Efficient Stochastic Algorithms for Semiconductor Device Modeling

The Boltzmann equation is well suited to describe carrier transport in highly down-scaled semiconductor devices. The Monte Carlo algorithms, which are used to date to solve the Boltzmann equation, are imitating the real transport process by calculating physical carrier trajectories. With these algorithms severe problems are encountered when scarcely populated regions of the phase space are to be considered. This is more or less always the case in device applications where transport is controlled by energy barriers. From the Boltzmann equation represented as a path integral equation, generalized Monte Carlo algorithms can be derived, as has been demonstrated by the weighted ensemble and the backward Monte Carlo algorithms. While these two algorithms solve the transient Boltzmann equation, this project aims at the development of new algorithms for the steady state. The purpose of the new algorithms is variance reduction in scarcely populated device regions of interest, and to avoid simulation of too many carrier trajectories in equilibrium regions, where the distribution function is known. Thus, the computation time of the expensive Monte Carlo method can be reduced, and the operating conditions can be extended, for example, to MOSFET in the subthreshold region or to reverse biased p-n junctions. The new algorithms will be implemented in the device simulator MINIMOS.