A GaN layer is grown on a sapphire substrate, an SiO2 film is formed on the GaN layer, and a GaN semiconductor layer including an MQW active layer is then grown on the GaN layer and the SiO2 film using epitaxial lateral overgrowth. The GaN based semiconductor layer is removed by etching except in a region on the SiO2 film, and a p electrode is then formed on the top surface of the GaN based semiconductor layer on the SiO2 film, to join the p electrode on the GaN based semiconductor layer to an ohmic electrode on a GaAs substrate. An n electrode is formed on the top surface of the GaN based semiconductor layer.