Abstract
As devices shrink to dimensions below 0.1 μm, it becomes essential to treat impurities and carriers as individual charges. We describe some approaches to ionised impurity scattering where the potential of the impurities is included directly in the dynamics of a Monto Carlo type simulation rather than as a scattering rate. The divergence in the Coulomb potential creates difficulties for mesh-based solutions of Poisson's equation, which we have compared with more accurate Ewald summation. However, we find that the mesh does not introduce significant errors, and reproduces well the expected mobility as a function of doping. Highly accurate integration of the equation of motion is needed for free carriers, and the initial distribution is problematic. In contrast, a simple treatment of phonon scattering by Brownian dynamics is more tolerant of errors because it tends to restore the system to equilibrium.