Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection.

Cone-shaped nanostructures with controllable side-wall angle are success- fully fabricated with a SiO(2) nanosphere lithography (NSL) etching mask. Vertical LEDs with cone-shaped nanostructures with a 24.1° side-wall angle provide 6% more light output power compared to those using hexagonal pyramids formed by photochemical etching. This achievement is attributed to effective elimination of total internal reflection by angle-controlled nanostructures.