The present invention provides a process for the production of an AlxGa(1-x)N single crystal (10) (wherein 0xGa(1-x)N single crystal (10) by a sublimation method, which comprises the step of preparing a substrate, the step of preparing a high-purity raw material, and the step of sublimating the raw material to grow an AlxGa(1-x)N single crystal (10) on the substrate. The AlxGa(1-x)N single crystal (10) exhibits a refractive index of 2.4 or above for a light having a wavelength of 250 to 300nm and a refractive index of 2.3 or above for a light having a wavelength which exceeds 300nm and is shorter than 350nm, each refractive index being determined at 300K.