A new derivation of the drift-diffusion equations for electrons and phonons

A new model, based on an asymptotic procedure for solving the generalized kinetic equations of electrons and phonons, is proposed. The linearized equations turn out to be solvable and lead naturally to the displaced Maxwellian approximation. The constitutive laws for the electric and thermal currents are derived and the Onsager relations are verified. The balance equations for the electron number and the total energy density for the whole system constitute now, together with the Poisson equation, a system of three equations for the electron chemical potential, the temperature of the system, and the electric potential.