發光二極體是在1950年末代由實驗室發展出來的。隨著科技的進步，現在已可以生產全系列的顏色(由藍色460nm至暗紅色660nm)，且其擁有發熱度低、省電、反應速率快、壽命長的優點奠定了其在固態照明的重要地位，目前被廣泛應用在照明、液晶螢幕背光、交通指示燈…等。然而發光二極體一直存在著一個問題，就是它的外部量子效率低。若是能提升其外部量子效率，使在發光層產生的光子可以更有效率的被粹取出來，整體的發光效率便能提升許多。利用光子晶體來提升出光效率是最普遍的方法之一，有藉由其表面週期性而產生的繞射特性成功的提升了63%出光效率[5]，也有在基板背部建立一一維光子晶體來利用其能隙特性而提升出光效率[7]。因此本研究中主要目的是利用二維光子晶體的能隙特性來增強往上傳播的光子量與光子晶體的繞射特性修正原本應該被全反射的光子行進方向，而允許更多的光子被萃取出以提升發光二極體的出光效率。並針對此結構建立了一套完整的分析流程，可以清楚知道光子晶體在發光二極體元件上的調變機制；以及建立了一完整的整體出光效率模擬模型，儘可能趨近實際發光二極體發光情形，來提高模擬的正確性。

中文摘要..................................................i
英文摘要.................................................ii
致謝....................................................iii
目錄.....................................................iv
表目錄.................................................viii
圖目錄...................................................ix
符號說明...............................................xvii
第一章 導論...............................................1
1.1 引言..................................................1
1.2 研究動機與目的........................................3
第二章 基本理論...........................................4
2.1 波動方程式............................................6
2.2 光子晶體能隙..........................................8
2.3 繞射理論.............................................13
第三章 模擬架構與理論....................................18
3.1 模擬工具.............................................18
3.2 有限差分時域法.......................................20
3.2.1 FDTD形式.........................................20
3.2.2 空間格點大小.....................................27
3.3 光子晶體之模擬分析...................................28
3.3.1 模擬架構.........................................28
3.3.2 模擬區域邊界條件─Bloch boundary.................30
3.3.3 發光光源─平面波(plane wave).....................34
3.3.4 數據接收型式─power monitor......................35
3.4 LED出光效率之模擬....................................41
3.4.1 模擬架構.........................................41
3.4.2 模擬區域邊界條件─PML(Perfectly Matched Layer)...43
3.4.3 發光光源─電偶極(electric dipole)................54
第四章 模擬環境參數設定之討論與模擬結果..................60
4.1 基本環境參數設定.....................................60
4.1.1 PML設定..........................................62
4.1.2 空間格點大小.....................................64
4.2 光子晶體特性之模擬結果..............................67
4.2.1 頻譜.............................................67
4.2.2 光子晶體特性之模擬數據整理流程...................71
4.2.3 數據分析之解析度討論.............................78
4.2.4 數據分析結果與討論...............................84
4.3 LED出光效率之模擬分析結果與模擬環境參數討論..........91
4.3.1 LED出光效率的模擬知數據整理流程..................91
4.3.2 模擬寬度.........................................96
4.3.3 模擬結果與討論..................................106
第五章 結論與未來展望...................................108
5.1 結論................................................108
5.2 未來展望............................................108
參考文獻................................................109
附錄A 光子晶體繞射理論─TE wave.........................112
附錄B 電偶極輻射........................................116
B.1 電偶極輻射電磁場....................................116
B.2 電偶極輻射強度(intensity)...........................118
B.3 電偶極輻射總能量....................................122
附錄C 決定dipole個數....................................125
C.1 二維光子晶體LED.....................................125
C.1.1 遠場對不同位置的關係............................125
C.1.2 對稱位置之間的遠場關係..........................134
C.1.3 source個數與位置................................138
C.1.4 本節結論........................................144
C.2 一維光子晶體LED.....................................145
附錄D...................................................149
D.1 干涉理論............................................149
D.2 決定sapphire厚度....................................155

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