Semiconductor transport simulation with the local iterative Monte Carlo technique

In typical particle simulations applied to device problems, it is desirable to simulate regions having widely different carrier concentration with similar resolution of the energy distribution function. Standard Monte Carlo (MC) algorithms use variance reduction techniques to limit the statistical error in regions of low carrier density. Here, we describe an alternative approach, based on a local iterative MC algorithm, where the carrier distribution is calculated by an iterative application of short MC steps for test particles that represent the local density. The information obtained from the local MC procedure is used to compute directly the evolution of the energy distribution function from an initial distribution until a steady state is reached. This local iterative procedure treats the charge density, represented by the MC, with arbitrary weight, independently of the actual number of physical particles corresponding to a given density. In this way, the computation time is the same for low- or high-density regions, leading to a more efficient use of computational resources and uniform statistical error. The computation time can be reduced also by tabulating and using more than once the results from the local MC steps in the overall iteration process. While the local iterative MC approach does not have the generality of the standard MC technique, much faster calculations and greatly reduced statistical noise are possible when applied to steady-state problems. We present a number of simulation examples for silicon devices, which illustrate the capabilities of the approach.