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

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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.