  We investigate a recombination-drift-diffusion model coupled to Poisson's
equation modelling the transport of charge within certain types of
semiconductors. In more detail, we study a two-level system for electrons and
holes endowed with an intermediate energy level for electrons occupying trapped
states. As our main result, we establish an explicit functional inequality
between relative entropy and entropy production, which leads to exponential
convergence to equilibrium. We stress that our approach is applied uniformly in
the lifetime of electrons on the trap level assuming that this lifetime is
sufficiently small.
