  Operation of semiconductor lasers in the 20--50 $\mu$m wavelength range is
hindered by strong non-radiative recombination in the interband laser diodes,
and strong lattice absorption in GaAs-based quantum cascade structures. Here,
we propose an electrically pumped laser diode based on multiple HgTe quantum
wells with band structure engineered for Auger recombination suppression. Using
a comprehensive model accounting for carrier drift and diffusion, electron and
hole capture in quantum wells, Auger recombination, and heating effects, we
show the feasibility of lasing at $\lambda = 26...30$ $\mu$m at temperatures up
to 90 K. The output power in the pulse can reach up to 8 mW for
microsecond-duration pulses.
