In the case in which a ZnO based oxide semiconductor layer is to be hetero-epitaxially grown on a substrate formed of a material which is different from that of a ZnO based oxide semiconductor, the ZnO based oxide semiconductor layer is grown at a high temperature of 500° C. or more, and supply of oxygen is stopped and gradual cooling is carried out until a substrate temperature is lowered to 350° C. or less after the growth of the ZnO based oxide semiconductor layer is completed. As a result, it is possible to suppress the generation of dislocations or crystal defects over an epitaxial grown layer based on the atmosphere while the substrate temperature is lowered after the growth of the semiconductor layer and a difference in a coefficient of thermal expansion, thereby obtaining a semiconductor device having a high quality ZnO based oxide semiconductor layer which has an excellent crystalline property and a semiconductor light emitting device having the high characteristics.