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We demonstrate the numerical study results of the enhancements of internal quantum efficiency (IQE) and external quantum efficiency (EQE) of a semiconductor quantum well when it is coupled with surface plasmons (SPs) induced on a grating interface between Ag and semiconductor. The IQE and EQE enhancements depend on the emission dipole position and the assigned intrinsic IQE. The SP dissipation in metal and the grazing-angle SP radiation lead to a significant difference between IQE and EQE. The enhancement of EQE is less significant when the intrinsic IQE becomes larger. In applying the SP coupling phenomenon to an InGaN-GaN quantum-well light-emitting diode, the efficiency enhancement is more significant in the green-red range, in which the intrinsic IQE is normally quite low.