Time-step stability for self-consistent Monte Carlo device simulation

Abstract

An important numerical constraint on self consistent Monte Carlo device simulation is the stability limit on the time step imposed by plasma oscillations. The widely quoted stability limit for the time step between Poisson field solutions, {Delta}t<2/{omega}{sub p} where {omega}{sub p} is the plasma frequency, is specific to the leapfrog particle advance used in collisionless plasma simulation and does not apply to typical particle advance schemes used for device simulation. The authors present a stability criterion applicable to several algorithms in use for solid state modeling; this criterion is verified with numerical simulation. This work clarifies the time step limitation due to plasma oscillations and provides a useful guide for the efficient choice of time step size in Monte Carlo simulation. Because frequent solution of the Poisson equation can be a sizable computational burden, methods for allowing larger time step are desirable. The use of advanced time levels to allow stability with {omega}{sub p}{Delta}t{much_gt}1 is well known in the simulation of collisionless plasmas; they have adapted these implicit methods to semiconductor modeling and demonstrated stable simulation or time steps larger than the explicit limit.