Correlation between subband population and threshold current densities in GaAs/(Al,Ga)As quantum-cascade structures/lasers with different barrier heights

The laser parameters such as threshold current density and characteristic temperature of GaAs/AlxGa1-xGaAs/AlxGa1-xAs quantum-cascade lasers (QCLs) with x=0.45x=0.45 are superior compared to QCLs with x=0.33x=0.33. This improvement is usually attributed to smaller leakage currents due to the higher conduction band offset for x=0.45x=0.45, since the QCLs for the two barrier compositions are designed in such a way that the population ratios ρpρp for the laser levels are the same. The experimental investigation of undoped GaAs/AlxGa1-xGaAs/AlxGa1-xAs quantum-cascade structures reveals a significantly smaller value of ρpρp for x=0.33x=0.33 than the calculated one, while for x=0.45x=0.45 it agrees with it. In the framework of a linear rate equation model, we estimate the effect of the experimentally observed reduction of ρpρp on the threshold current density. We conclude that the increased threshold current density for x=0.33x=0.33 has to be attributed to both, a larger leakage current and a reduced population ratio.