2012 tus lecture 2
- 2. Lecture 2. Nanocarbon C60, CNT’s Synthesis and e-beam lithography Graphene (synthesis, relativistic QM nature, transport)
- 6. Aligned Carbon Nanotubes AAO template CNT array in AAO CVD @ CAER, Dr. Rodney Andrews Group
- 7. TEM of smallest MWNT We have fabricated CNT arrays in AAO template with varying pore diameter. Our observations indicate that, CNT inner core diameter decreases with decreasing AAO pore diameter, while the wall thickness remains almost the same. AA4 CNT- MWNT with a 2 nm inner diameter
- 9. Graphene
- 11. Obtaining Graphene • Micromechanical cleavage from bulk graphite (on oxidized Si) • Thermal decomposition of 4-H SiC (Si terminated surface) in UHV • Vapor deposition from hydrocarbons (e.g. CVD from xylene as is done for CNT’s) • Pulsed Laser Deposition • Exfoliation by Ultasonification of Graphite and Spin- on Coating • Plasma-enhanced Chemical Vapor Deposition
- 20. A carbon nanotube is a honeycomb lattice rolled up into a cylinder. Although carbon nantoube seems to have a 3D structure, it can be considered as 1D because of their small size, which is in size of nano-order. The specifying of carbon naonotube is very simple. To define the structure, 2 numbers known as the chiral index is used. In Fig. 1, 2 unit vectors, a1 and a2, are defined on the hexagonal lattice. These 2 vectors define the chiral vector Ch, and equation is shown below. Ch= n a1+m a2≡ (n, m), (n, m are integers, 0≤|m|≤n) (n, m) is called the chiral index, or it is just called chirality. The example of (3, 3) is shown in Fig. 2. This chirality is important because it tells the characteristic of a carbon nanotube. For example, if the difference of n and m is the multiple of 3, then that carbon nanotube is metal. If not, it is semiconductor.
- 24. The first two of these, known as “armchair” (top left) and “zig-zag” (middle left) have a high degree of symmetry. The terms "armchair" and "zig-zag" refer to the arrangement of hexagons around the circumference. The third class of tube, which in practice is the most common, is known as chiral, meaning that it can exist in two mirror-related forms. An example of a chiral nanotube is shown at the bottom left. The structure of a nanotube can be specified by a vector, (n,m), which defines how the graphene sheet is rolled up. This can be understood with reference to figure on the right. To produce a nanotube with the indices (6,3), say, the sheet is rolled up so that the atom labelled (0,0) is superimposed on the one labelled (6,3). It can be seen from the figure that m = 0 for all zig-zag tubes, while n = m for all armchair tubes.
- 26. To calculate the band structure of CNT’s, it is useful to discuss graphene first. We’ll then do a simple modification to this calculation for CNT’s.
- 27. Band Structure of Graphene
- 29. a1 a2 Figure 1 Two unit vectors
- 46. Left: Diagram of the Brillouin zone of graphite. Center: Dirac fermions in momentum space near corner H of the Brillouin zone are characterized by a sharply linear Λ-shaped dispersion relation, similar to that found in graphene. Right: As a result of interlayer interactions, other regions of momentum space (near corner K) display a parabola-shaped dispersion, signifying the existence of quasiparticles with finite mass whose energy is quadratically dependent on momentum.
- 66. Schibli group University of Colorado/JILA
- 73. Band Structure of CNT’S
- 79. Other Materials with (Possible) Dirac Fermions
- 80. Left: Diagram of the Brillouin zone of graphite. Center: Dirac fermions in momentum space near corner H of the Brillouin zone are characterized by a sharply linear Λ-shaped dispersion relation, similar to that found in graphene. Right: As a result of interlayer interactions, other regions of momentum space (near corner K) display a parabola-shaped dispersion, signifying the existence of quasiparticles with finite mass whose energy is quadratically dependent on momentum.
- 82. Fig. 3. Electric field effect in single-atomic-sheet crystals Novoselov, K. S. et al. (2005) Proc. Natl. Acad. Sci. USA 102, 10451-10453 Copyright ©2005 by the National Academy of Sciences
- 86. We’ll see in Lecture 6 that MoS2 is useful as a gate in graphene FET’s
- 87. Devices
- 100. Can Graphene be a Superconductor? • Plasmon-mediated SC possible (Uchoa et al) PRL 98 146801 (2007) • Proximity effect supercurrents observed (Heersche et al) Solid State Comm.143, 72 (2007) • SC consistent with LAMH resistive transition theory in Single-walled CNT (Zhao) PRB 71 113404 (2005)