Analysis of the stochastic error of stationary Monte Carlo device simulations

Without proper analysis of the stochastic error, it is not possible to assess the accuracy or efficiency of Monte Carlo device simulations, and misleading results might be obtained. This is demonstrated for the so-called variance-minimizing estimator for the steady-state terminal currents which turns out to be not more efficient than a standard estimator. Self-consistent (with respect to the electric field) and non self-consistent device simulations are analyzed. In contrast to previously published results both methods have the same efficiency with respect to terminal currents, but in the case of internal distributions, like the particle density, self-consistent simulations are much more efficient. In addition, it is shown that non self-consistency increases the relaxation times of fluctuations by orders of magnitude necessitating extremely long simulation times. The efficiency of statistical enhancement is found to be degraded by strong interparticle correlation due to particle splitting.