Chapter 4 Properties of nanomaterials
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Frenkel excitons<br />
In materials with a small dielectric constant, the Coulomb interac;on between electron and<br />
hole may be strong and the excitons thus tend to be small, <strong>of</strong> the same order as the size <strong>of</strong> the<br />
unit cell. Molecular excitons may even be en;rely located on the same molecule, as in<br />
fullerenes. In these cases, the electron and hole lie within the same unit cell. This Frenkel<br />
exciton, named aver Yakov Frenkel, has a typical binding energy on the order <strong>of</strong> 0.1 to 1 eV.<br />
Frenkel excitons are realized in alkalihalide crystals and in organic molecular crystals<br />
composed <strong>of</strong> aroma;c molecules. Anthracene, Tetracene, Pentacene, Phenanthrene,<br />
Porphyrin, Phenazine, PTCDA,etc<br />
Wannier-Mot excitons<br />
In semiconductors, the dielectric constant is generally large. Consequently, electric field<br />
screening tends to reduce the Coulomb interac;on between electrons and holes. The result is<br />
a Wannier exciton, which has a radius larger than the lajce spacing. As a result, the effect <strong>of</strong><br />
the lajce poten;al can be incorporated into the effec;ve masses <strong>of</strong> the electron and hole.<br />
Likewise, because <strong>of</strong> the lower masses and the screened Coulomb interac;on, the binding<br />
energy is usually much less than a hydrogen atom, typically on the order <strong>of</strong> 0.01eV. This type<br />
<strong>of</strong> excitons are typically found in semiconductor crystals with small energy gaps and high<br />
dielectric constant, but have also been iden;fied in liquids, such as liquid xenon. In single-wall<br />
carbon nanotubes, excitons have both Wannier-Mot and Frenkel character.