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Dependence of hot carriers temperature on lattice temperature in CdS
Solid State Communications,
Vol. 13, pp. 245—248, 1973.
Pergamon Press.
Printed in Great Britain
DEPENDENCE OF HOT CARRIERS TEMPERATURE ON LATFICE TEMPERATURE IN CdS E.A. Meneses, N. Jannuzziand R.C.C. Leite Instituto de Fisica ‘Gleb Wataghin’, Universidade Estadual de Campinas, Campinas, S.P., Brasil (Received 2 April 1973 by R. Loudon)
Non-equilibrium carrier distributions were obtained in CdS at various temperatures from 77 to 400K. A study is made of the influence of the lattice temperature on the carrier temperature. It is found that the higher the lattice temperature the lower is the difference between carrier and lattice temperatures, though carriers are always thermalized among themselves. The results can be accounted for by carrier relaxation through optical polar phonon emission.
RECENTLY it was observed1 that the radiative emission band observed in GaAs at high photoexcitation intensities contained a large portion of its photons with energies hv larger than the energy gap, E~.With increas-
The hot ~carrierdistribution was observed for a lattice temperature of 2°K.The carrier temperature T 1 The effective tempera0 attained a value of 76°K. ture T 0 reached for the hot phonons in GaAs was 800°K for a lattice temperature of 420°K. Attempts to observe non-equilibrium carrier distributions at temperatures above that of liquid He with C.W. Argon laser failed. Only with pulsed N2 lasers (100KW) were we able to observe hot electrons in GaAs for lattice temperatures of liquid N2 and above. The effect was so small however that it was impossible to make a detailed study as performed here for the case of CdS. However, very high optical phonon temperatures were easily observed with C.W. Ar lasers (5W) several in 3’4 in Typically semiconductors at room temperature. an experiment with a C.W. Argon laser, capable of a few watts, the energetic carrier generation rate per unit volume is some two to three orders of magnitude lower than in a N 2 pulsed laser experiment (100 kW).
lag excitation that radiation component increased substantially. It was concluded that carriers were thermalized among themselves defining a carrier temperature T~,different from the lattice temperature 7. The experiment was restricted to 7~~ 2°K.The following sequence of events was suggested: (a) mono-energetic carriers are created by photon absorption (photons of energy hv, > E, were provided by a C.W. Ar laser with maximum power of 1.0W); (b) these high energy electrons lose energy by two competing mechanisms,with namely, phonons coffisions otheremission carriers;of (c)optical this last processand raises the temperature of the carriers which are thermalized among themselves through carrier—carrier collisions; (d) the thermalized carrier system then loses energy through ‘~
the emission of polar optical phonons. Therefore the temperature of the carrier system was determined by the interplay between the power supplied to it by the high energy photocreated electrons and the power it loses to the lattice through the emission of optical phonons.
If the polar optical phonon temperature is higher than that of the electron system, no energy transfer from the latter to the former seems to be possible, and therefore the hot electrons cannot relax through polar optical phonon emission. In order to search for other possible relaxation mechanisms we have repeated on CdS the experiments performed on GaAs at 2 but now at higher temperatures, from 77 to 400°K.
Subsequently it was shown under similar conditions of high density mono-energetic carrier production that a non-equilibrium distribution of LO 2 phonons also obtained in GaAs.
,
245
HOT CARRIERS TEMPERATURE ON LATFIC TEMPERATURE IN CdS
246
Vol. 13, No.3
Figure 1 gives the high-energy tail of the radiative emission band for several excitation intensities when the sample was immersed in liquid N2. For all laser powers
I
used, the high-energy tail can be characterized by a well-defused temperature T~which increases with increasing laser excitation intensities. The maximum
II .
power density used here was between two and three orders1 of magnitude of that used the GaAs The same experiment was in repeated forexperiseveral ment. temperatures up to 400°K with similar results. sample Figure 2 give the effective temperature 7~,of the hot electron system as a function of the excitation photon flux F. For comparison the results from GaAs are also included. F is normalized in both cases to each respective maximum flux. Approximately the same behaviour is observed for GaAs and CdS. The results in Fig. 2 can be accounted for by polar optical phonon emission, the model proposed for the case of GaAs at low temperatures. This apparently conflicts with results from hot phonon studies as we have pointed out before. However, if we recall that (1) the phonon generation due to relaxation of the energetic photo-carriers is limited to a certain volume in K-space, (2) that surface Raman scatteringprobes a small and well-defined portion of that volume in K-space and (3) that the carrier system may interact mainly with phonons belonging to a different range in K-space, it
~.
II Iwz4tai I ~ I
b IILN(,Ins I S ISNI.IIIS
I
Ii I
.. 3
~tIt2 N
S
~ ~
2.~,
~
INERSY (IV)
FIG. 1. The high tails in the photoluminescence spectra of CdS at energy different excitation intensities.
a
CdS
S $.As
tb-
.1;-
~ I
I
%o1
•1
-~
DITUtbU% CF IJ~N (~IT~MYhIlTS)
FIG. 2. The effective carrier temperature 1, expressed as I/(T~ 7) is plotted as a function of the photon flux F in arbitrary units. 7 is the lattice temperature. —
Vol. 13, No.3
HOT CARRIERS TEMPERATURE ON LATFICE TEMPERATURE IN CdS
1.1
247
—
S.-
•.10
I 100
I 450 T
1CK)
FIG. 3. Dependence of the fractional carrier temperature increase (T~
—
is still likely that the model proposed in reference I is 5 pertinent to the present case. Notice that the slope of the straight portion of the curve in Fig. 2 gives with good approximation the energy of the LO-phonon in CdS (‘-35 mY). Similar plots to those of Figs. 1 and 2 were obmined for several temperatures from 77 to 400°K.The higher the temperature of the sample the more difficult it was to increase the carrier temperature T~.The results in Fig. 3 illustrate this fact. The fractional increase in carrier temperature with reference to the lattice temperature 7~is plotted as a function of T,. This result may be understood as due to added competition to photocarrier relaxation through carrier—carrier collisions as the temperature increases. Such competition may arise from direct scatteringby acoustic phonons.6 The present work leaves open a few questions. A
on the lattice temperature 1~.
complete calculation of the three volumes in K-space determined by the three scattering mechanisms demands a better knowledge of dispersion curves for electrons and phonons than presently available and is beyond the scope of the present work. We have not attempted to account quantitatively for the results of Fig. 3. We have however demonstrated that non-equilibrium carrier distributions are readily obtainable at all easilyworkable temperatures, and that under the assumption of no scattering among optical phonons of the same branch, the hot carrier distribution may be accounted for by the same mechanism proposed for GaAs at He temperatures, i.e. by carrier relaxation through polar optical phonon emission.
Acknowledgements The authors are indebted to Dr. D.C. Reynolds for the samples used here. Grants Conselho Nacional de Pesquisas, Ministério do from 1~anejamentoe Fundação de Amparo a Pesquisa do Estado de São Paulo are gladly acknowledged. —
REFERENCES
I. 2.
SHAH JAGDEEP and LEITE R.C.C.,Phys. Rev. Lett. 22, 1304 (1969). SHAH JAGDEEP, LEITE R.C.C. and SCOTT J.F., Solid State Commun. 8, 1089 (1970).
248
HOT CARRIERS TEMPERATURE ON LATFICE TEMPERATURE IN CdS
Vol. 13, No.3
3.
MATFOS J.C.V. and LEITE R.C.C., Solid State Commun. 12, 465 (1973).
4.
MATTOS J.C.V., GUIMARAES W.O.N. and LEITE R.C.C., Optics Commun. (in press).
5.
Here, as it was in the case in reference 1, it is implied that scattering among phonons of the same branch is not important.
6.
CONWELL E.M., Solid State Phys. Suppi. 9, 1 (1967).
Des distributions non équilibrées des porteurs on été observées dans le CdS
a plusieurs temperatures de 77 jusqu’a 400°K.Nous avons etudié l’influence
de la temperature du réseau sur celle des porteurs. Nous avons trouvé que la difference entre Ia temperature des porteurs et celle de réseau décroit avec l’augmentation de la temperature du réseau, bien que les porteurs sont toujours temalizés entre aux-mémes. Les résultats sont d’accord avec la relaxation des pOrteurs par l’intermédiaire de l’émission des phonons optiques longitudinaux.
Vol. 13, pp. 245—248, 1973.
Pergamon Press.
Printed in Great Britain
DEPENDENCE OF HOT CARRIERS TEMPERATURE ON LATFICE TEMPERATURE IN CdS E.A. Meneses, N. Jannuzziand R.C.C. Leite Instituto de Fisica ‘Gleb Wataghin’, Universidade Estadual de Campinas, Campinas, S.P., Brasil (Received 2 April 1973 by R. Loudon)
Non-equilibrium carrier distributions were obtained in CdS at various temperatures from 77 to 400K. A study is made of the influence of the lattice temperature on the carrier temperature. It is found that the higher the lattice temperature the lower is the difference between carrier and lattice temperatures, though carriers are always thermalized among themselves. The results can be accounted for by carrier relaxation through optical polar phonon emission.
RECENTLY it was observed1 that the radiative emission band observed in GaAs at high photoexcitation intensities contained a large portion of its photons with energies hv larger than the energy gap, E~.With increas-
The hot ~carrierdistribution was observed for a lattice temperature of 2°K.The carrier temperature T 1 The effective tempera0 attained a value of 76°K. ture T 0 reached for the hot phonons in GaAs was 800°K for a lattice temperature of 420°K. Attempts to observe non-equilibrium carrier distributions at temperatures above that of liquid He with C.W. Argon laser failed. Only with pulsed N2 lasers (100KW) were we able to observe hot electrons in GaAs for lattice temperatures of liquid N2 and above. The effect was so small however that it was impossible to make a detailed study as performed here for the case of CdS. However, very high optical phonon temperatures were easily observed with C.W. Ar lasers (5W) several in 3’4 in Typically semiconductors at room temperature. an experiment with a C.W. Argon laser, capable of a few watts, the energetic carrier generation rate per unit volume is some two to three orders of magnitude lower than in a N 2 pulsed laser experiment (100 kW).
lag excitation that radiation component increased substantially. It was concluded that carriers were thermalized among themselves defining a carrier temperature T~,different from the lattice temperature 7. The experiment was restricted to 7~~ 2°K.The following sequence of events was suggested: (a) mono-energetic carriers are created by photon absorption (photons of energy hv, > E, were provided by a C.W. Ar laser with maximum power of 1.0W); (b) these high energy electrons lose energy by two competing mechanisms,with namely, phonons coffisions otheremission carriers;of (c)optical this last processand raises the temperature of the carriers which are thermalized among themselves through carrier—carrier collisions; (d) the thermalized carrier system then loses energy through ‘~
the emission of polar optical phonons. Therefore the temperature of the carrier system was determined by the interplay between the power supplied to it by the high energy photocreated electrons and the power it loses to the lattice through the emission of optical phonons.
If the polar optical phonon temperature is higher than that of the electron system, no energy transfer from the latter to the former seems to be possible, and therefore the hot electrons cannot relax through polar optical phonon emission. In order to search for other possible relaxation mechanisms we have repeated on CdS the experiments performed on GaAs at 2 but now at higher temperatures, from 77 to 400°K.
Subsequently it was shown under similar conditions of high density mono-energetic carrier production that a non-equilibrium distribution of LO 2 phonons also obtained in GaAs.
,
245
HOT CARRIERS TEMPERATURE ON LATFIC TEMPERATURE IN CdS
246
Vol. 13, No.3
Figure 1 gives the high-energy tail of the radiative emission band for several excitation intensities when the sample was immersed in liquid N2. For all laser powers
I
used, the high-energy tail can be characterized by a well-defused temperature T~which increases with increasing laser excitation intensities. The maximum
II .
power density used here was between two and three orders1 of magnitude of that used the GaAs The same experiment was in repeated forexperiseveral ment. temperatures up to 400°K with similar results. sample Figure 2 give the effective temperature 7~,of the hot electron system as a function of the excitation photon flux F. For comparison the results from GaAs are also included. F is normalized in both cases to each respective maximum flux. Approximately the same behaviour is observed for GaAs and CdS. The results in Fig. 2 can be accounted for by polar optical phonon emission, the model proposed for the case of GaAs at low temperatures. This apparently conflicts with results from hot phonon studies as we have pointed out before. However, if we recall that (1) the phonon generation due to relaxation of the energetic photo-carriers is limited to a certain volume in K-space, (2) that surface Raman scatteringprobes a small and well-defined portion of that volume in K-space and (3) that the carrier system may interact mainly with phonons belonging to a different range in K-space, it
~.
II Iwz4tai I ~ I
b IILN(,Ins I S ISNI.IIIS
I
Ii I
.. 3
~tIt2 N
S
~ ~
2.~,
~
INERSY (IV)
FIG. 1. The high tails in the photoluminescence spectra of CdS at energy different excitation intensities.
a
CdS
S $.As
tb-
.1;-
~ I
I
%o1
•1
-~
DITUtbU% CF IJ~N (~IT~MYhIlTS)
FIG. 2. The effective carrier temperature 1, expressed as I/(T~ 7) is plotted as a function of the photon flux F in arbitrary units. 7 is the lattice temperature. —
Vol. 13, No.3
HOT CARRIERS TEMPERATURE ON LATFICE TEMPERATURE IN CdS
1.1
247
—
S.-
•.10
I 100
I 450 T
1CK)
FIG. 3. Dependence of the fractional carrier temperature increase (T~
—
is still likely that the model proposed in reference I is 5 pertinent to the present case. Notice that the slope of the straight portion of the curve in Fig. 2 gives with good approximation the energy of the LO-phonon in CdS (‘-35 mY). Similar plots to those of Figs. 1 and 2 were obmined for several temperatures from 77 to 400°K.The higher the temperature of the sample the more difficult it was to increase the carrier temperature T~.The results in Fig. 3 illustrate this fact. The fractional increase in carrier temperature with reference to the lattice temperature 7~is plotted as a function of T,. This result may be understood as due to added competition to photocarrier relaxation through carrier—carrier collisions as the temperature increases. Such competition may arise from direct scatteringby acoustic phonons.6 The present work leaves open a few questions. A
on the lattice temperature 1~.
complete calculation of the three volumes in K-space determined by the three scattering mechanisms demands a better knowledge of dispersion curves for electrons and phonons than presently available and is beyond the scope of the present work. We have not attempted to account quantitatively for the results of Fig. 3. We have however demonstrated that non-equilibrium carrier distributions are readily obtainable at all easilyworkable temperatures, and that under the assumption of no scattering among optical phonons of the same branch, the hot carrier distribution may be accounted for by the same mechanism proposed for GaAs at He temperatures, i.e. by carrier relaxation through polar optical phonon emission.
Acknowledgements The authors are indebted to Dr. D.C. Reynolds for the samples used here. Grants Conselho Nacional de Pesquisas, Ministério do from 1~anejamentoe Fundação de Amparo a Pesquisa do Estado de São Paulo are gladly acknowledged. —
REFERENCES
I. 2.
SHAH JAGDEEP and LEITE R.C.C.,Phys. Rev. Lett. 22, 1304 (1969). SHAH JAGDEEP, LEITE R.C.C. and SCOTT J.F., Solid State Commun. 8, 1089 (1970).
248
HOT CARRIERS TEMPERATURE ON LATFICE TEMPERATURE IN CdS
Vol. 13, No.3
3.
MATFOS J.C.V. and LEITE R.C.C., Solid State Commun. 12, 465 (1973).
4.
MATTOS J.C.V., GUIMARAES W.O.N. and LEITE R.C.C., Optics Commun. (in press).
5.
Here, as it was in the case in reference 1, it is implied that scattering among phonons of the same branch is not important.
6.
CONWELL E.M., Solid State Phys. Suppi. 9, 1 (1967).
Des distributions non équilibrées des porteurs on été observées dans le CdS
a plusieurs temperatures de 77 jusqu’a 400°K.Nous avons etudié l’influence
de la temperature du réseau sur celle des porteurs. Nous avons trouvé que la difference entre Ia temperature des porteurs et celle de réseau décroit avec l’augmentation de la temperature du réseau, bien que les porteurs sont toujours temalizés entre aux-mémes. Les résultats sont d’accord avec la relaxation des pOrteurs par l’intermédiaire de l’émission des phonons optiques longitudinaux.