We present a grating model of two-dimensional(2D)rigorous coupled wave analysis(RCWA)to study top diffraction gratings on light-emitting diodes(LEDs).We compare the integrated-transmission of the non-grating,rectangular-grating,and triangular-grating cases for the same grating period of 6μm,and show that the triangular grating has the best performance.For the triangular grating with 6-μm period, the LED achieves the highest light transmission at 6-μm grating bottom width and 2.9-μm grating depth. Compared with the non-grating case,the optimized light transmission improvement is about 74.6%.The simulation agrees with the experimental data of the thin polymer grating encapsulated flip-chip(FC) GaN-based LEDs for the light extraction improvement.
