Self-consistent Monte Carlo particle modelling of small semiconductor elements

A self-consistent Monte Carlo particle model aimed at a profound physical understanding of small semiconductor components of arbitrary geometries is presented. The simulation technique consists briefly of following the transport histories of individual charge carriers in detail. After a discussion of the stochastic distribution of the time of free flight, the scattering mechanisms and the scattering angles of the particles, a brief review of the relevant semiconductor physics is given. As an example to illustrate the salient points of the technique, the results of simulating a GaAs field-effect transistor will be discussed. The presentation of the transistor characteristics is used to establish a link between theoretical physics and the view of the electrical engineer. A short discussion of statistical phenomena such as noise, negative differential resistivity and substrate currents has also been included.