Short-range electron-electron scattering in silicon with a non-parabolic band structure

Abstract

In this paper we propose a new methodology to treat the short-range electron-electron interaction within both deterministic and stochastic Boltzmann Transport Equation (BTE) solvers, while accounting for a spherical and non-parabolic band structure. Our approach is based on a suitable transformation of the integration variable within the scattering integrals, which allows us to perform analytically the integration in the angular part of crystal momenta. This methodology is applied to a deterministic BTE solver based on the expansion of the distribution function in spherical harmonics: we start from a double vector-integral, and we are left with a standard double integral to be numerically computed. Quantitatively large corrections to the high-energy tail of the distribution are found.