ABSTRACT
This chapter focuses on Monte Carlo methods for the solution of the Boltzmann transport equation. The ensemble Monte Carlo techniques have been used for well over 40 years as a numerical method to simulate nonequilibrium transport in semiconductor materials and devices and have been the subject of numerous books and reviews. The Monte Carlo algorithm consists of generating random free-flight times for each particle, choosing the type of scattering occurring at the end of the free flight, changing the final energy and momentum of the particle after scattering, and then repeating the procedure for the next free flight. In the bulk Monte Carlo method, particle motion is assumed to consist of free flights terminated by instantaneous scattering events, which change the momentum and energy of the particle after scattering. As in the case of solving the drift-diffusion, hydrodynamic, for a stable Monte Carlo device simulation, one has to choose the appropriate time step, and the spatial mesh size.
