由於常見的MIR雷射時常需要操作在低溫環境下，原因是其使用的材料通常為III-V族半導體，而III-V族半導體在室溫下的載子遷移率偏低且電子電洞容易發生非輻射的複合效應，這是導致常見的MIR雷射在室溫下效率不佳的原因。
本論文主要是於SOI基板上設計一維光子晶體雷射共振腔(包含2^nd order surface emission DFB lasers 以及 1st order phase-shifted edge emission DFB lasers)搭配二維材料-黑磷作為雷射增益介質的混成雷射，目的是為了製作出一個能操作在室溫環境、低閾值且單模輸出的中紅外光雷射(波段約為3.6 um左右)。
並基於耦合模態理論(Coupled Mode Theory)以及傳遞矩陣法(Transfer Matrix Method)，透過撰寫MATLAB scripts數值模擬運算，來分析二階面射型DFB(2^nd order surface emission DFB lasers)與一階相位平移邊射型DFB雷射(1st order phase-shifted edged emission DFB lasers)各共振模態之閾值增益係數以及共振波長。
並以Duty Cycle以及蝕刻深度為變因進行優化，分析這些變因對於二階面射型DFB與一階相位平移DFB雷射的閾值增益係數之影響，設計出較低閾值增益且共振波長落在大約 3.6 um 左右的中紅外光雷射共振腔。 

Common MIR lasers often need to operate in low-temperature environments because the materials used are usually III-V semiconductors. The carrier mobility of III-V semiconductors at room temperature is low and electron holes are prone to occur non-radiative recombination effect are the reasons why common MIR lasers are not efficient at room temperature.
In this thesis , we mainly designs a one-dimensional photonic crystal laser resonant cavity (including 2^nd order surface emission DFB lasers and 1st order phase-shifted edged emission DFB lasers) on an SOI substrate with a two-dimensional material - black phosphorus as the laser gain medium . The purpose of the hybrid laser is to create a mid-infrared light laser that can operate at room temperature, has a low threshold and has a single-mode output (the band is about 3.6 um).
Based on the Coupled Mode Theory and Transfer Matrix Method, we wrote MATLAB scripts to perform numerical simulation operations and to analyze the threshold gain coefficient and resonance wavelength of each resonance mode between 2^nd surface emission DFB lasers and 1st edged emission DFB lasers.
Optimization was carried out using Duty Cycle and etching depth as variables, and analyze the impact of these variables on the threshold gain coefficients of the 2^nd order surface-emitting DFB and 1st order phase-shifted DFB lasers , to design a mid-infrared laser resonant cavity with a lower threshold gain and the resonance wavelength falling within of approximately 3.6 um.

摘要 1
Abstract 2
致謝 3
目錄 5
圖目錄 8

第一章 緒論 13
1.1 研究動機 (Motivation) 13
1.2 光子晶體雷射(Photonics Crystal Laser) 15
1.3 二維材料 – 黑磷 (Black phosphorus) 18

第二章 理論介紹 21
2.1 耦合模態理論 (Coupled Mode Theory) 21
2.1.1 色散關係 (Dispersion Relation) 35
2.1.2 有限長度光柵結構的反射與穿透 (Reflectance and Transmittance of a Finite Length Grating) 37
2.1.3 閾值條件 (Threshold Condition) 39
2.2 傳遞矩陣法 (Transfer Matrix Method) 41
2.2.1 一般光柵結構的傳遞矩陣 42
2.2.2 利用傳遞矩陣得到振盪條件方程式 44
2.2.3 π/2相位平移DFB雷射原理 45
2.2.4 π/2相位平移DFB雷射的傳遞矩陣 48

第三章 元件設計與模擬 53
3.1 DFB結構簡介 (Introduction of DFB structures) 53
3.2 模擬流程圖 (Flow Chart of Simulation) 56
3.3 模擬分析 (Analysis of Simulation Results) 58
3.3.1 變因 :「Duty Cycle」對耦合係數的影響 58
3.3.2 變因 :「蝕刻深度」對耦合係數的影響 60
3.3.3 變因 :「蝕刻深度」對閾值增益的影響 62
3.3.4 邊界散射結構 (Scattering Structure on edges) 78
3.3.5 Final Design 88

第四章 元件製程 96
4.1 製程流程 (Process Flow) 96
4.2 詳細製程介紹 (Fabrication) 96

第五章 元件量測 99
5.1 量測結果 (Measurement Results) 99
5.2 問題與討論 (Problems & Discussions) 102
5.3 未來改善方向 (Directions for Improvements) 104
5.3.1 材料方面 (Material Improvements) 104
5.3.2 元件設計方面 (Device Design Improvements) 106
5.3.3 製程方面 (Fabrication Improvements) 111
5.3.4 量測方面 (Measurement Improvements) 112

第六章 結論 113

參考文獻 115

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