Unified quadruple-coupled model for terahertz quantum cascade lasers

Progress toward room-temperature operation of terahertz quantum cascade lasers is limited by the lack of active regions that sustain efficient transport at elevated temperature. Designing such active regions requires predictive models that quantitatively connect microscopic transport and nonequilibrium energy evolution to device-level temperature characteristics. We propose a unified quadruple-coupled model that incorporates energy evolution via a time-dependent electron-temperature equation and self-consistently couples electron, phonon, and photon populations on a common timescale. The model captures the overheating-relaxation dynamics of the average electron temperature, stabilizing within a few picoseconds but delayed relative to the carrier population. The framework extends to above-threshold transport with radiative processes explicitly included and simulations show that their effect on electron temperature is smaller than that of electron-phonon coupling, thereby providing quantitative evidence that thermal relaxation is dominated by electron-phonon interactions. Across ten representative active regions, the predicted maximum operating temperatures show significant linear correlation with experiment ($r=0.909$), demonstrating the model's predictive capability for active-region temperature performance. These results identify electron energy dynamics as the key controlling factor at elevated temperature and provide a physics-based tool for designing high-temperature active regions toward near-room-temperature operation, with applicability to broader nonequilibrium semiconductor laser systems.