A new Monte Carlo method is presented for the evaluation of the density matrix from the solution of the Liouville–von Neumann equation for an ensemble of noninteracting electrons in a semiconductor crystal. The method is applied to the study of the electron transient response to a high external electric field in Si and to the relaxation of photoexcited electrons in GaAs in absence of external electric fields. The phonon population is always assumed at equilibrium, but no assumptions are made about the strength of the electron-phonon interaction. Results show that typical quantum features such as energy-nonconserving transitions, intracollisional field effect, and multiple collisions change the very first transient of the system with respect to a semiclassical description.

• Received 28 November 1988

DOI:https://doi.org/10.1103/PhysRevB.39.10781