Energy conservation in collision broadening over a sequence of scattering events in semiclassical Monte Carlo simulation

In this paper, we discuss energy conservation when collisional broadening is considered, and a Lorentzian lineshape assumed, in a Monte Carlo simulation of electron transport. We show that collisional broadening with a Lorentzian distribution does not lead to energy conservation on the average over many electron-phonon collision events. We compute the expected value of departure from energy conservation for a realistic silicon bandstructure, and compare it to results from full-band Monte Carlo simulation to show good agreement. Finally, we propose a corrected distribution approach, where the Lorentzian distribution is divided by the density-of-states curve to obtain a distribution which is able to conserve energy in the average over many electron-phonon collisions.