Analysis of variance-reduction schemes for ensemble monte carlo simulation of semiconductor devices

A detailed discussion of variance-reduction techniques for Monte Carlo device simulation is presented. The use of variable statistical particle weights is examined from the point of view of numerical accuracy and physical consistency. An improved splitting/gathering technique is presented, which operates on the entire ensemble of particles rather than on particles located in one region of phase space. Application of the method to self-consistent ensemble simulation is also discussed, showing that the use of variable-weight techniques is limited to cases where the effect of short-range Coulomb interaction is negligible. Examples are given for simple space-homogeneous and one-dimensional cases, and for a submicron n-MOSFET device.