Phase space multiple refresh: A general purpose statistical enhancement technique for Monte Carlo device simulation

A new Multiple Refresh technique is presented, which can be applied to the enhancement of statistics in phase space during Monte Carlo device simulation without being restricted to ergodic or stationary systems. The method allows to specify the number of particles simulated in different regions of phase space and therefore to control directly the noise in those regions. It can improve the statistics of rare events like for example hot electron effects by many orders of magnitude without prohibitive CPU times. The problem of noise and correlation inherent to statistical enhancement methods which manipulate particle numbers is minimized. It is shown that the method does not impair the one particle distribution function and that it is more stable in a stochastic sense than other equally general methods, because it conserves particle charge exactly. The method itself consumes only a few percent of the total CPU time spent for a simulation and does not cause any computational overhead in parallel calculations. The method is very flexible and easy to apply, because it acts only on the particle ensemble at certain times and does not interfere with the Monte Carlo simulation itself. The potential of the Multiple Refresh technique is demonstrated for different important device applications.