SCALED ENSEMBLE MONTE CARLO STUDIES OF IMPACT IONIZATION

We introduce a scaled ensemble Monte Carlo (SEMQ technique to simulate high field electron transport. This technique is designed to improve the accuracy of the phase-space statistics of the non-equilibrium carrier distribution. As recognized in weighted-ensemble Monte Carlo, increasing the number of simulated particles is inefficient, since it substantially increases the computation times without ensuring adequate representation of the sparsely populated regions of phase space. A scaled scheme is especially important for these transient simulations, since one cannot average the electronic trajectories over sufficiently long times. The SEMC technique we propose overcomes this problem by redistributing the computational effort to weight the low-density regions of k-space more heavily. This is done through a formulation which uses an energy-dependent factor to scale the distribution functions and the scattered rates. The technique has the advantage of flexibility and simplicity in coding, is very similar to the traditional non-weighted approach, and doesn't involve particle-splitting. In the present work, the SEMC procedure is applied to simulate impact ionization for high-field transport, using a soft threshold. Since the impact ionization coefficient is strongly affected by the high-energy tail of the distribution function, we apply SEMC to evaluate this. In general, results depend sensitively on band structure and on coupling to other energy dissipation modes. I