臺灣博碩士論文加值系統

本研究旨在以密度泛函理論(density functional theory, DFT)原理與方法，模擬三族氮化物(Ⅲ-N族)半導體材料不同大小量子點之材料特性與光電性質做微觀分析及理論預測，並同時以光學測試驗證其正確性。
半導體材料特性在發光二極體研究中扮演著重要的角色，本論文主要在研究Ⅲ-N族半導體量子點之光學及材料特性，首先從微觀的角度開始出發，根據二元及三元三族氮化物(Ⅲ-N族)半導體材料─氮化鎵(GaN)n、氮化銦鎵(InxGa1-xN) 的纖維鋅礦(wurtzite)結構，分別建立各不同大小的clusters與量子點分子模型，計算結構最佳化、分子間之振動頻率、單點能量，再將模擬出來之結果進行分析，最後得到所需要的能隙 (band gap)、結合能(binding energy)、態密度函數(DOS)、紫外線可見光光譜(UV/Vis spectrum)。
在激發態部份，針對各個不同量子點(GaN)n之n值，進行激發態能量及其結構最佳化、計算螢光激發光譜及螢光發射光譜(fluorescence spectrum)、史托克位移(Stokes shift)、及溶劑效應下的各種n值情況之光學特性及電性，希望能可以作為奈米尺度下三族氮化物(Ⅲ-N族)特性的一個參考依據，期望能分析出符合實驗值量子點大小的模型，預測三族氮化物(Ⅲ-N族)量子點之實驗結果。

摘要 I
Abstract II
致謝 IV
目錄 V
圖目錄 VIII
表目錄 X
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 3
1.3 III-N半導體發光二極體簡介 4
1.4 文獻回顧 9
1.4.1 發光二極體的發展 9
1.4.2 理論計算 10
第二章 理論計算原理與方法 12
2.1 前言 12
2.2 密度泛函理論(DFT) 13
2.2.1 Hohenberg-Kohn理論 13
2.2.2 Kohn-Sham方法 15
2.2.3 自洽場(Self-Consistent Field)計算 17
2.3 與時間相關泛函密度理論(TD-DFT) 19
2.3.1 The Roung-Gross Theorem 19
2.3.2 Time-dependent Kohn-Sham System 20
2.3.3 Linear Response TDDFT 21
2.4 B3LYP理論 23
第三章 模型建構與模擬方法 25
3.1 模擬流程 25
3.2模擬模型建立 26
3.3密度泛函理論模擬 28
3.3.1 COM檔及LOG檔 28
3.3.2模擬設定 28
3.3.3量子侷限效應 (Quantum Confinement Effect) 32
3.3.4 能隙(Band Gap)與狀態密度函數 (Density of States) 33
3.3.5結合能 (Binding Energy) 34
3.3.6吸收和放射波長計算部份 35
3.3.7史托克位移 (Stokes Shift) 35
3.3.8實驗量測 36
第四章 結果與討論 39
4.1最佳化之clusters與量子點結構 39
4.2 結合能 (Binding Energy) 43
4.3能隙(Band Gap)與狀態密度函數(Density of States) 44
4.4吸收光譜 52
4.5激發態最佳化及放射光譜 (Emission Spectrum) 54
4.6 史托克位移 62
4.7 量子點大小估算 64
4.8 氮化鎵薄膜光學特性量測 66
第五章 結論與未來建議 69
5.1結論 69
5.2未來建議 70
參考文獻 72
附錄A 76
附表一 (GaN)9的TDDFT計算結果 76

[1] http://www.ledinside.com.tw/
[2] Arturas Zukauskas, Michael S. Shur, Remis Gaska, Introduction to Solid-State Lighting, Wiley-Interscience, 2002.
[3] E.F. Schubert, Light-Emitting Diodes, 2nd ed., Cambridge University Press, Cambridge, 2006.
[4] Donald A. Neamen, Semiconductor Physics &Devices, Third Edition, 2006.
[5] S. Nakamura, T. Mukai, M. Senoh, “High-power GaN P-N Junction Blue-Light Emitting Diodes”, Jpn. J. Appl. Phys., Vol. 30, p.p. 1998-2001, 1991.
[6] S. Nakamura, T. Mukai, “High-Quality InGaN films Grown on GaN Films” Junction Blue-Light Emitting Diodes” Jpn. J. Appl. Phys., Vol. 31, p.p. 1457-1457, 1992.
[7] S. Nakamura, T. Mukai, M. Senoh, “Candela-Class High-Brightness InGaN/AlGaN Double-Heterostructure Blue-Light-Emitting Diodes” Applied Physics Letters, Vol. 64, pp. 1687-1689, 1994.
[8] S. Nakamura, M. Senoh, N. Iwasa and S. Nagahama, “High-Brightness InGaN Blue, Green and Yellow Light-Emitting Diodes with Quantum Well Structures”, Jpn. J. Appl. Phys., Vol. 34, p.p. 797-799, 1995.
[9] S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, Y. Sugimoto, T. Kozaki, H. Umemoto, M. Sano, and K.” Continuous-wave Operation of InGaN/GaN/AlGaN-Based Laser Diodes Grownon GaN Substrates” Appl. Phys. Lett., Vol. 72, 2014, 1998.
[10] C. Stampfl and C. G. Van de Walle, “Density-Functional Calculations for III-V Nitrides Using The Local-Density Approximation and The Generalized Gradient Approximation” Physical Review B, Vol. 59, p.p. 5521-5535, 1999.
[11] J. P. Perdew and W. Yue, “Accurate and Simple Density Functional for the Electronic Exchange Energy: Generalized Gradient Approximation,” Phys. Rev. B, Vol. 33, pp. 8800−8802, 1986.
[12] J. P. Perdew, J. A. Chevary, S.H. Vosko, K. A. Jackson, M. R. Pederson, and D. J. Singh, “Atoms, Molecules, Solids, and Surfaces: Applications of The Generalized Gradient Approximation for Exchange and Correlation,” Phys. Rev. B, Vol. 46, pp. 6671−6687, 1992.
[13] B. Song, P. Cao, “Geometric and Electronic Structures of Small GaN Clusters” Physics Letters A, Vol. 328, p.p. 364–374, 2004.
[14] H. Wu,*, F.Zhang, X.Xu, C. Zhang, and H. Jiao, “Geometric and Energetic Aspects of Aluminum Nitride Cages”, J. Phys. Chem. A, Vol.107, p.p. 204- 209, 2003.
[15] J. Zhao, B Wang, X. Zhou, X. Chen, W. Lu, “Structure and Electronic Properties of Medium-Sized GanNn Clusters (n = 4–12)” Chemical Physics Letters, Vol. 422, p.p. 170–173, 2006.
[16] A. Loiseau, F. Willaime, N. Demoncy, G. Hug, and H. Pascard,”Boron Nitride Nanotubes with Reduced Numbers of Layers Synthesized by Arc Discharge” Physics Rev. Lett., Vol. 76, p.p.4737-4740, 1996.
[17] S. Lee, Y. Lee, Y. Hwang, J. Elsner, D. Porezag, T. Frauenheim,”Stability and Electronic Structure of GaN Nanotubes from Density-Functional Calculations” Physical Review B, Vol. 16, p.p. 7788-7791, 1999.
[18] Y. Chou, H. Wang, Y. Lin, W. Chen, B. Wang, “Infinite Single-Walled Boron-Nitride Nanotubes Studies by LGTO-PBC-DFT Method” Diamond & Related Materials, Vol.18, p.p. 351-354, 2009.
[19] Y. Guo, X. Yan, Y.Yang,”First-Principles Study of Narrow Single-Walled Nanotubes” Physics Letters A, Vol. 173, p.p. 367-370, 2009.
[20] H. Pan, Y.Feng, and J.Lin “Electronic Structures of AlGaN2 Nanotubes and AlN-GaN Nanotube Superlattice” J. Chem. Theory Comput, Vol. 4, p.p. 703-707, 2008.
[21] B. Brena and L. Ojama, “Surface Effects and Quantum Confinement in Nanosized GaN Clusters: Theoretical Predictions” J. Phys. Chem. C, Vol.112, p.p.13516–13523, 2008.
[22] R. Yang and A. Rendell, “First Principles Study of Gallium Atom Adsorption on the α-Al2O3 (0001) Surface” J. Phys. Chem. B ,Vol. 110, p.p. 9608-9618,2006.
[23] D. Tzeli, I. Petsalakis, and G. Teodorakopoulos,”Theoretical Study of Group III-A Nitrides on Si (111)”, J. Phys. Chem. C, Vol. 113, p.p. 5563-5567, 2009.
[24] Monkhorst, M. J., and Pack, J. D., “Special Point for Brillouin-Zone Integrations”, Physical Review B, Vol. 13, No. 12-15, p.p. 5188-5192 , 1976.
[25] 蔡岳璁 (洪哲文指導),” 計算量子力學於CO在直接甲醇燃料電池觸媒之毒化研究”, 清華大學動力機械系碩士論文,2006.
[26] M.A.L.Marques, Time-dependent density functional theory, Berlin: Springer, 2006.
[27] A. D. Becke,” Density-Functional Thermochemistry. III. The Role of Exact Exchange” J. Chem. Phys. Vol. 98, p.p. 5648-5652, 1993.
[28] G. Martínez-Criado, A. Somogyi, and S. Ramos,” Mn-rich Clusters in GaN: Hexagonal or Cubic Symmetry?” Appl. Phys. Lett., Vol. 86, p.p. 131927, 2005.
[29] Yen-Kuang Kuo, Wen-Wei Lin, and Jiann Lin,”Band –Gap Bowing Parameter of the InxGa1-xN Derived from Theoretical Simulation” Jpn. J. Appl. Phys., Vol. 40, p.p. 3157-3158, 2001.
[30] R. Kudrawiec, M. Nyk, M. Syperek, A. Podhorodecki, and J. Misiewisz,” Photoluminescence from GaN Nanopowder: The Size Effect Associated with the Surface-to-volume Ratio” Appl. Phys. Lett., Vol. 88, p.p.18916, 2006.
[31] M. Nyk, R. Kudrawiec, J. Misiewisz, R. Paszkiewicz, R. Korbutowicz, J. Kozlowski, J. Serafinczuk, M. Syperek, “Structure and Optical Properties of MOVPE and HVPE GaN Films Grown on GaN Nanocrystalline Powder Substrate ” J. Cryst. Growth, Vol. 277, p.p. 149-153, 2005.