The present invention provides a semiconductor device having a semiconductor multi-layer structure which includes at least an active layer having at least a quantum well, and the active layer further including at least a luminescent layer of In_xAl_yGa_1-x-yN (0x1, 0y0.2), wherein a threshold mode gain of each of the at least quantum well is not more than 12 cm^-1, and wherein a standard deviation of a microscopic fluctuation in a band gap energy of the at least luminescent layer is in the range of 75 meV to 200 meV.