Lecture 5奈米碳管之導電性與導電路徑

共軛結構 – C=C-C=

2D-view ( 骨架式 )

- 電子之共振結構

Isotropic conduction

-electron

捲成管狀後 isotropic conduction 仍然維持

3D-view

-bond (sp2)

-Wave function (electron cloud)

-bond-wave function

價電子雲位於二個碳原子間 , 導電之電子雲位於上下二處

骨架式

120

e-

e-

- 電子可於圓形 3D 空間內運行

- 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

如果重疊區域少 , 電子需藉由 hopping( 或是 tunneling) 方能穿梭

電阻小

電阻大

六連環俯視圖 側視圖

骨架 + 電子雲 ( 形成 3D view)

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

x

y

z

也就是說電子可延三個方向前進

1Å

z

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

x

y

x

y

x

y

無外加電場沿管軸方向外加電場時

E spiral conduction

2D: isotropic conduction ( 骨架式共軛結構 )

碳管之導電路徑

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

Standing wave pattern

Wave function image

STM images

碳管之能帶結構

石墨晶格 1st Brillourin zone

CB

VB

6 k-points

平面圖

3D-view

能量最大

CB joins with VB at k-points

k-point

VB

CB

EF

Above means that if any sub-bands cross at k-points would be metallic natureotherwise tube is a semiconducting property.

One atom one energy level (sub-band) with unpaired electron

Two atoms two energy levels with one bondingand one anti-bonding

bonding

anti-bonding

Three atoms three energy levels with one bonding, one anti-bonding and one unpaired electron

Each sub-band has own velocity and wave vectorIf any of these vectors cross at k-pointsor 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

zigzag edge

armchair

30

: Semiconducting

: metallic

(0,0) (1,0) (2,0) (3,0) (4,0)

(1,1)

(2,2)

(3,3)

(2,1) (3,1) (4,1)

m

n

(n,m) notation

(3,2)

(n,0): zigzag tubes(n,n): armchair tubes(n,m): chiral tubes

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

= 15 = 25

Determination by tube Chirality

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

armchairzigzag

M1/3M, 2/3S

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

STM TIP

Localized state (local Schottky device)

波向量在六連環結構上可來回

波向量不可逆

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

Outermost layer

Innermost layer

電極

e-e-

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 .

M

S

Science,292, 706, 2001

Removal of carbon layers byElectrical breakdown

MS

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

Defect extension

Removal of carbon layer on the order of ms

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).

Summaries

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

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.

Summaries of nanotube resistivity measurements

Temp (k)

R

Positive temp coefficient of resistivity

Negative temp coefficient of resistivity

VG

dI/dV(G) VG independent

VG dependentVG dependent

ll

By Baumgartner et al, PRB, 55, 6704, 1997

Resistivity of CNT films

e-hopping

Resistivity of CNT-polymer composites

CNTs polymer

electrodes1. 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

CNT load

R

Electrical threshold

Adv.Mater, 10, 1091, 1998

Adv.Mater, 11, 937, 1999

Technical challenges for CNTs in polymer

2. Interfacial binding between CNTs and polymers

1. Dispersion of CNTs in polymers

Uneven distribution of CNTs

CNT enriched regions

CNT deficit regions

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 enriched region

CNT deficit regions

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

Polymer coating

凸出

Adv.Mater, 10, 1091, 1998

APL, 76, 2868, 2000

APL, 79, 4225, 2001

2. Treated CNTs + polymers

a. Functionalized CNTs (on tube surfaces)

-OH

=CO

=O

PVA, PVC

Polymers containing amino-acid CH3

親水性疏水性

b. Surfactants

CNT親水性疏水性

polymer