許多研究致力於提升發光二極體(Light Emitting Diode，LED)之光萃取效率，並運用各種數值計算方法，其中一種是將二維光子晶體平板（2D photonic crystal slab, 2D PhC slab）結構置入LED之中。本文藉由平面波展開法（plane wave expansion method）及時域有限差分法(finite difference time domain method)來研究氮化鎵發光二極體(GaN LED)包覆層厚度，來分析光子晶體空氣柱之半徑及深度對LED光萃取率的影響，當深度及半徑參數設定適當時，可大幅提升光萃取效率。 進一步將點缺陷(point defect)置入光子晶體之中形成共振腔(resonance cavity)結構加以比較。被置入的缺陷類型分別為，H1、H2及H2之變型（回音廊型），三類共振腔。經比較，置入光子晶體發光二極體與原始發光二極體，光萃取率及光強度有明顯增加的現象。

The two dimensional photonic crystal slab with designated defects, namely H1, H2, and WGM type cavities, are investigated aiming at achieving more efficient light extraction. By using the finite–difference time–domain method, effects of finite air-hole radius and depth, and the thickness of cladding layer on the light extraction efficiency are examined. For the selected Gallium Nitrogen blue light emitting LED, values of radius, depth, thickness, that achieved improved photoluminescence, are identified.

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