發光二極體（LED）晶片的界面菲涅爾效應會限制其光的萃取率， 藉由圖形化LED晶片中的異質材料的接合界面，可有效抑制其界面菲 涅爾效應，因而提高光萃取率。本論文主要探討LED晶片之藍寶石基 板圖形化的奈微米圖形結構之設計技術。我們將奈微米圖形結構尺寸 分成三個範圍，並考慮分別使用有限時域差分法（FDTD）、嚴格耦 合波分析（RCWA）與蒙地卡羅光線追跡法等演算法的三種模擬工具， 來探討與分析藍寶石基板圖形化的奈微米圖形結構的模擬演算法的 應用問題與適用度。根據研究結果顯示，適當模擬演算法的選用與適 用模擬演算法的工具之參數設定，對LED晶片的奈微米圖形結構設計 影響很大，且每件結構模擬的時間差異也很大。我們的研究結果可提 供圖形化LED晶片中異質材料的接合界面之奈微米圖形結構的可靠 的、有效率的模擬參考。我們也分析了奈米到微米範圍的奈微米半球 結構對覆晶式LED晶片的光萃取率影響，模擬發現在奈米以及微米尺 寸在高寬比0.8 時，能達到最佳的光萃取率。;The light-extraction efficiency of light-emitting diodes (LEDs) is strictly limited by the Fresnel reflection. The patterned sapphire substrate technique can reduce the Fresnel reflection and enhance the light extraction efficiency. In this thesis, the size range of patterned structure is considered from a few microns to hundreds of nanometers. To obtain fast and accurate simulation, three simulation algorithms: finite time difference domain, rigorous coupled-wave analysis and Monte carlo ray tracing method are considered and found the preferred range of applications. The results show that appropriate simulation algorithms and parameter settings of simulation tools have obvious influence on simulation time and simulation accuracy. We also analyze influence of sphere-shape nano-patterned and micronpatterned sapphire substrate on LED, and we found that the largest light extraction efficiency can be obtained when the aspect ratio is 0.8.
