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We consider a family of drift-diffusion-recombination systems, where therecombination of electrons and holes is facilitated by an intermediateenergy-level for electrons in so-called trapped states. In particular, it hasbeen proven in [GMS07] that the associated quasi-stationary state limit of aninstantaneously fast trapped dynamics yields the famous Shockley--Read-Hallmodel for electron and hole recombination in semiconductor devices.  The main result of this paper proves exponential convergence to equilibriumuniformly in the fast reaction limit for the drift-diffusion-recombinationsystems and the limiting Shockley-Read-Hall model. The proof applies theso-called entropy method and the key results is to establish an entropy-entropyproduction inequality uniformly in the fast reaction limit.  Moreover, we prove existence of global solutions and show a-priori estimates,which are necessary to rigorously verify that solutions satisfy theentropy-entropy production law.

Uniform convergence to equilibrium for a family of drift-diffusion  models with trap-assisted recombination and the limiting Shockley--Read--Hall  model