在本論文中，我們使用蒙地卡羅光線追跡法建立出LED之光子循環效應的光學模型，並探討在不同的主動層吸收係數之條件下，光子循環效應對於GaN LED和AlGaInP LED之光萃取效率的影響。此外，我們更進一步地選取了表面結構之薄型氮化鎵和圖案式藍寶石基板兩種GaN LED結構，分析當微結構陣列之角錐的角度改變時，其對於晶片之指向性和光萃取效率的提升幅度。

In this thesis, we build the optical model for photon recycling effect of LEDs based on Monte Carlo ray tracing method. According to this model, under different absorption coefficients of the active layer, we analyze the light extraction efficiency with respect to GaN and AlGaInP LEDs. Furthermore, we select two kinds of GaN LED structures such as surface texture of ThinGaN LEDs and patterned substrate of sapphire-based LEDs. Based on these two structures, we analyze the enhancement of the directionality and the light extraction efficiency when the slanted angles of the pyramid array are different.

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