Hydrodynamic Model for Charge Carriers

Abstract

A set of hydrodynamic equations modeling strong ionization in semiconductors is formally derived from a kinetic framework. To that purpose, a system of Boltzmann transport equations governing the distribution functions of conduction electrons and holes is considered. Apart from impact ionization, the model accounts for phonon, lattice defects, and particle-particle scattering. Also degeneracy effects are included. The band diagram models are approximations close to the extrema of actual band diagrams. Ionization initiated by a charge carrier (and its reverse recombination) is the leading order collisional process. The resulting set of hydrodynamic equations for strong ionization differs from the usual hydrodynamic system for semiconductors, which corresponds to weak ionization. Indeed, it governs the total charge, the crystal momentum, and the energy, but the total mass is not a conservation variable. This system is supplemented by an entropy inequality and proved to be hyperbolic. The particular case of a parabolic band diagram is discussed.