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Photoexcited hot phonons and phonon lifetimes in GaAs
Volume
8, number
I
PHOTOEXCITED
HOT PHONONS
AND PHONON
J.C.V. MATTOS, W.O.N. GUIMARXES Institute
May 1973
OPTICS COMMUNICATIONS
LIFETIMES
IN GaAs
and R.C.C. LEITE
de Fkica “Gleb Wataghin”, Universidade Estadual de Campinas, Campinas, S.P., Bras2 Received
18 January
1973
A study of optical phonon lifetimes as determined from surface conditions is made through Raman lineshape analysis and non-equilibrium phonon distributions induced by energetic photoelectrons. Results indicate that firstorder Raman scattered linewidths are lifetime determined and that phonon lifetimes depend upon surface conditions. Our observations also give strong support to the mechanism and analysis proposed earlier for hot phonon generation through photoelectron relaxation.
Recent results obtained from different CdS samples showed that linewidths of surface Raman scattered radiation was dependent upon surface conditions [ 11. This raises an important question: are line-widths determined by phonon lifetimes in surface Raman scattering (SRS)? This is an increasingly important technique to study small gap semiconductors, metals and other opaque materials. In order to answer this question we have made a detailed analysis of lifetimes of photoexcited nonequilibrium phonon distributions from several samples of GaAs [2]. Our results not only demonstrate that linewidths are frequently lifetime determined but also bring strong support to the mechanism proposed earlier for the photo-generation of hot optical phonons in semiconductors. Such non-equilibrium phonon distributions were obtained subsequently for many different semiconductors and have shown promises of becoming an interesting technique for studies of electron-phonon coupling mechanisms [3] . The simple fact that linewidths change from sample to sample rules out the trivial cases of dispersion and anisotropy determined linewidths. We are left with two basically different mechanisms. Inhomogeneous broadening may arise from the fact that a finite area in the semiconductor surface probed by the incident radiation includes small regions where, due to stress and other effects, phonons are characterized by dif-
ferent frequencies. In this case the resulting lineshape is the convolution of these lines which may also be characterized by different lifetimes. The only other possibility is that surface conditions will determine a single phonon lifetime which will consequently display a lorentzian shape. We found that mechanical polishing and etching may result in non-lorentzian, somewhat asymmetrical lineshapes, whereas naturally grown epitaxial samples and cleaved surfaces give good lorentzians even for cases in which the light penetration depth is close to 1000 A. In the present communication we shall concentrate our attention to the cases where good lorentzians are obtained. A typical lorentzian shape obtained for the LO-phonon Raman scattered radiation is shown in fig. 1 *. In ref. [2], a rather simple relationship was obtained between the incident radiation power P and the resulting phonon population as described by the measured ratio of Stokes to anti-Stokes Raman scattered intensities (S/A). This may be written as:
1 -PP=PO r S/A-l
1 exp(hwLo/kr)-1
’
* The experimental procedure in the present described in detail in refs. [2,3].
work was
73
Volume 8, number 1
OPTICS COMMUNICATIONS
lit
May 1973
it 29
_1
g E
/
28c
Fig. 1. Observed lineshape and best fit lorentzian for one of the samples studied.
28C
273
373
473
573
TEMPERATURE (°K)
Fig. 2. Raman shift dependence on lattice temperature. where 13= (hv/25~2Po) 2Ad K m K 2, P is the laser power (W), P0 the maximum laser power used, Ad the active volume, K m and Kp twice the photo-electron and the p h o t o n wave vectors, respectively, r the phonon lifetime, T the lattice temperature, and hv the incident p h o t o n energy ( ~ 2.5 eV). In order to be sure that local heating is properly accounted for, we have measured the phonon frequencies and linewidths as a function of the sample temperature. To this end a furnace was built with optical
accesses. The sample was in an argon atmosphere. The results shown in fig. 2 for SRS indicate that the lattice temperature is properly described by the S/A ratio for the TO phonon in GaAs as was implied in the analysis of ref. [2]. Four examples were selected for the present work. For these we have plotted ( S / A - l ) -1 as a function of P/Po in fig. 3. The four slopes obtained in this way are values of r/j3, which may now be compared with
(
i
A
i
.5 0
Po
Fig. 3. (S/A-1) a as a function of the laser powerP/Po. 74
Volume 8, number 1
OPTICS COMMUNICATIONS
May 1973
Table 1
Sample
(r/(3)
linewidth (cm -1 )
r' X 1012sec
1 2 3 4
0.505 0.600 0.730 0.763
8.0 5.5 4.5 4.0
0.665 0.965 1.18 1.33
the four values of 7' as obtained from the measured linewidths in the four samples. A summary of results is included in table 1. If the mechanism and calculations of ref. [2] were correct a single value of/3 should be obtained for the different samples of the same material, once of course the active volume is constant. Indeed, results in fig. 4, where 7//3 is plotted against r', give a well defined value of/3 from which we may calculate the actiw~ volume A d . The value of 3.3 × 1 0 - 9 c m 3 thus obtained is in good agreement with the value used which of course cannot be measured with much precision. The results in figs. 3 and 4 bring good support to the general treatment given in ref. [2] to the problem of photon induced non-equilibrium distributions of optical phonons. Moreover these same results strongly support earlier contentions [ 1] that for good surface conditions as obtained in as-grown epitaxial material or through simple cleavage, phonon lifetimes though a function of surface condition, determine first-order Raman scattered linewidths. Some of the samples used in this work were kindly furnished b y Dr. Dale Hill. Grants from Conselho Nacional de Pesquisas, Funda~go de Amparo
I.¢
.5
t
t
.6
.7
t B
~/0 ~
Fig. 4. r', the lifetime determined from Raman linewidth as a function of r/f3 determined from hot phonons rate equation. Pesquisa do Estado de S~o Paulo and Minist6rio do Planejamento and Coordena~go are acknowledged.
References
[ 1 ] T.C. Damen, R.C.C. Leite and J. Shah, Proc. of the Xth International Conference on the Physics of Semiconductors, ed. S.P. Keller (U.S. Atomic Energy Comission, Washington, 1970). [2] J. Shah, R.C.C. keite and J.F. Scott, Solid State Commun. 8 (1970) 1089. [3] J.C.V. Mattos and R.C.C. Leite, Solid State Commun., to be published.
75
8, number
I
PHOTOEXCITED
HOT PHONONS
AND PHONON
J.C.V. MATTOS, W.O.N. GUIMARXES Institute
May 1973
OPTICS COMMUNICATIONS
LIFETIMES
IN GaAs
and R.C.C. LEITE
de Fkica “Gleb Wataghin”, Universidade Estadual de Campinas, Campinas, S.P., Bras2 Received
18 January
1973
A study of optical phonon lifetimes as determined from surface conditions is made through Raman lineshape analysis and non-equilibrium phonon distributions induced by energetic photoelectrons. Results indicate that firstorder Raman scattered linewidths are lifetime determined and that phonon lifetimes depend upon surface conditions. Our observations also give strong support to the mechanism and analysis proposed earlier for hot phonon generation through photoelectron relaxation.
Recent results obtained from different CdS samples showed that linewidths of surface Raman scattered radiation was dependent upon surface conditions [ 11. This raises an important question: are line-widths determined by phonon lifetimes in surface Raman scattering (SRS)? This is an increasingly important technique to study small gap semiconductors, metals and other opaque materials. In order to answer this question we have made a detailed analysis of lifetimes of photoexcited nonequilibrium phonon distributions from several samples of GaAs [2]. Our results not only demonstrate that linewidths are frequently lifetime determined but also bring strong support to the mechanism proposed earlier for the photo-generation of hot optical phonons in semiconductors. Such non-equilibrium phonon distributions were obtained subsequently for many different semiconductors and have shown promises of becoming an interesting technique for studies of electron-phonon coupling mechanisms [3] . The simple fact that linewidths change from sample to sample rules out the trivial cases of dispersion and anisotropy determined linewidths. We are left with two basically different mechanisms. Inhomogeneous broadening may arise from the fact that a finite area in the semiconductor surface probed by the incident radiation includes small regions where, due to stress and other effects, phonons are characterized by dif-
ferent frequencies. In this case the resulting lineshape is the convolution of these lines which may also be characterized by different lifetimes. The only other possibility is that surface conditions will determine a single phonon lifetime which will consequently display a lorentzian shape. We found that mechanical polishing and etching may result in non-lorentzian, somewhat asymmetrical lineshapes, whereas naturally grown epitaxial samples and cleaved surfaces give good lorentzians even for cases in which the light penetration depth is close to 1000 A. In the present communication we shall concentrate our attention to the cases where good lorentzians are obtained. A typical lorentzian shape obtained for the LO-phonon Raman scattered radiation is shown in fig. 1 *. In ref. [2], a rather simple relationship was obtained between the incident radiation power P and the resulting phonon population as described by the measured ratio of Stokes to anti-Stokes Raman scattered intensities (S/A). This may be written as:
1 -PP=PO r S/A-l
1 exp(hwLo/kr)-1
’
* The experimental procedure in the present described in detail in refs. [2,3].
work was
73
Volume 8, number 1
OPTICS COMMUNICATIONS
lit
May 1973
it 29
_1
g E
/
28c
Fig. 1. Observed lineshape and best fit lorentzian for one of the samples studied.
28C
273
373
473
573
TEMPERATURE (°K)
Fig. 2. Raman shift dependence on lattice temperature. where 13= (hv/25~2Po) 2Ad K m K 2, P is the laser power (W), P0 the maximum laser power used, Ad the active volume, K m and Kp twice the photo-electron and the p h o t o n wave vectors, respectively, r the phonon lifetime, T the lattice temperature, and hv the incident p h o t o n energy ( ~ 2.5 eV). In order to be sure that local heating is properly accounted for, we have measured the phonon frequencies and linewidths as a function of the sample temperature. To this end a furnace was built with optical
accesses. The sample was in an argon atmosphere. The results shown in fig. 2 for SRS indicate that the lattice temperature is properly described by the S/A ratio for the TO phonon in GaAs as was implied in the analysis of ref. [2]. Four examples were selected for the present work. For these we have plotted ( S / A - l ) -1 as a function of P/Po in fig. 3. The four slopes obtained in this way are values of r/j3, which may now be compared with
(
i
A
i
.5 0
Po
Fig. 3. (S/A-1) a as a function of the laser powerP/Po. 74
Volume 8, number 1
OPTICS COMMUNICATIONS
May 1973
Table 1
Sample
(r/(3)
linewidth (cm -1 )
r' X 1012sec
1 2 3 4
0.505 0.600 0.730 0.763
8.0 5.5 4.5 4.0
0.665 0.965 1.18 1.33
the four values of 7' as obtained from the measured linewidths in the four samples. A summary of results is included in table 1. If the mechanism and calculations of ref. [2] were correct a single value of/3 should be obtained for the different samples of the same material, once of course the active volume is constant. Indeed, results in fig. 4, where 7//3 is plotted against r', give a well defined value of/3 from which we may calculate the actiw~ volume A d . The value of 3.3 × 1 0 - 9 c m 3 thus obtained is in good agreement with the value used which of course cannot be measured with much precision. The results in figs. 3 and 4 bring good support to the general treatment given in ref. [2] to the problem of photon induced non-equilibrium distributions of optical phonons. Moreover these same results strongly support earlier contentions [ 1] that for good surface conditions as obtained in as-grown epitaxial material or through simple cleavage, phonon lifetimes though a function of surface condition, determine first-order Raman scattered linewidths. Some of the samples used in this work were kindly furnished b y Dr. Dale Hill. Grants from Conselho Nacional de Pesquisas, Funda~go de Amparo
I.¢
.5
t
t
.6
.7
t B
~/0 ~
Fig. 4. r', the lifetime determined from Raman linewidth as a function of r/f3 determined from hot phonons rate equation. Pesquisa do Estado de S~o Paulo and Minist6rio do Planejamento and Coordena~go are acknowledged.
References
[ 1 ] T.C. Damen, R.C.C. Leite and J. Shah, Proc. of the Xth International Conference on the Physics of Semiconductors, ed. S.P. Keller (U.S. Atomic Energy Comission, Washington, 1970). [2] J. Shah, R.C.C. keite and J.F. Scott, Solid State Commun. 8 (1970) 1089. [3] J.C.V. Mattos and R.C.C. Leite, Solid State Commun., to be published.
75