Ensemble Monte Carlo simulation of electron-electron scattering: Improvements of conventional methods

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Abstract
Ensemble Monte Carlo (EMC) simulation is performed to study the electron-electron (e-e) scattering of a two-dimensional electron gas. Two commonly utilized EMC methods, the first proposed by Lugli and Ferry [Physica B 117, 251 (1983)], the second by Brunetti and co-workers [Physica B 134, 369 (1985)], are used and discussed in detail. Both methods are found to lead to erroneous simulation results because they introduce either extra e-e collisions or artificial energy dissipation into the simulation procedure. To improve these methods, some simple corrections are proposed. With these corrections, both methods provide significantly different results, especially for the thermalization rate of the transient distribution function. An EMC approach, based on the concept of the N-particle e-e scattering rate, is developed. This approach gives the same results as conventional EMC methods with our corrections and provides insight into the simulation of e-e scattering. Unlike recent publications we conclude that e-e scattering can be taken into account exactly by EMC methods.