Optimization of the Cone Pattern in Patterned Sapphire Substrates for the Enhancement of the Light Extraction Efficiency of Light-Emitting Diode

We experimentally investigated the conditions for the enhancement of light extraction efficiency (LEE) in light-emitting diodes (LEDs) with cone patterned-sapphire substrates in terms of a base diameter of the cone pattern (d), pattern-to-pattern pitch (p), and pattern height (h). The LEE increased as both the base diameter of the cone pattern and height increase on the condition of the base diameter of the cone pattern being a certain value or lower. However, after the base diameter of the cone pattern exceeded this value, the LEE did not increase as the cone height increased, but the maximum LEE was realized under the optimum condition of the pattern height being equal to half of the base diameter. We present specific numerical values of the patterns on two different conditions of the base diameter of the cone pattern.