Stability of self-consistent Monte Carlo Simulations: effects of the grid size and of the coupling scheme

In this paper, the authors show that the grid spacing affects the stability of self-consistent Monte Carlo device simulations. An analytical model is derived to describe this effect. Guidelines for the choice of the grid size are provided, showing that, when the linear Poisson scheme is used, source/drain extensions with doping level as high as 10²⁰ cm^-3 require grid spacing lower than 1 nm in order to have stable simulations. On the other hand, the nonlinear coupling scheme does not impose any constraint, provided that the time between two solutions of the Poisson equation is so long that each solution can be considered as a stationary solution of the Boltzmann transport equation.