Numerical simulation of non-homogeneous submicron semiconductor devices by a deterministic particle method

Abstract

This paper is devoted to the description and application of a deterministic particle method (the weighted particle method) for the numerical solution of the semiconductor Boltzmann equation self-consistently with Poisson equation. 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. 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. The aim of thi spaper is to show that this method gives accurate results on physically relevant problems. Numerical results are presented, in comparison with other methods, for the modelling of a N +- N- N + structure.