Optoelectronics with Carbon Nanotubes

(a) (b)
metallic
Figure I-4. One-dimensional energy dispersion of (a) metallic and (b)
semiconducting SWNTs according to the single-particle interband theory.
Corresponding density of states with van Hove singularities are indicated in green.
In an undoped SWNT at zero temperature, the bands are filled up to the Fermi level
because there is only one extra electron per atom. The energy gap in semiconducting SWNTs
are in the order of 1 eV, meaning that we can expect to see transition effects from electrically or
optically excited carriers across the gap at room temperature. However, the unique
dimensionality of carbon nanotubes has a further consequence that needs to be considered first,
namely, many-body effects.
2. Electron-electron and electron-hole interactions in SWNTs
There are two main effects that significantly modify the single-particle bandgap, Eg,
described in the previous section. One is the electron-electron repulsion, which contributes to
the self energy Eee of the system. The other is the creation of localized electron-hole pairs bound
by the Coulomb attraction, forming hydrogen-like particles called excitons, each with a series of
Rydberg states. The energies of these two effects are both significant fractions of the single-
particle bandgap in one-dimension and considerably affect the electrical and optical excitations
of carriers and emission of photons. Initially the single-particle model served adequately enough
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semiconducting