Quantum versus classical scattering in semiconductor charge transport: a quantitative comparison

Abstract

A first-principle analysis is presented of the effect on transport phenomena of the relaxation of the semiclassical assumptions of energy conservation and point-like nature in space/time of the scattering processes. Quantitative estimates for the quantum case have been obtained within the Wigner-function approach with the use of the concept of Wigner paths. This formulation of the transport problem, although rigorous from the point of view of quantum mechanics, is very close to the classical language, so that comparisons are very straightforward. Results of the analysis of phonon scattering show that multiple collisions reduce collisional broadening and contribute to understanding the success of the semiclassical approximation. An analogous formulation in terms of the density matrix confirms the obtained results.