A significant improvement of output power and external quantum efficiency (EQE) for nonpolar a-plane (11-20) GaN light-emitting diodes (LEDs) on r-plane sapphire substrates has been demonstrated by using embedded pyramid-shape air-gap arrays on hexagonally patterned SiO<sub>2</sub> layer. The air-gap structure was realized based on asymmetrical growth behavior of a-plane epitaxial lateral overgrowth (ELO) GaN along +c-axis and -c-axis. The output power and EQE of the a-plane LEDs with the air-gaps on patterned SiO<sub>2</sub> have increased by more than 50% when compared to those of the conventional a-plane LEDs. Theoretical fit to the measured EQE suggested that the significant improvement of EQE was mainly attributed to the increase in light extraction efficiency (EXE). Light emission pattern analysis and ray-tracing simulation revealed that the air-gap arrays on top of patterned SiO<sub>2</sub> enlarged the guided-light scattering at the air-gap surface due to the significant refractive index contrast with the GaN layer, followed by the improvement of EXE of nonpolar a-plane LEDs.
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