Enhanced light extraction through nano-textured GaN interfaces via supercritical angle scattering

A novel theoretical approach combining scattering theory with supercritical angle transmission is introduced for treating light incidence on nanotextured surfaces. The theory is used to evaluate enhanced light extraction from interfaces with sub-wavelength feature sizes, where the ray tracing approach breaks down. A unified analytic formula covering the transition from periodic to random surface texturing is obtained. The results will be compared with experimental enhanced light extraction results from GaN textured interfaces. The extraction efficiency is studied as a function of the average feature size and the rms deviation from the average values. It is argued that enhanced extraction occurs due to both supercritical transmission for single wave incidence, and the quick randomization of the incident wave-vector directions via internal scattering.