Electrons and Phonons

International audienceThe aim of this Chapter is not to produce a complete course on electrons and phonons, but rather to give a concise outline of a certain number of their basic properties in order to be able to describe transport phenomena in crystalline solids. Indeed, transport phenomena will provide the guiding motivation.Transport phenomena in dilute media were discussed with the help of the Boltzmann equation in the Chapter on Transport in Dilute Media by Carminati in this volume, in the context of the kinetic approach. The idea is to establish an expression for the particle flux through a given area. We then deduce the flux of any quantity transported by each particle. The Boltzmann equation is used to determine the velocity distribution of the particles. It can be solved fairly straightforwardly if the system is close to equilibrium. We thus introduce the idea of local thermodynamic equilibrium (LTE). As we have seen, this notion can only be defined for length and time scales greater than the mean free path and the average time between consecutive collisions, respectively