Spintronics of a bipolar semiconductor with Fermi–Dirac statistics

A new model, based on an asymptotic procedure for solving the spinor kinetic equations of carriers and phonons is proposed, which gives naturally the displaced Fermi–Dirac distribution function at the leading order. The balance equations for the carrier number, energy densities, and momentum, constitute now a system of eight equations for the carrier chemical potentials, the temperatures and the drift velocities. Moreover two equations for the evolution of the spin densities are added, which account for a general dispersion relation. The treatment of spin-flip processes, derived from first principles, is new and leads to an explicit expression of the relaxation times as functions of the temperatures. The novelty here is twofold. The presence of holes is accounted for. Moreover carriers are correctly described by means of the Fermi–Dirac statistics.