- Email: [email protected]
A solution of the core-exciton issue for silicon and germanium
~
Solid S t a t e Communications, Voi.36, pp.297-300. Pergamon Press Ltd. 1980. Printed in Great Britain.
A SOLUTION OF THE CORE-EXCITON ISSUE FOR SILICON AND GERMANIUM. G. Margarltondo, § A. Franclosl, t N. G. Stoffel § and H. S. Edelman § §Department of Physics, University of Wisconsin, Madison, Wis. 53706 #Synchrotron Radiation Center, University of Wisconsin, Stoughton, Wis.53589 (Received 30 July 1980 by F. Bassani) The large discrepancies among the Si L 2 3 core-excitonic shifts measured by different techniques can be'explalned by the recently discovered surface shifts of the St 2p level. New, accurate photoemlssion measurements of both the L 2 ~ edge and of the 2p binding energy with equal surface sensitivity h~ve been performed. Our present results and those of previous experiments are consistent with a single value 0 . 3 ~ 0 1 ~ eV for the Si L2, 3 core excitonlc shift. Preliminary results for t~e~3d core exclton in Ge give a shift of 0.35 ± 0.25 eV.
complete breakdown of the effective mass approximation and of the statlc-screenlng condltlons. I0 Along this llne Dow and coworkers II have recently developed a model of "Frenkel" core excltons localized to the unit cell. Bassanl, however, argued I0 that the theoretical conditions for non-statlc screening are unlikely to be met by most common semiconductors including sllicon. He also hinted that intervalley interaction could explain the enhancement of the electron-core hole interaction in semiconductors. However, different theoretical calculations recently gave 12,13 divergent predictions about the strength of this correction. At this time the theory does not provide clear evidence that the electron-core hole interaction is sufficiently enhanced in silicon to give the large excltonlc binding energies obtained experimentally. This could of course raise some doubts about these experimental results. There is, indeed, a large divergence among the Si L2, 3 core excltonlc shifts measured by different authors. The published values I-3 range b~tween 0.18 and 0.9 eV. It is usually assumed- that this divergence is due to the intrinsic uncertainty in the core-excitonic shift measurements which consist of estimating the small difference between two large quantities, the L 2 q edge position and E c - E2p. This assumption~seems excessive since th e experimental uncertainty should not exceed 0.3 - 0.4 eV. Therefore the above discrepancies are likely to be real and in fact they could not be removed by careful revisions of the corresponding experimental results (one should observe that discrepancies may occur within absolute energy calibrations in dlfferent laboratories but the corresponding systematic errors should be reduced when estimating energy differences). We propose here that the recently dlscovered 4 surface-lnduced shifts of the Si 2p level are the key to explaining the above discrepancies -- and to placing the experimental evidence for a large Si L2, 3 core
In this letter we propose a solution for the long-standlng controversy concerning the L2, 3 core exclton in sillcon. I-3 The controversy arises primarily from a %0.7 eV discrepancy between the eore-excltonlc shifts of the L2, 3 edge as measured by electron energy loss spectroscopy 3 and as measured by partlal-yleld spectroscopy. I We argue that this discrepancy can be explained if one takes into account the large surface shifts in the Si 2p bln41ng energy recently discovered by HLmpsel et al. 4 We also observe that surface shifts of core levels necessitate measuring the absorption edge and the core-level binding energy with the same surface sensitivity In order to estimate core excltonlc shifts. New measurements of this kind give a Si L2, 3 core excltonle shift of 0.3 eV. This value is consistent with the lower limit for the core excltonlc binding energy deduced from electroreflectance data. 2 Similar preliminary experiments on the 3d core exclton in germanium give a shift of comparable magnitude, 0.35 eV. The existence of large (~ I00 meV) excltonic shifts at the core absorption edges of semiconducting crystals has been a very controversial issue for severa~ years. I-6 Early theoretlcal 5 and experlmental u results seemed to favor a binding energy smaller than 50 meV for the L2, 3 exclton in silicon. In 1976-78, however, several groups I-3 found larger discrepancies between the measured position of the L2, 3 edge and the one-electron absorption threshold (given by Si 2p binding energy measured with respect to the bottom of the conduction band, E c - E~,) ~ • Furthermore e_xperimental evidence was found by Brown et al. 7 and by Eberhardt et al. I0 for a strong localization of the states involved at the onset of the L 2 3 edge. This localization could result In large central-cell corr~ctlons to the excltonlc binding energy 8-IO and possibly lead to a Research supported in part by the Office of Naval Research, grant NR-392039.
297
298
A SOLUTION OF THE CORE-EXCITON
excitonic shift on more solid ground. The largest discrepancy is found between the Si L2, 3 excitonic shift edge as measured by electron energy loss spectroscopy 3 and the corresponding partlal-yield spectroscopy results. 1 We emphasize that these two techniques have different surface sensitivity. The degree of surface sensitivity of partlal-yleld spectroscopy depends upon the selected photoelectron kinetic energy. Even under the conditions for best surface sensitivity, however, all photoemlsslon techniques including partialyield spectroscopy appear qualitatively less surface sensitive than low-energy (~250 eV) electron energy loss. For example contamination of the Si(lll)Tx7 surface induces detectable changes in the 100-200 eV energy loss spectra long before any change is detected in photoemlssion spectra at kinetic energies of 15-35 eV. Therefore the L2, 3 edge measurements by electron energy loss are more sensitive to surface-related effects than the corresponding partlal-yleld measurements. This makes extremely relevant the recent observation by Himpsel et al. 4 of a surface-lnduced fine structure in the soft-X-ray photoemisslon spectrum of the Si 2p level. They found Si 2P3/2 photoemisslon peaks shifted in energy with respect to the "bulk" peak with a general prevalence of shifts toward smaller binding energies. In particular they observed a 2P3/2 peak arising from atoms in the top layer of Si(lll)7x7 with 0.7 eV less binding energy than the bulk 2P3/2 peak. We propose that the L 2 3 edge measured by energy loss on Si(lll)7x7 ~as strong contributions from transitions involving these surfaceshifted states. In the (unrealistic) limit of a 100% contribution from these transitions the corresponding core-excitonlc shift estimate becomes as low as 0.2. A more realistic correction should give a larger value. The surface-shifts of the 2p level induce systematic errors in the core-excltonlc shift measurements whenever different surface sensitivity is used to measure the core-level binding energy and the position of the edge. For example this makes strongly questionable the use of bulk optical me asurements 6 as a complement of surface-sensltlve soft-X-ray binding energy measurements. 2 Similarly this rules out the use of photoelectrons of different kinetic energies when measuring the edge by partlal-yield spectroscopy and the core-level binding energy by ordinary photoemisslon. Therefore we decided to measure both quantities on Si(lll)2xl surfaces cleaved in sltu using the same photoelectron kinetic energy range, %25 eV. The photoelectron energy analysis was performed by a modified double-pass cylindrical mirror analyzer in an ultrahigh vacuum chamber (pressure 7-9 x I0 -II torr). The photons were emitted by the storage ring Tantalus of the University of Wisconsin Synchrotron Radiation Center and monochromatized by a toroidal-grating monochromator. Due to the nature of the experiment extreme care was used in calibrating the monochromator by detecting the AI L 2 3 edge of a filter and by measuring the shirr'with photon energy of the Fermi edge for a freshly evaporated metal film (Tm). Figure 1 shows one of the Si(lll)2xl partlal-yield spectra taken for a photoelectron
ISSUE FOR SILICON AND GERMANIUM
Vol. 36, No. 4
kinetic energy of 25 eV. As is well knownl4 the spectral behavior of the photoelectron yield in a given energy window reproduces that of the absorption coefficient in a region near the surface. The thickness of the region depends on the position of the energy window via the photoelectron escape depth. The surface sensitivity of the partial yield spectrum of Fig. i is emphasized by the long tail below the absorption edge which corresponds to transitions involving surface states. 4 The vertical line at 99.68 eV shows the position of the L 3 edge as defined by a broadened step-function, l,4 The one-electron L 3 edge was deduced from the measured distance in energy between the Si 2p level and the top of the valence band, 99.05 eV, from the spinorbit splitting, 0.62 eV, and from the value of the indirect gap in Si, i.ii eV. The corresponding value of 99.96 eV corresponds in Fig.l to the vertical llne labelled E u - E2P3/2. From the discrepancy between the measured L 3 edge and its one-electron estimated value including the experimental uncertainty we obtain an L 2 3 excitonic shift of 0.3 ± 0.2 eV. ~ e uncertainty associated with this value can be reduced by a comparative analysis of this and other experimental results. 2,3 A lower limit for the core-exclton binding energy is set at 0.3 eV by the electroreflectance measurements of Bauer et al. 2 We also observe that defining the edge as the point of maximum slope of a broadened step-function as we and other authorsl,3, 4 did could lead to a slight underestimate of the core excltonlc shift. Using a broadened square-root llneshape instead of a broadened step-function we find this possible error to be of the order of 0.06 - 0.07 eV or less (an exact determination is not possible unless the lineshape is known and this in turn would require a detailed understanding 9 priori of the excitonlc effects). It appears therefore entirely reasonable to take 0.3 eV as the lower limit for the core excltonic shift. On the other hand the results of Ref. 1 (which agree within the experimental uncertainty with our present findings) would give an upper limit of 0.38 eV to the excitonic shift. Taking into account the above possible systematic errors induced by the definition of the edge this upper limit becomes ~0.45 eV. All things considered, therefore, the best value of the Si L2, 3 core excitonic shift is 0.3 -0.0 eV. +0.15 Measurements of the excitonlc shift were also performed on a cleaved Si(lll) surface covered by %1 monolayer of germanium. The purpose of this experiment was to search for possible changes in the value of the core exclton binding energy induced by the changes in the chemical environment -- as one should qualitatively expect based on the "optical alchemy" core-exciton theory by Dow and coworkers, llThe germanium adatoms, however, failed to induce any measurable change in the core excitonlc shift. Further experiments with other kinds of adatoms are therefore required before drawing any conclusion about the validity of the "optical alchemy" approach. II Finally, preliminary measurements were carried out on the core excitonlc shift for the 3d absorption edge in germanium. Measurements on a 200
Vol. 36, No. 4
A SOLUTION OF THE CORE-EXCITON
ISSUE FOR SILICON AND GERMANIUM
299
Si(111) 2X1 PARTIAL YIELD CK.E. = 25eV)
Z
49
16,
163
Fig. I - The L2, 3 edge of Si measured by partialyield spectroscopy energy of 25 eV.
at a photoelectron The vertical
marks the position of the L 3 edge. labelled E c - E2P3/2 corresponds one-electron
The llne
to the estimated
L 3 edge from the measured position
energy of the 2p level.
The distance
between the two lines corresponds excitonic
kinetic
llne at 99.68 eV
in
in energy
to a core
shift of 0.3 eV.
Ge film grown on top of a cleaved SI(III) substrate give for this edge a core excitonlc shift of 0.35 t 0.25 eV. This is further evidence that the core exciton binding energies in group IV semiconductors are substantially larger than those of valence excitons. Many unsolved problems still remain in the field of core excitons in semiconductors. In particular no satisfactory theoretical explanation has been found yet for the enhancement of the electron-hole interaction. I0 Our present results and the critical revision of previous experiments should hopefulIy contribute to the solution of these problems. In particular we have illustrated how the present and past experimental results can be reconciled with a single value, 0.3 eV, for the Si L 2 3 core excitonic shift. Further experiments should involve the study of
same crystal as well as very careful lineshape several different absorption edges in the analysis in spectra taken with high surface sensitivity. These experiments should clarify the possible role of surface effects in strengthening the electron-core hole interaction. Acknowledgement - We are extremely grateful to Franz Hlmpsel for having disclosed to us the results of Ref. 4 prior to publication. Thanks are due to F. Bassanl, W. Eberhardt, D. E. Aspnes and J. D. Dow for illuminating discussions. The collaboration of E. M. Rowe, J. H. Weaver, C. Pruett, D. Peterman and the entire staff of the University of Wisconsin Synchrotron Radiation Center (supported by NSF, grant 77-21888) was essential to the success of our experiments.
300
A SOLUTION OF THE CORE-EXCITON ISSUE FOR SILICON AND GERMANIUM
Vol. 36 No. 4
REFERENCES I. W. Eberhardt, C. Kalkoffen, C. Kunz, D. E. Aspnes and M. Cardona, Phys. Star. Sol. (b) 88, 135 (1978). 2. R. S. Bauer, R. S. Bachrach, J. C. McMenamin and D. E. Aspnes, Nuovo Cimento %98, 409 (1977). 3. G. Margaritondo and J. E. Rowe, Phys. Lett. A59, 464 (1977). 4. F. J. Himpsel, P. Helmann, T.-C. Chlang and D. E. Eastman, private c o ~ u n i c a t i o n and to be published. 5. M. Altarelli and D. L. Dexter, Phys. Rev. Lett. 29, ii00 (1972). 6. F. Brown and O. P. Rustgi, Phys. Rev. Lett. 28, 497 (1972). 7. F. C. Brown, R. S. Bachrach, and M. Skibowskl, Phys. Rev. BI~5, 4781 (1977). 8. C. Kunz, J. Physique Colloq. C4, 119 (1978). 9. k. Quattropanl, F. Bassanl, G. Margarltondo and G. Tinlvella, Nuove Clmento B51, 335 (1979).
I0. F. Bassanl, Proc. VI Intern. Conf. on Vacuum Ultraviolet Radiation Physics (to be published in Applied Optics). ii. J. D. Dow, H. P. Hjalamarson, O. F. Sankey, R. E. Allen and H. BUttner, Extended Abstracts of the VI Intern. Conf. on Vacuum Ultraviolet Radiation Physics, Charlottesville, VA. 1980, Vol. i, n.88. 12. M. Altarelll and W. Y. Hsu, Phys. Rev. Lett. 43, 1346 (1979); M. Altarelli, W. Y. Hsu and A. Baldereshl, Phys. Rev. B (to appear). 13. L. Resca and R. Resta, Sol. State Commun. 29, 375 (1979) and Phys. Rev. Lett. 44, 1340 (1980). 14. W. Gudat and C. Kunz, Phys. Rev. Lett. 29, 169 (1972).
Solid S t a t e Communications, Voi.36, pp.297-300. Pergamon Press Ltd. 1980. Printed in Great Britain.
A SOLUTION OF THE CORE-EXCITON ISSUE FOR SILICON AND GERMANIUM. G. Margarltondo, § A. Franclosl, t N. G. Stoffel § and H. S. Edelman § §Department of Physics, University of Wisconsin, Madison, Wis. 53706 #Synchrotron Radiation Center, University of Wisconsin, Stoughton, Wis.53589 (Received 30 July 1980 by F. Bassani) The large discrepancies among the Si L 2 3 core-excitonic shifts measured by different techniques can be'explalned by the recently discovered surface shifts of the St 2p level. New, accurate photoemlssion measurements of both the L 2 ~ edge and of the 2p binding energy with equal surface sensitivity h~ve been performed. Our present results and those of previous experiments are consistent with a single value 0 . 3 ~ 0 1 ~ eV for the Si L2, 3 core excitonlc shift. Preliminary results for t~e~3d core exclton in Ge give a shift of 0.35 ± 0.25 eV.
complete breakdown of the effective mass approximation and of the statlc-screenlng condltlons. I0 Along this llne Dow and coworkers II have recently developed a model of "Frenkel" core excltons localized to the unit cell. Bassanl, however, argued I0 that the theoretical conditions for non-statlc screening are unlikely to be met by most common semiconductors including sllicon. He also hinted that intervalley interaction could explain the enhancement of the electron-core hole interaction in semiconductors. However, different theoretical calculations recently gave 12,13 divergent predictions about the strength of this correction. At this time the theory does not provide clear evidence that the electron-core hole interaction is sufficiently enhanced in silicon to give the large excltonlc binding energies obtained experimentally. This could of course raise some doubts about these experimental results. There is, indeed, a large divergence among the Si L2, 3 core excltonlc shifts measured by different authors. The published values I-3 range b~tween 0.18 and 0.9 eV. It is usually assumed- that this divergence is due to the intrinsic uncertainty in the core-excitonic shift measurements which consist of estimating the small difference between two large quantities, the L 2 q edge position and E c - E2p. This assumption~seems excessive since th e experimental uncertainty should not exceed 0.3 - 0.4 eV. Therefore the above discrepancies are likely to be real and in fact they could not be removed by careful revisions of the corresponding experimental results (one should observe that discrepancies may occur within absolute energy calibrations in dlfferent laboratories but the corresponding systematic errors should be reduced when estimating energy differences). We propose here that the recently dlscovered 4 surface-lnduced shifts of the Si 2p level are the key to explaining the above discrepancies -- and to placing the experimental evidence for a large Si L2, 3 core
In this letter we propose a solution for the long-standlng controversy concerning the L2, 3 core exclton in sillcon. I-3 The controversy arises primarily from a %0.7 eV discrepancy between the eore-excltonlc shifts of the L2, 3 edge as measured by electron energy loss spectroscopy 3 and as measured by partlal-yleld spectroscopy. I We argue that this discrepancy can be explained if one takes into account the large surface shifts in the Si 2p bln41ng energy recently discovered by HLmpsel et al. 4 We also observe that surface shifts of core levels necessitate measuring the absorption edge and the core-level binding energy with the same surface sensitivity In order to estimate core excltonlc shifts. New measurements of this kind give a Si L2, 3 core excltonle shift of 0.3 eV. This value is consistent with the lower limit for the core excltonlc binding energy deduced from electroreflectance data. 2 Similar preliminary experiments on the 3d core exclton in germanium give a shift of comparable magnitude, 0.35 eV. The existence of large (~ I00 meV) excltonic shifts at the core absorption edges of semiconducting crystals has been a very controversial issue for severa~ years. I-6 Early theoretlcal 5 and experlmental u results seemed to favor a binding energy smaller than 50 meV for the L2, 3 exclton in silicon. In 1976-78, however, several groups I-3 found larger discrepancies between the measured position of the L2, 3 edge and the one-electron absorption threshold (given by Si 2p binding energy measured with respect to the bottom of the conduction band, E c - E~,) ~ • Furthermore e_xperimental evidence was found by Brown et al. 7 and by Eberhardt et al. I0 for a strong localization of the states involved at the onset of the L 2 3 edge. This localization could result In large central-cell corr~ctlons to the excltonlc binding energy 8-IO and possibly lead to a Research supported in part by the Office of Naval Research, grant NR-392039.
297
298
A SOLUTION OF THE CORE-EXCITON
excitonic shift on more solid ground. The largest discrepancy is found between the Si L2, 3 excitonic shift edge as measured by electron energy loss spectroscopy 3 and the corresponding partlal-yield spectroscopy results. 1 We emphasize that these two techniques have different surface sensitivity. The degree of surface sensitivity of partlal-yleld spectroscopy depends upon the selected photoelectron kinetic energy. Even under the conditions for best surface sensitivity, however, all photoemlsslon techniques including partialyield spectroscopy appear qualitatively less surface sensitive than low-energy (~250 eV) electron energy loss. For example contamination of the Si(lll)Tx7 surface induces detectable changes in the 100-200 eV energy loss spectra long before any change is detected in photoemlssion spectra at kinetic energies of 15-35 eV. Therefore the L2, 3 edge measurements by electron energy loss are more sensitive to surface-related effects than the corresponding partlal-yleld measurements. This makes extremely relevant the recent observation by Himpsel et al. 4 of a surface-lnduced fine structure in the soft-X-ray photoemisslon spectrum of the Si 2p level. They found Si 2P3/2 photoemisslon peaks shifted in energy with respect to the "bulk" peak with a general prevalence of shifts toward smaller binding energies. In particular they observed a 2P3/2 peak arising from atoms in the top layer of Si(lll)7x7 with 0.7 eV less binding energy than the bulk 2P3/2 peak. We propose that the L 2 3 edge measured by energy loss on Si(lll)7x7 ~as strong contributions from transitions involving these surfaceshifted states. In the (unrealistic) limit of a 100% contribution from these transitions the corresponding core-excitonlc shift estimate becomes as low as 0.2. A more realistic correction should give a larger value. The surface-shifts of the 2p level induce systematic errors in the core-excltonlc shift measurements whenever different surface sensitivity is used to measure the core-level binding energy and the position of the edge. For example this makes strongly questionable the use of bulk optical me asurements 6 as a complement of surface-sensltlve soft-X-ray binding energy measurements. 2 Similarly this rules out the use of photoelectrons of different kinetic energies when measuring the edge by partlal-yield spectroscopy and the core-level binding energy by ordinary photoemisslon. Therefore we decided to measure both quantities on Si(lll)2xl surfaces cleaved in sltu using the same photoelectron kinetic energy range, %25 eV. The photoelectron energy analysis was performed by a modified double-pass cylindrical mirror analyzer in an ultrahigh vacuum chamber (pressure 7-9 x I0 -II torr). The photons were emitted by the storage ring Tantalus of the University of Wisconsin Synchrotron Radiation Center and monochromatized by a toroidal-grating monochromator. Due to the nature of the experiment extreme care was used in calibrating the monochromator by detecting the AI L 2 3 edge of a filter and by measuring the shirr'with photon energy of the Fermi edge for a freshly evaporated metal film (Tm). Figure 1 shows one of the Si(lll)2xl partlal-yield spectra taken for a photoelectron
ISSUE FOR SILICON AND GERMANIUM
Vol. 36, No. 4
kinetic energy of 25 eV. As is well knownl4 the spectral behavior of the photoelectron yield in a given energy window reproduces that of the absorption coefficient in a region near the surface. The thickness of the region depends on the position of the energy window via the photoelectron escape depth. The surface sensitivity of the partial yield spectrum of Fig. i is emphasized by the long tail below the absorption edge which corresponds to transitions involving surface states. 4 The vertical line at 99.68 eV shows the position of the L 3 edge as defined by a broadened step-function, l,4 The one-electron L 3 edge was deduced from the measured distance in energy between the Si 2p level and the top of the valence band, 99.05 eV, from the spinorbit splitting, 0.62 eV, and from the value of the indirect gap in Si, i.ii eV. The corresponding value of 99.96 eV corresponds in Fig.l to the vertical llne labelled E u - E2P3/2. From the discrepancy between the measured L 3 edge and its one-electron estimated value including the experimental uncertainty we obtain an L 2 3 excitonic shift of 0.3 ± 0.2 eV. ~ e uncertainty associated with this value can be reduced by a comparative analysis of this and other experimental results. 2,3 A lower limit for the core-exclton binding energy is set at 0.3 eV by the electroreflectance measurements of Bauer et al. 2 We also observe that defining the edge as the point of maximum slope of a broadened step-function as we and other authorsl,3, 4 did could lead to a slight underestimate of the core excltonlc shift. Using a broadened square-root llneshape instead of a broadened step-function we find this possible error to be of the order of 0.06 - 0.07 eV or less (an exact determination is not possible unless the lineshape is known and this in turn would require a detailed understanding 9 priori of the excitonlc effects). It appears therefore entirely reasonable to take 0.3 eV as the lower limit for the core excltonic shift. On the other hand the results of Ref. 1 (which agree within the experimental uncertainty with our present findings) would give an upper limit of 0.38 eV to the excitonic shift. Taking into account the above possible systematic errors induced by the definition of the edge this upper limit becomes ~0.45 eV. All things considered, therefore, the best value of the Si L2, 3 core excitonic shift is 0.3 -0.0 eV. +0.15 Measurements of the excitonlc shift were also performed on a cleaved Si(lll) surface covered by %1 monolayer of germanium. The purpose of this experiment was to search for possible changes in the value of the core exclton binding energy induced by the changes in the chemical environment -- as one should qualitatively expect based on the "optical alchemy" core-exciton theory by Dow and coworkers, llThe germanium adatoms, however, failed to induce any measurable change in the core excitonlc shift. Further experiments with other kinds of adatoms are therefore required before drawing any conclusion about the validity of the "optical alchemy" approach. II Finally, preliminary measurements were carried out on the core excitonlc shift for the 3d absorption edge in germanium. Measurements on a 200
Vol. 36, No. 4
A SOLUTION OF THE CORE-EXCITON
ISSUE FOR SILICON AND GERMANIUM
299
Si(111) 2X1 PARTIAL YIELD CK.E. = 25eV)
Z
49
16,
163
Fig. I - The L2, 3 edge of Si measured by partialyield spectroscopy energy of 25 eV.
at a photoelectron The vertical
marks the position of the L 3 edge. labelled E c - E2P3/2 corresponds one-electron
The llne
to the estimated
L 3 edge from the measured position
energy of the 2p level.
The distance
between the two lines corresponds excitonic
kinetic
llne at 99.68 eV
in
in energy
to a core
shift of 0.3 eV.
Ge film grown on top of a cleaved SI(III) substrate give for this edge a core excitonlc shift of 0.35 t 0.25 eV. This is further evidence that the core exciton binding energies in group IV semiconductors are substantially larger than those of valence excitons. Many unsolved problems still remain in the field of core excitons in semiconductors. In particular no satisfactory theoretical explanation has been found yet for the enhancement of the electron-hole interaction. I0 Our present results and the critical revision of previous experiments should hopefulIy contribute to the solution of these problems. In particular we have illustrated how the present and past experimental results can be reconciled with a single value, 0.3 eV, for the Si L 2 3 core excitonic shift. Further experiments should involve the study of
same crystal as well as very careful lineshape several different absorption edges in the analysis in spectra taken with high surface sensitivity. These experiments should clarify the possible role of surface effects in strengthening the electron-core hole interaction. Acknowledgement - We are extremely grateful to Franz Hlmpsel for having disclosed to us the results of Ref. 4 prior to publication. Thanks are due to F. Bassanl, W. Eberhardt, D. E. Aspnes and J. D. Dow for illuminating discussions. The collaboration of E. M. Rowe, J. H. Weaver, C. Pruett, D. Peterman and the entire staff of the University of Wisconsin Synchrotron Radiation Center (supported by NSF, grant 77-21888) was essential to the success of our experiments.
300
A SOLUTION OF THE CORE-EXCITON ISSUE FOR SILICON AND GERMANIUM
Vol. 36 No. 4
REFERENCES I. W. Eberhardt, C. Kalkoffen, C. Kunz, D. E. Aspnes and M. Cardona, Phys. Star. Sol. (b) 88, 135 (1978). 2. R. S. Bauer, R. S. Bachrach, J. C. McMenamin and D. E. Aspnes, Nuovo Cimento %98, 409 (1977). 3. G. Margaritondo and J. E. Rowe, Phys. Lett. A59, 464 (1977). 4. F. J. Himpsel, P. Helmann, T.-C. Chlang and D. E. Eastman, private c o ~ u n i c a t i o n and to be published. 5. M. Altarelli and D. L. Dexter, Phys. Rev. Lett. 29, ii00 (1972). 6. F. Brown and O. P. Rustgi, Phys. Rev. Lett. 28, 497 (1972). 7. F. C. Brown, R. S. Bachrach, and M. Skibowskl, Phys. Rev. BI~5, 4781 (1977). 8. C. Kunz, J. Physique Colloq. C4, 119 (1978). 9. k. Quattropanl, F. Bassanl, G. Margarltondo and G. Tinlvella, Nuove Clmento B51, 335 (1979).
I0. F. Bassanl, Proc. VI Intern. Conf. on Vacuum Ultraviolet Radiation Physics (to be published in Applied Optics). ii. J. D. Dow, H. P. Hjalamarson, O. F. Sankey, R. E. Allen and H. BUttner, Extended Abstracts of the VI Intern. Conf. on Vacuum Ultraviolet Radiation Physics, Charlottesville, VA. 1980, Vol. i, n.88. 12. M. Altarelll and W. Y. Hsu, Phys. Rev. Lett. 43, 1346 (1979); M. Altarelli, W. Y. Hsu and A. Baldereshl, Phys. Rev. B (to appear). 13. L. Resca and R. Resta, Sol. State Commun. 29, 375 (1979) and Phys. Rev. Lett. 44, 1340 (1980). 14. W. Gudat and C. Kunz, Phys. Rev. Lett. 29, 169 (1972).