PHYSICAL REVIEW B VOLUME 43, NUMBER 5 15 FEBRUARY 1991-I Hot-electron relaxations and hot phonons in GaAs studied by subpicosecond Raman scattering Dai-sik Kim and Peter Y. Yu Department of Physics, University of California, Berkeley, California 94720 and Materials and Chemical Sciences Division, Laurence Berkeley Laboratory, 1 Cyclotron Road, Berkeley, California 94720 (Received 11 June 1990; revised manuscript received 13 September 1990) We have utilized subpicosecond laser pulses to excite and probe hot electrons and nonequilibrium longitudinal-optical (LO) phonons in bulk GaAs by Raman scattering. We find that the photoexcit- ed hot electrons cool at a rate much faster than predicted by intravalley scattering of LO phonons via the Frolich interaction. On the other hand, this fast cooling rate can be accounted for satisfac- torily by intervalley scattering. As a result of this very rapid cooling, the temperature of the hot LO phonons generated by the hot electrons temporarily overshoots the electron temperature. From the electron cooling curve and the dependence of the hot-phonon temperature on the excited-electron density, we determined the deformation potential for scattering between the I and L conduction- band valleys in GaAs. I. INTRODUCTION It has been known for many years that energetic elec- trons in GaAs relax predominantly via electron-phonon interactions. ' Of the many types of electron-phonon in- teractions possible in GaAs, the interaction between elec- trons and the zone-center longitudinal-optical (LO) pho- nons and the zone-edge optical phonons are known to occur in subpicosecond time scale. Recently, with the appearance of femtosecond dye lasers, it becomes possible to study these fast interactions in real time. So far there have been many reports on the study of fast relaxation of hot electrons in GaAs excited by femtosecond lasers us- ing optical techniques such as absorption and emis- sion. Comparatively, there are very few studies of hot- electron relaxation using Raman scattering. ' Raman scattering has the advantages of being an instantaneous process and being able to probe both electrons and pho- nons in the same experiment. However, Raman scatter- ing also has the disadvantages that the Raman signals due to photoexcited hot electrons and phonons are very small. In this paper we present the results of a study of hot- electron relaxation using subpicosecond Raman scatter- ing. We overcome the difficulty of weak Raman signals by using the same subpicosecond laser beam to excite and probe the hot electrons and phonons. We have shown elsewhere ' by using model calculations how the cooling rate of hot electrons can be determined in such a single- beam Raman experiment by varying the laser pulse width. In this paper we applied the single-beam tech- nique to measure the dependence of electron temperature and phonon population on photoexcited electron densi- ties. We find that at electron densities higher than 10' cm the "effective phonon temperature" overshoots that of the electrons (a phenomenon we have labeled phonon temperature overshoot). " By comparing our results with simple model calculations based on a realistic band struc- ture of GaAs we have been able to explain our results and to determine the electron-phonon scattering times for both intravalley and intervalley scatterings. Futhermore, we have clarified the role of hot phonons in the relaxation of hot electrons in GaAs. The organization of this paper is as follows. In Sec. II we present the background theories and models for un- derstanding the relaxation of hot electrons excited by femtosecond laser pulses. We will start with a commonly used model in which the conduction band is assumed to have only one minimum at the Brillouin-zone center. Since the photoexcited electrons in GaAs often have sufficient energy to scatter into the higher conduction- band valleys, we also consider a multivalley conduction- band model. The effects of the laser pulse width are then included in the theory. Following the theoretical con- siderations, we describe the details of our experimental setup and sample configurations. The technique of using a single subpicosecond laser beam to perform Raman scattering from photoexcited hot electrons and hot pho- nons will be presented. The kind of information one can extract using this technique is discussed. The electron and phonon temperatures measured with this technique as a function of excited carrier densities and of laser pulse length are presented. Finally, by comparing the experi- mental results with the predictions of both the one-valley model and the multivalley model, we show that the ex- perimental results cannot be explained by the one-valley model, but are in good agreement with the predictions of the multivalley model. II. MODEL CALCULATIONS In this section we present simple model calculations of the cooling curves of photoexcited hot electrons in bulk GaAs and the corresponding increase in longitudinal- optical phonon population caused by the relaxation of hot electrons. We will consider two band models which have been commonly used in the literature. Both models are based on the schematic band structure of GaAs 43 4158 1991 The American Physical Society