Numerical Investigation of Light Extraction Efficiency of GaN-based Vertical Blue Micron-Scale Light-Emitting Diode Structures.

The light extraction efficiency (LEE) of GaN-based vertical blue micron-scale light-emitting diode (μ-LED) structures was investigated numerically using three-dimensional finite-difference timedomain (FDTD) methods. The entire μ-LED chip was included in the FDTD computational domain to determine the LEE accurately. As the lateral dimensions of μ-LEDs increased from 5 to 30 μm, the LEE decreased gradually because of the increased portion of light trapped inside the LED chip and the increased light absorption in the GaN layers with increasing chip size. The LEE varied strongly with the p-GaN thickness for the μ-LED with a flattop surface, which could be explained by the strong dependence of the spatial distribution of the emission patterns on the p-GaN thickness. This dependence on the p-GaN thickness decreased when the surface of the μ-LED chip was patterned. A high LEE of >80% could be achieved in LEDs with properly chosen parameters. The FDTD simulation results presented in this study are expected to be employed advantageously in designing μ-LED structures with a high LEE.