A complete multifluid model for bipolar semiconductors, with interacting carriers, phonons, and photons

If electrons (e) and holes (h) in metals or semiconductors are heated to the temperatures T e and T h greater than the lattice temperature, the electron–phonon interaction causes energy relaxation. In the non-uniform case a momentum relaxation occurs as well. In view of such an application, a new model, based on an asymptotic procedure for solving the kinetic equations of carriers, phonons, and photons, is proposed, which gives naturally the displaced Maxwellian at the leading order. Several generation–recombination (GR) events occur in bipolar semiconductors. In the presence of photons the most important ones are the radiative GR events, direct, indirect, and exciton-catalyzed. Phonons and photons are treated here as a participating species, with their own equation. All the phonon–photon interactions are accounted for. Moreover, carrier–photon (Compton) interactions are introduced, which make complete the model. After that, balance equations for the electron number, hole number, energy densities, and momentum densities are constructed, which constitute now a system of macroscopic equations for the chemical potentials (carriers), the temperatures (carriers and bosons), and the drift velocities (carriers and bosons). In the drift–diffusion approximation the constitutive laws are derived and the Onsager relations recovered, even in the presence of an external magnetic field.