“…1) To increase the luminous efficiency of LEDs, it is necessary to improve the external quantum efficiency, which is defined as the product of the internal quantum efficiency and extraction efficiency. Several methods, including the use of surface roughening techniques, [2][3][4][5] inclined side-wall etching, 6,7) patterned sapphire substrates, 8,9) and highly reflective omnidirectional reflectors (ODRs), 10) have shown improved light extraction efficiencies. Surface roughening is one of the most efficient methods to provide large enhancement for the extraction efficiency owing to the random scattering factors on the roughened surfaces.…”