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Effects of electron correlations on Auger-electron and appearance-potential spectra of solid surfaces
ijii!i~ii~i~ii~ii~iiiiii~iiiiiiii~ surface science ELSEVIER
Surface Science 307-309 (1994) 942-946
Effects of electron correlations on Auger-electron and appearance-potential spectra of solid surfaces M. Potthoff *'a, j. Braun a, W. Nolting b, G. Borstel
a
a Department of Physics, University of Osnabriick, D-49069 Osnabriick, Germany b Department of Physics, University of Valladolid, E-47011 Valladolid, Spain (Received 20 August 1993)
Abstract
In the past the Cini-Sawatzky model and its generalizations to arbitrary band-filling and orbital degeneracy have been employed extensively in the discussion of electron-correlation effects in CVV Auger-electron (AIE) and appearance-potential (AP) spectra of solid surfaces. In all these attempts, however, the strong inherent perturbation of the valence-band system due to the core-hole potential has been neglected up to now. We present results of a new theoretical approach for arbitrary band-filling, which for the first time accounts for the on-site Coulomb interaction among the valence-band electrons U and for the Coulomb interaction between valence-band and core electrons Uc as well. The AE- and AP-intensities are given by a three-particle Green function, which is calculated using a diagrammatic vertex-correction method. The spectra show a strong dependence on the valence-band-core interaction Uc and exhibit several satellite features in the strong-correlation case. They indicate the importance of an accurate description of the effects of the core-hole potential for AE- and AP-spectra of solids.
I. Introduction
One of the main advantages of CVV Augerelectron (ALES) and appearance-potential spectroscopy (APS) is their direct sensitivity to electron-correlation effects. There can be no doubt that for many systems electron-correlation effects even dominate the general form of the line shape. For this reason and because of their comparatively simple experimental setup, AES and APS appear as attractive tools for studying the electronic structure of solid surfaces. However, since just correlation effects prevent us from a simple
* Corresponding author. Fax: +49 (541) 969 2670.
interpretation of the measured line shape within a self-convolution model [1], there is an urgent need for a general theory of AES and APS, from which we can extract information on the electronic structure via comparison of experimental and theoretical results. Concerning the description of the effects due to correlations among the valence-band electrons (VV correlations), the Cini-Sawatzky model [2,3] has served as a paradigm for CVV AES and, to a less extent, APS line-shape analysis and was generalized with respect to arbitrary band-filling, orbital degeneracy, finite temperatures, etc. in the past [4-8]. In search of an adequate theoretical model for CVV Auger-electron and appearancepotential spectroscopy, however, the treatment of
0039-6028/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved
SSDI 0 0 3 9 - 6 0 2 8 ( 9 3 ) E 0 9 1 1 - D
M. Potthoff et aL /Surface Science 307-309 (1994) 942-946
VV correlations is only one part of the problem. The strong inherent perturbation of the system due to the core-hole potential must not be forgotten about. In the initial state for AES, the primary core hole causes the valence-band electrons to rearrange themselves and to screen the corehole potential partially. In the final state the valence-band electrons adjust to the sudden destruction of the core hole. For APS the valenceband electrons are scattered at the core-hole potential present in the final state. All those effects are a consequence of correlations between the valence-band and the core electrons (CV correlations). CV correlations, however, are not considered within the Cini-Sawatzky model. On the other hand, in the only approach that rigorously treats the CV correlations, VV correlations are neglected altogether [9]. Another serious attempt to
943
the problem has been performed by Cini [10], who considered a three-particle Green function thereby including VV as well as CV correlation effects. Actually, he treated an effective single impurity problem (Anderson model). His approach, however, is restricted to low hole (electron) concentrations from the very beginning. For this special case the three-particle Green function is simply given by the convolution of the core Green function with a two-particle valence-band Green function. Since this simplifying separation is no longer valid for the general case of arbitrary band-filling, and VV and CV final-state correlations are mixed in a more intricate way, one has to look for a completely different way to tackle the problem. Provided that the CV correlations are weak, we could show recently that perturbation theory is applicable for arbitrary band-filling [11]. The
i
A--
- ' + '
=
T;i,.
+
+i
i'i"l
I
77-
T>
+
+,, i"
,
~
~
,
,
+ " ' ~
Fig. 1. Diagrammatic representation of the three-particle Green function G (3) by means of the vertex function A (topmost equation). Diagrammatic decomposition of A into special vertex functions £, r/, and ~" (second equation). Diagrammatic form of coupled system of Dyson equations for £, 77, and ~" (last three equations). Double solid (wavy) lines represent renormalized valence-band (core) propagators. Dotted (dashed) lines represent the U (Uc) interaction.
944
M. Potthoff et al. / Surface Science 307-309 (1994) 942-946
purpose of this paper is to present the results of a new approach for the description of CVV AEand AP-spectra for the general case of arbitrary band-filling and arbitrary strengths of VV and CV correlations. Of course, for this most general case approximations are inevitable. Here, we consider a three-particle ladder approximation, which turns out to be exact for the limiting cases of the completely filled and the empty valence band [12] and which is assumed to give a reasonable interpolation in between, as it is assumed for the two-particle ladder approximation in the calculation of two-particle Green functions, too [4,7,13].
2. Theory The basic theory [11] gives the AE- and AP-intensities in terms of a three-particle Green function, which is built up in its Wannier representation from creation (annihilation) operators c~ and bti~ (c w and bi~) for valence-band and core electrons at the lattice site i and with spin index o-, respectively: -2
I ( E ) = --~-Im G ° ) ( E ) _
-2Im((bti~ci~ci h2
t
t
~; Ci_~rCi~rbitr))E.
(1)
For AES the three-particle Green function G (3) has to be evaluated in the subspace of all states with a hole in the core level with spin index tr at the site i. For APS the subspace of all states with this core level filled has to be taken into account. For distinctness we consider a non-degenerate valence band, characterized by the hopping integrals T~j, and a non-degenerate s-like core level with one-particle energy E~. Let ni~r = Cti~rCicr and - b ~ b i , ~ be the occupation-number operators n i,r -for valence-band and core electrons, respectively. Then our model Hamiltonian reads:
H = Y'~ Tijcti,,cj, ~ + ec~_,bti~bi~ + ½UY'~ni~ni_,~ ijo,
itr
-t- U c E i o - o -r
llitrnie ' .
io"
(2)
The U-interaction term is the usual Hubbard interaction describing the VV correlations, while the Uc-interaction term accounts for the CV correlations. For the calculation of the three-particle Green function G (3) within the considered model, we employ a diagrammatic vertex-correction method (see Fig. 1). The approach is described in detail in Ref. [14]. Here, we briefly sketch the most essential points only. According to the first diagrammatic equation in Fig. 1, G (3) may be expressed in terms of a three-particle vertex function A, which is defined as the sum of all diagram parts with two connection points for external valence-band propagators and one connection point for an external core propagator. A is thought to be irreducible in the sense that it is impossible to split off full self-energy diagrams of the oneparticle propagators. Generally, the three-particle vertex function cannot be determined exactly. In analogy to the ladder approximation for two-particle Green functions, we calculate A considering only threeparticle ladder diagrams, thereby neglecting diagrams that involve the creation or annihilation of electron-hole pairs in the valence band. This generalized ladder approximation turns out to be exact for the limiting cases of the completely filled and the empty valence band and is reduced to a generalized Cini-Sawatzky model for Uc = 0. As it is shown schematically by the second equation in Fig. 1, the vertex function d can be decomposed into three parts sc, 77, and ~" that belong to special subclasses of ladder-diagram parts. Within the generalized ladder approximation the functions ~, r/, and ~ can be calculated from the Dyson equations shown in diagrammatic form in Fig. 1. The Dyson equations form a set of three coupled linear integral equations, which is solved numerically. The "dressed" one-particle propagators are calculated by means of the equation-of-motion method employing simple Stoner-like mean-field decouplings for higher-order Green functions [14]. Additionally, a small constant imaginary part of i0.25 eV has been added to the resulting self-energies for computational reasons. For a first impression of the qualitative effects of VV and CV
M. Potthoff et aL / Surface Science 307-309 (1994) 942-946
correlations on the spectra, this procedure should be sufficient. In principle, there is no difficulty to consider more elaborate techniques for calculating the one-particle self-energies.
eV. We have calculated AE- and AP-spectra for U = 10 eV and different values for Uc and the band-filling ( n ) (see Fig. 2). For Uc = 0 eV, the calculated AE- and APspectra separate into a band-like part of rather small spectral weight and a strong satellite, as it is known from the generalized Cini-Sawatzky model [7]. The considerable width of the satellite is due to the finite imaginary constant, which has been added to the self-energies. This well-known situation changes drastically, however, if the valenceb a n d - c o r e interaction is switched on. For APS
3. Results and discussion
The numerical calculations have been performed for a paramagnetic tight-binding valence band of a simple-cubic crystal. The corresponding density of states has an approximate width of 3
I
I
i
AES
~ - 1.0 ~
i
L
I
J
//
i
= 080
' <'~:'"'-: °~'°-1
U
1.0
~.
..
Xo1
c-
~
I
I
k.....
t
I
I
0.20
=
uC
0.5
-=4
0
i
APS
9
.d k_
945
0.5
,
,
-4 -2
o
-4 -2 0
V
2
4 .,"
I I
~
•,
-....
A
2
2
>,,,
ov
.m
03 I= ¢-. eV
c2 v
= lO ~
~ , .
U
0.5
q -4 -2 0
2
k
5 eV
__JUL.
E-E~ ..__ I I I I -25-20-15-10
4 eV
I -5
I 0
I 5
Energy
I I -10-5
//
I 0
6 eV I 5
I 10
I 15
(eV)
Fig. 2. Calculated AE- and AP-spectra for U = 10 eV and different indicated values for Uc. Band-filling: ( n ) = 0.80 for AES ( ( n ) = 0.47 for the last AE-spectrum), ( n ) = 0.20 for APS. Parts of the spectra are enhanced by a factor 10 (dotted lines). The energy zero is chosen to be the center of gravity of the self-convolution of the density of states. For AES, the insets show the respective local density of states (LDOS) corresponding to the values for Uc and the local valence-band occupation n u m b e r ( n ) * at the site, where the transition takes place. For APS, the inset shows the (translationally invariant) density of states (DOS). E F denotes the Fermi energy.
946
M. Potthoff et al. / Surface Science 307-309 (1994) 942-946
even small values for Uc cause substantial changes of the line shape. Generally, the spectra are observed to be strongly dependent on Uc, and for strong CV correlations several sharp satellite features come into existence due to a complex combination of VV and CV final-state correlations. In contrast, the Auger spectra, calculated for an average number of holes in the valence band 1 - ( n ) = 0.20 that is equal to the average number of valence-band electrons considered for APS, do not exhibit as complex structures as the APspectra. However, in the case of AES, we have to bear in mind that there are non-trivial initial-state CV correlations. Since in the initial state for AES the valence-band electrons rearrange to screen the core-hole potential partially, the density of states becomes site-dependent. At the lattice site i, where the transition takes place, the local density of states generally moves downwards in energy (see insets in Fig. 2). For Uc = 4 eV and ( n ) = 0.80 this results in a local valence-band occupation number ( n ) * = 0.96. So at the site i the valence states are almost completely filled. Since it is known [12] that there are no deviations from the Cini-Sawatzky line shape for a completely filled valence band ( ( n ) = ( n ) * = 1.0), the deviations from the Cini-Sawatzky line shape for AES for ( n ) = 0.80 are not as pronounced as for APS for ( n ) = 0.20. For Uc= 4 eV and ( n ) = 0 . 2 0 the AP-spectrum should be compared with the Auger spectrum for Uc = 4 eV and ( n ) = 0.47. In this case the CV correlations in the initial state for AES result in ( n ) * = 0.80, and now, as for APS, the Auger spectrum shows more pronounced satellite structures. Both, the AE- and the AP-spectrum, exhibit a rather long tail on the respective low- or high-energetic side of the main satellites.
Concludingly, we can state that in the case of partially filled valence bands AE- and AP-spectra may be substantially affected by the core-hole potential, which is not considered within the Cini-Sawatzky model. In a theory of electroncorrelation effects for AES and APS both, VV and CV correlations, should be treated with equal importance. With the presented diagrammatic vertex-correction method we have shown a reasonable way to tackle this problem.
4. Acknowledgement Financial support of this work by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.
5. References [1] J.J. Lander, Phys. Rev. 91 (1953) 1382. [2] M. Cini, Solid State Commun. 24 (1977) 681. [3] G.A. Sawatzky, Phys. Rev. Lett. 39 (1977) 504. [4] G. Tr6glia, M.C. Desjonqu~res, F. Ducastelle and D. Spanjaard, J. Phys. C 14 (1981) 4347. [5] C. Presilla and F. Sacchetti, J. Phys. F 17 (1987) 779. [6] M. Kotrla and V. Drchal, J. Phys.: Condensed Matter 1 (1989) 4783. [7] W. Nolting, Z. Phys. B 80 (1990) 73. [8] W. Nolting, G. Geipel and K. Ertl, Phys. Rev. B 45 (1992) 5790. [9] M. Natta and P. Joyes, J. Phys. Chem. Solids 31 (1970) 447. [10] M. Cini, Surf. Sci. 87 (1979) 483. [11] M. Potthoff, J. Braun, G. Borstel and W. Nolting, Phys. Rev. B 47 (1993) 12480. [12] M. Potthoff, J. Braun, W. Nolting and G. Borstel, J. Phys.: Condensed Matter 5 (1993) 6879. [13] V. Drchal and J. Kudrnovsk~, J. Phys. F 14 (1984) 2443. [14] M. Potthoff, J. Braun and G. Borstel, to be published.
Surface Science 307-309 (1994) 942-946
Effects of electron correlations on Auger-electron and appearance-potential spectra of solid surfaces M. Potthoff *'a, j. Braun a, W. Nolting b, G. Borstel
a
a Department of Physics, University of Osnabriick, D-49069 Osnabriick, Germany b Department of Physics, University of Valladolid, E-47011 Valladolid, Spain (Received 20 August 1993)
Abstract
In the past the Cini-Sawatzky model and its generalizations to arbitrary band-filling and orbital degeneracy have been employed extensively in the discussion of electron-correlation effects in CVV Auger-electron (AIE) and appearance-potential (AP) spectra of solid surfaces. In all these attempts, however, the strong inherent perturbation of the valence-band system due to the core-hole potential has been neglected up to now. We present results of a new theoretical approach for arbitrary band-filling, which for the first time accounts for the on-site Coulomb interaction among the valence-band electrons U and for the Coulomb interaction between valence-band and core electrons Uc as well. The AE- and AP-intensities are given by a three-particle Green function, which is calculated using a diagrammatic vertex-correction method. The spectra show a strong dependence on the valence-band-core interaction Uc and exhibit several satellite features in the strong-correlation case. They indicate the importance of an accurate description of the effects of the core-hole potential for AE- and AP-spectra of solids.
I. Introduction
One of the main advantages of CVV Augerelectron (ALES) and appearance-potential spectroscopy (APS) is their direct sensitivity to electron-correlation effects. There can be no doubt that for many systems electron-correlation effects even dominate the general form of the line shape. For this reason and because of their comparatively simple experimental setup, AES and APS appear as attractive tools for studying the electronic structure of solid surfaces. However, since just correlation effects prevent us from a simple
* Corresponding author. Fax: +49 (541) 969 2670.
interpretation of the measured line shape within a self-convolution model [1], there is an urgent need for a general theory of AES and APS, from which we can extract information on the electronic structure via comparison of experimental and theoretical results. Concerning the description of the effects due to correlations among the valence-band electrons (VV correlations), the Cini-Sawatzky model [2,3] has served as a paradigm for CVV AES and, to a less extent, APS line-shape analysis and was generalized with respect to arbitrary band-filling, orbital degeneracy, finite temperatures, etc. in the past [4-8]. In search of an adequate theoretical model for CVV Auger-electron and appearancepotential spectroscopy, however, the treatment of
0039-6028/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved
SSDI 0 0 3 9 - 6 0 2 8 ( 9 3 ) E 0 9 1 1 - D
M. Potthoff et aL /Surface Science 307-309 (1994) 942-946
VV correlations is only one part of the problem. The strong inherent perturbation of the system due to the core-hole potential must not be forgotten about. In the initial state for AES, the primary core hole causes the valence-band electrons to rearrange themselves and to screen the corehole potential partially. In the final state the valence-band electrons adjust to the sudden destruction of the core hole. For APS the valenceband electrons are scattered at the core-hole potential present in the final state. All those effects are a consequence of correlations between the valence-band and the core electrons (CV correlations). CV correlations, however, are not considered within the Cini-Sawatzky model. On the other hand, in the only approach that rigorously treats the CV correlations, VV correlations are neglected altogether [9]. Another serious attempt to
943
the problem has been performed by Cini [10], who considered a three-particle Green function thereby including VV as well as CV correlation effects. Actually, he treated an effective single impurity problem (Anderson model). His approach, however, is restricted to low hole (electron) concentrations from the very beginning. For this special case the three-particle Green function is simply given by the convolution of the core Green function with a two-particle valence-band Green function. Since this simplifying separation is no longer valid for the general case of arbitrary band-filling, and VV and CV final-state correlations are mixed in a more intricate way, one has to look for a completely different way to tackle the problem. Provided that the CV correlations are weak, we could show recently that perturbation theory is applicable for arbitrary band-filling [11]. The
i
A--
- ' + '
=
T;i,.
+
+i
i'i"l
I
77-
T>
+
+,, i"
,
~
~
,
,
+ " ' ~
Fig. 1. Diagrammatic representation of the three-particle Green function G (3) by means of the vertex function A (topmost equation). Diagrammatic decomposition of A into special vertex functions £, r/, and ~" (second equation). Diagrammatic form of coupled system of Dyson equations for £, 77, and ~" (last three equations). Double solid (wavy) lines represent renormalized valence-band (core) propagators. Dotted (dashed) lines represent the U (Uc) interaction.
944
M. Potthoff et al. / Surface Science 307-309 (1994) 942-946
purpose of this paper is to present the results of a new approach for the description of CVV AEand AP-spectra for the general case of arbitrary band-filling and arbitrary strengths of VV and CV correlations. Of course, for this most general case approximations are inevitable. Here, we consider a three-particle ladder approximation, which turns out to be exact for the limiting cases of the completely filled and the empty valence band [12] and which is assumed to give a reasonable interpolation in between, as it is assumed for the two-particle ladder approximation in the calculation of two-particle Green functions, too [4,7,13].
2. Theory The basic theory [11] gives the AE- and AP-intensities in terms of a three-particle Green function, which is built up in its Wannier representation from creation (annihilation) operators c~ and bti~ (c w and bi~) for valence-band and core electrons at the lattice site i and with spin index o-, respectively: -2
I ( E ) = --~-Im G ° ) ( E ) _
-2Im((bti~ci~ci h2
t
t
~; Ci_~rCi~rbitr))E.
(1)
For AES the three-particle Green function G (3) has to be evaluated in the subspace of all states with a hole in the core level with spin index tr at the site i. For APS the subspace of all states with this core level filled has to be taken into account. For distinctness we consider a non-degenerate valence band, characterized by the hopping integrals T~j, and a non-degenerate s-like core level with one-particle energy E~. Let ni~r = Cti~rCicr and - b ~ b i , ~ be the occupation-number operators n i,r -for valence-band and core electrons, respectively. Then our model Hamiltonian reads:
H = Y'~ Tijcti,,cj, ~ + ec~_,bti~bi~ + ½UY'~ni~ni_,~ ijo,
itr
-t- U c E i o - o -r
llitrnie ' .
io"
(2)
The U-interaction term is the usual Hubbard interaction describing the VV correlations, while the Uc-interaction term accounts for the CV correlations. For the calculation of the three-particle Green function G (3) within the considered model, we employ a diagrammatic vertex-correction method (see Fig. 1). The approach is described in detail in Ref. [14]. Here, we briefly sketch the most essential points only. According to the first diagrammatic equation in Fig. 1, G (3) may be expressed in terms of a three-particle vertex function A, which is defined as the sum of all diagram parts with two connection points for external valence-band propagators and one connection point for an external core propagator. A is thought to be irreducible in the sense that it is impossible to split off full self-energy diagrams of the oneparticle propagators. Generally, the three-particle vertex function cannot be determined exactly. In analogy to the ladder approximation for two-particle Green functions, we calculate A considering only threeparticle ladder diagrams, thereby neglecting diagrams that involve the creation or annihilation of electron-hole pairs in the valence band. This generalized ladder approximation turns out to be exact for the limiting cases of the completely filled and the empty valence band and is reduced to a generalized Cini-Sawatzky model for Uc = 0. As it is shown schematically by the second equation in Fig. 1, the vertex function d can be decomposed into three parts sc, 77, and ~" that belong to special subclasses of ladder-diagram parts. Within the generalized ladder approximation the functions ~, r/, and ~ can be calculated from the Dyson equations shown in diagrammatic form in Fig. 1. The Dyson equations form a set of three coupled linear integral equations, which is solved numerically. The "dressed" one-particle propagators are calculated by means of the equation-of-motion method employing simple Stoner-like mean-field decouplings for higher-order Green functions [14]. Additionally, a small constant imaginary part of i0.25 eV has been added to the resulting self-energies for computational reasons. For a first impression of the qualitative effects of VV and CV
M. Potthoff et aL / Surface Science 307-309 (1994) 942-946
correlations on the spectra, this procedure should be sufficient. In principle, there is no difficulty to consider more elaborate techniques for calculating the one-particle self-energies.
eV. We have calculated AE- and AP-spectra for U = 10 eV and different values for Uc and the band-filling ( n ) (see Fig. 2). For Uc = 0 eV, the calculated AE- and APspectra separate into a band-like part of rather small spectral weight and a strong satellite, as it is known from the generalized Cini-Sawatzky model [7]. The considerable width of the satellite is due to the finite imaginary constant, which has been added to the self-energies. This well-known situation changes drastically, however, if the valenceb a n d - c o r e interaction is switched on. For APS
3. Results and discussion
The numerical calculations have been performed for a paramagnetic tight-binding valence band of a simple-cubic crystal. The corresponding density of states has an approximate width of 3
I
I
i
AES
~ - 1.0 ~
i
L
I
J
//
i
' <'~:'"'-: °~'°-1
U
1.0
~.
..
Xo1
c-
~
I
I
k.....
t
I
I
0.20
=
uC
0.5
-=4
0
i
APS
9
.d k_
945
0.5
,
,
-4 -2
o
-4 -2 0
V
2
4 .,"
I I
~
•,
-....
A
2
2
>,,,
ov
.m
03 I= ¢-. eV
c2 v
= lO ~
~ , .
U
0.5
q -4 -2 0
2
k
5 eV
__JUL.
E-E~ ..__ I I I I -25-20-15-10
4 eV
I -5
I 0
I 5
Energy
I I -10-5
//
I 0
6 eV I 5
I 10
I 15
(eV)
Fig. 2. Calculated AE- and AP-spectra for U = 10 eV and different indicated values for Uc. Band-filling: ( n ) = 0.80 for AES ( ( n ) = 0.47 for the last AE-spectrum), ( n ) = 0.20 for APS. Parts of the spectra are enhanced by a factor 10 (dotted lines). The energy zero is chosen to be the center of gravity of the self-convolution of the density of states. For AES, the insets show the respective local density of states (LDOS) corresponding to the values for Uc and the local valence-band occupation n u m b e r ( n ) * at the site, where the transition takes place. For APS, the inset shows the (translationally invariant) density of states (DOS). E F denotes the Fermi energy.
946
M. Potthoff et al. / Surface Science 307-309 (1994) 942-946
even small values for Uc cause substantial changes of the line shape. Generally, the spectra are observed to be strongly dependent on Uc, and for strong CV correlations several sharp satellite features come into existence due to a complex combination of VV and CV final-state correlations. In contrast, the Auger spectra, calculated for an average number of holes in the valence band 1 - ( n ) = 0.20 that is equal to the average number of valence-band electrons considered for APS, do not exhibit as complex structures as the APspectra. However, in the case of AES, we have to bear in mind that there are non-trivial initial-state CV correlations. Since in the initial state for AES the valence-band electrons rearrange to screen the core-hole potential partially, the density of states becomes site-dependent. At the lattice site i, where the transition takes place, the local density of states generally moves downwards in energy (see insets in Fig. 2). For Uc = 4 eV and ( n ) = 0.80 this results in a local valence-band occupation number ( n ) * = 0.96. So at the site i the valence states are almost completely filled. Since it is known [12] that there are no deviations from the Cini-Sawatzky line shape for a completely filled valence band ( ( n ) = ( n ) * = 1.0), the deviations from the Cini-Sawatzky line shape for AES for ( n ) = 0.80 are not as pronounced as for APS for ( n ) = 0.20. For Uc= 4 eV and ( n ) = 0 . 2 0 the AP-spectrum should be compared with the Auger spectrum for Uc = 4 eV and ( n ) = 0.47. In this case the CV correlations in the initial state for AES result in ( n ) * = 0.80, and now, as for APS, the Auger spectrum shows more pronounced satellite structures. Both, the AE- and the AP-spectrum, exhibit a rather long tail on the respective low- or high-energetic side of the main satellites.
Concludingly, we can state that in the case of partially filled valence bands AE- and AP-spectra may be substantially affected by the core-hole potential, which is not considered within the Cini-Sawatzky model. In a theory of electroncorrelation effects for AES and APS both, VV and CV correlations, should be treated with equal importance. With the presented diagrammatic vertex-correction method we have shown a reasonable way to tackle this problem.
4. Acknowledgement Financial support of this work by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.
5. References [1] J.J. Lander, Phys. Rev. 91 (1953) 1382. [2] M. Cini, Solid State Commun. 24 (1977) 681. [3] G.A. Sawatzky, Phys. Rev. Lett. 39 (1977) 504. [4] G. Tr6glia, M.C. Desjonqu~res, F. Ducastelle and D. Spanjaard, J. Phys. C 14 (1981) 4347. [5] C. Presilla and F. Sacchetti, J. Phys. F 17 (1987) 779. [6] M. Kotrla and V. Drchal, J. Phys.: Condensed Matter 1 (1989) 4783. [7] W. Nolting, Z. Phys. B 80 (1990) 73. [8] W. Nolting, G. Geipel and K. Ertl, Phys. Rev. B 45 (1992) 5790. [9] M. Natta and P. Joyes, J. Phys. Chem. Solids 31 (1970) 447. [10] M. Cini, Surf. Sci. 87 (1979) 483. [11] M. Potthoff, J. Braun, G. Borstel and W. Nolting, Phys. Rev. B 47 (1993) 12480. [12] M. Potthoff, J. Braun, W. Nolting and G. Borstel, J. Phys.: Condensed Matter 5 (1993) 6879. [13] V. Drchal and J. Kudrnovsk~, J. Phys. F 14 (1984) 2443. [14] M. Potthoff, J. Braun and G. Borstel, to be published.