DIFFUSION-APPROXIMATION OF NONLINEAR ELECTRON-PHONON COLLISION MECHANISMS

We study the behaviour of the solutions of the Boltzmann equation of s olid state physics when the mean free path tends to zero. The nonlinea r Boltzmann operator considered in this paper models collisions betwee n electrons and phonons with constant energy. Taking into account dege neracy effects we show that distribution functions relax to local equi librium functions similar to Fermi Dime distributions depending on ene rgy dependent chemical potentials, which are periodic with period equa l to the phonon energy. In the fluid limit these chemical potentials s olve an energy dependent drift diffusion equation.