The dependence of the stimulated emission of radiation in semiconductors on temperature and on impurity concentration has been calculated using a Kane model with a Gaussian band tail for the density of states, and an optical model with a constant matrix element and no selection rule for the radiative transitions. The screening length and the characteristic energies for the widths of the conduction- and valence-band tails are calculated by a self-consistent procedure, and the calculation has no adjustable parameters. Numerical results are obtained using parameters appropriate for GaAs injection lasers. The presence of band tails leads to a more nearly linear dependence of gain on excitation level, in better agreement with experiment, than did the calculation without band tails by Lasher and Stern. Increasing impurity concentration leads to a weaker temperature dependence of the excitation rate required to reach a given gain.

• Received 21 March 1966

DOI:https://doi.org/10.1103/PhysRev.148.186