Methods for anisotropic selection of final states in the full band ensemble Monte Carlo simulation framework

In this paper we discuss different algorithms to select final states after scattering within the full band ensemble Monte Carlo (MC) simulation framework. Faster computers have made it possible to use more elaborated microscopic models for simulation of advanced semiconductor devices. Microscopic details like the band structures, the phonon dispersions and k-vector dependent deformation potentials are becoming accessible, which demand good algorithms for the selection of final states after scattering. The algorithm should also be adapted for a numerical representation of the band structure. Such an algorithm based on the rejection method is presented, which has been studied and compared in terms of efficiency and accuracy with two other algorithms for final state selection. The rejection algorithm is considered as suitable for anisotropic scattering mechanisms and when a relatively slow method is used for calculation of the wave-function overlap integral. It is shown that an accurate model of acoustic phonon scattering results in two characters of the process: one short-q process and one long-q process, very similar to a nonpolar optical intervalley process.