The importance of doping or alloying with In for obtaining high external quantum efficiency was shown for GaN-based single-quantum-well (SQW) structures in terms of localization effects due to quantum-disk (Q-disk [M. Sugawara, Phys. Rev. B 51, 10743 (1995)])-size potential minima in the QW plane. The ultraviolet light-emitting diode with lightly In-alloyed InGaN SQW exhibited an electroluminescence peak from the band-tail states. Monochromatic cathodoluminescence mapping images of In0.03Ga0.97N SQW indicated the presence of Q-disk-size effective bandgap variation. Furthermore, cubic InGaN QW which does not suffer from the piezoelectric field normal to the QW plane, also exhibited a broad band-tail.