Runaway Phenomena and Fluid Approximation Under High Fields in Semiconductor Kinetic Theory

The problem of existence of homogeneous stationary solutions of the semiconductor Boltzmann equation is studied. We give a classification of the results according to the behaviour of the collision frequency for high velocities. We underline the case where a critical value of the electric field appears. When the collision frequency is bounded from below, these results allow to derive a fluid approximation of the kinetic equation. It is obtained as a limit of a perturbation which is convenient for high electric fields.