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

Abstract

The equations for threshold-current density Jth 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 Jth and d, denoted by T0 and T1, respectively, are found to reach values as high as 278 and 285 K over the 20 to 90°C temperature range, which means that Jth 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