Simulation of GaN-Based Light-Emitting Diodes With Hemisphere Patterned Sapphire Substrate Based on Poynting Vector Analysis

The GaN-based light-emitting diodes (LEDs) with hemisphere patterned sapphire substrate (PSS) have been investigated numerically using a combined method of ray tracing and finite-difference time-domain techniques based on Poynting vector. Our method has been verified using unpatterned sapphire substrate for which analytical formulas exist. The simulated results show that the hemisphere PSS can improve the light extraction efficiency by increasing the reflection angle, decreasing the transmission angle, enhancing the reflectance of light incident on it, and enlarging the escape cone at its interface. Moreover, it is found that the hemisphere pattern size has significant influence on the improvement of the LED emission efficiency. The optimal radius of the hemisphere is about the emission wavelength of GaN-based LEDs, which can be attributed to the strong effect of wave properties of light at the PSS interface.