ece440—nanoelectronicszyang/teaching/20192020fallece440/downloads/10.pdfece440—nanoelectronics...
TRANSCRIPT
Carbon nanotubes (Part I)Geometric and Band Structures
ECE440—Nanoelectronics
Zheng Yang
Department of Electrical and Computer Engineering
University of Illinois at Chicago
2
Dimensionality & Nanostructures
ρ3D(E)
Bulk Quantum Walls Quantum Wires Quantum Dots
Energy Energy Energy Energy
ρ1D(E)ρ2D(E) ρ0D(E)
ρ3D(E) ~ E1/2 ρ2D(E) ~ E0 ρ1D(E) ~ E-1/2 ρ0D(E) ~δ(E)
Fullerene (C60)Carbon Nanotube
Graphene
Graphite(Discovered in 1985)(1996 Nobel Prize
in Chemistry)
(Discovered in 1991 &1993) (on
the waiting list for Noble Prize)
(Discovered in 2004)(2010 Nobel Prize
in Physics)(Ancient times)Diamond
Discovery of Carbon Nanotube
4
Discovery of Carbon Nanotubes
Multi-Walled CNTsby
Sumio Iijima, NEC Lab, Japan,1991
Single-Walled CNTs (SWNTs)by
Sumio Iijima’s group, NEC Lab, Japan [Nature 363, 603 (1993)]
& Donald Bethune’s group,
IBM Lab, US, [Nature 363, 605 (1993)] Sumio Iijima and his HRTEMDiscovery of Single-Walled CNTs
Nature 363, 603 (1993)
5
Discovery of Carbon Nanotubes
Multi-Walled CNTsby
Sumio Iijima, NEC Lab, Japan,1991
Single-Walled CNTs (SWNTs)by
Sumio Iijima’s group, NEC Lab, Japan [Nature 363, 603 (1993)]
& Donald Bethune’s group,
IBM Lab, US, [Nature 363, 605 (1993)] Sumio Iijima and his HRTEMDiscovery of Multi-Walled CNTs
Nature 354, 56 (1991)Discovery of Single-Walled CNTsNature 363, 603 (1993)
6
Discovery of Carbon Nanotubes
Multi-Walled CNTsby
Sumio Iijima, NEC Lab, Japan,1991
Single-Walled CNTs (SWNTs)by
Sumio Iijima’s group, NEC Lab, Japan [Nature 363, 603 (1993)]
& Donald Bethune’s group,
IBM Lab, US, [Nature 363, 605 (1993)] Sumio Iijima and his HRTEMDiscovery of Multi-Walled CNTs
Nature 354, 56 (1991)Discovery of Single-Walled CNTsNature 363, 603 (1993)
Extraordinary Properties of Carbon Nanotubes
8
Properties and Synthesis of Carbon Nanotubes
They are stronger than steel, but the most important uses for these threadlike macromolecules may be in faster, more efficient and more durable electronic devices.—”Science American”
They can behave like metals or semiconductors, can conduct electricity better than copper, can transmit heat better than diamond, and they rank among the strongest materials known. —”Physics World”
(1) Arc-Discharge, (2) Pulsed Laser Deposition (PLD), (3) Chemical Vapor Deposition (CVD).
9
Applications of CNTs——Beyond Electronics
10
Applications of CNTs ——Beyond Electronics (continued)
Geometric/crystal structure of carbon nanotubes
12
Lattice of Graphene
Å42.1cca
13
Geometric Structure of Carbon Nanotubes
Ch
21 aaC mnh Chiral Vector
ccamnmn
d
)(3 22
)(3
arctgmn
mnÅ42.1cca
14
Cylindrical Boundary condition of Carbon Nanotube
Periodic Boundary Conditions of CNs)Z(2 qqh Ck
ji
aaC
amnamn
mnh
)(21)(
23
21
)Z(4)()(3 qqakmnakmn yx
Å46.23 ccaa
jia
jia
223
223
2
1
aa
aa
Band structure of carbon nanotubes
16
Band Structure of Graphene
)2
3cos()2
cos(4)2
(cos41)( 20
akakakE xyyn
graphene k
17
Band Structure of Carbon Nanotube
Periodic Boundary Conditions of CNs)Z(2 qqh Ck
ji
aaC
amnamn
mnh
)(21)(
23
21
)Z(4)()(3 qqakmnakmn yx
)(2)(4
cos2
cos42
cos41)( 20 mn
akmnqakakkE yyy
yqtube
2
3cos)(2
3)(4cos4)(2
3)(4cos41)( 20
akmn
akmnqmn
akmnqkE xxxx
qtube
or
Employing the energy dispersion of graphite
18
Band Structure of ArmchairCarbon Nanotube (1)
)(2)(4
cos2
cos42
cos41)( 20 mn
akmnqakakkE yyy
yqtube
)2,,1(
cos2
cos42
cos41)( 20
nq
nqakak
kE yyy
qarmchair
Armchair Carbon Nanotubes: n = m
19
Band Structure of ArmchairCarbon Nanotube (2)
0.0 0.2 0.4 0.6 0.8 1.0
-3
-2
-1
0
1
2
3
E( 0)
ky( / a)0.0 0.2 0.4 0.6 0.8 1.0
-3
-2
-1
0
1
2
3
E( 0
)
ky ( / a)
(5, 5) (6, 6)
All armchair CNTsare Metallic!
20
Band Structure of ZigzagCarbon Nanotube (1)
Periodic Boundary Conditions of Zigzag CNTs
)Z(2 qqh Ck
jaC nanh 1
)Z(2 qqnaky
Å46.23 ccaa
jia
ja
223
2
1
aaa
21
Band Structure of ZigzagCarbon Nanotube (2)
Zigzag Carbon Nanotubes: m = 0
)2,,1(
23coscos4cos41)( 2
0
nq
aknq
nqkE x
xqzigzag
)2
3cos()2
cos(4)2
(cos41)( 20
akakakE xyyn
graphite k
qanky 2
22
Band Structure of ZigzagCarbon Nanotube (3)
0.0 0.2 0.4 0.6 0.8 1.0
-3
-2
-1
0
1
2
3
E( 0
)
kx)3/( a
(6, 0)
0.0 0.2 0.4 0.6 0.8 1.0
-3
-2
-1
0
1
2
3E( 0
)
kx )3/( a
(7, 0) (8, 0)
0.0 0.2 0.4 0.6 0.8 1.0
-3
-2
-1
0
1
2
3
E( 0
)
kx
(9, 0)
)3/( a)3/( a0.0 0.2 0.4 0.6 0.8 1.0
-3
-2
-1
0
1
2
3
E( 0)
kx
23
Summary
)2,,1(2
3coscos4cos41)( 20 nqak
nq
nqkE x
xqzigzag
)2,,1(cos2
cos42
cos41)( 20 nq
nqakak
kE yyy
qarmchair
)(2)(4
cos2
cos42
cos41)( 20 mn
akmnqakakkE yyy
yqCNT
All Carbon Nanotubes
Armchair Carbon Nanotubes
Zigzag Carbon Nanotubes
24
Semiconducting or Metallic
If n–m=3p, the CNT is metallic, or the CN is semiconducting.
Among all the CNTs, 1/3 are metallic while the other 2/3 are semiconducting.