Light Extraction Efficiency of GaN-Based Micro-Scale Light-Emitting Diodes Investigated Using Finite-Difference Time-Domain Simulation

We conducted a systematic investigation of the light extraction efficiency (LEE) of GaN-based vertical micro-scale light-emitting diode (mu-LED) structures using three-dimensional finite-difference time-domain (FDTD) simulations. The LEE of mu-LED structures was found to have a strong dependence on structural parameters such as the shape of the chip cross section, chip dimension, and p-GaN thickness. The LEE of a mu-LED with a circular cross section was lower than that of a mu-LED with a square cross section by 5 similar to 10% owing to the coupling of light with high-quality-factor whispering gallery modes. The LEE of a mu-LED structure decreased as the chip dimension increased, which could be attributed to the increased portion of trapped light inside the LED chip and increased light absorption in the GaN with an increasing chip dimension. In addition, the LEE varied significantly with the thickness of the p-GaN layer, which could be explained by the strong dependence of the angular distribution of the emission pattern on the p-GaN thickness. The FDTD simulation method presented in this study is expected to be advantageously employed in designing mu-LED structures with high LEE.