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Nanomaterials

Which statement about the structure and properties of graphene is correct?

  1. AIt is a single atomic layer of carbon atoms linked tetrahedrally by sp³ bonds and, like diamond, is an electrical insulator
  2. BIt is a single atomic layer of carbon atoms arranged in hexagons by sp² bonds, but the quantum size effect makes it a semiconductor with a large band gap of 1 eV or more
  3. CIt is a single atomic layer of carbon atoms arranged in a hexagonal (honeycomb) lattice by sp² bonds, with an essentially zero band gap and very high in-plane electron mobility
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Answer: C. It is a single atomic layer of carbon atoms arranged in a hexagonal (honeycomb) lattice by sp² bonds, with an essentially zero band gap and very high in-plane electron mobility

Graphene is a single layer taken from graphite, in which carbon atoms form a honeycomb network of hexagons through strong sp²-hybridized covalent bonds. The conduction and valence bands touch at a single point at the K point (the Dirac cone), so it behaves as a semimetal with an essentially zero band gap, and its carrier mobility is very high even at room temperature. The in-plane sp² bonds are extremely strong, so its in-plane strength, elastic modulus and thermal conductivity are also high. Tetrahedral sp³ bonding and insulating behavior are characteristics of diamond. Also, clean single-layer graphene does not have a band gap on the order of 1 eV; opening a gap requires measures such as cutting it into narrow nanoribbons or applying a perpendicular electric field to bilayer graphene.

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  1. For CdSe quantum dots (bulk band gap 1.74 eV), assume a simple model in which the confinement energy increase is inversely proportional to the square of the radius R, and that it is 0.30 eV for R = 3.0 nm. Which value is closest to the effective band gap of a quantum dot with R = 2.0 nm? Neglect the Coulomb interaction between electron and hole.
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