AlInGaN materials have found applications in the fabrication of high efficiency blue, white, and UV light emitters. Indium is believed to significantly improve the efficiency of semiconductor lasers and light emitting diodes due to carrier localization in the potential fluctuations caused by In clustering in the alloy. Such localization prevents nonradiative carrier recombination. At low temperatures, exciton transport in In-containing nitrides is only possible by phonon-assisted hopping. Observed "anomalous" S- and W-shaped temperature dependences of the photoluminescence (PL) band peak and width, respectively, serve as a signature of exciton hopping.
We report on Monte Carlo simulation of the localized exciton hopping in quaternary AlInGaN. The simulation results enabled a qualitative and quantitative interpretation of the measured temperature behaviour of the PL band peak position and width. Our calculations are based on a model of clusters with different In content, where excitons are hopping through the states dispersed due to potential fluctuations. The model successfully accounts for the inhomogeneous PL band broadening caused by the size fluctuations of individual clusters, i.e. by fluctuations of average localization energy. It provides a quantitative description of the temperature dependence of the PL band peak and width in the temperature range from 8 to 150 K. The simulation results for quaternary AlInGaN containing 1% of In yield 16 meV for the roughness of the potential profile in individual clusters and 42 meV for their distribution in average localization energy.

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