Random Population of Quantum Dots in InAs–GaAs Laser Structures

We have measured the spontaneous emission rates, absorption, and gain spectra of quantum dots between 20 K and 350 K using the segmented contact method, exploiting self assembled dots with a bimodal size distribution. At 20 K, we find a linear relationship between the radiative rates of the ground states of small and large sets of dots, and using absorption data we show the slope corresponds to random population of states at different energy with equal probability. The emission spectra indicate relaxation of carriers from excited to ground states in the same set of dots at 20 K. We have developed a rate equation model to describe the transition from thermal to random population, including relaxation between excited and ground states in the same dot. This produces a Fermi-Dirac occupation distribution of electrons in all states at 350 K with a global quasi Fermi level. At 20 K all ground states have the same occupation probability, irrespective of their energy. Using values for spontaneous lifetime and gain cross section from absorption data, these rate equations give a very good description of the experimental results for radiative threshold current density as a function of temperature, reproducing the minimum at 200 K, and thereby modeling the transition from the thermal regime at high temperature, to the random regime at low temperature.