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The Boltzmann equation in presence of boundary and initial conditions, which describes the general case of carrier transport in microelectronic devices is analysed in terms of Monte Carlo theory. The classical Ensemble Monte Carlo algorithm which has been devised by merely phenomenological considerations of the initial and boundary carrier contributions is now derived in a formal way. The approach allows to suggest a set of event-biasing algorithms for statistical enhancement as an alternative of the population control technique, which is virtually the only algorithm currently used in particle simulators. The scheme of the self-consistent coupling of Boltzmann and Poisson equation is considered for the case of weighted particles. It is shown that particles survive the successive iteration steps.

Mixed initial-boundary value problem in particle modeling of microelectronic devices