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The dependencies of quantum-well (QW) internal quantum efficiency (IQE) and device behaviors on the p-layer thickness in a high-indium InGaN/GaN QW light-emitting diode (LED) are demonstrated. During the high-temperature growths of the p-AlGaN and p-GaN layers, the QWs are thermally annealed to increase their IQEs and blue-shift the emission with increasing p-layer thickness. Meanwhile, the quantum-confined Stark effect is enhanced with increasing p-layer thickness to decrease the IQEs and red-shift the emission. Based on the counteraction between the two effects, the maximum IQE and the shortest emission wavelength are observed in a sample with an optimized p-layer thickness, which includes a p-AlGaN layer of 20 nm and a p-GaN layer of 60 nm in thickness under our growth conditions. The fabricated LEDs of different p-GaN thicknesses show the similar variation trends in emission efficiency and wavelength.