自西元1991年發現奈米碳管, 由於其獨特的物理、化學及力學特性，引起各界人士廣泛的研究和討論。奈米碳管可看作是由石墨烯層片捲成的奈米尺度空心圓柱，用理論的方法預測了理想奈米碳管之電學特性發現與石墨烯層捲曲的角度及直徑有直接的關係。然而，現今所有製造出來的奈米碳管都存在著各種不同的缺陷。因此其特性往往和之前理論預測有所出入。因此研究存在缺陷的奈米碳管的基本特性，將會是一件非常重要及有趣的事情。從一些理論和實驗都證明，當有空缺陷存在於奈米碳管時，將會造成奈米碳管的結構發生重構現象，進而影響其能帶結構和電子傳輸特性。但是還有很多特性仍是未知的。例如，空缺陷的密度如何造成電性的改變、缺陷間的作用力如何導致電性變化、以及有缺陷的奈米碳管在外加電場下，電性又將是如何的改變。因此在本論文中，我們將應用理論計算，研究存在空缺陷之奈米碳管的能帶結構及電子傳輸特性，並探討利用空缺陷來控制奈米碳管能隙的可行性。希望透過此研究能對未來奈米碳管在電子元件上的應用有所幫助。

1 Introduction 1
2 Overview of Single-Walled Carbon Nanotube 5
2.1 Geometrical Structures of Single-Walled Carbon Nanotube5
2.1.1 Chiral Vector . . . . . . . . . . . . 6
2.1.2 Translation Vector . . . . . . . . . . 7
2.1.3 Reciprocal Lattice Vector. . . . . . . 9
2.2 Electrical Properties of Single-Walled Carbon Nanotubes9
2.3 Structural Defects in Single-Walled Carbon Nanotubes 12
2.3.1 Vacancy Defects . . . .. . . . . . . . 15
2.3.2 Topological Defects . . . . . . . . . 20
3 Density Functional Theory . . . . . . . . . 23
3.1 Density Functional Computational Methods .23
3.1.1 Density Function Approach . . . . . . . 24
3.1.2 Local Density Approximation . . . . . . 26
3.1.3 Bloch’s Theorem . . . . . . . . . . . 27
3.1.4 Plane Wave Basis Set . . . . . . . . . . 28
3.1.5 Supercell Approach . . . . . . . . . . . 28
3.2 CASTEP . . . . . . . . . . . . . . . . . . 29
3.3 Approach . . . . . . . . . . . . . . . . . 30
3.4 Computational Equipment . . . . . . . . . 31
4 Characterization of Vacancy Defects and Defects Interaction 33
4.1 Characterization of an Isolated Vacancy Defect in Zigzag SWNTs 36
4.1.1 Vacancy Defect Density Modeling . . . . . 36
4.1.2 Calculation Methods . . . . . . . . . . . 37
4.1.3 Effect of an Isolated Vacancy Defect . . 37
4.1.4 Conclusion .. . . . . . . . . . . . . . . 43
4.2 Characterization of Vacancy Defects Interaction on the Electric Properties of Zigzag Single-Walled Carbon Nanotube 43
4.2.1 Divacancy Defects Interaction Modeling . . . 44
4.2.2 Calculation Methods . . . . . . . . . . . .. 44
4.2.3 Influence of Vacancy Defects Interaction .. . 45
4.2.4 Conclusion . . . . . . . . . . . . . . . . . 49
4.3 Influence of Vacany Defects Density on Electrical Properties of Armchair Single-Walled Carbon Nanotube 50
4.3.1 Vacancy Defect Density Modeling . . . . .. . 51
4.3.2 Calculation Methods . . . . . . . . . . . . 51
4.3.3 Influence of Vacany Defects Density . . . . 52
4.3.4 Conclusion . . . . . . . . . . . . . . . . 54
5 Defective Carbon Nanotubes Under a Transverse Electrical Field 57
5.1 Zigzag Single-walled Carbon Nanotubes . . . . 58
5.1.1 Model of Zigzag SWNTs under Transverse Electric Field 58
5.1.2 Calculation Methods . . . . . . . . 59
5.1.3 Bandgap Modification . . . . . . . . . . . 60
5.1.4 Conclusion . . . . . . . . . . . . . . . . . 65
5.2 Chiral Single-Walled Carbon Nanotube . . . . . 66
5.2.1 Model of Chiral SWNTs Under Transverse Electric Field . 66
5.2.2 Effect of Vacancy Defect on Electrical Properties 68
5.2.3 Conclusion . . . . . . . . . . . . . . . . 74
6 Summary . . . . . . . . . . . . . .75

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