Convergence estimation for stationary ensemble Monte Carlo simulations

A criterion for the convergence of the stochastic Monte Carlo simulations is necessary to ensure the reliability of their results and to guarantee efficiency. Due to the finite scattering rate in Monte Carlo simulations all quantities are in general correlated in time. This makes the estimation of the stochastic error of the sampled statistics difficult. In this work the theoretical basis of a method found in literature is explored which allows to calculate the stochastic error of stationary Ensemble Monte Carlo simulations and which requires only a rough estimate of the magnitude of the largest correlation time of the sampled quantities. The feasibility of the method is demonstrated by application to substrate current calculations for nMOSFETs.