A deterministic particle method for the kinetic model of semiconductors: The homogeneous field model

Abstract

We present a new particle method for the simulation of the semiconductor Boltzmann equation—the weighted particle method. This method differs from the Monte-Carlo method by the approximation of the collision operator—we allocate each particle a weight which varies in time according to the collision integral. This integral is evaluated by means of a quadrature formula, which does not require the use of random numbers. The aim of this paper is to show that this method gives accurate results on physically relevant problems. Linear as well as non-linear collision integrals can be handled the same way by this method. Precise representations of the distribution functions are available, which allow a good insight into the physical processes. In this paper, we only consider the homogeneous field model with an emphasis on the collision operator. Numerical results are presented with a comparison with the Monte-Carlo method.