Population inversion and threshold current densities: A comparison of GaAs∕(Al,Ga)As quantum-cascade structures with different barrier heights

The population of the laser levels in undoped GaAs∕AlxGa1−xAs quantum-cascade structures (QCSs) is investigated by interband photoluminescence spectroscopy. We compare similar QCSs with different barrier heights (x=0.33 and x=0.45), for which the calculated population ratios ρpca are equal. While the experimental value ρpme for x=0.45 agrees with the theoretical one, ρpme for x=0.33 is much smaller than ρpca. At the same time, the threshold current densities jth are significantly smaller for x=0.45 than for x=0.33. In the framework of a linear rate equation model, we estimate the effect of the experimentally observed reduction of the population ratio on jth. We show that the increased value of jth for x=0.33 cannot only be attributed to a larger leakage current due to the lower barriers, but also to the reduced population ratio.