On the convergence of the Boltzmann equation for semiconductors toward theenergy transport model

The diffusion limit of the Boltzmann equation of semiconductors is analyzed . The dominant collisions are the elastic collisions on one hand and the el ectron-electron collisions with the Pauli exclusion terms on the other hand . Under a nondegeneracy hypothesis on the distribution function. a lower bo und of the entropy dissipation rate of the leading term of the Boltzmann ke rnel for semiconductors in terms of a distance to the space of Fermi-Dirac functions is proved. This estimate and a mean compactness lemma are used to prove the convergence of the solution of the Boltzmann equation to a solut ion of the energy transport model.