Electron leakage and its suppression via deep-well structures in 4.5- to 5.0-μm-emitting quantum cascade lasers

The equations for threshold-current density J_th and external differential quantum efficiency _d of quantum cascade lasers (QCLs) are modified to include electron leakage and the electron-backfilling term corrected to take into account hot electrons in the injector. We show that by introducing both deep quantum wells and tall barriers in the active regions of 4.8-μm-emitting QCLs, and by tapering the conduction-band edge of both injector and extractor regions, one can significantly reduce electron leakage. The characteristic temperatures for J_th and _d, denoted by T₀ and T₁, respectively, are found to reach values as high as 278 and 285 K over the 20 to 90C temperature range, which means that J _th and _d display ≈ 2.3 slower variation than conventional 4.5- to 5.0-μm-emitting, high-performance QCLs over the same temperature range. A model for the thermal excitation of hot injected electrons from the upper laser level to the upper active-region energy states, wherefrom some relax to the lower active-region states and some are scattered to the upper miniband, is used to estimate the leakage current. Estimated T₀ values are in good agreement with experiment for both conventional QCLs and deep-well QCLs. The T₁ values are justified by increases in both electron leakage and waveguide loss with temperature.