Variance of the ensemble Monte Carlo algorithm for semiconductor transportmodeling

The ensemble Monte Carlo algorithm (EMC) is the most frequently used tool f or 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 expe riment rather than as a numerical method. Recently it has been shown that t he 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 appro ach has been further used to prove under a general condition the convergenc e 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 vari ance and an analytical result is derived. This allows to assign the precisi on estimates of the numerical MC method to the EMC. (C) 2001 IMACS. Publish ed by Elsevier Science B.V. All rights reserved.