Evolution of a nonthermal electron energy distribution in GaAs

We have observed the thermalization of conduction electrons in GaAs from a nonthermal to a Maxwell-Boltzmann kinetic-energy distribution. A streak camera is used to observe the time-resolved spectrum of the band-to-acceptor luminescence following a short (5-ps) near-resonant laser pulse of very low excitation power. At electron density less than ${10}^{14}$ ${\mathrm{cm}}^{\mathrm{-}3}$ the thermalization of the electron energy distribution occurs with a rate independent of density on a time scale of 50 ps. Inelastic electron-phonon scattering is too slow to produce this thermalization. We examine electron-donor scattering in detail, and find that this scattering mechanism also does not cause the thermalization at low density. We conclude that the primary scattering mechanism at low density is electron-hole scattering in which electrons are spatially correlated with holes. At higher density, thermalization occurs via electron-electron scattering. We have performed extensive modeling of the thermalization with a Boltzmann-equation approach. In the case of the low-density thermalization, we find that a model of short-range electron-hole scattering provides a good fit to the nonthermal distribution we observe. At higher density, we calculate the time scale of weakly screened Coulomb scattering and find that it agrees with our observations. We compare our results to those of other experiments on electron thermalization in GaAs and ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As.