Relaxation of Energy and Momentum in an Carrier-Phonon System

Abstract

If electrons (e) and holes (h) in metals or semiconductors are heated to the temperatures Te and Th greater than the lattice temperature Tp, the electron-phonon interaction causes energy relaxation. In the non-uniform case a momentum relaxation occurs as well. In view of such an application, a new model, based on an asymptotic procedure for solving the generalized kinetic equations of carriers and phonons is proposed, which gives naturally the displaced Maxwellian at the leading order. After that, balance equations for the electron number, hole number, energy densities, and momentum densities are constructed, which constitute now a system of five equations for the electron chemical potential, the temperatures and the drift velocities. In the drift-diffusion approximation the constitutive laws are derived and the Onsager relations recovered.