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We have grown GaN films with a thickness of about 1.2 $\mu$m on Si (111) substrates by using metalorganic chemical vapor deposition and a AlN/GaN superlattice. In order to optimize the pair number of the AlN/GaN superlattice, we have grown GaN films on Si (111) substrates having various pair numbers of the AlN/GaN superlattices. When the pair number of the AlN/GaN superlattices is 15 pairs, no cracks are observed in the GaN film grown on Si (111), and the GaN film shows the best surface and crystal quality. Also, the GaN micro-cavity structure with SiO$_2$/ZrO$_2$ dielectric-distributed Bragg reflectors as both cavity mirrors has been fabricated by means of transferring a InGaN/GaN multiple quantum well structure from the Si (111) substrate onto a sapphire carrier and wet-chemical etching of the Si substrate. Dips in the reflectivity spectrum of the fabricated micro-cavity structure have been observed at wavelengths of 405 nm 433 nm, indicating the resonance mode of the cavity.