Theory of the Monte Carlo method for semiconductor device simulation

A brief review of the semiclassical Monte Carlo (MC) method for semiconduct or device simulation is given, covering the standard MC algorithms, varianc e reduction techniques, the self-consistent solution. and the physical semi conductor model . A link between physically based MC methods and the numeri cal method of MC integration is established. The integral representations t he transient and the steady-state Boltzmann equations are presented as well as the corresponding conjugate equations. The structure of the iteration t erms of the Neumann series and their evaluation by MC integration is discus sed. Using this formal mathematical approach, the standard algorithms and v ariety of new algorithms are derived. The basic ideas of the weighted ensem ble MC and the MC backward algorithms are explained.