The radiative recombination of carriers in a two-dimensional electron gas (2DEG) in undoped and modulation-doped AlxGa1-xN/GaN heterostructures grown by metalorganic chemical vapor deposition is investigated at low temperature using photoluminescence measurements. Temperature-dependent Hall effect and Shubnikov-de Haas measurements, verify the formation of a high-quality 2DEG. Radiative recombination is observed between the 2DEC in quantum states at the hetero-interface and the holes in the flat-band region or bound to residual accepters both in undoped and top AlGaN layer is removed by reactive ion etching. In addition, the effect of the growth interruption time, laser excitation intensity, and doping conditions upon the photoluminescence is also described.