carbon nanotubes - university of california,...
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![Page 1: Carbon Nanotubes - University of California, Irvinernelson/EECS174-2006/EECS174-LectureNotes-9.pdf · Allotropes of Carbon Diamond, graphite, lonsdalerite, C60, C70, carbon, amorphous](https://reader031.vdocument.in/reader031/viewer/2022021505/5ae7986d7f8b9ae1578f3ce3/html5/thumbnails/1.jpg)
Carbon NanotubesMaterials
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Allotropes of Carbon
Diamond, graphite, lonsdalerite, C60, C70, carbon, amorphous carbon, carbon nanotube
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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
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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
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CNT Geometry
(n,n) armchair vector (n,0) zigzag vector
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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
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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
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Bandgap CNTEgap=2 y0 acc / d
Where:y0 = C-C bonding energy [2.7 ev]
acc = nearest neighbor distance [0.142nm]
d = CNT diameter
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Density of States
Source: http://www.pa.msu.edu/cmp/csc/ntproperties/opticalproperties.html
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Metallic vs Semiconductor CNTs
m=n metallic
n-m = 3i semimetallic
n = m ≠ 3i semiconducting
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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
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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
−
−
= < >
=
< > =
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Amorphous vs Crystalline
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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)
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Gated pn Junction
Intrinsic conductivity type = p n-type by vapor exposure
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