Theory of the Monte Carlo method for semiconductor device simulation

A brief review of the semiclassical Monte Carlo (MC) method for semiconductor device simulation is given, covering the standard MC algorithms, variance reduction techniques, the self-consistent solution, and the physical semiconductor model. A link between physically based MC methods and the numerical method of MC integration is established. The integral representations the transient and the steady-state Boltzmann equations are presented as well as the corresponding conjugate equations. The structure of the iteration terms of the Neumann series and their evaluation by MC integration is discussed. Using this formal mathematical approach, the standard algorithms and variety of new algorithms are derived. The basic ideas of the weighted ensemble MC and the MC backward algorithms are explained.