A BGK type approximation for the collision operator of the transport equation for semiconductors

In the attempt of obtaining macroscopic models which describe the flow of electrons through a semiconductor crystal, many authors start from the Boltzmann transport equation, often using a generalized BGK type approximation for the collision operator. In this work, by means of this approximation, we shall show that it is possible to obtain a new drift-diffusion equation valid in the high electric field regime.