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
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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
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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)
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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
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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
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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 10
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
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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)
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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
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Electronic Structure STM of Metallic & Semiconducting CNT
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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.
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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
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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
20 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. 21
