Bipolar spintronics with generation-recombination of electrons and holes: Macroscopic equations

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 Maxwellian at the leading order. The balance equations for the carrier numbers, total energy density and total momentum for the whole system constitute now a system of four equations for the carrier chemical potentials, the temperature of the system and the drift velocity. In the drift-diffusion approximation, the constitutive laws are derived and the Onsager relations recovered. Moreover, 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 time tau(sf) as a function of the temperature.