Parameters optimization of nanopatterned sapphire substrates for enhancing light extraction efficiency of GaN-based LEDs

The nanopatterned structures play an important role in enhancing the light extraction efficiency (LEE) of GaN-based light-emitting diodes (LEDs). Three-dimensional finite-difference time-domain (3D-FDTD) method was carried out to calculate the LEE enhancement of GaN-based LEDs designed on periodic nanostructures with different geometries. Orthogonal experiment method was employed to obtain the optimal structure parameters and analyze the weighting factor of critical parameters affecting the LEE enhancement. The results of orthogonal experiment showed that the height/depth of the periodic nanostructures is the dominated factor to influence the LEE enhancement, followed by the diameter and the spacing of the periodic nanostructures. It was also found that the far-field intensities of LEDs with periodic convex nanostructures were stronger than those with periodic concave nanostructures. The critical parameters of periodic convex nanostructures were further optimized by single factor method, and their optimal parameters were obtained. The optimal LEE enhancement of GaN-based LEDs grown on cone-shaped nanopillar and column-shaped nanopillar array patterned sapphire substrates are 1.95 and 1.97, respectively. This means the cone-shaped and column-shaped nanopillar structures have almost identical LEE enhancement of GaN-based LEDs.