Ray-tracing study of Bragg diffraction-assisted light extraction efficiency of GaN-based light-emitting diodes with vertical sidewalls

摘要

Ray-tracing method is used to investigate the light extraction efficiency (LEE) of Bragg diffraction-assisted GaN-based light-emitting diodes (LED's) with vertical sidewalls. The ray tracing is based on the analytical formulae of the LEE in the incoherent regime for LED model with infinite lateral size. It is shown that without considering the sidewalls, the change of the LEE with the absorption or backside reflectivity is too small and thus not reasonable. And the enhancement with respect to the unpatterned case could be overestimated by ignoring the finite-size effect. Numerical calculations show that the enhancement of the LEE due to the sidewalls when compared to the infinite model could be up to 10% or even higher. Besides, the extracted energy from the sidewalls decreases due to the increased extraction from the PhC when compared to the unpatterned LED.