Kinetic theory of high-field transport in semiconductors

The paper deals with electron transport in a semiconductor of arbitrary band structure and electron-phonon interaction, subjected to a high, but not necessarily homogeneous, electric field. The Boltzmann transport equation is simplified under the assumption that the occupation of momentum space is almost isotropic, as is the case for a drifting, not ballistic, electron. A closed-form equation for the electron energy distribution ensues: the equation is of the multivariate Fokker-Planck type in four-dimensional energy-position space. The typical relative departure between the Boltzmann and Fokker-Planck transport equations is the ratio of the hard-phonon energy to the average electron energy. Previous electron-transport equations in solids and gases are recovered as instantiations of ours. The hierarchies of scales underlying the derivation of the Fokker-Planck equation are those used in the lucky-drift model.