Properties of Spontaneous and Stimulated Emission in GaAs Junction Lasers. II. Temperature Dependence of Threshold Current and Excitation Dependence of Superradiance Spectra

The spontaneous and stimulated emission spectral functions are calculated using a band model consisting of the self-consistent densities of states calculated in a previous paper and an optical model with an energy-dependent matrix element and no selection rule for the radiative recombinations. The energy dependence of the matrix element is that for a transition from a parobolic conduction band to an acceptor level and should be a suitable one, because of a small conduction band tail and the occupancy of most of the holes in the vicinity of the acceptor ionization energy. General properties, such as the spontaneous emission band shape, the gain-current relationship, and the temperature dependence of current required to maintain a given gain are compared with those calculated without band tails and with band tails given by Kane's model. Considerable differences are found among various models and these are discussed. The calculations on the temperature dependence of the threshold current and the current dependence of the superradiance spectra are then applied to GaAs-diffused diodes with substrate doping of 3 × ${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$, taking into account the temperature dependence of the cavity loss and the non-uniform acceptor distribution in the $p$ layer. Detailed comparison with experimental data is made and good quantitative agreement is obtained in both cases, giving strong support to our conclusions concerning the band-tail structure.