  HgCdTe-based quantum cascade lasers operating in the GaAs phonon Reststrahlen
band with a target wavelength of 36 mkm are theoretically investigated using
the balance equations method. The optimized active region designs, which are
based on three and two quantum wells, exhibit a peak gain exceeding 100 cm(-1)
at 150 K. We analyze the temperature dependences of the peak gain and predict
the maximum operation temperatures of 170 K and 225 K for three- and two-well
designs, respectively. At high temperatures (T > 120 K), the better temperature
performance of the two-well design is associated with a larger spatial overlap
of the weakly localized lasing wavefunctions as well as a higher population
inversion.
