Hydrodynamic model for charge carriers involving strong ionization in semiconductors

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. The charge carriers obey a degenerate gas statistics and their kinetic energy relations are arbitrary. The umklapp collisions are supposed to be negligible. 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 diiers 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. Within this frame, the set of conservation equations modeling strong ionization is also proved to be strictly hyperbolic.