本論文的研究主題是以光波導的概念來探討發光二極體(light emitting diode, LED)的光萃取效率，利用有限差分光束傳播法(Finite-Difference Beam Propagation Method, FD-BPM)計算氮化鎵 LED光波導內最強模態的角度，根據此角度設計最佳穿透效率的光柵結構於氮化鎵的表面上，目的使其達到最佳的光萃取效率，研究方法利用(FD-BPM)來計算多重量子井(Multi Quantum Wells, MQWs)的位置與最強模態角度的關係，根據此模擬結果得到最強模態的角度，將此角度運用嚴格耦合波搭配基因演算法做系統性的參數優化，找出最佳穿透效率的光柵結構參數，在發光波長為460 nm，其光柵週期為2.07 ?m、填充因子為0.51、蝕刻深度為0.2 ?m，根據此模擬結果LED的光萃取效率相較於平板結構約可增強36 %，利用FD-BPM可以快速的決定LED表面的粗化程度，並結合嚴格耦合波與基因演算法的優化，達到最佳的光萃取效率。

The subject of this thesis is to promote the light extraction of light emitting diodes by using the concept of optical waveguide. We use the Finite-Difference Beam Propagation Method (FD-BPM) to simulate the GaN LED waveguide and calculate the angle ( ) corresponding to strongest guided mode. According to the simulation results of FD-BPM, we can design the maximum transmission efficiency grating structure to roughen the surface of the GaN to increase the light extraction. First, we used FD-BPM to compute the relationship between the position of the Multi Quantum Wells (MQWs) and the strongest modes. From the simulation results, the angles of the strongest modes can be obtained. According to the angles of the strongest modes obtained by FD-BPM, we adopted the Rigorous Coupled Wave Analysis (RCWA) to compute the transmission efficiency of the grating structure and the Genetic Algorithms (GAs) to optimize the parameters of the grating structure to find the maximum transmission efficiency. From the results of the GAs, the optimum parameters of the grating structure at the wavelength of 460 nm the grating period were 2.07 ?m, filling factor 0.51 and etching depth 0.2 ?m. The light extraction efficiency of the grating structure compared to the slab structure was promoted to 36 %. The LED with the periodic structure can be rapidly determined by the FD-BPM and the RCWA based on the GAs to optimize the light extraction.

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