One-dimensional model of drift-diffusion in a high electric field

The relationship between drift and diffusion in an electric field is studied by using a distribution function which takes into account the anisotropy introduced into electronic motion by the electric field. This puts some order into otherwise completely random motion. The transition from linear to nonlinear behavior is obtained when the energy gained by an electron in traversing a mean free path is comparable to the thermal energy. The diffusion coefficient is found to be independent of an electric field in the absence of quantum emission. But quantum emission degrades the diffusion coefficient. The drift velocity is shown to be limited to the thermal velocity. This indicates an independence of the saturation velocity on momentum-randomizing scattering events which control the mobility. The emission of a quantum of energy by emitting a phonon or photon degrades the carrier velocity. The saturation velocity is lower in the presence of a quantum emission while ohmic mobility is not affected. Einstein ratio enhances because of the mobility degradation effect. Hot electron temperature concepts under ac and de conditions are elaborated.