  In this paper we develop a class of Implicit-Explicit Runge-Kutta schemes for
solving the multi-scale semiconductor Boltzmann equation. The relevant scale
which characterizes this kind of problems is the diffusive scaling. This means
that, in the limit of zero mean free path, the system is governed by a
drift-diffusion equation. Our aim is to develop a method which accurately works
for the different regimes encountered in general semiconductor simulations: the
kinetic, the intermediate and the diffusive one. Moreover, we want to overcome
the restrictive time step conditions of standard time integration techniques
when applied to the solution of this kind of phenomena without any
deterioration in the accuracy. As a result, we obtain high order time and space
discretization schemes which do not suffer from the usual parabolic stiffness
in the diffusive limit. We show different numerical results which permit to
appreciate the performances of the proposed schemes.
