Moment inequalities and high-energy tails for electron distribution   function of the Boltzmann transport equation in semiconductors
  In this paper we prove the existence of the high-energy tails for electron distribution function of the Boltzmann equation for semiconductors, in the stationary and homogeneous regime, in the analytic band approximation and scattering with acoustic and optical phonons and impurities. We also prove numerically that the tail is a global maxwellian in the parabolic band approximation, and in the quasi parabolic band case, a power law of the global maxwellian. 
Orazio Muscato