FDTD Analysis on Extraction Efficiency of GaN Light-Emitting Diodes With Microsphere Arrays

The improvement of light extraction efficiency of InGaN light-emitting diodes (LEDs) using microsphere arrays with various refractive indices was analyzed. Finite-difference time-domain (FDTD) simulations show that the use of microsphere ( ${d}_{\rm \\musphere} = 500$ nm) arrays with refractive indices of 1.8 and 2.5 led to increase in light extraction efficiency of InGaN LEDs by 1.9 times and 2.2 times, respectively. The enhancement in light extraction efficiency is attributed to the decrease in the Fresnel reflection and increase in effective photon escape cone due to graded refractive index and curvature formed between microsphere and free space. The maximum enhancement of light extraction efficiency of InGaN quantum well LEDs was achieved by employing the refractive index matched anatase-TiO $_{2}$ microsphere arrays. The effects of microsphere diameters on the light extraction efficiency were also investigated and 2.4 times enhancement was achieved by employing 400-nm refractive index matched TiO $_{2}$ sphere arrays.