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研究生： 林明寬
Lin, Ming-Kuan
論文名稱： 奈米碳管電極之間分子結的電子傳輸研究
Electron Transport Study of Molecular Junctions in between Carbon Nanotube Electrodes
指導教授： 陳穎叡
學位類別： 碩士
Master
系所名稱： 物理學系
Department of Physics
論文出版年： 2017
畢業學年度： 105
語文別： 英文
論文頁數： 55
中文關鍵詞： 奈米碳管 、分子結 、緊密束縛模型 、第一原理
英文關鍵詞： carbon nanotube, molecular junction, tight-binding model, ab initio
DOI URL： https://doi.org/10.6345/NTNU202202651
論文種類： 學術論文
相關次數： 點閱：122  下載：5 
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    • 本篇論文以斜切的armchair奈米碳管(carbon nanotube)作為分子結(molecular junction)中的電極。使用緊密束縛模型(tight-binding model)計算斜切的armchair奈米碳管、直切的armchair奈米碳管和直切的zigzag奈米碳管從表面到內部的局域態密度(local density of states)。直切的armchair奈米碳管和直切的zigzag奈米碳管的每一層局域態密度分別顯示三層循環的週期性振盪和局域的邊緣態(edge state)。斜切的armchair奈米碳管不只具有週期性振盪，也具有局域的邊緣態。在局域態密度的研究之後，我們把一條或兩條多烯(polyene)接在兩個斜切的armchair奈米碳管之間作為分子結。使用緊密束縛模型和第一原理(ab initio)方法研究分子結的電子傳輸性質。One-polyene分子結在費米能量(Fermi energy)的傳輸(transmission)數值接近1，所以它恢復了一條電子傳輸通道。Two-polyene分子結在費米能量的傳輸數值在0和2之間變化，所以它顯示了干涉效應。儘管緊密束縛模型和第一原理的結果大致相同，但是從這兩種方法得到的結果還是有不一致之處。藉由調整緊密束縛模型中參數的大小，研究分子結的傳輸性質如何變化。我們發現分子結的傳輸性質會受到來自於分子內的鍵結(intra-molecular bonding)強度、耦合(coupling)強度和on-site energy的影響。

    In the thesis, we study the angled-cut armchair carbon nanotubes (CNTs) taken as the electrodes in a molecular junction. Using a one-parameter tight-binding model, we investigate the local density of states (LDOS) from the edge to the interior of the angled-cut armchair CNTs, and similarly for the cross-cut armchair CNTs and the cross-cut zigzag CNTs. We find the periodic oscillation of a 3-layer-cycle and the localized edge states from the layer-by-layer LDOS of the cross-cut armchair CNTs and the cross-cut zigzag CNTs, respectively. The angled-cut armchair CNTs possess not only the periodic oscillation but also the localized edge states. Following the LDOS study, we consider one or two polyenes bridging two angled-cut armchair CNTs as our molecular junction system. We use both the tight-binding model and the ab initio approach to study the electronic transport properties of these molecular junctions. For the one-polyene cases where the polyene has odd number of carbon atoms, the value of the transmission reaches one at the Fermi energy, meaning that one electronic channel is restored by the polyene. For the two-polyene cases, the value of the transmission varies between zero and two at the Fermi energy, which shows the interference effect. Despite the qualitative agreement between the tight-binding and the ab initio results, we look into the discrepancies between the transmissions obtained from the two methods. Tuning the magnitude of the parameters in the tight-binding model, we investigate the corresponding responds in the transmission. We find that the transmission of the molecular junction suffers the influences from the intra-molecular bonding strength, the coupling strength, and the on-site energy.

    致謝 i 摘要 ii Abstract iii Chapter 1 Introduction 1 Chapter 2 Theory 3 2.1 Quantum transport 3 2.1.1 Green’s function 3 2.1.2 Surface Green’s function 4 2.1.3 Density matrix 5 2.1.4 Transmission function 6 2.2 Density functional theory (DFT) 7 2.3 Quantum transport calculations using Nanodcal 9 2.3.1 Two-probe device model 9 2.3.2 The procedure of the lead calculation in Nanodcal 9 2.3.3 Boundary condition 10 2.3.4 Green’s function of the scattering region 11 2.3.5 Density matrix of the scattering region 12 Chapter 3 Method 14 3.1 The layer-by-layer LDOS of the semi-infinite carbon nanotube 14 3.1.1 Introduction to the system 14 3.1.2 Calculation using the tight-binding model 16 3.2 The transmission of the polyene junctions in between angled-cut armchair carbon nanotube leads 18 3.2.1 Introduction to the system 18 3.2.2 Tight-binding model calculations 21 3.2.3 Ab initio calculations 22 3.2.4 The contributions from the even and odd channels in the two-polyene junctions 24 Chapter 4 Result and Discussion 26 4.1 The semi-infinite carbon nanotube 26 4.1.1 The LDOS of the outermost layer 26 4.1.2 The layer-by-layer LDOS at the Fermi energy 33 4.2 The polyene junctions in between angled-cut armchair carbon nanotube leads 38 4.2.1 The band structure and the transmission of the armchair carbon nanotube bulk 38 4.2.2 The transmission of the polyene junctions in between angled-cut armchair carbon nanotube leads 40 4.3 The discrepancy of the transmission between the tight-binding model and the ab initio 44 4.3.1 The intra-molecular hopping energy 45 4.3.2 The contact coupling 46 4.3.3 The unbalanced contact couplings 47 4.3.4 The on-site energy 48 Chapter 5 Conclusion 53 References 54

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