GACR.
References 1. A.Jablonski, Surf. Interface Anal., 21(1994)758. 2. I.S.Tilinin, A.Jablonski and B.Lesiak-Orlowska, Acta Phys. Polonica, 86(1994)845 3. C.J.Powell and M.P.Seah, J. Vac. Sci. Technol., A8(1990)735. 4. A.Jablonski and J.Zemek, Phys. Rev., B48 (1993)4799. 5. I.S.Tilinin and W.S.M.Werner, Mikrochim. Acta, 114/115(1994) 485. 6. S.L.Dudarev and M.J.Whelan, Surf. Sci., 311 (1994) L687. 7. S.Chandrasekhar, Radiative Transfer, Clarendon Press, Oxford, 1950. 8. D.A.Shirley, Phys. Rev., B5(1972) 4709. 9. C.S.Fadley, R.Baird, W.Sichaus, T.Novakov and S.A.L.Bergstrom, J. Electron Spectrosc. Relat. Phenom., 4(1974) 93. 10. S.Tanuma, C.J.Powell and D.R.Penn, J. Surf. Interface Anal., 17(1991 ) 927. 11. I.S.Tilinin, Sov. Phys. JETP, 67(1988) 1570.
Photoelectron escape depth J. Zemek", S. Hucek ~, A. Jablonski b and I.S. Tilinin" ~Institute of Physics, Academy of Sciences, Cukrovarnickd 10, Prague 6, Czech Republic "Institute of Physical Chemistry, Polish Academy of Sciences, ul. Kasprzaka 44/52, 01-224 Warsaw, Poland
The average escape depth of AI 2s and O ls photoelectrons is determined for the A1/Al(oxide) system experimentally and theoretically (Monte Carlo simulations [ 1], analytical solution of the kinetic equation in the transport approximation [2]). Special attention is paid to a particular experimental geometry where pronounced effects of elastic scattering are expected [ 1]. The first results show that for the asymmetry parameter being equal to 2 and the emission directions close to that of x-ray propagation, the mean escape depth of electrons may differ noticeably from the value predicted by the usual XPS formalism (when elastic scattering is neglected). The results obtained may be of special practical interest in quantitative XPS analysis and transmission photoelectron microscopy.
I. Introduction In the usual XPS formalism widely used in practical surface analysis, the basic quantity characterizing the surface sensitivity is the product of the inelastic mean free path and the cosine of the emission angle measured from the normal. In particular, it is believed that at grazing emission, when the cosine of emission angle is small compared with unity, the thickness of the top surface layer contributing mostly to the recorded photoelectron intensity can be made as small as desired. This result follows from the assumption that elastic scattering of photoelectrons on their way out of the target can be neglected. Recent studies [1, 2] indicate, however, that disregard for elastic scattering may lead to over- or underestimating the probed volume in the near surface region. To account for the influence of elastic collisions they proposed to use the so-called attenuation length [3]. The concept of the attenuation length is based on the hypothesis about exponential behaviour of the escape probability as a function of the depth of origin. Unfortunately, in many cases the escape probability does not obey the exponential law and therefore the term "attenuation length" becomes questionable. In this connection making use of the mean escape depth of signal photoelectrons as a 0368-2048/95 $09.50 © 1995 ElsevierScience B.V. All rights reserved SSDI 0368- 2048 (95) 02507-3
measure of the analysed volume seems to be much more appropriate. The mean escape depth D is defined as the average value with respect to the depth distribution function [ 1, 2]:
t) = Iz,V(z)~/ I 'V(z)~
(1)
Here qb(z) is the depth distribution function characterizing the probability for an electron generated at a certain depth to leave the target in a particular direction and the integration is performed over all emission depths. The main advantage of the mean escape depth is that it is a strictly defined quantity and may be evaluated rapidly as soon as the function • is available. In a number of works [1, 2, 4] the mean escape depth was determined theoretically by means of the Monte Carlo approach and by solving analytically a kinetic equation with the corresponding boundary condition. Meanwhile, until recently no attempt has been made to determine the mean escape depth experimentally. This is primarily due to difficulties in measuring the depth distribution function. In this report a new experimental method is proposed to evaluate the mean escape depth of photoelectrons leaving the target without a considerable energy loss. The experimental values of the mean escape depth are compared with the corresponding theoretical predictions.
444
2. Theory First, we assume, for simplicity, that a broad beam of x-rays is incident at the angle 0 on a semiinfinite homogeneous sample. To find the depth distribution function and the mean escape depth of signal electrons it is necessary to solve a kinetic equation satisfying the corresponding boundary condition. In the medium energy range, when typical kinetic energies of photoelectrons are comparable with the average binding energy of atomic electrons, the electron transport can be described by a classical Boltzmann type kinetic equation [2, 5]. This refers to both amorphous and polycrystalline targets. The possibility of neglecting dynamical diffraction effects in the case of polycrystalline solids is substantiated by the fact that coherent scattering influences the electron motion far away from the directions of crystallographic axes insignificantly [6] and the electron momentum and energy relaxation processes are governed by incoherent scattering at least for temperatures exceeding several tens of Kelvins. On the other hand, the initial angular distribution of photoelectrons is characterized usually by a smoothly varying function and correlation of the initial emission direction and that of crystallographic axes is generally weak due to a random orientation of microcrystalline domains. The approach employing the transport equation usually encounters mathematical difficulties associated with a complex behaviour of the differential elastic scattering cross section. It turned out, however, that a highly accurate analytical solution to the boundary value problem may be obtained on the basis of the so-called generalized radiative field similarity principle [5]. According to this principle, the exact differential elastic scattering cross section may be replaced by an approximate one provided the typical angular distribution is not highly anisotropic and the approximate cross section yields the radiative field distribution similar to the exact one in the limiting cases of weak (~,i >> ~,r) and strong (~,i << ~,tr) absorption, where ~,i and ~,tr are the inelastic and the transport mean free paths of electrons in a solid. It can be shown that the transport approximation [2, 5] satisfies the requirements imposed by the radiative field similarity principle. In this approach the approximate scattering cross section is isotropic and
equal to the corresponding value of the momentum transfer cross section. Making use of the transport approximation allows us to obtain a relatively simple analytical expression for the mean escape depth [2] D = ~k,~,tr(~,i + ~Ltr)-u (cos 0t + S)
(2)
where cz is the polar emission angle with respect to the surface normal, while the quantity S is determined by the ratio (3)
S = $1/$2
of the two functions depending on a specific geometry and the asymmetry parameter lB. Within an accuracy of a few percent the functions Sn and $2 can be evaluated by means of the formulas 1
$1 = [o)/2(1 - to)] f0/.tH(I,t, to)dla
(4)
$2 = (1 - to)-l/2_ (lB/4)(3 cos20 - l)/H(cos tx, to) (5) Here to = ~,i(~,i + ~tr) -j is the single scattering albedo, O is the angle between the photoelectron emission direction and that of x-ray propagation and H(la, to) is the H-function of Chandrasekhar [7]. The mean escape depth can be also calculated employing the Monte Carlo method. The major assumptions underlying this approach are discussed in detail elsewhere [1]. In Table 1 we present the comparison of the analytical (AT) and Monte Carlo (MC) results for the mean escape depth of Cu 3p (Ek = 1180 eV, lB= 1.04) photoelectrons from different targets. The electrons are collected in the solid angle of +4.1 degrees along the surface normal (ct=0) while the x-ray angle of incidence 0 is varied from 0 to 80 degrees. It is seen that the Monte Carlo data are in close agreement with the analytical predictions. In contrast to this the corresponding D-values found in the straight line approximation are 5-30% larger than those presented in the table. An analytical solution of the secondary emission problem is also possible in the case of an overlayer/substrate target under the condition that the ratios of the inelastic to the transport mean free paths for the overlayer and the substrate are identical or differ little from each other. In the latter
445 Table 1. Comparison of the Monte Carlo (MC) and analytical (AT) results for the mean escape depth of Cu 3p photoelectrons, excited by Mg Ktz x-rays. 0, deg
Mean escape depth D,/~ AI
Cu
Ag
W
Pt
MC
AT
MC
AT
MC
AT
MC
AT
MC
AT
0.0
21.0
21.1
15.2
15.2
13.4
13.1
11.7
!1.6
11.2
11.2
20.0
20.9
20.9
15.2
15.0
13.1
13.0
11.5
11.4
11.2
11.0
40.0
20.9
20.6
14.2
14.6
12.9
12.7
11.1
11.1
10.7
10.6
60.0
19.9
20.5
14.1
14.4
12.3
12.4
10.7
10.8
10.5
10.4
80.0
19.6
20.4
13.8
14.2
12.4
12.3
10.6
10.7
10.3
10.3
case the mean escape depths from the overlayer (o) and substrate (s) materials can be found by simple formulas
D~ = ~o l,.(t)dt
(6)
D,, = ~o[1 - l,,(t)ldt
(7)
where lo(t) and l,.(t) are the photoelectron line intensities of the overlayer and the substrate respectively as functions of the overlayer thickness t. The functions Io and I,. are normalized in such a way that /o(oo) = / A 0 ) = 1
(8)
The accuracy of expressions (6) and (7) is about 8-Aco= Ico,,-co.,.I, where coo and co,. are the single scattering albedos for the overlayer and the substrate. Hence the mean escape depth can be determined by measuring the overlayer or the substrate signals in overlayer experiments.
3. Experimental X-ray photoelectron spectra were measured by the ADES-400 (V. G. Scientific) angle-resolved photoelectron spectrometer at room temperature using AI K(~ radiation (1486 eV, 200 W) at normal
incidence angle. The hemispherical energy analyzer was operated in the constant energy mode at a pass energy of 50 eV. The acceptance angle of the analyzer was set to _+ 4.1 degrees. Spectra were recorded in regions of AI 2s and O Is lines at fixed position of the sample at emission angles, ct, equal to 0, 5, 10 and 60 degrees with respect to the surface normal. Areas of the peaks were determined by applying the non-linear inelastic background subtraction procedure [8]. The target consisting of a 2 larn thick polycrystaline AI foil was carefully adjusted to the axis of analyzer rotation by a laser beam technique in order to keep the uncertainty in take-off angles below 1 degree. Unrestricted analyzer rotation at emission angles close to the x-ray propagation direction was ensured by the x-ray source positioning at the opposite side of the AI foil with respect to the analyzer. The AI foil was sputter-cleaned by means of a 4000 eV Ar ÷ ion beam incident at an angle 60 degrees relative to the surface normal. The beam current was 2x105 A into a spot of diameter 1 cm at the target. Then the surface was exposed to molecular oxygen of spectroscopic purity first at room temperature and later (to obtain higher values of the oxide thickness) at temperatures up to 400°C and pressures in the range of l x l 0 7 tO 10 Torr. After each consecutive oxygen exposure the target was cooled down to room temperature, the AI 2s and O ls spectra were recorded and the overlayer thickness was determined.
446 Table 2. The values of the inelastic (~i) and the transport (X~r) mean free paths used for estimation of the AI203 overlayer thickness. Photoelectron line
E k, eV
~,~, A
Z~r, A
)~e,f,/~
AI 2s
1368.0
27.4
142.6
23.0
O ls
956.0
20.9
82.5
16.7
up to about 3~,i. The behaviour of the escape probability as a function of the depth of origin at larger depths has little influence on the recorded intensity since the contribution of photoelectrons generated at depths exceeding 3Xi to the photoelectron current is negligible. It should be stressed that the AI 2s spectrum consists of the two overlapping peaks corresponding to the photoelectrons originating in the overlayer and the substrate. These peaks are located at (1367.0- 1366.5) eV and 1369.0 eV on the kinetic energy scale (Ek) respectively. The chemical shift has been found to be overlayer-thickness dependent and to vary from 2.0 eV for very small thicknesses to 2.5 eV for a semiinfinite overlayer. The lower kinetic energy of AI 2s photoelectrons from AI203 is associated with a higher binding energy of the AI 2s core shell in the oxide. To obtain true Ai 2s line intensities from the overlayer and the substrate the total spectrum was decomposed by the standard curve synthesis procedure of the program SPECTRA (VG).
4. Results and discussion The aluminum oxide thickness was estimated on the basis of the ratio of oxide and substrate AI 2s peak intensities recorded for 60 degrees emission angle assuming a simple overlayer/substrate model [9] corrected for electron elastic scattering. This correction consists in replacing the inelastic mean free path by the effective mean free path )~eff:
eff--"i
+ ~,;1
(9)
where )~i is the inelastic mean free path [10] and ~,tr is the transport mean free path [11]. The values of ~,i, )~tr, )~eg used for the oxide thickness determination are shown in Table2. Such a procedure to determine the overlayer thickness is justified by the Monte Carlo simulation data for the A! 2s line in aluminum [4]. From them it follows, in particular, that the depth distribution function obeys approximately the exponential law for the emission angle ot = 60 degree [4] in the emission depth range Table 3.
The mean escape depth D of O ls and AI 2s photoelectrons excited by AI Kcx radiation in AI203 , for different polar emission angles or. The x-rays are normally incident on the target. The notation Exp, SLA, AT and MC refers to the D-values found experimentally, in the straight line approximation, analytically by formula (2) and by the Monte Carlo method, respectively. Ct, deg
Mean escape depth D, ]k O 1s
AI 2s
Exp
SLA
AT
MC
Exp
SLA
AT
MC
0.0
24.2
20.9
21.2
24.1
30.7
27.4
29.0
34.7
5.0
23.2
20.8
21.0
23.8
30.3
27.3
28.6
33.2
10.0
20.7
20.6
20.2
22.9
29.8
27.0
27.4
31.9
60.0
9.1
10.5
9.1
8.5
11.5
13.7
12.3
11.6
447 The mean escape depth D for the O Is and AI 2s photoelectrons was calculated from the experimentally obtained dependence lo(t) by making use of Eq.(7). In addition, the corresponding D-values were evaluated by the Monte Carlo technique and analytically from Eq.(2). Experimental and theoretical results are summarized in Table 3. From Table 3 it follows that the values of the mean escape depth measured experimentally and calculated theoretically compare quite well. The deviations of the theoretical results obtained when accounting for elastic scattering effect (AT and MC) do not differ too much from those found in the straight line approximation (SLA) disregarding elastic collisions. This is mainly due to weak scattering properties of A1203. However, the SLA predicts a twofold decrease in the quantity D with increasing the emission angle from 0 to 60 degrees. Meanwhile the experimental, analytical and MC results clearly indicate that the mean escape depth for the normal emission is by a factor of 2.3 - 2.6 larger than the corresponding value at a = 6 0 degrees. Thus we conclude that elastic scattering influences the average depth of analysis even for elements with relatively low atomic numbers. This effect is expected to be much more strongly pronounced for heavy elements. In this connection further experimental studies of the mean escape depth from elements with higher Z-values are desirable.
Acknowledgements This work was partially supported by grant of 202/95/0032 GACR.
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