High-field electron transport for ellipsoidal multivalley band structure of silicon

Abstract

High-field electron-transport properties of bulk silicon are studied taking into account the multivalley band structure with ellipsoidal energy surface. A distribution function that takes into account the anisotropy introduced in electron motion by the high electric field is described. This puts some order in the 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 drift velocity is shown to be limited to the random thermal velocity for nondegenerate electrons and to the Fermi velocity for degenerate electrons. This indicates independence of the saturation velocity on momentum-randomizing scattering events which control the mobility. The emission of an optical phonon is significant when inelastic scattering length is comparable to the momentum randomizing mean free path. This further lowers the saturation velocity. When an electric field is applied along the <100≳ direction in silicon, an intervalley transfer from valleys with lower mean free path to the ones with higher mean free path is obtained. When compared with the experimental data on silicon, an excellent agreement is obtained.