Weighted Monte Carlo approach to electron transport in semiconductors

Abstract

The theory of electron transport in semiconductors is traditionally formulated in terms of the semiclassical Boltzmann equation. In nonlinear transport such an equation must be solved without linearization with respect to the external driving fields. This task is practically impossible by analytical means, but for many years a Monte Carlo numerical technique has been successfully applied to all sorts of problems in semiconductor electron transport. In this paper a new approach to Monte Carlo simulation of electron transport in semiconductors, which has recently appeared in the literature, is reviewed. In the traditional Monte Carlo approach a direct simulation of the electron motion is realized, where all possible events (scattering processes) occur with the same probability as in the 'real' world. On the contrary, in the new approach, called the weighted Monte Carlo technique, events occur with arbitrary probabilities, and the weight of the particle in the simulation is accordingly modified in such a way as to maintain an unbiased result. In this way it is possible to emphasize, during the simulation, the analysis of the effect of rare events that in standard simulations would occur too rarely. The traditional Monte Carlo approach is recovered as a special case of this new more general technique. Applications of the weighted Monte Carlo technique to the evaluation of high-energy tails of the distribution function and of the electron current through a potential barrier are presented. A generalization of the method to quantum electron transport is also reviewed.