Electronic Interactions

Abstract

Together with the band shape and semiclassical dynamics, electronic interactions in crystals form the basic ingredients for any semiclassical theory of electron transport in semiconductors. In general terms, to write down the Boltzmann transport equation (BE), we need the transition rate, or transition probability per unit time, from a state with crystal momentum k to a state with crystal momentum k’, due to the various possible interaction mechanisms. Most of the times the latter are considered independent from each other, and the corresponding transition rates are calculated by means of the Fermi golden rule, described in Appendix E. This formula contains a δ function of energy conservation. However, this result is correct in the limit of long times between collisions, i.e., in the completed-collision approximation. When this condition is not satisfied, we need a more precise theory that accounts for collisional broadening, as will be discussed later in this book.