- Email: [email protected]
The phosphorus Auger L2.3VV spectrum of InP(110)
Solid State Communications, Vol. 79, No. 2, pp. 191-195, 1991. Printed in Great Britain. THE PHOSPHORUS AUGER
L2.3VVS P E C T R U M
0038-1098/91 $3.00 + .00 Pergamon Press plc OF InP(1 1 0)
P.O. Nilsson Department of Physics, Chalmers University of Technology, S-412 96 G6teborg, Sweden and S.P. Svensson Martin Marietta Laboratories, Baltimore, MD 21227, USA
(Received 4 March 1991 by B. Lundqvist) The L2,3VVAuger spectrum of InP(1 1 0) has been measured using synchrotron radiation excitation. In a first step a one-body theory was applied for analysis, involving convolutions of partial, local density of states functions obtained from a band calculation. The effect of holehole correlations in the valence band was then evaluated using the Cini-Sawatzky model. 1. I N T R O D U C T I O N
bonding of the constituents, in particular for more complicated compounds such as ternaries and quarternaries. Valence Auger spectra of metals have been treated in the literature in some detail [3], while spectra from semiconductors are more scarse [4]. Essentially only the Si L2,3VVspectrum has been thoroughly analyzed [5]. As there is now a very intensive research taking place on the electronic structure of surfaces and interfaces of semiconductors it is of great importance to find out if a simple model can be applied to the analysis of CVV spectra for these materials. Specifically we want to determine the influence of the many-body effects on the CVV transitions and relate it to earlier studies on Si [5]. From the outset it is not clear whether a single-particle model is at all adequate. For example, even the application of the cited Ue~/W rule is not trivial for a semiconductor since several bands are involved, in some cases separated by a gap; the heteropolar gap in compound semiconductors. This means for example that one single value for Ueermay not be sufficient.
A U G E R electron spectroscopy has mainly been used as a routine tool for qualitative and quantitative analysis, in particular of surfaces. However, the technique can also be used for investigations of the electronic structure of solids. For studies of valence bands the CVV transitions are of special interest. In such a process the initial state consists of one core hole while the final state contains two holes in the valence band and an escaping Auger electron. The final state rule [1] says that the detected energies are those of the final state, while the transition amplitudes also depend on the initial state. Thus, as the final state contains no core hole in the CVV process (in contrast to e.g. the CCV process) we expect to test the unscreened band structure in an independent particle model. This situation should prevail when the effective Coulomb interaction Uar is much smaller than the valence band width W. In the Cini-Sawatzky model [2] the condition is U~J2W ~< 1. In the independent particle picture the measured spectrum is a sum of weighted convolutions of ground state density of states functions. As the perturbation operator in the Auger pro2. E X P E R I M E N T A L D E T A I L S cess is the Coulomb interaction the selection rules are very much relaxed compared to the dipole selection The P L2.3VV transition in InP waschosen due to rule for optical transitions. However, combined with its favourable energy position relative to other specsimple theory, information may be extracted about tral features. Only a few other, very weak, transitions partial (i.e. angular momentum decomposed) density from either of the constituents are expected to overlap of states functions. In addition one of the most valu- with the peaks we are studying [6]. Furthermore, the able characteristics of Auger transitions is that the P Lz,3VV transition appears at a sufficiently high local valence density of states is tested. This site sen- energy so that the large background of the low energy sitivity, not present in e.g. photoemission, is of par- secondary electrons does not interfere with the low ticular importance for investigations of alloys and energy part of the peak. These facts make it possible compounds since it may reveal information about the to obtain a very clean spectrum without complicated 191
192
THE PHOSPHORUS A U G E R I
I
L2.3VVSPECTRUM
!i.il
t~
pr(r, E) ~ f IWL(r)I26(E- e)de.
I(Ef)
= ~" PL ® PL' WLL'(E/),
I
I
I
100
110
120
where ® denotes convolution: 130
PL ® PL' = f d~opL(E - ~o)pL'(E, + oJ).
Fig. 1. The upper curve is the experimental L2,3VV phosphorus Auger spectrum of InP(1 1 0) excited by synchrotron radiation (hv = 150 eV). The lower curve is calculated in an one-electron approximation using results from a band calculation.
background subtraction. The P L2,3VVtransition has also been studied earlier for Si [5] which makes direct comparison possible between a binary and an elemental semiconductor. The InP(1 1 0) surface was produced by cleavage in ultrahigh vacuum (UHV). The surface produced a sharp LEED pattern with only a weak background. The Auger excitation was done by synchrotron light of 150eV from the MAX storage ring in Lund, Sweden. The advantage of using synchrotron light is the low background compared with electron excitation. The Auger electrons were detected under normal emission using a semi-spherical analyzer. No essential difference was detected for various emission angles. The spectrum as recorded is reprodficed in Fig. 1. 3. THEORY In an independent particle description the CVV Auger current can be expressed as [7] --
Z L I L'I L 2 L~
(3)
LL'
Kine~cenergy(eV)
I(Es)
(2)
The line shape of the Auger spectrum becomes
Theory 90
Vol. 79, No. 2
general smallness of the off-diagonal elements of FLL.(E) it should be enough to consider the diagonal part of the matrices. This approximation results in a simple theory based on the conventional local, partial density of states functions
I
InP ,6
OF InP(1 1 0)
fdO~FL,L~(EI-a~)FL2L~
x (E,, + cO)WL, LiL:L~(Ef).
(4)
The presented model relies on the one-particle approximation, i.e. the valence electrons are assumed frozen in their ground state during the Auger process. This cannot be rigorously true because the Auger process itself requires an interaction to occur between two electrons. The essential many-body effects may be discussed in terms of screening effects in the initial and final states [8]. One of the most important contributions is the final state hole-hole interaction in the valence band. The interaction can be characterized by an effective net Coulomb repulsion U~. For a single, filled band the Cini-Sawatzky model gives [5] N(E)LL, =
pL(E) ® pL,(E) [1 -- UeerlLL,(E)]2 + rflUZ~r[pL(E) ® pL,(E)] 2' (5)
where the folded one-electron density of states is denoted by pL(E) ® pL,(E). The function ILL'(E) is the Hilbert transform of pL(E) ® pL'(E). When Uefr is increased from zero peaks are expected to shift towards higher binding energies, while the upper and lower boundaries of the total spectrum are unchanged. For Uaf larger than twice the band width a satellite splits off below the spectrum. One may argue that such a model is too simple to apply here. However, UCfrwill turn out to be fairly small and we assume that any error can be absorbed in the U,fr parameter. 4. RESULTS AND DISCUSSION
(1)
Here EI is the energy of the Auger electron and E,. the core hole energy. The FLL,(E) functions are the elements of local, occupied density of states matrices with angular momentum L = (1,m). The WL,LIL2L~ factors denote transition probabilities affd contain Auger matrix elements and geometrical factors. These can with good accuracy be represented by atomic integrals. It has been shown [7] that because of the
The band structure of InP was calculated using a semi-empirical LCAO method [6]. The parameters were chosen to fit the bands of Chelikowski et al. [9]. These bands were recently confirmed by angleresolved photoelectron spectroscopy to an accuracy of about 0.1 eV [10]. The local, partial density of states functions were calculated by a Monte Carlo method. Out of these only the phosphorus functions will contribute to this particular Auger spectrum. The ss-, sp-,
Vol. 79, No. 2 I
I
I
I
I
I
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pp-foM
P in InP
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I
0
EnergyrelativeVBM(eV) Fig. 2. The folds of the phosphorus s and p partial density of states functions. These were weighted by transition probabilities and added, which resulted in the theory curve in Fig. 1. pp-convolutions are shown in Fig. 2. According to equation (3) these should be weighted with their transition probabilities WLL" and added together. The WLL' values were estimated from theoretical and experimental atomic matrix elements in the literature [11] and taken a s p p : sp: ss = 1.0 : 0.3 : 0.03. As we will see below the exact choices of these numbers will not be critical for our final analysis. The result is compared with the experimental data in Fig. 1. Note that the background of inelastically scattered electrons has not been removed from the experimental curve. As the experimentally observed peaks can all be identified from this simple independent-particle model, meaning that correlation effects do not dominate the spectrum. The two uppermost peaks A and B entirely correspond to p-states (pp-fold) of the phosphorus atom because the sp-contribution is small in this energy region and moreover contributes very little due to its lower transition probability. Peaks C and D derive completely from the sp-fold while the E peak comes from the ss-fold. Peaks C, D, and E are located on a background and it is difficult to get any precise measure of their absolute positions, heights and widths. It appears, however, that peaks C and E are more broadened than peaks A, B and D. One may speculate that multiplet splitting play a role here. In the following we focus our attention on the A and B-peaks where a more quantitative analysis appears possible. The peaks appear on a low background and moreover are pure pp-folds, so we are not concerned with the transition probabilities. Various theories for background subtraction have been published [12]. We have, however, decided not to do a detailed analysis. One reason is that there are some
80
I
! Ueff = 2 eV i', 2 , ,
-25
193
THE PHOSPHORUS A U G E R L2.3W SPECTRUM OF InP(1 1 0)
I
I
84
88
:) ;I, j),,
I
I
92
96
100
Electronenergy(eV) Fig. 3. The effect of hole-hole correlation on the calculated one-electron Auger spectrum in Fig. 1 using the Cini-Sawatzky model. The U~ parameter is the net Coulomb repulsion. uncertainties in the scattered part of our experimental data. Spectra taken with different pass energies of the electron analyzer gave somewhat different shapes of the background signalling a varying transmission of the analyzer. We have decided to simply subtract a linear backgound. For comparison of the theoretical curve with experiment a broadening (Gaussian) was applied to the latter. Only a moderate agreement was found. The two major discrepancies are: (i) the ratio of the amplitudes of the two theoretical peaks is too large and (ii) the peaks were somewhat too far. apart in energy ( ~ 0.2 eV). The experimental and theoretical spectra were aligned at the A-peak, because we do not know the absolute energy scale experimentally, nor theoretically. To investigate possible influences of hole-hole correlation we applied the Cini-Sawatzky model discussed above. Figure 3 shows the effect on the unbroadened theoretical spectrum in Fig. 1 when Ucfr is successively increased. The most striking effect is the increase of the amplitude of the B-peak. Both the A and B peaks increase their binding energies, however, the A peak moves faster than the B-peak, thus resulting in a decrease in their separation. It is encouraging that both the desired corrections are obtained simultaneously by adjustment of the single parameter Ucfr. Finally, the curve was broadened to take into account the core hole life time as well as possible multiplet splittings. We find a very good agreement with experiment using Uofr = 0.8 eV and FGau~ = 2.3 eV as illustrated in Fig. 4. When applying the U~er/(W/2)-rule it seems clear that the total valence band width (11 eV) should not be used. For the pp-fold only the valence band part above the heteropolar band gap is involved which
THE PHOSPHORUS AUGER
194
t2'3A w Exp. __
105
I
110
I
I
115 120 125 Electron energy (eV)
Fig. 4. The Uefr = 0.8 eV spectrum (see Fig. 3) convoluted with a Gaussian (F = 2.3 eV). It is compared with the experimental curve in Fig. 1, the background of which has been removed by linear interpolation. gives us W = 2.3 eV. This is the width of the broader of the two bands that extend from F to the X-point. The second band that covers this direction has a width of about 2.7 eV. The small Uoerof 0.8 eV compared to either W-number tells us that the independent particle model should be quite accurate, as we have indeed seen is the case. The A-peak is a self-fold of the more narrow band, while the B-peak is a fold of the broad and the narrow bands. If one considered using a varying Uar the value for the A-peak could therefore be expected to be larger. The two discrepancies between the experimental data and the independent particle model calculation, i.e. the difference in the peak separation and the A/B peak ratio, could to some degree be due to inacctlracies in the assumed band structure and the background subtraction. The relative positions of the calculated Auger lines are dependent on the position of the energies used in the fit for the tight-binding calculation. Specifically, the energy separation between peaks A and B are mainly dependent on the energy o f the two top bands at the X-point and to some degree at the L-point (measured relative to the valence band maximum at F). The data we used is the best available and we believe the accuracy is of the order of 0.1 eV. We note in passing that bands were confirmed in photoemission measurements [10], which measures the one-hole spectrum. We think that the small shift of 0.2 eV in the calculated A - B peak separation is significant, but can hardly be taken alone as evidence for the need for a many-body model. With regards to the background simulation we did attempt to generate a background at an energy E that is proportional to the integral of the number of Auger electrons emitted between E and infinity. How-
L2,3VVS P E C T R U M
OF InP(1 1 0)
Vol. 79, No. 2
ever, we found that in order to be able to raise the calculated B-peak sufficiently, the level of the spectrum at lower energies, say 95 eV, was significantly higher than in the experimental spectrum. We take this as strong evidence for our assumptions that the linear background separation is adequate and that a manybody correction to the single-particle model is needed. A remaining question concerns distortion of the spectrum due to surface effects. It is known that the local density of states is somewhat different in the outermost atomic layers, where also the main contribution to the Auger spectrum occurs. We believe the effect is not decisive for the present conclusions because the Auger spectrum is an integration over the product of density of state functions according to above, which smears details. However, observable effects have been found for metals [13]. We are for the present calculating the spectrum taking the surface density of states into account [14]. Considering all uncertainties involved our conclusion is that the upper part of the Auger spectrum (the pp-fold) is subject to a correlation energy of about 0.8eV. It is interesting to observe that this value is about twice as large as the value found for the pp-fold part of Si L2.3VV spectrum [5], which is 0.4 eV. We do not know the reason for the difference. We note, however, that the Si spectrum does not sh'ow as much structure as InP, which may make the fitting more uncertain. 5. C O N C L U S I O N S The LVV Auger spectrum of InP(1 1 0) has been measured using synchroton radiation excitation. The five observed features can all be identified using a simple independent particle model involving convolutions of partial, local density of states functions obtained from a band calculation. The effect of holehole correlation Ueer in the valence band has been evaluated using the Cini-Sawatzky model and found to be of the order of 0.8 eV at the top of the valence band (pp-fold part). Relative displacements of the band energies due to this were found to be a few tenths of an eV. The amplitude changes were, however, appreciable. We believe that this is a typical situation for the III-V and II-VI semiconductor compounds, although we are not aware of any other results on these materials. Calculations to take surface effects into account are in progress. - This work has been supported by grants from the Swedish Natural Science Research Council. We wish to thank the staff at MAX-lab for generous technical assistance.
Acknowledgements
Vol. 79, No. 2
THE PHOSPHORUS AUGER L2.3VV SPECTRUM OF InP(l 1 0) REFERENCES
1. 2. 3. 4.
5. 6. 7.
U. von Barth & G. Grossmann, Phys. Rev. B25, 5150 (1982). M. Cini, Solid State Commun. 20, 605 (1976); Phys. Rev. B17, 2788 (1978); G.A. Sawatzky, Phys. Rev. Lett. 39, 504 (1977). See e.g.P. Weightman, Physica Scripta T25, 165 (1989). For a review see C.O. Almbladh, in Proceedings of the lOth Taniguchi International Symposium, (Edited by J. Kanamori & A. Kotani), p. 263, Springer, Berlin (1988). D.E. Ramaker, F.L. Houston, N.H. Turner & W.N. Mei, Phys. Rev. B33, 2574 (1986). S.P. Svensson, P.O. Nilsson & T.G. Andersson, Phys. Rev. B31, 5272 (1985). P.J. Feibelman, E.J. McGuire & K.J. Pandey,
8. 9. 10. 11. 12. 13. 14.
195
Phys. Rev. B15, 2202 (1977); P.J. Feibelman & E.J. McGuire, Phys. Rev. B17, 690 (1978). J.E. Houston, J.W. Rogers, R.R. Rye, F.L. Hutson & D.E. Ramaker, Phys. Rev. B34, 1215 (1986). R. Chelikowski & M.L. Cohen, Phys. Rev. BI4, 556 (1976). H. Qu, J. Kanski, P.O. Nilsson & U.O. Karlsson, Surf. Sci. (in press). D.E. Ramaker, in Chemistry and Physics of Solid Surfaces, Springer, Berlin (1982). See e.g.E.M. Sickafus, Phys. Rev. B16, 1448 (1977) and references therein. C.O. Almbladh & A.L. Morales, J. Phys. 48, C9-879 (1987). P.O. Nilsson, Y. Khazmi & S.P. Svensson, to be published.
L2.3VVS P E C T R U M
0038-1098/91 $3.00 + .00 Pergamon Press plc OF InP(1 1 0)
P.O. Nilsson Department of Physics, Chalmers University of Technology, S-412 96 G6teborg, Sweden and S.P. Svensson Martin Marietta Laboratories, Baltimore, MD 21227, USA
(Received 4 March 1991 by B. Lundqvist) The L2,3VVAuger spectrum of InP(1 1 0) has been measured using synchrotron radiation excitation. In a first step a one-body theory was applied for analysis, involving convolutions of partial, local density of states functions obtained from a band calculation. The effect of holehole correlations in the valence band was then evaluated using the Cini-Sawatzky model. 1. I N T R O D U C T I O N
bonding of the constituents, in particular for more complicated compounds such as ternaries and quarternaries. Valence Auger spectra of metals have been treated in the literature in some detail [3], while spectra from semiconductors are more scarse [4]. Essentially only the Si L2,3VVspectrum has been thoroughly analyzed [5]. As there is now a very intensive research taking place on the electronic structure of surfaces and interfaces of semiconductors it is of great importance to find out if a simple model can be applied to the analysis of CVV spectra for these materials. Specifically we want to determine the influence of the many-body effects on the CVV transitions and relate it to earlier studies on Si [5]. From the outset it is not clear whether a single-particle model is at all adequate. For example, even the application of the cited Ue~/W rule is not trivial for a semiconductor since several bands are involved, in some cases separated by a gap; the heteropolar gap in compound semiconductors. This means for example that one single value for Ueermay not be sufficient.
A U G E R electron spectroscopy has mainly been used as a routine tool for qualitative and quantitative analysis, in particular of surfaces. However, the technique can also be used for investigations of the electronic structure of solids. For studies of valence bands the CVV transitions are of special interest. In such a process the initial state consists of one core hole while the final state contains two holes in the valence band and an escaping Auger electron. The final state rule [1] says that the detected energies are those of the final state, while the transition amplitudes also depend on the initial state. Thus, as the final state contains no core hole in the CVV process (in contrast to e.g. the CCV process) we expect to test the unscreened band structure in an independent particle model. This situation should prevail when the effective Coulomb interaction Uar is much smaller than the valence band width W. In the Cini-Sawatzky model [2] the condition is U~J2W ~< 1. In the independent particle picture the measured spectrum is a sum of weighted convolutions of ground state density of states functions. As the perturbation operator in the Auger pro2. E X P E R I M E N T A L D E T A I L S cess is the Coulomb interaction the selection rules are very much relaxed compared to the dipole selection The P L2.3VV transition in InP waschosen due to rule for optical transitions. However, combined with its favourable energy position relative to other specsimple theory, information may be extracted about tral features. Only a few other, very weak, transitions partial (i.e. angular momentum decomposed) density from either of the constituents are expected to overlap of states functions. In addition one of the most valu- with the peaks we are studying [6]. Furthermore, the able characteristics of Auger transitions is that the P Lz,3VV transition appears at a sufficiently high local valence density of states is tested. This site sen- energy so that the large background of the low energy sitivity, not present in e.g. photoemission, is of par- secondary electrons does not interfere with the low ticular importance for investigations of alloys and energy part of the peak. These facts make it possible compounds since it may reveal information about the to obtain a very clean spectrum without complicated 191
192
THE PHOSPHORUS A U G E R I
I
L2.3VVSPECTRUM
!i.il
t~
pr(r, E) ~ f IWL(r)I26(E- e)de.
I(Ef)
= ~" PL ® PL' WLL'(E/),
I
I
I
100
110
120
where ® denotes convolution: 130
PL ® PL' = f d~opL(E - ~o)pL'(E, + oJ).
Fig. 1. The upper curve is the experimental L2,3VV phosphorus Auger spectrum of InP(1 1 0) excited by synchrotron radiation (hv = 150 eV). The lower curve is calculated in an one-electron approximation using results from a band calculation.
background subtraction. The P L2,3VVtransition has also been studied earlier for Si [5] which makes direct comparison possible between a binary and an elemental semiconductor. The InP(1 1 0) surface was produced by cleavage in ultrahigh vacuum (UHV). The surface produced a sharp LEED pattern with only a weak background. The Auger excitation was done by synchrotron light of 150eV from the MAX storage ring in Lund, Sweden. The advantage of using synchrotron light is the low background compared with electron excitation. The Auger electrons were detected under normal emission using a semi-spherical analyzer. No essential difference was detected for various emission angles. The spectrum as recorded is reprodficed in Fig. 1. 3. THEORY In an independent particle description the CVV Auger current can be expressed as [7] --
Z L I L'I L 2 L~
(3)
LL'
Kine~cenergy(eV)
I(Es)
(2)
The line shape of the Auger spectrum becomes
Theory 90
Vol. 79, No. 2
general smallness of the off-diagonal elements of FLL.(E) it should be enough to consider the diagonal part of the matrices. This approximation results in a simple theory based on the conventional local, partial density of states functions
I
InP ,6
OF InP(1 1 0)
fdO~FL,L~(EI-a~)FL2L~
x (E,, + cO)WL, LiL:L~(Ef).
(4)
The presented model relies on the one-particle approximation, i.e. the valence electrons are assumed frozen in their ground state during the Auger process. This cannot be rigorously true because the Auger process itself requires an interaction to occur between two electrons. The essential many-body effects may be discussed in terms of screening effects in the initial and final states [8]. One of the most important contributions is the final state hole-hole interaction in the valence band. The interaction can be characterized by an effective net Coulomb repulsion U~. For a single, filled band the Cini-Sawatzky model gives [5] N(E)LL, =
pL(E) ® pL,(E) [1 -- UeerlLL,(E)]2 + rflUZ~r[pL(E) ® pL,(E)] 2' (5)
where the folded one-electron density of states is denoted by pL(E) ® pL,(E). The function ILL'(E) is the Hilbert transform of pL(E) ® pL'(E). When Uefr is increased from zero peaks are expected to shift towards higher binding energies, while the upper and lower boundaries of the total spectrum are unchanged. For Uaf larger than twice the band width a satellite splits off below the spectrum. One may argue that such a model is too simple to apply here. However, UCfrwill turn out to be fairly small and we assume that any error can be absorbed in the U,fr parameter. 4. RESULTS AND DISCUSSION
(1)
Here EI is the energy of the Auger electron and E,. the core hole energy. The FLL,(E) functions are the elements of local, occupied density of states matrices with angular momentum L = (1,m). The WL,LIL2L~ factors denote transition probabilities affd contain Auger matrix elements and geometrical factors. These can with good accuracy be represented by atomic integrals. It has been shown [7] that because of the
The band structure of InP was calculated using a semi-empirical LCAO method [6]. The parameters were chosen to fit the bands of Chelikowski et al. [9]. These bands were recently confirmed by angleresolved photoelectron spectroscopy to an accuracy of about 0.1 eV [10]. The local, partial density of states functions were calculated by a Monte Carlo method. Out of these only the phosphorus functions will contribute to this particular Auger spectrum. The ss-, sp-,
Vol. 79, No. 2 I
I
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EnergyrelativeVBM(eV) Fig. 2. The folds of the phosphorus s and p partial density of states functions. These were weighted by transition probabilities and added, which resulted in the theory curve in Fig. 1. pp-convolutions are shown in Fig. 2. According to equation (3) these should be weighted with their transition probabilities WLL" and added together. The WLL' values were estimated from theoretical and experimental atomic matrix elements in the literature [11] and taken a s p p : sp: ss = 1.0 : 0.3 : 0.03. As we will see below the exact choices of these numbers will not be critical for our final analysis. The result is compared with the experimental data in Fig. 1. Note that the background of inelastically scattered electrons has not been removed from the experimental curve. As the experimentally observed peaks can all be identified from this simple independent-particle model, meaning that correlation effects do not dominate the spectrum. The two uppermost peaks A and B entirely correspond to p-states (pp-fold) of the phosphorus atom because the sp-contribution is small in this energy region and moreover contributes very little due to its lower transition probability. Peaks C and D derive completely from the sp-fold while the E peak comes from the ss-fold. Peaks C, D, and E are located on a background and it is difficult to get any precise measure of their absolute positions, heights and widths. It appears, however, that peaks C and E are more broadened than peaks A, B and D. One may speculate that multiplet splitting play a role here. In the following we focus our attention on the A and B-peaks where a more quantitative analysis appears possible. The peaks appear on a low background and moreover are pure pp-folds, so we are not concerned with the transition probabilities. Various theories for background subtraction have been published [12]. We have, however, decided not to do a detailed analysis. One reason is that there are some
80
I
! Ueff = 2 eV i', 2 , ,
-25
193
THE PHOSPHORUS A U G E R L2.3W SPECTRUM OF InP(1 1 0)
I
I
84
88
:) ;I, j),,
I
I
92
96
100
Electronenergy(eV) Fig. 3. The effect of hole-hole correlation on the calculated one-electron Auger spectrum in Fig. 1 using the Cini-Sawatzky model. The U~ parameter is the net Coulomb repulsion. uncertainties in the scattered part of our experimental data. Spectra taken with different pass energies of the electron analyzer gave somewhat different shapes of the background signalling a varying transmission of the analyzer. We have decided to simply subtract a linear backgound. For comparison of the theoretical curve with experiment a broadening (Gaussian) was applied to the latter. Only a moderate agreement was found. The two major discrepancies are: (i) the ratio of the amplitudes of the two theoretical peaks is too large and (ii) the peaks were somewhat too far. apart in energy ( ~ 0.2 eV). The experimental and theoretical spectra were aligned at the A-peak, because we do not know the absolute energy scale experimentally, nor theoretically. To investigate possible influences of hole-hole correlation we applied the Cini-Sawatzky model discussed above. Figure 3 shows the effect on the unbroadened theoretical spectrum in Fig. 1 when Ucfr is successively increased. The most striking effect is the increase of the amplitude of the B-peak. Both the A and B peaks increase their binding energies, however, the A peak moves faster than the B-peak, thus resulting in a decrease in their separation. It is encouraging that both the desired corrections are obtained simultaneously by adjustment of the single parameter Ucfr. Finally, the curve was broadened to take into account the core hole life time as well as possible multiplet splittings. We find a very good agreement with experiment using Uofr = 0.8 eV and FGau~ = 2.3 eV as illustrated in Fig. 4. When applying the U~er/(W/2)-rule it seems clear that the total valence band width (11 eV) should not be used. For the pp-fold only the valence band part above the heteropolar band gap is involved which
THE PHOSPHORUS AUGER
194
t2'3A w Exp. __
105
I
110
I
I
115 120 125 Electron energy (eV)
Fig. 4. The Uefr = 0.8 eV spectrum (see Fig. 3) convoluted with a Gaussian (F = 2.3 eV). It is compared with the experimental curve in Fig. 1, the background of which has been removed by linear interpolation. gives us W = 2.3 eV. This is the width of the broader of the two bands that extend from F to the X-point. The second band that covers this direction has a width of about 2.7 eV. The small Uoerof 0.8 eV compared to either W-number tells us that the independent particle model should be quite accurate, as we have indeed seen is the case. The A-peak is a self-fold of the more narrow band, while the B-peak is a fold of the broad and the narrow bands. If one considered using a varying Uar the value for the A-peak could therefore be expected to be larger. The two discrepancies between the experimental data and the independent particle model calculation, i.e. the difference in the peak separation and the A/B peak ratio, could to some degree be due to inacctlracies in the assumed band structure and the background subtraction. The relative positions of the calculated Auger lines are dependent on the position of the energies used in the fit for the tight-binding calculation. Specifically, the energy separation between peaks A and B are mainly dependent on the energy o f the two top bands at the X-point and to some degree at the L-point (measured relative to the valence band maximum at F). The data we used is the best available and we believe the accuracy is of the order of 0.1 eV. We note in passing that bands were confirmed in photoemission measurements [10], which measures the one-hole spectrum. We think that the small shift of 0.2 eV in the calculated A - B peak separation is significant, but can hardly be taken alone as evidence for the need for a many-body model. With regards to the background simulation we did attempt to generate a background at an energy E that is proportional to the integral of the number of Auger electrons emitted between E and infinity. How-
L2,3VVS P E C T R U M
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Vol. 79, No. 2
ever, we found that in order to be able to raise the calculated B-peak sufficiently, the level of the spectrum at lower energies, say 95 eV, was significantly higher than in the experimental spectrum. We take this as strong evidence for our assumptions that the linear background separation is adequate and that a manybody correction to the single-particle model is needed. A remaining question concerns distortion of the spectrum due to surface effects. It is known that the local density of states is somewhat different in the outermost atomic layers, where also the main contribution to the Auger spectrum occurs. We believe the effect is not decisive for the present conclusions because the Auger spectrum is an integration over the product of density of state functions according to above, which smears details. However, observable effects have been found for metals [13]. We are for the present calculating the spectrum taking the surface density of states into account [14]. Considering all uncertainties involved our conclusion is that the upper part of the Auger spectrum (the pp-fold) is subject to a correlation energy of about 0.8eV. It is interesting to observe that this value is about twice as large as the value found for the pp-fold part of Si L2.3VV spectrum [5], which is 0.4 eV. We do not know the reason for the difference. We note, however, that the Si spectrum does not sh'ow as much structure as InP, which may make the fitting more uncertain. 5. C O N C L U S I O N S The LVV Auger spectrum of InP(1 1 0) has been measured using synchroton radiation excitation. The five observed features can all be identified using a simple independent particle model involving convolutions of partial, local density of states functions obtained from a band calculation. The effect of holehole correlation Ueer in the valence band has been evaluated using the Cini-Sawatzky model and found to be of the order of 0.8 eV at the top of the valence band (pp-fold part). Relative displacements of the band energies due to this were found to be a few tenths of an eV. The amplitude changes were, however, appreciable. We believe that this is a typical situation for the III-V and II-VI semiconductor compounds, although we are not aware of any other results on these materials. Calculations to take surface effects into account are in progress. - This work has been supported by grants from the Swedish Natural Science Research Council. We wish to thank the staff at MAX-lab for generous technical assistance.
Acknowledgements
Vol. 79, No. 2
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