I. Introduction
Recently, GaN-based semiconductors have attracted great attention for application in solid-state lighting. In many applications, such as full color displays, traffic signals, automobile headlights, and daily lighting, we still need to further improve the output power and external quantum efficiency of the light-emitting diodes (LEDs). Currently, GaN-based LEDs are grown on planar sapphire substrates by metal–organic chemical vapor deposition (MOCVD) systems. Large lattice mismatch and thermal expansion coefficient differences between GaN and sapphire substrates make GaN films contain a high density of threading dislocations (TDs). The TDs will provide a pathway for electrons to leak through the active region which reduced internal quantum efficiency [1]. In addition, it is known that the light extraction efficiency of LEDs is limited by total internal reflection due to the large difference in refractive index between the GaN film, the sapphire substrate , and the surrounding air according to Snell's law.