A self-consistent event biasing scheme for statistical enhancement

Statistical enhancement aims at reduction of the time necessary for computation of the desired device characteristics. Enhancement algorithms are especially useful when the device behavior is governed by rare events in the transport process. Such events are inherent for sub-threshold regime of device operation, simulations of effects due to discrete dopant distribution as well as tunneling phenomena. Virtually all Monte Carlo device simulators with statistical enhancement use population control techniques (Wordelman et al., 1998). They are based on the heuristic idea for splitting of the particles entering given phase space region D of interest. The alternative idea - to enrich the statistic in D by biasing the probabilities associated with the transport of classical carriers - gives rise to the event-biasing approach. Due to the event biasing the behavior of the simulated numerical particles differs from that of Boltzmann carriers. Nevertheless the Boltzmann distribution function f is recovered by using the proper weights associated to the particles. The approach, first proposed for evolution of an initial condition (Rota et al., 1989), has been recently extended for stationary transport determined by boundary conditions (Kosina et al., 2003). Biased could be the events for particle evolution and/or the initial or boundary distributions. The approach is derived from the integral form of the linear Boltzmann equation (BE), where Coulomb interactions are neglected.