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Resonant Raman scattering in germanium and zincblende-type semiconductors temperature dependence
Solid State Communications,Vol. 9, Pp. 1235—1238, 1971.Pergamon Press.
Printed in Great Britain
RESONANT RAMAN SCATTERING IN GERMANIUM AND ZINCBLENDE-TYPE SEMICONDUCTORS TEMPERATURE DEPENDENCE* by J.B. Renucci, M.A. Renucci,t and Manuel Cardona Department of Physics, Brown University, Providence, Rhode Island 02912 (Received 11 May 1971 by E. Burstem)
We have measured the resonance in the Raman scattering near the E1 gaps of InAs and of a Ge0 77 Si023 alloy at 77, 300 and 594°K. In contrast to the E1 gap determined in absorption and transmission measurements, the corresponding peak in the spectral dependence of the scattering cross section shifts very little with temperature; it occurs at all temperatures very near the energy of the absorption peak measured at low temperatures (~ 77°K).
INTRODUCTION
is seen for the Ge—Si alloy and only a small shift (~ 0.08 eV) is observed for InAs between 77 and 594°K. A shift larger than 0.2 eV would be expected on the basis of the temperature dependence of the structure in the absorption and
THE PHENOMENON of resonant Raman scattering in solids has recently received in the 5.Resonances considerable attention~ scattering cross section have been reported at the E 0 gap 2 5 (lowest direct absorption edge at k = 0) and at the E1 gap (nearly two-dimensional 34. direct the[1111 of direction In this critical note wepoints reportalong measurements the
reflection spectra. This is the first observation of large differences in gap energies obtained by different techniques at finite temperatures. bi-product of this work we have proved the As a existence of an E 1 resonance in the Raman scattering cross section of germanium, hitherto unobserved.
resonant Raman scattering near E for InAs and for a Ge—Si alloy with 23 at.% of 0Si at several temperatures between 77 and 594 K. The shift in the resonant energy with temperature is considerably less than expected from the known temperature dependence of theE1 peaks in the optical constants (absorption and reflection). Actually, no shift at all (to within ±0.02 eV) *
Our measurements were performed with the five lines of a Coherent Radiation 54 A Argon-ion laser [2.41, 2.47, 2.50, 2.54 and 2.60eV]. The cross sections were determined from the measured intensities by comparison with the scattered intensities of calcite, assumed proportional to c~.~ It is then not necessary to know the spectral response of the photomultiplierand the transfer function of the monochromator. However, we checked the proportionality of the scattering cross section to w’ for calcite independently, on the basis of the known spectral response of the
Supported by the Army Research Office, Durham, and the National Science Foundation. Fellows of French government on leave from the University of Toulouse, Laboratoire de Physique Expérimentale. 1235
1236
RESONANT RAMAN SCATTERING IN SEMICONDUCTORS
photomultiplier (ITT FW 130) and the intensity of exciting radiation measured with a laser power
compatible with Fig. 1. We should point out that we have measured the E 1 resonace for lower Si concentrations: these measurements indicate, by extrapolation, that the E1 resonance also occurs in pure Ge. However, it cannot be observed with an argon-ion laser since it falls below the frequency of the available laser lines.
meter. The sample was placed inside a glass Dewar and immersed in liquid nitrogen for the low temperature measurements. For measurements at high temperature it was heated in vacuum with a resistance heater attached to a copper block onto which the sample was glued. The scattered light was analyzed with a Jarrel_Ash double monochromator and detected by phonon counting. Because of the opacity of the samples the measurements were performed in the backscattering configuration.
laser Ge—Si frequencies alloys will be published elsewhere.
I
I
A 7. 77~Ic 0 T.3O0~K -
~
0~gIn ~h~tt.d by.0 C
The concentration of the polycrystalline Ge—Si alloy (23 at. % Si was chosen so as to bring the E1 energy the center of our available 6. to Raman measurements on other
Vol. 9, No. 14
25
~h~iIed by .1.50
-
~;0
-
(/)
E
2
-
E~5945()
E 1 300 K)
Figure 1 shows the E, resonance observed for
0
~E1)77~K)
0
this alloy at 77, 300 and 594 K. The sample was p 5 x 1015 cm-s. These measurements were performed on the Raman line which extrapolates 7. Measureto the on one-phonon line ofcorresponds germanium to Ge—Si ments the line which pairs yield similar results. Since these data were obtained by comparison with the scattering of calcite they are automatically corrected for the dependence of the scattering cross section. However, we have not performed a correction for absorption in view of the lack of absorption data at several temperatures. The absorption spectrum 8 indicates of a Ge—Si alloy at room temperature that this correction should produce no substantial shift of in the the Eposition of the resonance. The position 1 gap expected from 6 measurements reflection ~ and electroreflectance at room temperature is indicated by an arrow. We have also indicated by arrows the E 1 energies at &~
0
594 and 77 K expected on the basis of the value at dependence of the E 300°Kand the temperature 9 The three resonances 1 reflection peak in Ge. in Fig. 1 have approximately the same width and occur at the same energy (to ±0.02 eV). Possible temperature broadening is undoubtedly masked by the alloy broadening. The shift expected on the basis of the shift in the reflection spectrum of germanium (0.22 eV) is an order of magnitude larger than any shift in the Raman resonance
0220
I 2,30
I ExcilaI)on 2.40 Energy
C
I eV) 2.50
I 2.60
FIG. the 1. Resonant near E, gap ofRaman a Ge scattering (Stokes) 0 ~ — Si0 23 sample at several temperatures. The origins of the vertical scales have been shifted as indicated.
Figure 2 shows thenear resonances observed for the TO phonon of InAs E 1 at 77, 300 and 594°K. We used for this work an n-typetook sample 3. The scattering place with N 6 x i0’~cm’ on a [llOj surface and thus only TO-phonons were Raman allowed although a strong, presumably surface field induced ~ LO line was seen at low temperatures. We have also included in Fig. 1 the data obtained by Leite and Scott for a3[1111 surface at room temperature line). in the Considerable broadening(dashed is observed resonance line of Fig. 2 at high temperatures. The temperature independent alloy scattering present in the Ge—Si alloys is now absent. A shift in the resonant energy of about 0.08 eV to lower energies is seen between 77 and 594°K. This shift is much smaller than the shift in the corresponding absorption and reflection peak
Vol. 9, No. 14
RESONANT RAMAN SCATTERING IN SEMICONDUCTORS
(0.28 eV). ‘° It is somewhat larger than the shift expected solely on the basis of the change in lattice constant due to thermal expansion (9.034eV estimated from the linear expansion coefficient,~ the elastic coast ants, 12 and the hydrostatic pressure coefficient of the gap). 13 We have also measured the resonance in the LO forbidden line at several temperatures. The position of the resonance shows the same temperature dependence as the data of Fig. 2. However, a much stronger temperature effect on the strength of the LO resonance is seen. The forbidden LO line is very strong at 773 K but it becomes very weak (as expected for a forbidden line) at high temperatures.
I 30
I
C
I
7. 77~K 0 7.594~K OT~300~O 7 . 300~K [Ref 3
-
~
—
I II
I
II
I I
III
I
I
I EI594KI
RI
117 ~I5
I
I
I
-
E
-
I300~6II I
‘
2
I 0
~IO
,/
-
-
0
of CrORS $CCtIOC sfrlft.d by —75
OrIgIn
0
C 2.30
C
2.40 ExcItatIon
C 250 Energy Ccv)
2.60
FIG. 2. Resonant Raman scattering (Stokes) for the TO phonon line of InAs near the E 1 gap at several temperatures. The data given in reference 3 for room temperature are also included (dashed line),
We believe this phenomenon is similar to that reported by Pinczuk and Burstein for InSb; ~ it is not due to a shift in the resonant energy with temperature, as suggested in reference 4, but to a change in the height of the resonance line probably related to a strong excitonic contribution to the LO resonance. The existence of this contribution 4 has also been proposed by Pinczuk and Burstein. We have not investigated ourselves whether
1237
Raman resonances near E
0 also have an anomalously small temperature shift. However, measurements for GaP by Scott et a!. at 30 and 300°K do not indicate any shift in the resonance curves, within the experimental scatter. We point out that the energy of the E0 gap at 30°Khas been recent~y used to fit equally well both the 30 and 300°K E0 Raman resonance in GaP. 14 The question of whether a given energy gap at finite temperatures should be the same for different processes has been considered earlier. Brooks, ~ for instance, concluded on the basis of experimental evidence that the thermal gap and the corresponding optical gap are essentially the same at all temperatures. The gap which enters into the k-p expression of the effective mass at finite temperature is believed to be the zero temperature gap decreased only by thermal 16 expansion, but not by electron—phonon interaction. A similar result seems to apply to the resonant gaps in Raman scattering: in Figure 2 a shift approximately equal to the expected effect of thermal expansion is seen, while no shift whatsoever is seen in Figure 1. We do not have a detailed theoretical explanation of this effect. However, it is not too surprising to find a different effect of the electron—phonon interaction on energy gaps in optical absorption and in Raman scattering. In optical absorption the electron— phonon decrease in the gap with temperature is mostly produced by virtual absorption and emission of acoustical phonons by the electrons and holes. The Raman scattering is produced by real absorption and emission of optical phonons. It is clear that in a theory of the temperature dependence of the resonant Raman scattering both the acoustical gap-shifting phonons and the optical light-scattering phonons must be treated on the same footing. This theory is not available at present. Acknowledgements — We would like to thank Drs. J.P. Dismukes, L.E. Ekstrom and E.F. Hockins for the Ge—Si alloy sample used in this experiment.
.1238
RESONANT RAMAN SCATTERING IN SEMICONDUCTORS
Vol.9, No. 14
REFERENCES 1.
LOUDON R. Phys. 13, 423 (1964).
2.
LEITE R.C.C., DAMEN T.C. and SCOTT J.F. Light Scattering in Solids, p. 359 (edited by WRIGHT G.B.) Springer Verlag, N.Y., (1969).
3.
LEITE R.C.C. and SCOTT J.F. Phys. Rev. Lett. 21, 130 (1969).
4.
PINCZUK A. and BURSTEIN E. Phys. Rev. Lett. 21, 1073 (1968).
5.
SCOTT J.F., DAMEN T.C., LEITE R.C.C. and SILFVAST W.T. Solid State Commun. 7, 953 (1969).
6.
KLEIN J.S., POLLAK F.H. and CARDONA M. Helv. Phys. Ada 41, 968 (1968).
7.
FELDMAN D.W., ASHKIN A. and PARKER J.H. Phys. Rev. Leit. 17, 1209 (1966).
8.
SCHMIDT, E. Phys. Status Solidi 27, 57 (1968).
9.
CARDONA M. and SOMMERS, Jr. H.S. Phys.Rev. 122, 1382 (1961).
10.
CARDONA M. and HARBEKE G. J. appl. Phys. 34, 813 (1963).
11.
WELKER H. and WEISS Ii.. Solid State Phys. Vol. 3. Academic Press, N.Y. (1956).
12.
GERLICH D. J. appi. Phys. 34, 2915 (1963).
13.
ZALLEN R. and PAUL W. Phys. Rev. 155, 703 (1967).
14.
CARDONA M. Solid State Commun., to be published.
15.
BROOKS H. in Advances in Electronics and Electron Physics, p. 85. Vol. 7, (edited by MARTON L.) Academic Press, N.Y. (1955).
16.
CARDONA M. Phys. Rev. 121, 752 (1961) SMITH S.D., PIDGEON C.R. and PROSSER V. Proc. Conf. on the Physics of Semiconductors, Exeter, 1962 (1962) p. 301. The Institute of Physics and the Physical Society, London.
mt.
Nous avons étudié la resonance de la diffusion Raman InAs et d’un alliage Ge 0 77 Si0 23 au voisinage des gaps E1 a 77, 300 et 594°K. Contrairement a la valeur de E1 détermineé par des mesures d’absorption et de transmission, l’énergie correspondant au maximum de la section efficace de diffusion vane trés peu avec la temperature. Elle est trés voisine, a toutes temperatures, de celle détermineé par absorption a basse temperature (“~- 773 K).
Printed in Great Britain
RESONANT RAMAN SCATTERING IN GERMANIUM AND ZINCBLENDE-TYPE SEMICONDUCTORS TEMPERATURE DEPENDENCE* by J.B. Renucci, M.A. Renucci,t and Manuel Cardona Department of Physics, Brown University, Providence, Rhode Island 02912 (Received 11 May 1971 by E. Burstem)
We have measured the resonance in the Raman scattering near the E1 gaps of InAs and of a Ge0 77 Si023 alloy at 77, 300 and 594°K. In contrast to the E1 gap determined in absorption and transmission measurements, the corresponding peak in the spectral dependence of the scattering cross section shifts very little with temperature; it occurs at all temperatures very near the energy of the absorption peak measured at low temperatures (~ 77°K).
INTRODUCTION
is seen for the Ge—Si alloy and only a small shift (~ 0.08 eV) is observed for InAs between 77 and 594°K. A shift larger than 0.2 eV would be expected on the basis of the temperature dependence of the structure in the absorption and
THE PHENOMENON of resonant Raman scattering in solids has recently received in the 5.Resonances considerable attention~ scattering cross section have been reported at the E 0 gap 2 5 (lowest direct absorption edge at k = 0) and at the E1 gap (nearly two-dimensional 34. direct the[1111 of direction In this critical note wepoints reportalong measurements the
reflection spectra. This is the first observation of large differences in gap energies obtained by different techniques at finite temperatures. bi-product of this work we have proved the As a existence of an E 1 resonance in the Raman scattering cross section of germanium, hitherto unobserved.
resonant Raman scattering near E for InAs and for a Ge—Si alloy with 23 at.% of 0Si at several temperatures between 77 and 594 K. The shift in the resonant energy with temperature is considerably less than expected from the known temperature dependence of theE1 peaks in the optical constants (absorption and reflection). Actually, no shift at all (to within ±0.02 eV) *
Our measurements were performed with the five lines of a Coherent Radiation 54 A Argon-ion laser [2.41, 2.47, 2.50, 2.54 and 2.60eV]. The cross sections were determined from the measured intensities by comparison with the scattered intensities of calcite, assumed proportional to c~.~ It is then not necessary to know the spectral response of the photomultiplierand the transfer function of the monochromator. However, we checked the proportionality of the scattering cross section to w’ for calcite independently, on the basis of the known spectral response of the
Supported by the Army Research Office, Durham, and the National Science Foundation. Fellows of French government on leave from the University of Toulouse, Laboratoire de Physique Expérimentale. 1235
1236
RESONANT RAMAN SCATTERING IN SEMICONDUCTORS
photomultiplier (ITT FW 130) and the intensity of exciting radiation measured with a laser power
compatible with Fig. 1. We should point out that we have measured the E 1 resonace for lower Si concentrations: these measurements indicate, by extrapolation, that the E1 resonance also occurs in pure Ge. However, it cannot be observed with an argon-ion laser since it falls below the frequency of the available laser lines.
meter. The sample was placed inside a glass Dewar and immersed in liquid nitrogen for the low temperature measurements. For measurements at high temperature it was heated in vacuum with a resistance heater attached to a copper block onto which the sample was glued. The scattered light was analyzed with a Jarrel_Ash double monochromator and detected by phonon counting. Because of the opacity of the samples the measurements were performed in the backscattering configuration.
laser Ge—Si frequencies alloys will be published elsewhere.
I
I
A 7. 77~Ic 0 T.3O0~K -
~
0~gIn ~h~tt.d by.0 C
The concentration of the polycrystalline Ge—Si alloy (23 at. % Si was chosen so as to bring the E1 energy the center of our available 6. to Raman measurements on other
Vol. 9, No. 14
25
~h~iIed by .1.50
-
~;0
-
(/)
E
2
-
E~5945()
E 1 300 K)
Figure 1 shows the E, resonance observed for
0
~E1)77~K)
0
this alloy at 77, 300 and 594 K. The sample was p 5 x 1015 cm-s. These measurements were performed on the Raman line which extrapolates 7. Measureto the on one-phonon line ofcorresponds germanium to Ge—Si ments the line which pairs yield similar results. Since these data were obtained by comparison with the scattering of calcite they are automatically corrected for the dependence of the scattering cross section. However, we have not performed a correction for absorption in view of the lack of absorption data at several temperatures. The absorption spectrum 8 indicates of a Ge—Si alloy at room temperature that this correction should produce no substantial shift of in the the Eposition of the resonance. The position 1 gap expected from 6 measurements reflection ~ and electroreflectance at room temperature is indicated by an arrow. We have also indicated by arrows the E 1 energies at &~
0
594 and 77 K expected on the basis of the value at dependence of the E 300°Kand the temperature 9 The three resonances 1 reflection peak in Ge. in Fig. 1 have approximately the same width and occur at the same energy (to ±0.02 eV). Possible temperature broadening is undoubtedly masked by the alloy broadening. The shift expected on the basis of the shift in the reflection spectrum of germanium (0.22 eV) is an order of magnitude larger than any shift in the Raman resonance
0220
I 2,30
I ExcilaI)on 2.40 Energy
C
I eV) 2.50
I 2.60
FIG. the 1. Resonant near E, gap ofRaman a Ge scattering (Stokes) 0 ~ — Si0 23 sample at several temperatures. The origins of the vertical scales have been shifted as indicated.
Figure 2 shows thenear resonances observed for the TO phonon of InAs E 1 at 77, 300 and 594°K. We used for this work an n-typetook sample 3. The scattering place with N 6 x i0’~cm’ on a [llOj surface and thus only TO-phonons were Raman allowed although a strong, presumably surface field induced ~ LO line was seen at low temperatures. We have also included in Fig. 1 the data obtained by Leite and Scott for a3[1111 surface at room temperature line). in the Considerable broadening(dashed is observed resonance line of Fig. 2 at high temperatures. The temperature independent alloy scattering present in the Ge—Si alloys is now absent. A shift in the resonant energy of about 0.08 eV to lower energies is seen between 77 and 594°K. This shift is much smaller than the shift in the corresponding absorption and reflection peak
Vol. 9, No. 14
RESONANT RAMAN SCATTERING IN SEMICONDUCTORS
(0.28 eV). ‘° It is somewhat larger than the shift expected solely on the basis of the change in lattice constant due to thermal expansion (9.034eV estimated from the linear expansion coefficient,~ the elastic coast ants, 12 and the hydrostatic pressure coefficient of the gap). 13 We have also measured the resonance in the LO forbidden line at several temperatures. The position of the resonance shows the same temperature dependence as the data of Fig. 2. However, a much stronger temperature effect on the strength of the LO resonance is seen. The forbidden LO line is very strong at 773 K but it becomes very weak (as expected for a forbidden line) at high temperatures.
I 30
I
C
I
7. 77~K 0 7.594~K OT~300~O 7 . 300~K [Ref 3
-
~
—
I II
I
II
I I
III
I
I
I EI594KI
RI
117 ~I5
I
I
I
-
E
-
I300~6II I
‘
2
I 0
~IO
,/
-
-
0
of CrORS $CCtIOC sfrlft.d by —75
OrIgIn
0
C 2.30
C
2.40 ExcItatIon
C 250 Energy Ccv)
2.60
FIG. 2. Resonant Raman scattering (Stokes) for the TO phonon line of InAs near the E 1 gap at several temperatures. The data given in reference 3 for room temperature are also included (dashed line),
We believe this phenomenon is similar to that reported by Pinczuk and Burstein for InSb; ~ it is not due to a shift in the resonant energy with temperature, as suggested in reference 4, but to a change in the height of the resonance line probably related to a strong excitonic contribution to the LO resonance. The existence of this contribution 4 has also been proposed by Pinczuk and Burstein. We have not investigated ourselves whether
1237
Raman resonances near E
0 also have an anomalously small temperature shift. However, measurements for GaP by Scott et a!. at 30 and 300°K do not indicate any shift in the resonance curves, within the experimental scatter. We point out that the energy of the E0 gap at 30°Khas been recent~y used to fit equally well both the 30 and 300°K E0 Raman resonance in GaP. 14 The question of whether a given energy gap at finite temperatures should be the same for different processes has been considered earlier. Brooks, ~ for instance, concluded on the basis of experimental evidence that the thermal gap and the corresponding optical gap are essentially the same at all temperatures. The gap which enters into the k-p expression of the effective mass at finite temperature is believed to be the zero temperature gap decreased only by thermal 16 expansion, but not by electron—phonon interaction. A similar result seems to apply to the resonant gaps in Raman scattering: in Figure 2 a shift approximately equal to the expected effect of thermal expansion is seen, while no shift whatsoever is seen in Figure 1. We do not have a detailed theoretical explanation of this effect. However, it is not too surprising to find a different effect of the electron—phonon interaction on energy gaps in optical absorption and in Raman scattering. In optical absorption the electron— phonon decrease in the gap with temperature is mostly produced by virtual absorption and emission of acoustical phonons by the electrons and holes. The Raman scattering is produced by real absorption and emission of optical phonons. It is clear that in a theory of the temperature dependence of the resonant Raman scattering both the acoustical gap-shifting phonons and the optical light-scattering phonons must be treated on the same footing. This theory is not available at present. Acknowledgements — We would like to thank Drs. J.P. Dismukes, L.E. Ekstrom and E.F. Hockins for the Ge—Si alloy sample used in this experiment.
.1238
RESONANT RAMAN SCATTERING IN SEMICONDUCTORS
Vol.9, No. 14
REFERENCES 1.
LOUDON R. Phys. 13, 423 (1964).
2.
LEITE R.C.C., DAMEN T.C. and SCOTT J.F. Light Scattering in Solids, p. 359 (edited by WRIGHT G.B.) Springer Verlag, N.Y., (1969).
3.
LEITE R.C.C. and SCOTT J.F. Phys. Rev. Lett. 21, 130 (1969).
4.
PINCZUK A. and BURSTEIN E. Phys. Rev. Lett. 21, 1073 (1968).
5.
SCOTT J.F., DAMEN T.C., LEITE R.C.C. and SILFVAST W.T. Solid State Commun. 7, 953 (1969).
6.
KLEIN J.S., POLLAK F.H. and CARDONA M. Helv. Phys. Ada 41, 968 (1968).
7.
FELDMAN D.W., ASHKIN A. and PARKER J.H. Phys. Rev. Leit. 17, 1209 (1966).
8.
SCHMIDT, E. Phys. Status Solidi 27, 57 (1968).
9.
CARDONA M. and SOMMERS, Jr. H.S. Phys.Rev. 122, 1382 (1961).
10.
CARDONA M. and HARBEKE G. J. appl. Phys. 34, 813 (1963).
11.
WELKER H. and WEISS Ii.. Solid State Phys. Vol. 3. Academic Press, N.Y. (1956).
12.
GERLICH D. J. appi. Phys. 34, 2915 (1963).
13.
ZALLEN R. and PAUL W. Phys. Rev. 155, 703 (1967).
14.
CARDONA M. Solid State Commun., to be published.
15.
BROOKS H. in Advances in Electronics and Electron Physics, p. 85. Vol. 7, (edited by MARTON L.) Academic Press, N.Y. (1955).
16.
CARDONA M. Phys. Rev. 121, 752 (1961) SMITH S.D., PIDGEON C.R. and PROSSER V. Proc. Conf. on the Physics of Semiconductors, Exeter, 1962 (1962) p. 301. The Institute of Physics and the Physical Society, London.
mt.
Nous avons étudié la resonance de la diffusion Raman InAs et d’un alliage Ge 0 77 Si0 23 au voisinage des gaps E1 a 77, 300 et 594°K. Contrairement a la valeur de E1 détermineé par des mesures d’absorption et de transmission, l’énergie correspondant au maximum de la section efficace de diffusion vane trés peu avec la temperature. Elle est trés voisine, a toutes temperatures, de celle détermineé par absorption a basse temperature (“~- 773 K).