The Monte Carlo method for semi-classical charge transport in semiconductor devices Original Research Article

A brief review of the semi-classical Monte Carlo method for semiconductor device simulation is given, covering the standard Monte Carlo algorithms, variance reduction techniques, the self-consistent solution, and the physical semiconductor model including band structure and scattering mechanisms. The link between physically-based Monte Carlo methods and the numerical method of Monte Carlo integration is considered. The integral representations and the conjugate equations are presented for the transient and the steady-state Boltzmann equation. From these equations the standard algorithms as well as a variety of new algorithms can be derived in a formal way.