Hot phonon effects and suppressed Auger recombination on 3 $\mu$m room temperature lasing in HgTe-based multiple quantum well diodes

We propose an electrically pumped laser diode based on multiple HgTe quantum wells with band structure engineered for Auger recombination suppression. A model for accounting for hot phonons is developed for calculating the nonequilibrium temperature of electrons and holes. Using a comprehensive model accounting for carrier drift and diffusion, Auger recombination and hotphonon effects, we predict of lasing at $\lambda \sim 3 $ $\mu$m at room temperature in 2.2 nm HgTe/Cd$_{0.85}$Hg$_{0.15}$Te quantum well heterostructure. The output power in the pulse can reach up to 600 mW for 100 nanosecond-duration pulses.