本文以分子靜力學結合Basin-hopping 法建構二氧化矽奈米線之結構，再利用密度泛函理論探討幾何與電子性質，最後藉由分子動力學探討二氧化矽奈米線的機械性質。本文成功找到八種線徑大小不同的二氧化矽奈米線，並且4MR-4O 與實驗文獻得到二氧化矽奈米結構之排列方式相同，印證了使用Basin-hopping 法與密度泛函理論來預測二氧化矽奈米線結構之可行性。此外我們更預測出螺旋狀二氧化矽奈米線4MR-3f、4MR-4f以及4MR-5f。接著我們利用密度泛函理論來探討二氧化矽奈米線的投影態電子密度(Projected density of states, PDOS)、電子密度差(Electronic density difference)以及Mulliken 電荷，並且將此結果比對塊材石英的幾何結構與電子性質。最後則利用分子動力學來模擬二氧化矽奈米線在溫度10K 下受軸向拉伸應變的影響，可觀察到楊氏係數會隨線徑縮小而增加，而此結果與實驗以及模擬文獻所得結果相同。此外我們利用角度關係函數(Angular correlation function, ACF)來解釋二氧化矽奈米線經拉伸負載後的特徵角度變化。

In this study, we used the molecular statics, molecular dynamics, and density function theory to investigate structural, electronic, and mechanical properties of ultra-thin silica nanowires. There are two parts in this study. In the first part, we used basin-hopping method to get different diameters of silica nanowires, nemed 2MR, 2MR-2O, 3MR-3O, 4MR-4O, 5MR-5O, 4MR-3f, 4MR-4f, and 4MR-5f. The various silica nanowires were optimized by density function theory to obtain the projected density of states, Mulliken charge, and electronic density difference, and we also compared this results to α-quartz. In the second part, the molecular dynamics simulations were performed to investigate deformation behavior of silica nanowires under axial tensile loading at 10K. The Young’s modulus increases when the diameter decreases. We also
used angular correlation function to study the mechanical properties and variation of structures.

中文摘要………………………………………………………………………..I
英文摘要…………………………………………………………….....……...II
目錄…………………………………………………………………………...III
圖次…………………………………………………...…………………….....V
表次…………………………………………………………………….…..VIII
第一章 緒論 .................................................................................................. 1
1.1 研究目的與動機 .............................................................................. 1
1.2 二氧化矽奈米線文獻回顧 .............................................................. 4
1.3 本文架構 .......................................................................................... 8
第二章 模擬方法及理論介紹 ...................................................................... 9
2.1 密度泛函理論 .................................................................................. 9
2.1.1 Thomas-Fermi model (TF model) ......................................... 9
2.1.2 Hohenberg-Kohn model (HK model) .................................. 10
2.1.3 Kohn-Sham equation ........................................................... 10
2.1.4 CASTEP 介紹 ..................................................................... 12
2.2 分子靜力學與分子動力學理論 .................................................... 13
2.2.1 Basin-hopping 計算法 ........................ ……………………13
2.2.2 勢能函數 ............................................................................. 15
2.2.3 運動方程式 ......................................................................... 17
2.2.4 積分法則 ............................................................................. 17
2.2.5 時間步階選取 ..................................................................... 18
2.2.6 溫度修正 ............................................................................. 19
2.3 數值統計方法 ................................................................................ 21
2.3.1 鄰近表列數值方法 ............................................................. 21
2.3.2 原子級應力數值計算 ......................................................... 23
2.3.3 角度關係函數 ..................................................................... 27
第三章 結果與討論 .................................................................................... 28
3.1 二氧化矽奈米線幾何結構與電性分析 ........................................ 28
3.1.1 模擬模型建構 ..................................................................... 28
3.1.2 二氧化矽奈米線幾何結構特性 ......................................... 30
3.1.3 電子態密度與電子密度差分析 ......................................... 39
3.2 以分子動力學探討二氧化矽奈米線之機械性質與動態行為分析
....................................................................................................... 52
3.2.1 物理模型之建構 ................................................................. 52
3.2.2 機械性質與動態行為分析 ................................................. 53
第四章 結論與建議 .................................................................................... 66
4.1 結論 ................................................................................................ 66
4.2 建議與未來展望 ............................................................................ 68
參考文獻 ........................................................................................................ 69

[1] S. Jiang, H. W. Zhang, Y. G. Zheng, and Z. Chen, "Atomistic study of the mechanical response of copper nanowires under torsion", Journal of Physics D-Applied Physics, Vol. 42, p. 135408, 2009.
[2] V. K. Sutrakar and D. R. Mahapatra, "Stress-induced phase transformation and pseudo-elastic/pseudo-plastic recovery in intermetallic Ni-Al nanowires", Nanotechnology, Vol. 20, p. 295705, 2009.
[3] N. L. Netzer, R. Gunawidjaja, M. Hiemstra, Q. Zhang, V. V. Tsukruk, and C. Y. Jiang, "Formation and optical properties of compression induced nanoscale buckles on silver nanowires", Acs Nano, Vol. 3, p. 1795-1802, 2009.
[4] R. K. Joshi, Q. Hu, F. Am, N. Joshi, and A. Kumar, "Au decorated zinc oxide nanowires for CO sensing", Journal of Physical Chemistry C, Vol. 113, p. 16199-16202, 2009.
[5] K. D. Hirschman, L. Tsybeskov, S. P. Duttagupta, and P. M. Fauchet, "Silicon-based visible light-emitting devices integrated into microelectronic circuits", Nature, Vol. 384, p. 338-341, 1996.
[6] Z. G. Wu, J. B. Neaton, and J. C. Grossman, "Charge Separation via strain in silicon nanowires", Nano Letters, Vol. 9, p. 2418-2422, 2009.
[7] F. Marlow, M. D. McGehee, D. Y. Zhao, B. F. Chmelka, and G. D. Stucky, "Doped mesoporous silica fibers: A new laser material", Advanced Materials, Vol. 11, p. 632-636, 1999.
[8] I. Sokolov, H. Yang, G. A. Ozin, and C. T. Kresge, "Radial patterns in mesoporous silica", Advanced Materials, Vol. 11, p. 636-642, 1999.
[9] D. P. Yu, Q. L. Hang, Y. Ding, H. Z. Zhang, Z. G. Bai, J. J. Wang, Y. H. Zou, W. Qian, G. C. Xiong, and S. Q. Feng, "Amorphous silica nanowires: Intensive blue light emitters", Applied Physics Letters, Vol. 73, p. 3076-3078, 1998.
[10] K. W. Jin, B. D. Yao, and N. Wang, "Structural characterization of mesoporous silica nanowire arrays grown in porous alumina templates", Chemical Physics Letters, Vol. 409, p. 172-176, 2005.
[11] S. H. Li, X. F. Zhu, and Y. P. Zhao, "Carbon-assisted growth of SiOx nanowires", Journal of Physical Chemistry B, Vol. 108, p. 17032-17041, 2004.
[12] S. Kar and S. Chaudhuri, "Catalytic and non-catalytic growth of amorphous silica nanowires and their photoluminescence properties", Solid State Communications, Vol. 133, p. 151-155, 2005.
[13] V. A. Sivakov, R. Scholz, F. Syrowatka, F. Falk, U. Gosele, and S. H. Christiansen, "Silicon nanowire oxidation: the influence of sidewall structure and gold distribution", Nanotechnology, Vol. 20, p. 405607, 2009.
[14] S. H. Sun, G. W. Meng, M. A. Zhang, Y. F. Hao, X. R. Zhang, and L. D. Zhang, "Microscopy study of the growth process and structural features of closely packed silica nanowires", Journal of Physical Chemistry B, Vol. 107, p. 13029-13032, 2003.
[15] L. Jin, J. B. Wang, G. Y. Cao, and W. C. H. Choy, "Fabrication and characterization of amorphous silica nanostructures", Physics Letters A, Vol. 372, p. 4622-4626, 2008.
[16] X. J. Wang, B. Dong, and Z. Zhou, "Preparation and photoluminescence of high density SiOx nanowires with Fe3O4 nanoparticles catalyst", Materials Letters, Vol. 63, p. 1149-1152, 2009.
[17] J. C. Knight, T. A. Birks, P. S. Russell, and D. M. Atkin, "All-silica single-mode optical fiber with photonic crystal cladding", Optics Letters, Vol. 21, p. 1547-1549, 1996.
[18] H. R. Luckarift, J. C. Spain, R. R. Naik, and M. O. Stone, "Enzyme immobilization in a biomimetic silica support", Nature Biotechnology, Vol. 22, p. 211-213, 2004.
[19] G. Brambilla and D. N. Payne, "The ultimate strength of glass silica nanowires", Nano Letters, Vol. 9, p. 831-835, 2009.
[20] H. Ni, X. D. Li, and H. S. Gao, "Elastic modulus of amorphous SiO2 nanowires", Applied Physics Letters, Vol. 88, p. 043108, 2006.
[21] K. Zheng, C. C. Wang, Y. Q. Cheng, Y. H. Yue, X. D. Han, Z. Zhang, Z. W. Shan, S. X. Mao, M. M. Ye, Y. D. Yin, and E. Ma, "Electron beam assisted superplastic shaping of nanoscale amorphous silica", Nature Communications, Vol. 1, p. 1-8, 2010.
[22] E. Silva, L. M. Tong, S. Yip, and K. J. Van Vliet, "Size effects on the stiffness of silica nanowires", Small, Vol. 2, p. 239-243, 2006.
[23] T. Zhu, J. Li, S. Yip, R. J. Bartlett, S. B. Trickey, and N. H. De Leeuw, "Deformation and fracture of a SiO2 nanorod", Molecular Simulation, Vol. 29, p. 671-676, 2003.
[24] D. E. Taylor, K. Runge, and R. J. Bartlett, "Study of the effect of hydration on the tensile strength of a silica nanotube", Molecular Physics, Vol. 103, p. 2019-2026, 2005.
[25] E. Silva, J. Li, D. Liao, S. Subramanian, T. Zhu, and S. Yip, "Atomic scale chemo-mechanics of silica: nano-rod deformation and water reaction", Journal of Computer-Aided Materials Design, Vol. 13, p. 135-159, 2006.
[26] L. P. Davila, V. J. Leppert, and E. M. Bringa, "The mechanical behavior and nanostructure of silica nanowires via simulations", Scripta Materialia, Vol. 60, p. 843-846, 2009.
[27] A. K. Singh, V. Kumar, and Y. Kawazoe, "Structure of the thinnest most stable semiconducting and insulating nanotubes of SiOx (x=1,2)", Physical Review B, Vol. 72, p. 155422, 2005.
[28] L. A. Chernozatonskii, V. I. Artyukhov, and P. B. Sorokin, "Silica nanotube multi-terminal junctions as a coating for carbon nanotube junctions", Physical Review B, Vol. 74, p. 045402, 2006.
[29] X. F. Wei, D. J. Zhang, and C. B. Liu, "A DFT study on the hydrolysis stabilities of silica molecular chains and rings based on the two membered rings", Journal of Molecular Structure-Theochem, Vol. 859, p. 1-6, 2008.
[30] P. Hohenberg and W. Kohn, "Inhomogeneous electron gas", Physical Review B, Vol. 136, p. B864, 1964.
[31] W. Kohn and L. J. Sham, "Self-consistent equations including exchange and correlation effects", Physical Review, Vol. 140, p. 1133, 1965.
[32] R. H. Byrd, P. H. Lu, J. Nocedal, and C. Y. Zhu, "A limited memory algorithm for bound constrained optimization", Siam Journal on Scientific Computing, Vol. 16, p. 1190-1208, 1995.
[33] G. N. Vanderplaats, "Numerical Optimization Techniques for Engineering Design: With Applications", McGraw-Hill Book Company, 1984.
[34] S. Tsuneyuki, M. Tsukada, H. Aoki, and Y. Matsui, "First principles interatomic potentail of silica applied to molecular dynamics", Physical Review Letters, Vol. 61, p. 869-872, 1988.
[35] B. W. H. Vanbeest, G. J. Kramer, and R. A. Vansanten, "Force fields for silicas and aluminophosphates based on Ab Initio calculations ", Physical Review Letters, Vol. 64, p. 1955-1958, 1990.
[36] E. Flikkema and S. T. Bromley, "A new interatomic potential for nanoscale silica", Chemical Physics Letters, Vol. 378, p. 622-629, 2003.
[37] O. Teleman, B. Jonsson, and S. Engstrom, "A molecular-dynamics simulation of a water model with intramolecular degrees of freedom", Molecular Physics, Vol. 60, p. 193-203, 1987.
[38] S. Nose, "A unified formulation of the constant temperature molecular-dynamics methods", Journal of Chemical Physics, Vol. 81, p. 511-519, 1984.
[39] W. G. Hoover, "Canonical dynamics - equilibrium phase-space distributions", Physical Review A, Vol. 31, p. 1695-1697, 1985.
[40] N. Chandra, S. Namilae, and C. Shet, "Local elastic properties of carbon nanotubes in the presence of Stone Wales defects", Physical Review B, Vol. 69, p. 094101, 2004.
[41] N. Tokita, M. Hirabayashi, C. Azuma, and T. Dotera, "Voronoi space division of a polymer: Topological effects, free volume, and surface end segregation", Journal of Chemical Physics, Vol. 120, p. 496-505, 2004.
[42] D. Srolovitz, K. Maeda, V. Vitek, and T. Egami, "Structural defects in amorphous solids statistical analysis of a computer model", Philosophical Magazine a-Physics of Condensed Matter Structure Defects and Mechanical Properties, Vol. 44, p. 847-866, 1981.
[43] J. F. Lutsko, "Stress and elastic constants in anisotropic solids: Molecular dynamics techniques", Journal of Applied Physics, Vol. 64, p. 1152-1154,
1988.
[44] K. S. Cheung and S. Yip, "Atomic-level stress in an inhomogeneous system", Journal of Applied Physics, Vol. 70, p. 5688-5690, 1991.
[45] N. Miyazaki and Y. Shiozaki, "Calculation of mechanical properties of solids using molecular dynamics method", Jsme International Journal Series a-Mechanics and Material Engineering, Vol. 39, p. 606-612, 1996.
[46] Z. Liu, S. K. Joung, T. Okazaki, K. Suenaga, Y. agiwara, T. Ohsuna, K. Kuroda, and S. Iijima, "Self-assembled double ladder structure formed inside carbon nanotubes by encapsulation of H8Si8O12", Acs Nano, Vol. 3, p. 1160-1166, 2009.
[47] Z. X. Xi, M. W. Zhao, T. He, X. J. Zhang, H. Y. Zhang, Z. H. Wang, K. Y. Hou, Y. C. Fan, X. D. Liu, and Y. Y. Xia, "First-principles identification of two- and four-membered-ring hybrid structures of silica nanorings", Physics Letters A, Vol. 373, p. 4376-4380, 2009.
[48] V. I. Artyukhov and L. A. Chernozatonskii, "Theoretical study of two-dimensional silica films", Journal of Physical Chemistry C, Vol. 114, p. 9678-9684, 2010.
[49] X. Luo, B. Wang, and Y. Zheng, "Microscopic mechanism of leakage currents in silica junctions", Journal of Applied Physics, Vol. 106, p. 073711, 2009.
[50] G. Zhang, X. Li, C. H. Tung, K. L. Pey, and G. Q. Lo, "A nanoscale analysis of the leakage current in SiO2 breakdown", Applied Physics Letters, Vol. 93, p. 022901, 2008.
[51] T. Tamura, S. Ishibashi, S. Tanaka, M. Kohyama, and M. H. Lee, "First-principles analysis of the optical properties of structural disorder in SiO2 glass", Physical Review B, Vol. 77, p. 085207, 2008.
[52] T. Tamura, G. H. Lu, R. Yamamoto, and M. Kohyama, "First-principles study of neutral oxygen vacancies in amorphous silica and germania", Physical Review B, Vol. 69, p. 195204, 2004.
[53] Q. Sun, Q. Wang, Y. Kawazoe, and P. Jena, "Soft breakdown of an insulating nanowire in an electric field", Nanotechnology, Vol. 15, p. 260-263, 2004.
[54] J. Robertson, "Band offsets of wide-band-gap oxides and implications for future electronic devices", Journal of Vacuum Science & Technology B, Vol. 18, p. 1785-1791, 2000.
[55] C. Bosio, W. Czaja, and H. C. Mertins, "VUV reflectivity of crystalline alpha-SiO2 and of amorphous SiO2", Europhysics Letters, Vol. 18, p. 319-324, 1992.
[56] L. Levien, C. T. Prewitt, and D. J. Weidner, "Structure and elastic properties of quartz at pressure", American Mineralogist, Vol. 65, p. 920-930, 1980.
[57] R. B. Laughlin, J. D. Joannopoulos, and D. J. Chadi, "Bulk electronic structure of SiO2", Physical Review B, Vol. 20, p. 5228-5237, 1979.
[58] B. Fischer, R. A. Pollak, T. H. Distefano, and W. D. Grobman, "Electronic structure of SiO2, SiXGe1-XO2, and GeO2 from photoemission spectroscopy", Physical Review B, Vol. 15, p. 3193-3199, 1977.