Numerical simulations of light-extraction efficiencies of light-emitting diodes on micro and nanopatterned sapphire substrates

Numerical simulations are performed to investigate the light-extraction efficiencies (LEEs) of gallium nitride-based light-emitting diodes (LEDs) on patterned sapphire substrates (PSSs), using the three-dimensional finite-difference time-domain method. PSSs with hexagonal arrays of cone-shaped patterns were used, and the pitch of the pattern array, pattern fill factor and pattern height were varied from nanoscale to microscale. The relative LEE for each PSS-LED was calculated, and the geometrical parameters were analysed for optimised light extraction enhancement of the PSS-LEDs.