Spontaneous and Stimulated Recombination Radiation in Semiconductors

Spectral line shapes of the radiation produced by band-to-band recombination of excess carriers in semi-conductors are calculated under the assumption that the momentum matrix element is the same for all initial and final states, i. e. , that there is no momentum selection rule. The peak of the stimulated radiation falls at a lower photon energy than does the peak of the spontaneous radiation, except when T=0^. Some numerical results are given for simple parabolic bands, specifically for the case of electron injection into p-type GaAs, and are used to deduce the temperature dependence of the forward current which is necessary to maintain a fixed gain in the active region of a diode. The result is closely related to the temperature dependence of the threshold current in an injection laser, and gives reasonable agreement with experiment. The effect of a conduction band tail is briefly considered.