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Second indirect band gap in silicon
Solid State Communications,
Vol. 14, pp. 1007—1010, 1974.
Pergamon Press.
Printed in Great Britain
SECOND INDIRECT BAND GAP IN SILICON Richard A. Forman and W. Robert Thurber National Bureau of Standards, Washington, D.C. 20234, U.S.A. and David E. Aspnes Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A. (Received 26 October 1973 by M. Cardona)
We report the first observation of the F25’÷L1(second indirect) transition in Si based on optical absorption studies. The energy, (1650 ±10) meV, measured for this critical point shows that there remains a large discrepancy between theoretical band structure calculations and experimental results for this material.
BECAUSE of a confluence of critical points near 3.4eV, the energy band structure of silicon is not known with other semiconducting compoi nds despite a great deal the same degree of precision and certainty as those of of experimental and theoretic il effort. The wide vari-
_______________
~-sio
~
\
.
~
~
urn cm
—31 IKICK~.TYPi SILICSN .—soOI.~
~ —
ations in the predicted energies of nearly all highsymmetry critical points (with the exception of that for the unambiguous fundamental indirect absorption threshold) found1’9 in aprovide numberdirect of recent and calculations dramatic for this material evidence for the present uncertain situation.
IS
151214111211214
INIRCY SO)
However, recent modulation spectroscopy experi. ments1016 have made progress in identifying critical points, and it has been possible from these results to select two energy band calculations2’4 for which the correspondence between experiment and theory is reasonably good.15 In this Communication we report the first observation of the I’ 25’÷L1(second indirect) critical point, the remaining so-called ‘sensitive’ transition, and show that there still exists a reasonably large discrepancy between theory and experiment. Samples used in all measurements reported herein were high purity, high resistivity (p > 300 ~l-cm), and p-type silicon single crystals, polished, using a
lii
750 ISO ISO WAYFLENGIK sm~
FIG.l(a). The Temperatures absorption spectrum of silicon attovarious temperatures. listed correspond the bath temperature in the cold finger dewar(see text). FIG.1(b). Expanded scale of results in 1(a). Note curves have been displaced vertically for ease of presentation. The are straight continuations of the lowerdashed energylines portions of the line curves and are added to aid the reader. 7’8to commercial etch-polish (Lustrox)~ thicknesses ranging fromtechnique 25 to 300pm. Absorption measurements were performed using a Cary 14R18 foreprism grating double beam spectrophotometer
~.
1007
1008
SECOND INDIRECT BAND GAP IN SILICON
modified by the addition of a high intensity quartzhalogen source and a Hamamatsu18 R446 photomultiplier with extended S20 response. Scattered light was negligible over the entire spectral region. The sample temperature was controlled by means of a cold-finger dewar with a copper tail. Liquid helium, liquid nitrogen, dry ice-acetone, and boiling water were used as constant temperature baths in the dewar to obtain the various measurement temperatures. The samples were mounted the insulating copper tailvarnish, at onlyinone 18 Type on 7031 point, to using GEstrain, order avoid In Fig.l(a), we show the results of measurements at 373K, room temperature, and ‘~10K(and 80K) on one of the thinner samples. In Fig.l(b), we show an expanded scale of the region between 700 and 870nm. At room temperature and 373K, two quite small changes of slope are evident at 830 and at 760 nm, at low temperatures only one slope change can be seen at 758 nm. At intermediate temperatures. the feature near 830 becomes progressively weaker with decreasing temperature. The remainder of the spectrum is in good 19 agreement withthat results reported earlier by many We emphasize the only features observed in workers. the entire absorption spectrum are those due to the fundamental indirect threshold and the new structures noted above, that the temperature dependence and shape of the features near 760 and 830 nm appear very —
similar to those of the fundamental indirect gap, and that identical spectra are found for both n and p type samples. We interpret these new structures as indirect allowed transitions from the vicinity of the F~’maximum of the highest valence band to the L1 local minimum of lowest conduction band. Our interpretation is based on the detailed nature of the experimental observations as well as the correspondence with general theoretical predictions. First, the fact that two struCtures are observed at high temperatures but that only the higher-energy one is observable at low temperatures suggests immediately that an indirect transition is involved. Secondly, the temperature shift of the threshold energy is consistent with that observed for the analogous transition in Ge~(the fundamental indirect absorption edge). Thirdly, the apparent square. root nature of the threshold (visible in the data but not in Fig.l) is consistent with the lineshape expected for an indirect transition from an n = I exciton line and is not consistent with lineshapes of direct absorption
Vol. 14, No. 10
edges in low-dielectric-function materials.2’ Fourthly, the oscillator strength of the transition, obtained by direct comparison in Fig.1, is only about six times larger than that of the r 25.~~ transition, which is again consistent with an indirect transition. Fifthly, all band structure calculations show that one (and only one) indirect critical point, r’25+L1, should occur in this energy range, somewhere between 1.6 and 2.3eV, depending on the calculation. Finally, the observed energy separation, = 120meV, between the two thresholds is equal,~E within experimental uncertainty. to twice that of the TO phonon, 60.7meV,22 which is expected to be involved in the transition. Accordingly. we assign this threshold to the [‘ 25÷L1critical point. As is obvious from the data, finer details of the absorption shape as well as the exact position of the branch corresponding to phonon absorption are some~ what in the noise of the measurement; however, the totality of all of the observations provides the strength of this assignment. To obtain further information about this transition, we performed room and low electroabsorption temperatures usingmeasurements the techniquesat of Chester and Wendland,~but were unable to resolve any structure. However, we were able to determine an upper limit ~ < 0.003cm~fore = 6kV cm’ for this transition, which is at least a factor of 15 less than that for the easily measured F 25’-~&indirect transition. A quantitative comparison between the two transitions cannot be made because of the combination of exciton and broadening effects; broadening is the likely cause of lack of observation of electroabsorption signals. We mention that since uniform-field electroreflectance and electroabsorption signal magnitudes (peak to peak) are related approximately as X —
—.
P~P
—
7T
pp
where X is the wavelength and e the dielectric constant. then the electroreflectance response for this transition would be ~R/RI~.~< 108, and therefore completely beyond present experimental sensitivities. With both so-called ‘sensitive’ transitions now uniquely identified, it should be possible to calculate the band structure of Si to the same degree of accuracy and certainty as for those of other Group IV and Ill—V compounds .For comparison with present calculations, we summarize in Table I the present best
Vol. 14, No. 10
SECOND INDIRECT BAND GAP IN SILICON
1009
Table 1. Comparison of experimental and theoretical critical point energies for silicon Saravia Stukel Cohen Dresseihaus and and and Berg- Van Herman and 5 Vechtent et at1 Kanem Dresseihaush Type Experimental Brust” Euwemak stresser .
Transition r
25~(r;)~ &~ 1(fund. abs. edge) —
r’25~~(r8)—L1~ I ri5~ D(E~) A~,—A1~ D(E~) —
r2?~(r8’)—r2~D(E0) r’25•~(r,~) I’2’c D(E0 +
~)
1169.8 ±0.6~meV 0.9eV
1.10eV
1650±10b 3370 ±30c 3485 ±15d
L60 2.79 2.78 2.75
4185±l0e 4229 ±lo~ 34SO~
2.1 3.39 3.37, 3.54 4.2
0.8eV
1.04eV
1.13eV
1.15eV
1.9 3.4 —3.1
1.87 3.40 3.60
2.25 2.7 3.4
2.98 3.01
3.8
4.10
4.2
3.61
—
1.07eV 1.77 2.43 3.20
3.78 3.33 3.4 4570g 4.15 4.50 4.3 ~K.L. Shak]ee and R.E. Nahory, Reference 11. hG. Dresseihaus and Reference M.S. DTesselhaus, Reference 3. 1JA. Van Vechten, 5. bThis paper. CR.A Forman, D.E. Aspnes and M. Cardona, Reference 10. ~M.L. Cohen and T.K. Bergstresser, Reference 1. dD.E. Aspnes and A.A. Studna, to be published. kDJ Stukel and R.N. Euwema, Reference 6. eD.E Aspnes and A.A. Studna, Reference 15. 1F. Herman, R.L. Kortum, C.D. Kuglin and R.A. Short, ~i. Koo, YR. Shen and R.R.L. Zucca, Reference 13. Reference 2. Values pertain to third ‘E (PERT)’calculation. ~R.R.L Zucca, J.P. Walter, Y,R. Shen and M.L. Cohen, Reference 12. mEO Kane, Reference 7. “L.R. Saravia and D. Brust, Reference 4. Values pertain to their ‘Model 11.’ —
—
D D(E2)
3.49
—
—
—
experimental values for known critical point energies in Si, together with a selection of the more accurate band structure calculations. In the case of the pseudopotential calculations, good agreement is found in those regions for which the calculation was adjusted. In the most detailed pseudopotential calculation of Saravia and Brust4 the best fit to the transition r 25~r2~ produces an error of 0.4eV at the transition .In this calculation, it appears for the cases considered that the energies of these two transitions are coupled, and that substantial changes in the pseudopotentials would be required to fit both experimentally determined critical point 6energies. The has no adjustable calculation of Stukel and Euwema parameters and predicts with remarkable accuracy both the fundamental indirect gap energy and that of the new transition reported here, but it fails strongly at higher energy transitions. Possibly this failure is
—
—
—
—
—
due to correlation effects which could be expected to become more important at higher energies. The results obtained by Van Vechten in the dielectric theory5 can be considered to be reasonable as the fit at all the gaps including the second fundamental indirect edge, is within approximately 0.2eV. ,
Obviously, further experiments are indicated to determine other band-to-band energies. Wavelength modulation is an obvious experiment which should be performed. Another interesting possibility for further experiments would be to reexamine hot electron effects including possible contributions of excitation from ~the~ to L
1
~.
Acknowledgements We would like to thank M. Cosman for his careful sample preparation without which these experiments could not have been performed. —
REFERENCES 1. 2. 3.
COHEN M.L and BERGSTRESSER T.K.,Phys. Rev. 141, 789 (1966). HERMAN F., KORTUM R.L., KUGLIN C.D. and SHORT R.A., in Quantum Theory ofAtOms, Molecules, and the Solid State, p.381 (Edited by LOWDIN P.O.) Academic Press, New York (1966). DRESSELHAUS G. and DRESSELHAUS M.S., Phys. Rev. 160, 649 (1967).
1010
SECOND INDIRECT BAND GAP IN SILICON
4.
SARAVIA LR. and BRUST D,Thys. Rev. 171,916(1968).
5.
VANVECHTENJ.A,Phys. Rev. 187, 1007(1969).
6.
STUKELD.J. and EUWEMA R.N.,Phys. Rev. BI, 1635 (1970).
7.
KANE E.O.,Phys. Rev. B4, 1910 (1971).
8. 9.
KUNZ A.B,Fhys. Rev. Lett. 27, 567 (1971). CHANEY R.C., UN C.C. and LAFON E.E.,Fhys. Rev. B3, 459 (1971).
Vol. 14, No. 10
10.
FORMAN R.A., ASPNES DE. and CARDONA M.,J. Phys. Chem. Solids 31, 227 (1970).
11. 12.
SHAKLEE K.L and NAHORY R.E.,Phys. Rev. Lett. 24,942(1970). ZUCCA R.R.L, WALTER J.P., SHEN YR. and COHEN M.L, Solid Stare Commun. 8,627(1970).
13.
KOO J., SHEN Y.R. and ZUCCA R.R.L., Solid State Commun. 9,2229(1971).
14.
SCHMIDT E. and VEDAM K., Solid State Commun. 9, 1187 (1971).
15.
ASPNES D.E. and STUDNA A.A.,Solid Stare Commun. 11, 1375 (1972).
16.
POLLAK F.H. and RUBLOFF G.W.,Phys. Rev. Letr. 29, 789 (1972).
17. 18.
Lustrox 1000, manufactured by Tizon Chemical Co., Flemington, N.J. Certain commercial instruments and materials are identified in this paper in order to specify adequately the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the instrument or material identified is necessarily the best available for the purpose.
19.
See, e.g., MACFARLANE G.G., MC LEAN T.P., QUARRINGTON J.E. and ROBERTS V., Phvs. Rev. Ill, 1245 (1958). MACFARLANE G.G., MC LEAN T.P., QUARRINGTON J.E. and ROBERTS V., Proc. Phys. Soc. (London) 71, 863 (1958). MCLEAN T.P., in Progress in Semiconductors, Vol. 5, p.53, (Edited by GIBSON A.F.) John Wiley, New York (1960).
20. 21. 22.
DOLLING G., in Inelastic Scattering ofNeutrons in Solids and Liquids, Vol. 2, p.37, International Atomic Energy Agency, Vienna (1963).
23.
CHESTERM. and WENDLANDP.H.,Phys. Rev. Lert. 13,193 (1964).
Auf Grund optischer Absorptionsmessungen an Si benchten wir die erste Beobachtung des t)bergangs f’25’~L~. Die gemessene Energie für diesen Kritischen Punkt (der zweite indirekte) von 1650 ±10meV zeigt class noch em ziemlich grosser Unterschied zwischen unser Messung and Resultate theoretischer Bandstruktur Rechnungen verbleibt.
Vol. 14, pp. 1007—1010, 1974.
Pergamon Press.
Printed in Great Britain
SECOND INDIRECT BAND GAP IN SILICON Richard A. Forman and W. Robert Thurber National Bureau of Standards, Washington, D.C. 20234, U.S.A. and David E. Aspnes Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A. (Received 26 October 1973 by M. Cardona)
We report the first observation of the F25’÷L1(second indirect) transition in Si based on optical absorption studies. The energy, (1650 ±10) meV, measured for this critical point shows that there remains a large discrepancy between theoretical band structure calculations and experimental results for this material.
BECAUSE of a confluence of critical points near 3.4eV, the energy band structure of silicon is not known with other semiconducting compoi nds despite a great deal the same degree of precision and certainty as those of of experimental and theoretic il effort. The wide vari-
_______________
~-sio
~
\
.
~
~
urn cm
—31 IKICK~.TYPi SILICSN .—soOI.~
~ —
ations in the predicted energies of nearly all highsymmetry critical points (with the exception of that for the unambiguous fundamental indirect absorption threshold) found1’9 in aprovide numberdirect of recent and calculations dramatic for this material evidence for the present uncertain situation.
IS
151214111211214
INIRCY SO)
However, recent modulation spectroscopy experi. ments1016 have made progress in identifying critical points, and it has been possible from these results to select two energy band calculations2’4 for which the correspondence between experiment and theory is reasonably good.15 In this Communication we report the first observation of the I’ 25’÷L1(second indirect) critical point, the remaining so-called ‘sensitive’ transition, and show that there still exists a reasonably large discrepancy between theory and experiment. Samples used in all measurements reported herein were high purity, high resistivity (p > 300 ~l-cm), and p-type silicon single crystals, polished, using a
lii
750 ISO ISO WAYFLENGIK sm~
FIG.l(a). The Temperatures absorption spectrum of silicon attovarious temperatures. listed correspond the bath temperature in the cold finger dewar(see text). FIG.1(b). Expanded scale of results in 1(a). Note curves have been displaced vertically for ease of presentation. The are straight continuations of the lowerdashed energylines portions of the line curves and are added to aid the reader. 7’8to commercial etch-polish (Lustrox)~ thicknesses ranging fromtechnique 25 to 300pm. Absorption measurements were performed using a Cary 14R18 foreprism grating double beam spectrophotometer
~.
1007
1008
SECOND INDIRECT BAND GAP IN SILICON
modified by the addition of a high intensity quartzhalogen source and a Hamamatsu18 R446 photomultiplier with extended S20 response. Scattered light was negligible over the entire spectral region. The sample temperature was controlled by means of a cold-finger dewar with a copper tail. Liquid helium, liquid nitrogen, dry ice-acetone, and boiling water were used as constant temperature baths in the dewar to obtain the various measurement temperatures. The samples were mounted the insulating copper tailvarnish, at onlyinone 18 Type on 7031 point, to using GEstrain, order avoid In Fig.l(a), we show the results of measurements at 373K, room temperature, and ‘~10K(and 80K) on one of the thinner samples. In Fig.l(b), we show an expanded scale of the region between 700 and 870nm. At room temperature and 373K, two quite small changes of slope are evident at 830 and at 760 nm, at low temperatures only one slope change can be seen at 758 nm. At intermediate temperatures. the feature near 830 becomes progressively weaker with decreasing temperature. The remainder of the spectrum is in good 19 agreement withthat results reported earlier by many We emphasize the only features observed in workers. the entire absorption spectrum are those due to the fundamental indirect threshold and the new structures noted above, that the temperature dependence and shape of the features near 760 and 830 nm appear very —
similar to those of the fundamental indirect gap, and that identical spectra are found for both n and p type samples. We interpret these new structures as indirect allowed transitions from the vicinity of the F~’maximum of the highest valence band to the L1 local minimum of lowest conduction band. Our interpretation is based on the detailed nature of the experimental observations as well as the correspondence with general theoretical predictions. First, the fact that two struCtures are observed at high temperatures but that only the higher-energy one is observable at low temperatures suggests immediately that an indirect transition is involved. Secondly, the temperature shift of the threshold energy is consistent with that observed for the analogous transition in Ge~(the fundamental indirect absorption edge). Thirdly, the apparent square. root nature of the threshold (visible in the data but not in Fig.l) is consistent with the lineshape expected for an indirect transition from an n = I exciton line and is not consistent with lineshapes of direct absorption
Vol. 14, No. 10
edges in low-dielectric-function materials.2’ Fourthly, the oscillator strength of the transition, obtained by direct comparison in Fig.1, is only about six times larger than that of the r 25.~~ transition, which is again consistent with an indirect transition. Fifthly, all band structure calculations show that one (and only one) indirect critical point, r’25+L1, should occur in this energy range, somewhere between 1.6 and 2.3eV, depending on the calculation. Finally, the observed energy separation, = 120meV, between the two thresholds is equal,~E within experimental uncertainty. to twice that of the TO phonon, 60.7meV,22 which is expected to be involved in the transition. Accordingly. we assign this threshold to the [‘ 25÷L1critical point. As is obvious from the data, finer details of the absorption shape as well as the exact position of the branch corresponding to phonon absorption are some~ what in the noise of the measurement; however, the totality of all of the observations provides the strength of this assignment. To obtain further information about this transition, we performed room and low electroabsorption temperatures usingmeasurements the techniquesat of Chester and Wendland,~but were unable to resolve any structure. However, we were able to determine an upper limit ~ < 0.003cm~fore = 6kV cm’ for this transition, which is at least a factor of 15 less than that for the easily measured F 25’-~&indirect transition. A quantitative comparison between the two transitions cannot be made because of the combination of exciton and broadening effects; broadening is the likely cause of lack of observation of electroabsorption signals. We mention that since uniform-field electroreflectance and electroabsorption signal magnitudes (peak to peak) are related approximately as X —
—.
P~P
—
7T
pp
where X is the wavelength and e the dielectric constant. then the electroreflectance response for this transition would be ~R/RI~.~< 108, and therefore completely beyond present experimental sensitivities. With both so-called ‘sensitive’ transitions now uniquely identified, it should be possible to calculate the band structure of Si to the same degree of accuracy and certainty as for those of other Group IV and Ill—V compounds .For comparison with present calculations, we summarize in Table I the present best
Vol. 14, No. 10
SECOND INDIRECT BAND GAP IN SILICON
1009
Table 1. Comparison of experimental and theoretical critical point energies for silicon Saravia Stukel Cohen Dresseihaus and and and Berg- Van Herman and 5 Vechtent et at1 Kanem Dresseihaush Type Experimental Brust” Euwemak stresser .
Transition r
25~(r;)~ &~ 1(fund. abs. edge) —
r’25~~(r8)—L1~ I ri5~ D(E~) A~,—A1~ D(E~) —
r2?~(r8’)—r2~D(E0) r’25•~(r,~) I’2’c D(E0 +
~)
1169.8 ±0.6~meV 0.9eV
1.10eV
1650±10b 3370 ±30c 3485 ±15d
L60 2.79 2.78 2.75
4185±l0e 4229 ±lo~ 34SO~
2.1 3.39 3.37, 3.54 4.2
0.8eV
1.04eV
1.13eV
1.15eV
1.9 3.4 —3.1
1.87 3.40 3.60
2.25 2.7 3.4
2.98 3.01
3.8
4.10
4.2
3.61
—
1.07eV 1.77 2.43 3.20
3.78 3.33 3.4 4570g 4.15 4.50 4.3 ~K.L. Shak]ee and R.E. Nahory, Reference 11. hG. Dresseihaus and Reference M.S. DTesselhaus, Reference 3. 1JA. Van Vechten, 5. bThis paper. CR.A Forman, D.E. Aspnes and M. Cardona, Reference 10. ~M.L. Cohen and T.K. Bergstresser, Reference 1. dD.E. Aspnes and A.A. Studna, to be published. kDJ Stukel and R.N. Euwema, Reference 6. eD.E Aspnes and A.A. Studna, Reference 15. 1F. Herman, R.L. Kortum, C.D. Kuglin and R.A. Short, ~i. Koo, YR. Shen and R.R.L. Zucca, Reference 13. Reference 2. Values pertain to third ‘E (PERT)’calculation. ~R.R.L Zucca, J.P. Walter, Y,R. Shen and M.L. Cohen, Reference 12. mEO Kane, Reference 7. “L.R. Saravia and D. Brust, Reference 4. Values pertain to their ‘Model 11.’ —
—
D D(E2)
3.49
—
—
—
experimental values for known critical point energies in Si, together with a selection of the more accurate band structure calculations. In the case of the pseudopotential calculations, good agreement is found in those regions for which the calculation was adjusted. In the most detailed pseudopotential calculation of Saravia and Brust4 the best fit to the transition r 25~r2~ produces an error of 0.4eV at the transition .In this calculation, it appears for the cases considered that the energies of these two transitions are coupled, and that substantial changes in the pseudopotentials would be required to fit both experimentally determined critical point 6energies. The has no adjustable calculation of Stukel and Euwema parameters and predicts with remarkable accuracy both the fundamental indirect gap energy and that of the new transition reported here, but it fails strongly at higher energy transitions. Possibly this failure is
—
—
—
—
—
due to correlation effects which could be expected to become more important at higher energies. The results obtained by Van Vechten in the dielectric theory5 can be considered to be reasonable as the fit at all the gaps including the second fundamental indirect edge, is within approximately 0.2eV. ,
Obviously, further experiments are indicated to determine other band-to-band energies. Wavelength modulation is an obvious experiment which should be performed. Another interesting possibility for further experiments would be to reexamine hot electron effects including possible contributions of excitation from ~the~ to L
1
~.
Acknowledgements We would like to thank M. Cosman for his careful sample preparation without which these experiments could not have been performed. —
REFERENCES 1. 2. 3.
COHEN M.L and BERGSTRESSER T.K.,Phys. Rev. 141, 789 (1966). HERMAN F., KORTUM R.L., KUGLIN C.D. and SHORT R.A., in Quantum Theory ofAtOms, Molecules, and the Solid State, p.381 (Edited by LOWDIN P.O.) Academic Press, New York (1966). DRESSELHAUS G. and DRESSELHAUS M.S., Phys. Rev. 160, 649 (1967).
1010
SECOND INDIRECT BAND GAP IN SILICON
4.
SARAVIA LR. and BRUST D,Thys. Rev. 171,916(1968).
5.
VANVECHTENJ.A,Phys. Rev. 187, 1007(1969).
6.
STUKELD.J. and EUWEMA R.N.,Phys. Rev. BI, 1635 (1970).
7.
KANE E.O.,Phys. Rev. B4, 1910 (1971).
8. 9.
KUNZ A.B,Fhys. Rev. Lett. 27, 567 (1971). CHANEY R.C., UN C.C. and LAFON E.E.,Fhys. Rev. B3, 459 (1971).
Vol. 14, No. 10
10.
FORMAN R.A., ASPNES DE. and CARDONA M.,J. Phys. Chem. Solids 31, 227 (1970).
11. 12.
SHAKLEE K.L and NAHORY R.E.,Phys. Rev. Lett. 24,942(1970). ZUCCA R.R.L, WALTER J.P., SHEN YR. and COHEN M.L, Solid Stare Commun. 8,627(1970).
13.
KOO J., SHEN Y.R. and ZUCCA R.R.L., Solid State Commun. 9,2229(1971).
14.
SCHMIDT E. and VEDAM K., Solid State Commun. 9, 1187 (1971).
15.
ASPNES D.E. and STUDNA A.A.,Solid Stare Commun. 11, 1375 (1972).
16.
POLLAK F.H. and RUBLOFF G.W.,Phys. Rev. Letr. 29, 789 (1972).
17. 18.
Lustrox 1000, manufactured by Tizon Chemical Co., Flemington, N.J. Certain commercial instruments and materials are identified in this paper in order to specify adequately the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the instrument or material identified is necessarily the best available for the purpose.
19.
See, e.g., MACFARLANE G.G., MC LEAN T.P., QUARRINGTON J.E. and ROBERTS V., Phvs. Rev. Ill, 1245 (1958). MACFARLANE G.G., MC LEAN T.P., QUARRINGTON J.E. and ROBERTS V., Proc. Phys. Soc. (London) 71, 863 (1958). MCLEAN T.P., in Progress in Semiconductors, Vol. 5, p.53, (Edited by GIBSON A.F.) John Wiley, New York (1960).
20. 21. 22.
DOLLING G., in Inelastic Scattering ofNeutrons in Solids and Liquids, Vol. 2, p.37, International Atomic Energy Agency, Vienna (1963).
23.
CHESTERM. and WENDLANDP.H.,Phys. Rev. Lert. 13,193 (1964).
Auf Grund optischer Absorptionsmessungen an Si benchten wir die erste Beobachtung des t)bergangs f’25’~L~. Die gemessene Energie für diesen Kritischen Punkt (der zweite indirekte) von 1650 ±10meV zeigt class noch em ziemlich grosser Unterschied zwischen unser Messung and Resultate theoretischer Bandstruktur Rechnungen verbleibt.