Kinetic model of thermotransport in semiconductors

In this work we develop a semiclassical kinetic model to construct hydrodynamic equations to study the nonequilibrium behavior of an electron gas in a semiconductor. To describe the system we assume that the Boltzmann transport equation is valid and we solve it in terms of the first 13 moments, which become the basic fields to describe thermotransport in this system. The closure of the transport equations is achieved through an expansion around the nonequilibrium Fermi–Dirac distribution function. The nonconserved variables satisfy relaxation equations and their characteristic times are expressed in kinetic terms. The electric current density and the heat flux can be written as generalized constitutive equations, allowing us to obtain thermotransport coefficients as functions of the frequency, where the relaxation times play a very important role