Coherent transport in semiconductor heterostructures: A phenomenological approach

We propose a theoretical method for describing coherent quantum transport in semiconductor heterostructures and particularly in quantum cascade lasers (QCLs). The method is an extension of standard rate-equation models to include coherence. Instead of building the model from microscopic considerations, we construct it from the following requirements: invariance under basis change, non-negativity of the density matrix, and compatibility with existing rate-equation models. The computational effort associated with the proposed method is very modest. It is shown that the role of coherence in QCLs is crucial and omitting it from the calculation leads to unphysical results. The discussion in the paper is focused on QCLs but the approach applies in general to semiconductor heterostructures.