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In-depth concentration profile information through analysis of the entire XPS peak shape
332
Applied
Surface
Science 32 (1988) 332-337 North-Holland, Amsterdam
IN-DEPTH CONCENTRATION PROFILE INFORMATION THROUGH ANALYSIS OF THE ENTIRE XPS PEAK SHAPE S. TOUGAARD Fysisk Institut, Odense Uniuersitet, DK-5230 Odense M, Denmark
Received
26 October
1987; accepted
for publication
15 February
1988
A simple procedure, for non-destructive extraction of concentration depth profile information, through analysis of the ratio of the XPS peak area to the increase in the background signal below the peak, was previously developed. However, since only one point in the background is used in the analysis, the detailed in-depth profile cannot be determined. In the present paper, a method is defined which takes into account the shape of the inelastic background signal in a wide energy range. With the procedure, it is possible, through a simple analysis of a single XPS spectrum, to (a) decide whether the in-depth concentration varies roughly exponentially with depth and (b) determine the characteristic length of the depth profile.
1. Introduction A technique for non-destructive extraction of in-depth composition information based on an analysis of the inelastic background in XPS was previously developed [l-4]. The method relies on a simple analysis of the ratio of the XPS peak area to the increase in background signal associated with the peak. The procedure has been tested on metallic [l-4] as well as organic [5] solids. It is non-destructive, extremely fast and readily provides an estimate on the depth distribution of a given element. In the method, all physical information is deduced from a single experimentally determined number, namely the above-mentioned ratio. Since only a single point in the inelastic background signal is used in the analysis, details of the depth profiles cannot be determined [ 3,4]. In the present paper it is shown that it is possible to extract more detailed information if the full background signal associated with an XPS peak is used in the analysis. Thus, a simple procedure is defined from which it can be concluded whether the distribution of a given element is roughly exponential with depth and, in addition, the characteristic length of the in-depth profile can be determined. 0169-4332/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
333
S. Tougaard / In-depth concentration profile information
2. Theory
Assume an exponential concentration a function of depth x, i.e.
f(x)
profile, f(x)
of electron emitters, as
0)
a eCxlLa,
where L, is the attenuation length. Then the primary excitation spectrum F(E), after removal of all inelastically scattered electrons is given in terms of the measured spectrum j(E) by [6]
F(E)=j(E)-
j?C(E’-E)
,co;2+L a
j(E’)dE’,
(2)
E
where 8 is the electron exit angle with respect to the surface normal, X is the inelastic electron mean free path, and K( E' - E) is the differential inelastic scattering cross section for energy loss E' - E. For routine analysis of spectra, it was recently proposed to use a simple “universal” cross section [7]
AK(T)
=
BT (C+T*)*'
where B = 2866 eV* and C = 1643 eV2, as an approximation transition metals. Then, from eq. (2)
F(E) -j(E) -
x
Et-E cosL;+ Blm[c+(E'-E)*]* L
a
for noble and
j(E') dE’.
E
After proper background correction, we should have F(E) beyond 30-50 eV from the XPS main peak [8].
(4)
= 0 for all energies
3.Method Concentration depth profile information can now be obtained through the following simple procedure: First, the value of the parameter B, is adjusted so that after applying the equation:
F(E) =_dE)-
4J,”[c+
E'-E
j(E') dE’,
(5)
(E'-E)*]*
to the measured spectrum j(E), then F(E) = 0 in a reasonably wide energy range (e.g. from 30-100 eV) beyond - 30 eV below the XPS peak energy. If such a B, can be found, the following two conclusions can be made: (a) the depth distribution of the corresponding element is roughly exponential with depth, i.e. f(x) 2: c eexlLa;
S. Touganrd / In-depth concentration profile information
334
(b) the characteristic
L, =
&A
length is approximately
given by
cos 8. 1
If no B, exists that gives F(E) = 0 in a wide energy range below the peak, it can be concluded that the depth distribution is not exponential with depth.
4. Discussion Figs. 1A and 1B show model XPS with 8 = 0 o for two exponential in-depth distributions of impurities in copper, assuming L, = 30.6 A and L, = - 46.0 A respectively. The primary peak is of the Doniach-Sunjic form [9] with (Y= 3 eV and y = 0.1 centered around 1000 eV. For details of the method of calculation see refs. [3,6]. Now, eq. (5) was applied to these spectra adjusting the factor B,. With B, = 1900 eV2 and 4300 eV2 respectively, the resulting
920
940
960
ELECTRON
980
ENERGY
IOCKJ
(eV
l(
10
)
Fig. 1. Model XPS i(E) for exponential distributions in Cu of electron emitters with the energy distribution cl(E). In (A) and (B), the characteristic length of the distribution is L, = 30.6 A and L, = -46.0 A respectively. F(E) results when eq. (5) is applied to j(E) adjusting B, to give F(E) = 0 in a wide energy region below the peak.
S. Tougaard / In-depth concentration profile information
920
940
960
ELECTRON
960 ENERGY
1000
11
335
10
(eV)
Fig. 2. Model XPS j(E) for a depth distribution given by f(x) = 0 for 0 -Cx -C 40 A and f(x) = constant for x > 40 A. F,(E) is the primary electron energy distribution. The spectra F(E) result when eq. (5) is applied to j(E) for two values of B,. (The spectra j(E) are identical in the two figures but the scales are different.)
primary spectra are roughly zero in a wide energy range below the0 peak energy. Thus the conditions for (a) and (b) are fullfilied. With X = 16 A [lo], we find from eq. [6] L, = 30 A and L, = - 50 A respectively, in good agreement with the actual in-depth distribution profiles. Fig. 2 shows a similar model XPS for a depth distribution given by f(x) = 0 for 0 c x -C 40 A and f(x) = constant for x > 40 A. Also shown is the result after application of eq. (5) for two values of B,. It is clearly seen that there does not exist a B, which gives F(E) 2: 0 in a wide energy range below the peak. Then, from the above, it is concluded that the distribution is not exponential with depth in agreement with the true depth distribution. Finally, we apply eqs. (5) and (6) to experimental XPS for a homogeneous impurity depth distribution. Since the inelastic properties of the transition and noble metals are strikingly similar [7], we expect to first order the overall XPS peak shape to depend only on the in-depth concentration profile and to be independent of the impurity concentration. Furthermore, in view of the great
336
S. Tougaard / In-depth concentration
profile information
J
1100
1020
ELECTRON
ENERGY
1200
(eV)
Fig. 3. Al Ka excited XPS of pure gold in the energy range of the Au 4d peaks (upper curves). lower curves are obtained after application of eq. (5) using three different values of B,.
The
experimental difficulties in producing samples with a well known in-depth concentration profile we therefore illustrate the application of the method to experimental XPS of a pure metal. Measured XPS of pure gold is shown in fig. 3 in the region of the Au 4d peaks, after correcting for the analyser transmission function and after subtraction of a constant background. The lower curves in figs. 3A-3C are obtained by eq. (5) using B, = 2500 eV2, 2866 eV2, and 3400 eV2 respectively. It is clear that in fig. 3A, the inelastic background intensity in the corrected spectrum is still too high, while in fig. 3C it is too low. In fig. 3B, however, the intensity in the background corrected spectrum is roughly zero in the full - 30-100 eV energy range below the XPS peak structure. Consequently, in fig. 3B, the conditions for (a) and (b) are fulfilled with B, = 2900 eV2. It can then be concluded that the observed gold is, to a good approximation, exponentially distributed with depth in the sample and that the attenua-
S. Tougaard / In-depth concentration profile information
337
tion length (by eq. (6)) is L, 2: co i.e. the gold concentration is constant in the surface region of the solid. This is in perfect agreement with the fact that the spectrum is measured from a pure gold sample. If we take the calculated backgrounds in figs. 3A and 3C as the lower and upper error bar limits for B,, we get from eq. (6) L, 2 6.83 X and L, I -6.37 A. With X = 18 A [lo] this corresponds to L, 2 120 A and L, I -115 A respectively. This illustrates the depth scale within which the method proposed in this paper is sensitive. It is obvious that since the present method relies on an analysis of the full spectrum, it is less ambiguous compared to another method [l-4]. However, more investigations on inhomogeneous systems are necessary to more clearly define the limitations of the method.
References [l] [2] [3] [4] [5] [6] [7] [8] [9] [lo]
S. Tougaard and A. Ignatiev, Surface Sci. 129 (1983) 355. S. Tougaard, Surface Sci. 162 (1985) 875. S. Tougaard, Surface Interface Anal. 8 (1986) 257. S. Tougaard, J. Vacuum, Sci. Technol. A 5 (1987) 1275. S. Zeggane and M. Delamar, Appl. Surface Sci. 29 (1987) 411. S. Tougaard, Surface Sci. 139 (1984) 208. S. Tougaard, Solid State Commun. 61 (1987) 547. S. Tougaard, Phys. Rev. B 10 (1986) 6779. S. Doniach and M. Sunjic, J. Phys. C 3 (1970) 285. C.J. Powell, J. Vacuum Sci. Technol. A 3 (1985) 1338.
Applied
Surface
Science 32 (1988) 332-337 North-Holland, Amsterdam
IN-DEPTH CONCENTRATION PROFILE INFORMATION THROUGH ANALYSIS OF THE ENTIRE XPS PEAK SHAPE S. TOUGAARD Fysisk Institut, Odense Uniuersitet, DK-5230 Odense M, Denmark
Received
26 October
1987; accepted
for publication
15 February
1988
A simple procedure, for non-destructive extraction of concentration depth profile information, through analysis of the ratio of the XPS peak area to the increase in the background signal below the peak, was previously developed. However, since only one point in the background is used in the analysis, the detailed in-depth profile cannot be determined. In the present paper, a method is defined which takes into account the shape of the inelastic background signal in a wide energy range. With the procedure, it is possible, through a simple analysis of a single XPS spectrum, to (a) decide whether the in-depth concentration varies roughly exponentially with depth and (b) determine the characteristic length of the depth profile.
1. Introduction A technique for non-destructive extraction of in-depth composition information based on an analysis of the inelastic background in XPS was previously developed [l-4]. The method relies on a simple analysis of the ratio of the XPS peak area to the increase in background signal associated with the peak. The procedure has been tested on metallic [l-4] as well as organic [5] solids. It is non-destructive, extremely fast and readily provides an estimate on the depth distribution of a given element. In the method, all physical information is deduced from a single experimentally determined number, namely the above-mentioned ratio. Since only a single point in the inelastic background signal is used in the analysis, details of the depth profiles cannot be determined [ 3,4]. In the present paper it is shown that it is possible to extract more detailed information if the full background signal associated with an XPS peak is used in the analysis. Thus, a simple procedure is defined from which it can be concluded whether the distribution of a given element is roughly exponential with depth and, in addition, the characteristic length of the in-depth profile can be determined. 0169-4332/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
333
S. Tougaard / In-depth concentration profile information
2. Theory
Assume an exponential concentration a function of depth x, i.e.
f(x)
profile, f(x)
of electron emitters, as
0)
a eCxlLa,
where L, is the attenuation length. Then the primary excitation spectrum F(E), after removal of all inelastically scattered electrons is given in terms of the measured spectrum j(E) by [6]
F(E)=j(E)-
j?C(E’-E)
,co;2+L a
j(E’)dE’,
(2)
E
where 8 is the electron exit angle with respect to the surface normal, X is the inelastic electron mean free path, and K( E' - E) is the differential inelastic scattering cross section for energy loss E' - E. For routine analysis of spectra, it was recently proposed to use a simple “universal” cross section [7]
AK(T)
=
BT (C+T*)*'
where B = 2866 eV* and C = 1643 eV2, as an approximation transition metals. Then, from eq. (2)
F(E) -j(E) -
x
Et-E cosL;+ Blm[c+(E'-E)*]* L
a
for noble and
j(E') dE’.
E
After proper background correction, we should have F(E) beyond 30-50 eV from the XPS main peak [8].
(4)
= 0 for all energies
3.Method Concentration depth profile information can now be obtained through the following simple procedure: First, the value of the parameter B, is adjusted so that after applying the equation:
F(E) =_dE)-
4J,”[c+
E'-E
j(E') dE’,
(5)
(E'-E)*]*
to the measured spectrum j(E), then F(E) = 0 in a reasonably wide energy range (e.g. from 30-100 eV) beyond - 30 eV below the XPS peak energy. If such a B, can be found, the following two conclusions can be made: (a) the depth distribution of the corresponding element is roughly exponential with depth, i.e. f(x) 2: c eexlLa;
S. Touganrd / In-depth concentration profile information
334
(b) the characteristic
L, =
&A
length is approximately
given by
cos 8. 1
If no B, exists that gives F(E) = 0 in a wide energy range below the peak, it can be concluded that the depth distribution is not exponential with depth.
4. Discussion Figs. 1A and 1B show model XPS with 8 = 0 o for two exponential in-depth distributions of impurities in copper, assuming L, = 30.6 A and L, = - 46.0 A respectively. The primary peak is of the Doniach-Sunjic form [9] with (Y= 3 eV and y = 0.1 centered around 1000 eV. For details of the method of calculation see refs. [3,6]. Now, eq. (5) was applied to these spectra adjusting the factor B,. With B, = 1900 eV2 and 4300 eV2 respectively, the resulting
920
940
960
ELECTRON
980
ENERGY
IOCKJ
(eV
l(
10
)
Fig. 1. Model XPS i(E) for exponential distributions in Cu of electron emitters with the energy distribution cl(E). In (A) and (B), the characteristic length of the distribution is L, = 30.6 A and L, = -46.0 A respectively. F(E) results when eq. (5) is applied to j(E) adjusting B, to give F(E) = 0 in a wide energy region below the peak.
S. Tougaard / In-depth concentration profile information
920
940
960
ELECTRON
960 ENERGY
1000
11
335
10
(eV)
Fig. 2. Model XPS j(E) for a depth distribution given by f(x) = 0 for 0 -Cx -C 40 A and f(x) = constant for x > 40 A. F,(E) is the primary electron energy distribution. The spectra F(E) result when eq. (5) is applied to j(E) for two values of B,. (The spectra j(E) are identical in the two figures but the scales are different.)
primary spectra are roughly zero in a wide energy range below the0 peak energy. Thus the conditions for (a) and (b) are fullfilied. With X = 16 A [lo], we find from eq. [6] L, = 30 A and L, = - 50 A respectively, in good agreement with the actual in-depth distribution profiles. Fig. 2 shows a similar model XPS for a depth distribution given by f(x) = 0 for 0 c x -C 40 A and f(x) = constant for x > 40 A. Also shown is the result after application of eq. (5) for two values of B,. It is clearly seen that there does not exist a B, which gives F(E) 2: 0 in a wide energy range below the peak. Then, from the above, it is concluded that the distribution is not exponential with depth in agreement with the true depth distribution. Finally, we apply eqs. (5) and (6) to experimental XPS for a homogeneous impurity depth distribution. Since the inelastic properties of the transition and noble metals are strikingly similar [7], we expect to first order the overall XPS peak shape to depend only on the in-depth concentration profile and to be independent of the impurity concentration. Furthermore, in view of the great
336
S. Tougaard / In-depth concentration
profile information
J
1100
1020
ELECTRON
ENERGY
1200
(eV)
Fig. 3. Al Ka excited XPS of pure gold in the energy range of the Au 4d peaks (upper curves). lower curves are obtained after application of eq. (5) using three different values of B,.
The
experimental difficulties in producing samples with a well known in-depth concentration profile we therefore illustrate the application of the method to experimental XPS of a pure metal. Measured XPS of pure gold is shown in fig. 3 in the region of the Au 4d peaks, after correcting for the analyser transmission function and after subtraction of a constant background. The lower curves in figs. 3A-3C are obtained by eq. (5) using B, = 2500 eV2, 2866 eV2, and 3400 eV2 respectively. It is clear that in fig. 3A, the inelastic background intensity in the corrected spectrum is still too high, while in fig. 3C it is too low. In fig. 3B, however, the intensity in the background corrected spectrum is roughly zero in the full - 30-100 eV energy range below the XPS peak structure. Consequently, in fig. 3B, the conditions for (a) and (b) are fulfilled with B, = 2900 eV2. It can then be concluded that the observed gold is, to a good approximation, exponentially distributed with depth in the sample and that the attenua-
S. Tougaard / In-depth concentration profile information
337
tion length (by eq. (6)) is L, 2: co i.e. the gold concentration is constant in the surface region of the solid. This is in perfect agreement with the fact that the spectrum is measured from a pure gold sample. If we take the calculated backgrounds in figs. 3A and 3C as the lower and upper error bar limits for B,, we get from eq. (6) L, 2 6.83 X and L, I -6.37 A. With X = 18 A [lo] this corresponds to L, 2 120 A and L, I -115 A respectively. This illustrates the depth scale within which the method proposed in this paper is sensitive. It is obvious that since the present method relies on an analysis of the full spectrum, it is less ambiguous compared to another method [l-4]. However, more investigations on inhomogeneous systems are necessary to more clearly define the limitations of the method.
References [l] [2] [3] [4] [5] [6] [7] [8] [9] [lo]
S. Tougaard and A. Ignatiev, Surface Sci. 129 (1983) 355. S. Tougaard, Surface Sci. 162 (1985) 875. S. Tougaard, Surface Interface Anal. 8 (1986) 257. S. Tougaard, J. Vacuum, Sci. Technol. A 5 (1987) 1275. S. Zeggane and M. Delamar, Appl. Surface Sci. 29 (1987) 411. S. Tougaard, Surface Sci. 139 (1984) 208. S. Tougaard, Solid State Commun. 61 (1987) 547. S. Tougaard, Phys. Rev. B 10 (1986) 6779. S. Doniach and M. Sunjic, J. Phys. C 3 (1970) 285. C.J. Powell, J. Vacuum Sci. Technol. A 3 (1985) 1338.