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Carbon NanotubesMaterials

Allotropes of Carbon

Diamond, graphite, lonsdalerite, C60, C70, carbon, amorphous carbon, carbon nanotube

Carbon Nanotube (CNT)SWNT Single Wall is 1 atom thick

MWNT, Multi-walled is more than 1 atom thick

Typical diameter: 1 nm

Shown is zip-zag CNT

Note hemispherical cap

Chirality1. Pick an atom (A) on a blue

line and draw armchair vector to other blue line.

2. Find the atom on the other edge closest to the armchair intersection. Connect A & B w chiralvector R (red). Wrapping angle is angle between armchair and chiral vectors.

3. Cut tube parallel to axis, The edges correspond to the blue lines

4. a1 lines along zig-zag line. a2 is reflection of a1 about armchair vector.

5. na1 + ma2 = ROrgin: www.pa.msu.edu/cmp/csc/ntproperties/equilibriumstructure.html

CNT Geometry

(n,n) armchair vector (n,0) zigzag vector

DIAMETER CNT

2 23( )CCC ad m mn nπ π

= = + +

1 3tan2

nm n

− ⎡ ⎤Θ = ⎢ ⎥+⎣ ⎦

aCC = 0.142 nm C-C bond length

a = sqrt[3]aCC = 0.249 nm length unit vector

Importance of CNT Chirality

• Effects: conductance, density, lattice structure, and other properties.

• Metallic if n - m is divisible by three. Otherwise, semiconducting.

• CNT diameter: d = (n2 + m2 + nm)1/2 0.0783 nm

Bandgap CNTEgap=2 y0 acc / d

Where:y0 = C-C bonding energy [2.7 ev]

acc = nearest neighbor distance [0.142nm]

d = CNT diameter

Density of States

Source: http://www.pa.msu.edu/cmp/csc/ntproperties/opticalproperties.html

Metallic vs Semiconductor CNTs

m=n metallic

n-m = 3i semimetallic

n = m ≠ 3i semiconducting

CNT Bandgap - Crystalline

0.9( )( )gE eV

d nm=

0

0

2 1 ( 1) 2 cos(3 )

2.53 0.43 2 3

pCC CCa aEgd d

eV p n m i

γ β θ

γ β

⎡ ⎤= + −⎢ ⎥⎣ ⎦= = = − −

Simple formula

More accurate

Bandgap Amorphous CNT

2

23

1

32

(2 10 ),

(1600 )

CCC

C

aEg md

m mass of carbon g

average phonon energy cm

ω

ω

−

−

= < >

=

< > =

Amorphous vs Crystalline

CNT Electron Transport• Ballistic

conductor• Resistivity

CNT robes 10-4 Ω-cm

• Max current density > 1013 amp/cm2

Source: Stefan Frank, Science 280, 1744 (1988)

Gated pn Junction

Intrinsic conductivity type = p n-type by vapor exposure