We have investigated quantum corrections to the Boltzmann equation for transport in high, spatially uniform electric fields, with weak scattering. Parabolic bands show no effects for constant fields up to ${10}^7$ V/cm; nonparabolic bands or time-varying fields give quantum corrections by dis- torting the energy-conserving δ function in semiclassical transition rates. We have found that in practical cases the scale of this is less than that from collisional broadening, almost invariably neglected. These results extend greatly the known range of validity of the Boltzmann equation in semiconductors.

• Received 24 January 1986

DOI:https://doi.org/10.1103/PhysRevB.33.7263