Kinetic theory of thermotransport of degenerate polar semiconductor electrons

A kinetic theory approach is developed from the semiclassical Boltzmann transport equation for the thermotransport of electrons in polar semiconductors in the degenerate limit. The method of moments drives to a set of hydrodynamical equations which are closed up to thirteen relevant variables, including the stress tensor and the heat flux in the description. The closure of the balance equations is achieved by evaluating the higher order momenta, as well as the production terms, through a nonequilibrium Fermi-Dirac distribution function coming from the maximum entropy principle. Our main results are a set of characteristic relaxation times, which are evaluated under the consideration that electron-optical polar phonon interaction is the leading scattering process. Also, under degenerate conditions analytical expressions are obtained for the relaxation times and the usual thermoelectric coefficients.