On the validity of Fermi's golden rule for calculating scattering rates in the Boltzmann collision integral

Kristof Moors, Bart Sorée, Wim Magnus

Published 2016-02-16Version 1

Being a standard tool to calculate the scattering rates that enter the collision term of the Boltzmann transport equation, Fermi's golden rule underpins a semi-classical investigation of mobile carriers propagating through various solids. As such, it provides a perturbative estimate of the scattering rates under the implicit assumption that the effect of the interaction Hamiltonian which causes the scattering events is sufficiently small. In order to check the validity of this assumption, we have developed easy-to-handle criteria to assess whether the predicted transport properties can be trusted for the system under consideration. Depending on the system's statistical properties, such as average size, electron density, impurity density etc., the analysis underlying these criteria is carried out for, but not limited to the multi-subband Boltzmann transport equation describing electron transport in metallic nanowires subjected to several elastic scattering mechanisms.