Theory of the spectral line shape and gain in quantum wells with intersubband transitions

We investigate the spectral line shape of radiative intersubband transitions in a quantum well as determined by two factors: the electron scattering rate from states of given energy and the mass difference between the two subbands involved. The interplay between these factors leads to an essentially non-Lorentzian form of the spectral line. We develop an analytic theory of the line shape and calculate the dependence of the intersubband optical gain in a quantum well on both the population inversion and the temperature. Under typical conditions, the effect of electron temperature on the gain is similar to that of the lattice temperature, which points to the importance of hot carrier effects in understanding the behavior of intersubband lasers.