Extended density matrix model applied to tall barrier quantum cascade lasers

Quantum cascade lasers (QCLs) are promising sources of terahertz (THz) radiation that have applications such as security and medical screening. While optical output power has recently exceeded 1 W, their highest operating temperature is currently limited to ~200 K due to mechanisms such as thermal back filling and non-radiative phonon emission between lasing states. Another possible cause of performance degradation is parasitic leakage currents over barriers into continuum states as subband electron temperatures increase with lattice temperature. Novel designs with new injection schemes remain an intensive research area and new efforts are being made assuming that barrier heights no longer need to be constant. A possible advantage of this is using tall barriers to reduce the leakage current, and in this work we present a theoretical study of recent experimental evidence supporting this. Interface roughness (IFR) scattering scales with the conduction band discontinuity squared and the calculations also assume a typical correlation length Λ and root mean roughness value Δ which are related to growth quality of the individual sample. We take typical values of Λ=60 Å and Δ=3 Å for these parameters. The QCL gain and current output characteristics are calculated using an extended density matrix solver which models transport through the injection barrier coherently. We obtain similar current and gain values at resonance for both structures, indicating that the experimentally observed reduction in current density could be accredited to the reduction of parasitic current leakage. Additionally, this work attempted a similar design with all AlAs barriers which did not lase and it was conjectured that this was due to excessive IFR scattering as well as increased susceptibility to monolayer fluctuations with thinner layers. Our model, which accounts for the lifetime broadening in the gain calculation, confirms that modifying the IFR parameters to Λ=100 Å and Δ=1 Å (i.e. unrealistically sharp interfaces) leads to a significant improvement in performance as shown in Figure 1. We extend this work by proposing designs which aim to balance leakage current reduction and excessive scattering to achieve higher operating temperatures.