Scaled ensemble Monte Carlo

We introduce a scaled ensemble Monte Carlo technique for the simulation of semiconductor plasmas at ultrashort times after excitation. The error, from counting statistics, can be decreased directly either by a computationally expensive increase in the number of simulation trajectories or by averaging over long times. The latter approach cannot be applied in studying ultrafast, far-from-equilibrium phenomena. The remaining alternative is to redistribute the computational effort to weight more heavily those regions with low densities. Scaled EMC uses ordinary EMC weighting, but simulates a different function, related by an energy- dependent scaling factor to the usual particle distribution. The simulation trajectories obey the same free-flight equations of motion as ordinary EMC, with no `splitting' of particles or iteration of trajectories. We describe simulations of modulation-doped GaAs structures under applied fields. G-, L- and X-valley carrier populations are determined across more than seven orders of magnitude in density, using only ten thousand simulation points, with fractionally small sampling error across a one-volt energy range. Using standard EMC with the same number of points, sampling statistics necessarily limits the range of simulable densities to less than four decades overall.