Diffusion of charge carriers in high electric fields

Abstract

The diffusion constant of electrons in high electric fields is studied by solving the Boltzmann equation and incorporating the effect of the carrier density gradient on the distribution function. The relaxation-time description of the scattering mechanisms and a constant isotropic effective mass for the carriers are assumed. For charge diffusion in gases, the method yields values of the longitudinal to transverse diffusivity ratio D_L/D_T in excellent agreement with those obtained from other methods. The method has also been applied to study the hot-electron diffusion in semiconductors, namely, germanium and silicon. It is found that the quantity D_L/D_T is less than unity and differs markedly from the values calculated on the basis of modified Einstein's relations. Satisfactory agreement with recent experiments in the case of silicon has been obtained.