Compact model for the efficient simulation of the optical gain and transport properties in THz quantum-cascade lasers

We present a compact model for the efficient simulation of the gain characteristics in THz quantum-cascade lasers (QCLs) based on the self-consistent solution of the Schrödinger and Poisson equations in the framework of a one-dimensional scattering-rate approach. The total intersubband scattering rates are factorized into the squared modulus of the respective dipole matrix elements and an energy-dependent factor, which we use as an approximation for the various scattering processes. Intended for designing THz QCLs, this model allows the efficient calculation of the gain characteristics and current densities due to a significantly reduced numerical effort compared to a full quantum transport theory. In view of the large parameter space, which causes even small variations of the parameters to have a complex influence on the lasing properties, the accuracy of the predicted results appears to be sufficient. We explore the benefits and limits of this approach by applying it to various THz QCLs based on either the bound-to-continuum design or the resonant-longitudinal-optical-phonon design. A remarkable agreement between the numerical and experimental results, in particular for the energy position of the gain maximum and lasing energy, is found. Finally, we use our model to design a THz QCL operating at a voltage close to the lower theoretical limit in order to reduce excess heating.