Numerical Simulations of the Light-Extraction Efficiency of LEDs on Sapphire Substrates Patterned with Various Polygonal Pyramids

We report a numerical analysis of the light-extraction efficiency (LEE) of light-emitting diodes (LEDs) on patterned sapphire substrates (PSSs). We considered various n-sided, regular convex pyramids, where n is an integer and n ≥ 3. We then considered four cross sections: extruded, subtracted, truncated-extruded, and truncated-subtracted. Ray-tracing simulations were carried out with these polygonal pyramid patterns, and the dimensions of the patterns were systematically varied. Optimized pattern shapes were determined for large LEE. An extruded circular pyramid with a slant angle of 45° was found to be the optimal patterned shape. KCI Citation Count: 5