An Efficient Solution Scheme for the Spherical-Harmonics Expansion of the Boltzmann Transport Equation Applied to Two-Dimensional Devices

Abstract

This paper presents a novel numerical scheme applicable to the solution of the Boltzmann transport equation by means of a spherical-harmonics expansion. This scheme improves the solution at low energies, keeping the desired accuracy in the calculation of the mean quantities while saving a significant amount of CPU time. This is important in view of the applications of the method, since the typical number of nodes to be used in the combined space-energy domain is in the range of 10⁴–10⁵.