臺灣博碩士論文加值系統

在本論文中，我們利用等效折射率法(Effective Index method)及保角轉換法(Conformal transformation method)結合使用光束傳播法(Beam propagation method)來模擬脊型彎曲波導結構的模態，接著藉由這套模擬方法推廣應用到環形共振腔架構之矽電光調制器的光學特性分析上。
環形共振腔的架構採用脊型波導設計是為了有更大的橫截面尺寸能使波導的模態以單模的形式傳播，以及增加光纖與波導間的耦合效率。而脊型波導的橫截面依自由載子濃度分布改變的情況，分別為載子排空、載子累積、載子注入等三種模式，因此發展出p/n接面、金氧半導體和p-i-n結構等橫截面設計應用於矽電光調制器。
本論文主要討論非對稱p/n接面和金氧半導體此兩款為主的脊形橫截面設計，此兩款的操作機制都是藉由加入電壓造成自由載子色散效應進而調變模態的折射率和光學損耗係數，接著利用我們提供的一套模擬計算方法可以分別得到不同電壓切換下的模態折射率和光學損耗係數，之後代入環形共振腔之穿透率與波長的關係式得到環形共振腔的穿透光譜，從中分析出不同結構的光學特性如光學調變速率、消光比、插入損耗、品質因子等。在本論文中對於環形共振腔結構之矽電光調制器建立了完整的光學分析流程之外，同時藉此光學分析的結果給予未來在元件的製程設計上有指標性的參考價值。

目錄
摘要.................................................................................................................................I
誌謝..............................................................................................................................III
目錄..............................................................................................................................IV
圖目錄......................................................................................................................... VI
表目錄..........................................................................................................................IX
第一章 導論..................................................................................................................1
1.1 前言.........................................................................................................................1
1.2 矽電光調制器的介紹及應用.................................................................................2
1.3 文獻回顧.................................................................................................................5
1.4 論文架構.................................................................................................................8
第二章 彎曲波導理論與其相關模擬方法..................................................................9
2.1波導基本理論..........................................................................................................9
2.1-1 馬克士威方程式............................................................................................9
2.1-2 平面波導......................................................................................................12
2.2 等效折射率法.......................................................................................................16
2.3 保角轉換法...........................................................................................................19
2.4 光學模擬軟體原理介紹.......................................................................................27
2.4-1 Beam Propagation Method.........................................................................27
2.4-2 Finite Difference Time Domain.................................................................29
2.5 比較功率耦合係數(κ)與間隙尺寸關係的光學模擬方法..................................36
2.6 單臂環形共振腔之穿透關係式...........................................................................37
2.7 彎曲波導光學模擬流程.......................................................................................40
第三章 具有縱向非對稱p/n脊型橫截面之電光調制器.........................................42
3.1 電光調制器之縱向非對稱p/n脊型橫截面的設計.............................................42
3.1-1 單模條件....................................................................................................45
3.1-2 彎曲損耗....................................................................................................48
3.2具有縱向非對稱p/n橫截面之電光調制器的光學分析......................................52
3.2-1 自由載子濃度分布....................................................................................52
3.2-2 折射率係數變化及損耗係數變化分佈....................................................55
3.2-3 穿透光譜與切換光學特性........................................................................59
3.2-4 功率耦合係數(κ)與間隙尺寸的關係....................................................66
第四章 具有金氧半導體結構脊型橫截面之電光調制器........................................70
4.1 電光調制器之金氧半導體結構脊型橫截面的設計...........................................70
4.2 具有縱向非對稱MOS橫截面之電光調制器的光學分析................................72
4.2-1 比較TE模和TM模於偏壓切換之光學差異.........................................72
4.2-2 不同的閘極氧化層厚度造成的光學差異................................................76
第五章 結論與未來展望............................................................................................91
5.1 結論.......................................................................................................................91
5.2 未來展望...............................................................................................................92
參考文獻......................................................................................................................93
附錄A..........................................................................................................................95
附錄B..........................................................................................................................98

[1]X.Qianfan,B.Schmidt,S.Pradhan and M.Lipson,“Micrometre-scale silicon electro-optic modulator,”Nature,435,2005,1007-1009

[2]F.Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L.O'Faolain, F. Dong, J.M. Fedeli, P. Dumon, L. Vivien, T.F. Krauss, G.T. Reed, J. Martí, “High-speed modulation of a compact silicon ring resonator based on a reverse-biased pn diode,” OPTICS EXPRESS 21986, Vol. 17, No. 24, 23 November 2009

[3]F. Y. Gardes, G. T. Reed, N.G. Emerson, “A sub-micron depletion-type photonic modulator in Silicon On Insulator,”OPTICS EXPRESS 8845, Vol. 13, No. 22

[4]Kyle Preston, Sasikanth Manipatruni, Alexander Gondarenko,
Carl B. Poitras, and Michal Lipson,” Deposited silicon high-speed integrated electro-optic modulator”, OPTICS EXPRESS 5118, Vol. 17, No. 7

[5]Po Dong, Roshanak Shafiiha, Shirong Liao, Hong Liang, Ning-Ning Feng, Dazeng Feng, Guoliang Li, Xuezhe Zheng, Ashok V. Krishnamoorthy, and Mehdi Asghari,”Wavelength-tunable silicon microring modulator”, OPTICS EXPRESS 10941, Vol. 18, No. 11, 24

[6]K. Okamoto, ”Planar optical waveguides,” in Fundamentals of Optical
Waveguides, P. L. Kelley, I. P. Kaminow, and G. P. Agerawal, Eds., San
Diego: Academic Press, 2000, pp. 13-45.

[7]M. Munowitz and D. J. Vezzetti,“Numerical procedures for constructing equivalent slab waveguides. An alternative approach to effective-index theory,”J. Lightwave Technol., vol. 9, pp. 1068-1073, Sept. 1991.

[8]M. Heiblum and J. H. Harris,“Analysis of curved optical waveguides by conformal transformation,”IEEE J. Quantum Electron., vol. 11, pp. 75-83,Feb. 1975.

[9]C. T. Shih, and S. Chao, ” Simplified numerical method for analyzing TE-like modes in 3-D circularly bent dielectric rib waveguide by solving two 1-D eigenvalue equations,” J. Opt. Soc. Am. B, vol.5,pp.1031-1037,Jun. 2008.

[10]黃維傳,“在矽基板上使用金氧半導體電光效應之環形共振腔特性模擬與分析,”清華大學,碩士論文(2006)

[11]陳怡萍,“以自我複製式光子晶體提升藍光發光二極體出光效率之模擬,”清華大學, 碩士論文(2008)

[12]A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electronics Letters 36, 321-322 (2000)

[13] K. Okamoto, ”Coupled mode theory,” in Fundamentals of Optical
Waveguides, P. L. Kelley, I. P. Kaminow, and G. P. Agerawal, Eds., San
Diego: Academic Press, 2000, pp. 125-171.

[14]S Pogossian, L Vescan and A Vonsovici (1998), “The single mode condition for semiconductor rib waveguides with large cross-section,” J. Lightwave Technol., 16, 1851–1853.

[15]C. Vassallo,Optical Waveguide Concepts. Amsterdam, The Netherlands:Elsevier,1991.

[16]R. A. Soref and B. R. Bennett , “Electrooptical effects in silicon “ IEEE J. Quant. Electron. 23, 123-129 (1987)

[17]Chih T’sung Shih, Zhi Wei Zeng, and Shiuh Chao,”Design and Analysis of MOS-capacitor Microring Optical Modulator with SPC Poly-silicon Gate”,Journal of Lightwave Technology.

[18]C.T. Shih,Zhi Wei Zeng ,Y.C.Chang,Y.J.Lee and S.Chao,”Optical Design of Bent Rib waveguide with MOS cross-section”, J. Lightwave Technology.,2008
[19]江信東,”s型彎曲波導與微米小球共振腔之光耦合效率研究,”中央大學，碩士論文(2006)
[20]Daoxin Dai, Sailing He,”Analysis of characteristics of bent rib waveguides,” J. Opt. Soc. Am. A,Vol. 21, No. 1
[21]陳雲霜,“半導體環形濾波器之研製”,中山大學,碩士論文(2003)
[22]C. A. Barrios, M. Lipson, “Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration”, Journal of Applied Physics 96, 6008-6014 (2004)
[23]A.M. Ghosh,C.Fishman,and T.Feng,”Theory of the electrical and photovoltaic properties of polycrystalline silicon,”J. Appl. Phys.,51,446-454,(1980).