Evolution of multi-valley electron distributions in GaAs

An approach based on the physical evolution of the distribution function in the energy relaxation scale is used to study multi-valley distribution functions of electrons in GaAs subjected to a rapid change in electric field. This approach, which assumes the distribution can be determined by mean energy, is able to describe transport phenomena, including inter-valley transitions, in the scale as small as the energy relaxation time. Results show that, near the peak of velocity overshoot and bottom of undershoot in the Γ valley, the energy-dependent distribution cannot respond as fast as the distribution obtained from Monte Carlo method. This results in less pronounced overshoot and undershoot in the Γ valley when using the introduced approach than using the Monte Carlo method. However, in the L valley, overshoot and undershoot are not pronounced, and these two approaches are in very good agreement