A Deterministic Particle Method for Solving Kinetic Transport Equations: The Semiconductor Boltzmann Equation Case

Abstract

This paper is devoted to the description and implementation of a deterministic particle method: the weighted particle method. It is able to simulate kinetic transport equations with self-consistent force fields and collision terms. In this method, the particles move in the phase space according to the convective field, and collisions are accounted for by the time variation of a new degree of freedom, the weight of the particle. It is used here to simulate the Boltzmann equation of semiconductors and it is described in this case. An emphasis is put on the algorithms involved in the deterministic treatment of the collision term and in the computation of the self-consistent force field. Finally, numerical results of the simulation of a one-dimensional inhomogeneous semiconductor structure are shown.