本論文主要利用了「嚴格耦合波分析」，針對背部具自我複製式二維光子晶體[13][14]的氮化鎵材料之藍光發光二極體，建立了一套完整模擬具週期性結構的LED之出光特性的方法，並優化二維光子晶體之幾何形狀以其反射特性、繞射特性來提升光汲取效率。我們得到之最佳二維光子晶體結構為：「grating pitch=250nm、optical thickness=(1.3/4*中心波長)」，其光汲取效率為36.05%。相較於FDTD等演算法，利用這套計算方法可更加快速的得到二維光子晶體結構的最佳幾何參數，期望對於製程設計上能夠快速的給出一個明確的方向。

In this research, we used a “rigorous coupled wave analysis” to characterize the light extraction property of a two-dimension photonic crystal of GaN-based blue LED and optimize the geometric configuration of the photonic crystal via controlling the photonic band gap and the diffraction efficiency. An optimized geometric configuration of the photonic crystal obtained under such calculation is “grating pitch=250nm、optical thickness=(1.3/4*central wavelength)”the extraction efficiency achievable under such condition is 36.05%. This algorithm is more efficient than FDTD or other common by used algorithms. The optimized geometric configuration of the photonic crystal could serve as useful guidelines for fabrication and design.

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