Efficient silicon device simulation with the local iterative Monte Carlo method

Abstract

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. We introduced an alternative approach based on a local iterative Monte Carlo (LIMO) algorithm. The evolution of the energy distribution function from an initial distribution to steady state is calculated by an iterative application of short MC steps for test particles that represent the local density. Since the charge density represented by the test particle is proportional to the local density the number of particles simulated is the same for low and high density regions, leading to a more efficient use of computational resources and uniform statistical error. Meanwhile, a 2D version of the LIMO technique for the simulation of silicon devices, based on the full band structure, has been implemented and tested. In this contribution we focus on the possibility for a further computation time reduction by tabulating and using more than once the results from the local MC steps in the overall iteration process. Since the MC step simulations need most of the computation time, the use of each drift information in more than one iteration can significantly reduce the computational expenses. However, a lower number of simulated MC steps reduces the statistical representation of the underlying physics and leads to an increase in the statistical fluctuations.