Effect of inclusion of self-consistently determined electron temperature on the electron–plasmon interaction

Abstract

In this article, we present a comparison of three different formulations of the carrier–plasmon interaction in semiconductors that can be included within an ensemble Monte Carlo simulation. Two of the formulations, referred to here as the electron–field and electron–electron methods, can be considered as first-order quantum mechanical approaches in which the electron–plasmon interaction is treated as an additional scattering mechanism. The electron–field model formulation is corrected from previously published work following the approach of Popov, Solodkaya, and Bagaeva [Physica B 217, 118 (1996)]. The corrected electron–field model is compared to an improved, self-consistent electron–electron model and to the semiclassical method, by which the Poisson equation is solved self-consistently, for both steady-state bulk and transient transport. It is found that the corrected electron–field model, which is also formulated as self-consistent, and the new improved self-consistent electron–electron model predict nearly identical results in both steady and transient states. It is further found that the self-consistent quantum mechanical models compared to the semiclassical model do not yield precisely the same result, in agreement with previously published results. The addition of self-consistency to these models results in nearly equal plasmon occupation factors for both absorption and emission, leading to nearly equal absorption and emission rates at high carrier temperatures. Some caution must be exercised, however, in these results since a full temperature-dependent dielectric function has not been employed and it is possible that the quantum mechanical models may need some revision at high carrier temperatures. Nevertheless, the self-consistent quantum mechanical models predict the net average energy relaxation to be small, due to nearly equal absorption and emission rates, consistent with the semiclassical model.