Modeling of the non-equilibrium effects by high electric fields in small semiconductor devices

For the purpose of the future theory of energy and momentum relaxation in semiconductor devices, the introduction of two temperatures and two mean velocities for electron and phonons is required. A new model, based on an asymptotic procedure for solving the generalized kinetic equations of electrons and phonons is proposed, which gives naturally the displaced Maxwellian at the leading order. After that, balance equations for the electron number, energy densities, and momentum densities are constructed, which now constitute a system of five equations for the chemical potential of electrons, the temperatures and the drift velocities. In the drift-diffusion approximation the constitutive laws are derived and the Onsager relations recovered.