Chapter 4 Properties of nanomaterials

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