Journal of Statistical Physics, Vol. 98, Nos. 3/4, 2000. p. 835-870.
The diffusion limit of the Boltzmann equation of semiconductors is analyzed. The dominant collisions are the elastic collisions on one hand and the electron-electron collisions with the Pauli exclusion terms on the other hand. Under a nondegeneracy hypothesis on the distribution function, a lower bound of the entropy dissipation rate of the leading term of the Boltzmann kernel 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 solution of the energy transport model.