Metallic and Semiconducting
Properties of Carbon Nanotubes
by Egill Skúlason
Modern Physics, Nov 2005
CAMP, nanoDTU, Department of Physics, DTU
Contents
• Fullerenes
– Structure of e.g. C60 & Carbon Nanotubes (CNT)
– History
• Metals, Semiconductors & Insulators
– Band Gaps & Fermi Level
– Graphite is Semimetal, SWNT: Metals or Semiconductors
• Single-Wall NanoTubes (SWNT)
– Vector Notation, Atomic Structure
– Electronic Structure
– Magnetic Magic
• Electronic Transport in SWNT
– Metallic & Semiconducting SWNT
– Field Effect Transistor
• Summary
2
Fullerence & CNT
d: 1 - 10 nm, L: up to many µm
L/d can be as large as 104-105 ⇒ 1D
3
From presentation by C. Dekker at the Conference on Disorder and Interaction Quantum Hall and Mesoscopic Systems (1998)
History of CNT and C60
4
From presentation by D. Zhang & C-L Lin, Carbon Nanotubes (2003)
CNT and C60: Old Materials
First to make CNT and C60:
Neanderthals (230 to 29 thousand years ago)
Buckyball, C60
Carbon NanoTube
Could control fire
Candle’s soot
contains some
amount of fullerenes
(e.g. C60 & CNT)
5
Contents
• Fullerenes
– Structure of e.g. C60 & Carbon Nanotubes (CNT)
– History
• Metals, Semiconductors & Insulators
– Band Gaps & Fermi Level
– Graphite is Semimetal, SWNT: Metals or Semiconductors
• Single-Wall NanoTubes (SWNT)
– Vector Notation, Atomic Structure
– Electronic Structure
– Magnetic Magic
• Electronic Transport in SWNT
– Metallic & Semiconducting SWNT
– Field Effect Transistor
• Summary
6
Band Gaps & Fermi Level of Materials
Conduction band - The first unfilled energy level at T = 0 K (LUMO for molecules)
Valence band - The last filled energy level at T = 0 K (HOMO for molecules)
7
Britney's Guide to Semiconductor Physics, britneyspears.ac
Fermi-Dirac Distribution Changes with T
Doping of Semiconductors
Fermi-Level & Doping of
Semicontuctors
8
B.V. Zeghbroeck, Principles of Semiconductor Devices, Colarado University, ece-www.colorado.edu/~bart/
Metal, Semiconductor and Semimetal
Metals:
Conduct electricity
easily because many ehave easy access to
adjacent conduction
states
Semiconductors:
e- need an energy boost
from light or an
electrical field to jump
the gap to the first
available conduction
state
Graphite:
Semimetal that just
barely conducts. Only a
few electrons can access
the narrow path to a
conduction state
9
P.G. Collins & P. Avouris, Nanotubes for Electronics, Scientific American (2000)
SWNT: Metals or Semiconductors
Electronic Energy varies with the Wavevector
Fermi level = 0
a) armchair (5,5) nanotube
b) zigzag (9,0) nanotube
Infinitesimally small amount
of energy is needed to excite
an electron into an empty
excited state
⇒
metallic
A small increase in diameter
has a major impact on the
conduction properties of
carbon nanotubes.
c) zigzag (10,0) nanotube
A finite band gap between the
occupied and empty states
⇒
semicontucor
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physicsweb.org
Contents
• Fullerenes
– Structure of e.g. C60 & Carbon Nanotubes (CNT)
– History
• Metals, Semiconductors & Insulators
– Band Gaps & Fermi Level
– Graphite is Semimetal, SWNT: Metals or Semiconductors
• Single-Wall NanoTubes (SWNT)
– Vector Notation, Atomic Structure
– Electronic Structure
– Magnetic Magic
• Electronic Transport in SWNT
– Metallic & Semiconducting SWNT
– Field Effect Transistor
• Summary
11
Vector Notation
Chiral vector:
Ch = OA = na1 + ma2 ≡ (n,m)
(n, m are integers, 0 ≤ |m| ≤ n)
a1 & a2 are unit vektors
Chiral angle θ is defined as the
angle between the vectors Ch and
a1, with 0 ≤ |θ| ≤ 30° because of the
hexagonal symmetry of the
honeycomb lattice
Rule: n - m = 3i
⇒ Metallic if i is integer
⇒ Semicontuctor if i is non-integer
metal
semiconductor
M.S. & G. Dresselhaus, P. Avouris,
Carbon Nanotubes, Springer (2001)
12
Structure of SWNT
Direction of the 6-membered ring can be taken
almost arbitrarily. No distortion of the hexagons.
Only distortion due to the curvature of the CNT.
armchair
(n,n)
θ = 30˚
zigzag
(n,0)
θ = 0˚
chiral
(n,m)
0 < θ < 30˚
Chiral molecule:
Not identical to its
mirror image
Cannot be mapped to
its mirror image by
rotations and
translations alone
hemisphere
na1 + ma2 ≡ (n,m)
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R. Saito, G. & M.S. Dresselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press (2003)
Tutorial on Electronic Transport, Jesper Nygaard, Niels Bohr Institude, University of Copenhagen
DOS (sest
ekki)
DOS:
number of
available states
per unit volume
per unit energy
14
Electronic Structure
STM of Metallic & Semiconducting CNT
15
Cees Dekker, Physics Today (1999)
Magnetic Magic
a)
Magnetic field introduces a phase
factor to the electron wavefunction
in the circumferential direction.
As a result, the electronic
properties of a nanotube can be
modulated by a magnetic field.
b) The energy spectrum is a plot of
energy (E) versus wavevector (k).
As the magnetic flux increases the
energy-band structure of the
nanotube oscillates from that of a
metal to that of a semiconductor.
16
J.Kong, L.Kouwenhoven & C. Dekker, Quantum change for nanotubes, Physics in Action (2004)
Contents
• Fullerenes
– Structure of e.g. C60 & Carbon Nanotubes (CNT)
– History
• Metals, Semiconductors & Insulators
– Band Gaps & Fermi Level
– Graphite is Semimetal, SWNT: Metals or Semiconductors
• Single-Wall NanoTubes (SWNT)
– Vector Notation, Atomic Structure
– Electronic Structure
– Magnetic Magic
• Electronic Transport in SWNT
– Metallic & Semiconducting SWNT
– Field Effect Transistor
• Summary
17
a) Conductance Measurements
of Different Nanotubes
b) DOS for Different
Nanotubes
c) Energy Gap varying with
the Diameter
18
Presentation by Cees Dekker at the Conference on Disorder and Interaction Quantum Hall and Mesoscopic Systems (1998)
19
Presentation by Cees Dekker at the Conference on Disorder and Interaction Quantum Hall and Mesoscopic Systems (1998)
Field Effect Transistor
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Presentation by Cees Dekker at the Conference on Disorder and Interaction Quantum Hall and Mesoscopic Systems (1998)
Summary
• The vector notation, atomic structure and the electronic
structure of SWNT has been explained.
• SWNT are either chiral or achiral molecules and the cirality
of the nanotubes affects the properties.
• SWNT can either have metallic properties or semiconducting
properties. That can be seen by both calculations and
experiments of the Density of State around the Fermi level.
• Magnetic field can change conduction properties of SWNT,
varying them from being metallic to semiconducting and vice
versa.
• It is possible to use SWNT to make a Field Effect Transistor.
By applying a different gate voltage, one can change the
conduction by many orders of magnitude. Carbon nanotubes
could be used in molecular electronics in the future.
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