Analysis of the emission characteristics of photonic crystal LEDs

Photonic crystals are known to enhance the extraction efficiency of LEDs and simultaneously shaping the emission pattern. In order to determine the radiation pattern we developed a model based on coupled mode theory that takes into account the lattice pattern, etch depth and the mode distribution. From a basic geometrical consideration a fundamental limit for the directionality is predicted. The calculations fit well to experimental data obtained from green InGaN LEDs incorporating a hexagonal PhC revealing a maximum directionality of 31% within 30°. Additional FDTD simulations were performed for determining quantitatively the extraction efficiency of PhC LEDs compared to LEDs with a roughened surface. Despite its lower overall extraction efficiency, the PhC LED outperforms a standard LED with surface roughening within an acceptance angle of 34° due to the higher directionality of the extracted light.