Variance of the ensemble Monte Carlo algorithm for semiconductor transport modeling

The ensemble Monte Carlo algorithm (EMC) is the most frequently used tool for simulation of the transient transport in semiconductors and structures. The common definition of the algorithm is of a procedure based on imitation of the real transport phenomena. Often EMC is accepted as a simulated experiment rather than as a numerical method. Recently it has been shown that the EMC can be obtained by an application of the numerical Monte Carlo (MC) theory to the integral form of the Boltzmann equation (BE) [1–3]. The approach has been further used to prove under a general condition the convergence of the algorithm [4]. In this work we utilize the approach to investigate the variance of the EMC. It is proved that the algorithm has a finite variance and an analytical result is derived. This allows to assign the precision estimates of the numerical MC method to the EMC.