An event bias technique for Monte Carlo device simulation

Abstract

In Monte Carlo (MC) simulations of semiconductor devices it is necessary to enhance the statistics in sparsely populated regions of interest. In this work the Monte Carlo method for stationary carrier transport, known as the Single-Particle MC method, is considered. It gives a solution to the stationary boundary value problem defined by the semi-classical Boltzmann equation (BE). Using a formal approach which employs the integral form of the problem and the Neumann series expansion of the solution, the Single-Particle MC method is derived in a formal way. The independent, identically distributed random variables of the simulated process are identified. Estimates of the stochastic error are given. Furthermore, the extension of the MC estimators to the case of biased events is derived. An event bias technique for particle transport across an energy barrier is developed and simulation results are discussed.