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If you re-use any material in this presentation, please credit:

If you re-use any material in this presentation, please credit: Michael S. Fuhrer, University of Maryland. -. -. C. -. -. Why is Carbon Unique for Electronics?. Carbon. Graphite. Hexagonal lattice; 1 p z orbital at each site. 4 valence electrons. 1 p z orbital. 3 sp 2 orbitals.

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  1. If you re-use any material in this presentation, please credit: Michael S. Fuhrer, University of Maryland

  2. - - C - - Why is Carbon Unique for Electronics? Carbon Graphite Hexagonal lattice; 1 pz orbital at each site 4 valence electrons 1 pz orbital 3 sp2 orbitals Fundamental question: Is graphite a metal or a semiconductor?

  3. ε Solid State Physics in One Dimension 1 orbital (doubly degenerate) 1 atom 1 electron Ten atoms: Energy Levels: Excited state; Energy ε above ground state “metallic” Ground state: Fill lowest five (doubly degenerate) levels

  4. Eg Solid State Physics in One Dimension 1 orbital (doubly degenerate) 1 atom 1 electron Dimerization can lower energy: Energy Levels: Dimerization creates two bands Electrons fill lower band “semiconducting” Excited state costs energy Eg

  5. Graphite: Atoms or Dimers? Graphite: Metallic in some directions, Semiconducting in others! Atomic chain: metallic Dimer chain: semiconducting

  6. Rolling up graphene into a tube… Graphics courtesy Rick Smalley • Pick a lattice vector in graphite • Cut out a strip perpendicular • to that vector • Roll up the strip • to form a tube!

  7. Nanotubes: Metallic or Semiconducting? Metallic Semiconducting Whether nanotube is metallic or semiconducting… …depends on how nanotube is wrapped.

  8. kr krR = n (integer) Momentum around circumference is quantized Δ ~ 350 meV/[d(nm)] vF~ 9.3 x 107 cm/s E E 3Δ 0 -3Δ 2Δ Δ 0 -Δ -2Δ k k Metal Nanotube Band Structure E2 = (ħvFk)2 Semiconductor E2 = Δ2 + (ħvFk)2

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