Localized Auger Recombination in Quantum-Dot Lasers

We have calculated radiative and Auger recombination rates due to localized recombination in individual dots, for an ensemble of 10⁶ dots with carriers occupying the inhomogeneous distribution of energy states according to global Fermi-Dirac statistics. The recombination rates cannot be represented by simple power laws, though the Auger rate has a stronger dependence on the ensemble electron population than radiative recombination. Using single-dot recombination probabilities which are independent of temperature, the ensemble recombination rates and modal gain decrease with increasing temperature at fixed population. The net effect is that the threshold current density increases with increasing temperature due to the increase in threshold carrier density. The most significant consequence of these effects is that the temperature dependence of the Auger recombination rate at threshold is much weaker than in quantum wells, being characterized by a T₀ value of about 325 K. Observations of a strong temperature dependence of threshold in quantum dot lasers may have explanations other than Auger recombination, such as recombination from higher lying states, or carrier leakage.