The kinetic distribution function in multi-valley semiconductors evolving at the momentum relaxation scale

Abstract

A new approach to the non-equilibrium distribution function for carriers in multi-valley band structures is presented. The approach is derived from the evolution process of the kinetic distribution function in momentum space as a result of scattering and a rapid change in electric field. This physics-based approach offers a unique and efficient model to obtain non-equilibrium and hot-carrier distribution functions without directly solving the integro-differential Boltzmann transport equation. The fast transient distribution functions of electrons in multi-valley GaAs and are studied using the resultant model. A Monte Carlo (MC) simulation is also included to verify the validity of the developed approach. It is shown that the distribution function derived from the developed method can respond, as fast as the average velocity, to a drastic change in field. It can account for effects of velocity overshoot/undershoot and includes the highly non-Maxwellian nature of the kinetic distribution function in extreme non-equilibrium situations.