In this paper, the stability of self-consistent Monte Carlo (MC) device simulations is revised by developing a model that extends the existing ones by accounting for the effect of a carrier diffusion. Both the linear and the nonlinear Poisson schemes have been considered. The analysis of the linear Poisson scheme reveals that, consistently with the availablemodel, the time step between two Poisson solutions must be short compared to a
factor proportional to the scattering rate. On the other hand, it has been found that, contrary to the available stability models, the nonlinear Poisson scheme requires long time steps in order to provide stable simulations. For this reason, the nonlinear scheme is advantageous when considering steady-state simulations. The model predictions have been verified by comparison with MC simulations implementing both schemes.