KINETIC-THEORY OF HIGH-FIELD TRANSPORT IN SEMICONDUCTORS

The paper deals with electron transport in a semiconductor of arbitrar y band structure and electron-phonon interaction, subjected to a high, but not necessarily homogeneous, electric field. The Boltzmann transp ort equation is simplified under the assumption that the occupation of momentum space is almost isotropic, as is the case for a drifting, no t 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 recover ed as instantiations of ours. The hierarchies of scales underlying the derivation of the Fokker-Planck equation are those used in the lucky- drift model.