Collision broadening through sequences of scattering events: theory, consequences and modeling within semiclassical Monte Carlo

摘要

Recent developments in the understanding of the theory and consequences of collision broadening through sequences of scattering events are reviewed and expanded upon, particularly in regard to semiclassical Monte Carlo simulation. Using basic theory backed up by quantum transport simulations, it is demonstrated that the requirement for energy conservation in the coupled carrier-phonon system prohibits the accumulation of the uncertainty in the carrier energy associated with collision broadening through a sequence of scattering events. This accumulation, however, had been possible with the conventional treatment of collision broadening in semiclassical Monte Carlo. Accordingly, an improved, more physically accurate algorithm for connecting sequences of collision broadened scattering events within semiclassical Monte is described. The potential consequences of collision broadening are then reassessed using both the quantum transport simulations and semiclassical Monte Carlo simulations incorporating the new algorithm, including full-band Monte Carlo simulations for the first time. The broadening assisted runaway of the high-energy tail of the carrier distribution possible with the conventional algorithm is shown to be an artifact of that algorithm, not of the form of the collision broadening used (Lorentzian, etc.) as often assumed. Simulation results obtained with the new algorithm also demonstrate that for important cases, Golden-Rule-based Monte Carlo simulations can remain accurate despite the presence of significant collision broadening. A notable class of exceptions, however, is when collision broadening allows for a threshold or scattering bottleneck to be overcome, although the ultimate requirement for energy conservation remains critical. Specifically, it is shown that collision broadening lowers but does not eliminate the impact ionization threshold energy, producing simulated impact ionization coefficients for holes in silicon that accurately track experimental results as a function of field. Similarly, the quantum transport simulations illustrate how collision broadening can significantly affect optical absorption, but that simply subjecting low energy carriers to scattering induced collision broadening does not allow them to overcome large potential barriers.