TIME STABILITY OF MONTE-CARLO DEVICE SIMULATION

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, DELTAt < 2/omega(p) where omega(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. We derive 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.