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Lecture 5 奈米碳管之導電性與導電路徑 2D-view (骨架式) 共軛結構 –C=C-C= -電子之共振結構 -electron Isotropic conduction 捲成管狀後isotropic conduction 仍然維持 3D-view -wave function -bond -bond (sp2) 骨架式 -Wave function (electron cloud) 價電子雲位於二個碳原子間, 導電之電子雲位於上下二處 e120 e- -電子可於圓形3D空間內運行 電阻小 -電子雲重疊, 造成電子可於電子雲中自由穿梭, 形成導電路徑 電阻大 如果重疊區域少, 電子需藉由hopping(或是tunneling)方能穿梭 骨架 + 電子雲 (形成3D view) 六連環俯視圖 側視圖 z x 電子可視為電子波, 故具備向量性質 而空間中向量可分成三個分量, x, y, z y 也就是說電子可延三個方向前進 由於波函數(wave function)沿z軸方向只延伸約1Å距離, 故電子波向量 沿z軸方向受限制. 但沿x, y軸方向不受限制 z x 1Å y y y x x 無外加電場 E 沿管軸方向外加電場時 spiral conduction 碳管之導電路徑 2D: isotropic conduction (骨架式共軛結構) 3D: along x (circumference) and y (tube axial) axes conduction without external electric field 3D: spiral conduction occurs when external electric field is applied 電子雲于碳管表面 STM images Standing wave pattern Wave function image 碳管之能帶結構 石墨晶格 1st Brillourin zone 6 k-points CB 3D-view VB 平面圖 能量最大 CB joins with VB at k-points CB k-point EF VB Above means that if any sub-bands cross at k-points would be metallic nature otherwise tube is a semiconducting property. One atom one energy level (sub-band) with unpaired electron anti-bonding Two atoms two energy levels with one bonding and one anti-bonding bonding Three atoms three energy levels with one bonding, one anti-bonding and one unpaired electron Each sub-band has own velocity and wave vector If any of these vectors cross at k-points or intercept EF the nanotube would be a metallic nature. Metallic nature Wave vector Band-gap where a1 and a2 are unit vectors, and n and m are integers. A nanotube constructed in this way is called an (n,m) nanotube Chiral vector = Ch = na1 + ma2 d = (3)1/2aC-C(m2 +mn +n2)1/2/) Where aC-C = 1.42 Å: the nearest neighbor carbon-carbon distance = tan-1[(3)1/2n/(2m+n)] Example: for zigzag tube when = 0 with (n,0) = (9,0), d= 7.05 Å for armchair tube, (n,n) = (5,5), d= 6.83 Å (n,m) notation (n,0): zigzag tubes (n,n): armchair tubes (n,m): chiral tubes m zigzag edge n (0,0) (1,0) 30 (2,0) (1,1) (3,0) (2,1) (4,0) (3,1) (2,2) (4,1) (3,2) (3,3) armchair : Semiconducting : metallic 2n + m = 3q; (q: integer) 為何文獻總是說碳管之電性取決於管徑(tube diameter) 與螺旋性 (chirality) 波向量隨直徑變化而位移 Determination by tube Chirality = 15 = 25 波向量隨管之螺旋性而變化 文獻說不論直徑為何只要nanotubes是armchair edge 均是metallic nature (no band gap) 因為波向量永遠 座落於k-points上 且此六邊形對稱不 隨管直徑而變化 文獻說zigzag nanotube有三分之一會是metallic tube,三分之二是semiconductor Bent Nanotube- Nano-Schottky barrier 1/3M, 2/3S zigzag M armchair 假設為S-M(機率大), 此結構具整流效應, 也就是說電流只能由M流向S 無法回流 zigzag armchair STM tip Localized state (local Schottky device) 波向量不可逆 波向量在六連環結構上可來回 STM TIP Science by C.M. Leiber et al 多層碳管之導電路徑為那一層---每層均可導電, 但一般是最外層, 因為只有最外層與金屬電極接觸 (注意: 電子不可能跳躍層與層之 間距離而由內層跳至外層 Innermost layer 電極 Outermost layer ee- e- 前述碳管電性取決於直徑與螺旋性, 因此多壁碳管有可能 是每層電性不同. S Removal of carbon layers by Electrical breakdown M Science,292, 706, 2001 M S Contribution to total conductance from individual layers Carbon nanotubes can carry electrical current up to 109 A/cm2 So how to remove carbon layers in a vacuum via electrical breakdown? Current induced defect formation Self-heating Removal of carbon layer on the order of ms Defect extension Summaries 1. Alternative electronic property of MWNTs, M-S-M-S 2. Removal of each layer reduces current of 19 A. 3. A MWNT conducts electrical current only at outer-layer where they contact with electrodes. Nevertheless, when MWNTs are modulated at higher bias voltage the inner-layers also contribute to nanotube conductance via inter-layer barriers (thermally activated conduction). 4. Inner layers only contribute limitedly to nanotube conductance, because they have to overcome interlayer barriers of 0.34 nm spacing. 早期量測單根多壁碳管 1. J. Vac.Sci.Tech. B, 13, 327, 1995, by Rivera et al (STM) 2. Syn.Metals. 70, 1393, 1995, by Langer et al (STM + lithographic tech) 3. Nature, 382, 54, 1996, by Ebbesen et al (four terminal + lithographic tech) 4. Science, 272, 523, 1996, by Dai et al (four terminal + lithographic tech) Two terminal method Four terminal method Summaries of nanotube resistivity measurements 1. Averaged resistivity of nanotube tube is 10-4 ~ 10-5 m.(arc made) 2. Resistivity of metallic nanotubes is 10-6 m. (arc made) 3. Resistivity of defective carbon nanotubes is 10-2 ~ 10-3 m. (pyrolysis made) 4. Band gap of semiconducting nanotubes is 0.1 – 2 eV, and is thermally activated type (negative temp coefficient of resistivity), also is gate voltage dependent conductance. 5. Metallic nanotubes are gate voltage independent and positive temp coefficient of resistivity. Negative temp coefficient of resistivity R Positive temp coefficient of resistivity Temp (k) VG dependent dI/dV(G) VG dependent VG independent VG Resistivity of CNT films By Baumgartner et al, PRB, 55, 6704, 1997 ll e-hopping Resistivity of CNT-polymer composites CNTs polymer electrodes 1. Low content of CNT in polymer a. Primary capacitive phase b. High resistance c. No conduction paths between electrodes 2. CNT load increases a. capacitance decreases b. Resistance decrease c. conduction paths begins to establish 3. High CNT load a. Low capacitance b. Low resistance c. Conduction path formation Electrical threshold R Adv.Mater, 10, 1091, 1998 CNT load Adv.Mater, 11, 937, 1999 Technical challenges for CNTs in polymer 1. Dispersion of CNTs in polymers 2. Interfacial binding between CNTs and polymers CNT enriched regions CNT deficit regions Uneven distribution of CNTs Dispersion of CNTs in polymers 1. Lengthy mechanical blending, (ultra-sonicate, magnetic stirring) 2. Surfactant assistant (lowering interfacial strength, so CNTs move easily in polymer solution) surfactant CNT deficit regions CNT enriched region Chem.Mater, 12, 1049, 2000 Interfacial binding between CNTs and polymers Carbon, 40, 1605, 2002 Negative reinforcement 1. Untreated CNTs + polymer A. Weak bonding between nanotube defects and polymer functional groups CH3-CH2-CH2-OH B. Van der waals interaction (polymer chain wrapping around CNT) CPL, 342, 265, 2001 APL,74, 3317, 1999 APL, 73, 3842, 1998 凸出 Polymer coating Adv.Mater, 10, 1091, 1998 APL, 76, 2868, 2000 APL, 79, 4225, 2001 2. Treated CNTs + polymers a. Functionalized CNTs (on tube surfaces) -OH 疏水性 =CO PVA, PVC 親水性 Polymers containing amino-acid CH3 =O b. Surfactants polymer 疏水性 CNT 親水性