Temperature dependence of the radiative lifetime in GaN

Using time-resolved photoluminescence spectroscopy, we determine the temperature dependence of the radiative lifetime for GaN layers with doping levels from 10¹⁶ to 10¹⁸cm^-3. The experimental results are analyzed by a coupled rate-equation model taking into account band-to-band, free and bound excitons, as well as donor-to-band recombination. An analytic expression for the radiative lifetime of this coupled system is derived and fit to the data. Over the entire temperature range, radiative recombination is strongly affected by the decay of either bound or free excitons. The temperature dependence and the absolute values for the radiative lifetime are governed by the coupling between the individual populations. This coupling in turn is determined by the binding energies of the respective species. Using a binding energy of 26.4 meV for the free exciton, we obtain best-fit values of 30±6 and 36.3±2meV for the donor and the donor-bound exciton, respectively.