Drift diffusion and Einstein relation for electrons in silicon subjected to a high electric field

We present a theory that makes an explicit connection between scattering-limited Ohmic mobility and quantum-emission-limited saturation velocity. The theory is applied to electrons in bulk silicon by taking a quantum equal to the energy of an optical phonon. A modification in the mean-free path because of this quantum emission is indicated, an effect that appears only in the high-field regime. This modification is shown to lead to electric-field-induced degradation of the diffusion coefficient. The theory presented agrees well with the drift-diffusion experimental data and empirical relations used in modeling devices. The theory makes connections with an alternate description in terms of electron temperature under ac and dc conditions. Because drift-diffusion processes are central in performance evaluation of submicron-scale devices in which high fields are necessarily present, these results contribute significantly to reshaping thinking processes in the high-field regime.