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AlGaN/AlN/GaN high electron mobility transistor heterostructures grown by metal-organic chemical vapor deposition have been studied by temperature dependent time-resolved photoluminescence. The AlGaN-related emission is found to be sensitive to the excitation power and to the built-in internal electric field. In addition, this emission shows a shift to higher energy with the reduction in the excitation density, which is rather unusual. Using a self-consistent calculation of the band potential profile, we suggest a recombination mechanism for the AlGaN-related emission involving electrons confined in the triangular AlGaN quantum well and holes weakly localized due to potential fluctuations.