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Exciton (Read 2886 times)
Gerrit-Jan Linker
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Exciton
24.10.09 at 11:08:55
 
Exciton
 
The exciton is a quasi-particle or elementary excitation of a solid.
 
An excition in an insulator or semi-conductor is a bound state of an electron and an imaginary particle, a hole.
Since an exciton is a bound state of an electron and a hole, the overall charge for this quasiparticle is zero. Hence it carries no electric current.
 
The bound electron and hole pairs (excitons) provide a means to transport energy without transporting net charge.
 
The wavefunction of the bound state is hydrogenic. However, the binding energy is much smaller and the size much bigger than a hydrogen atom
 
There are two exciton sub-types:
  • Mott-Wannier exciton
    A Mott-Wannier exciton has a radius much larger than the lattice spacing. In materials with a high dielectric constant (in semi conductors) screening reduces the Coulomb interaction between electrons and holes. Typical binding energy: 0.1 eV.
  • Frenkel exciton
    When a material's dielectric constant is very small, the Coulomb interaction between electron and hole become very strong and the excitons tend to be much smaller, of the same order as the unit cell.
    Typical binding energy: 1 eV

 
Singlet excitons are short-lived (ns) and in some cases might be delicalized over more than one site in molecular crystals.
Triplet excitons are lon-lived (microseconds) and tend to be delocalised on a single site in molecular crystals.
 
Reference:
Exciton at Wikipedia
http://en.wikipedia.org/wiki/Exciton
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« Last Edit: 04.02.11 at 06:59:48 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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Gerrit-Jan Linker
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Coulomb interaction of an exciton
Reply #1 - 16.05.12 at 10:20:09
 
Coulomb interaction of an exciton
 
The hole and electron of an exciton attract and the Coulomb energy is -Ecoul=-e^2/r where e is the electronic charge and r the distance between the hole and the electron. In a material the electron charge is shielded from the hole due to the material that exists in between. Usually this is taken into account by using the dielectric constant to diminish the electronic charge: Ecoul= -e/ε * e/r where ε is the dielectric constant. Strictly speaking this may not be done as ε is a bulk property and r is not of macroscopic dimensions.
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Gerrit-Jan Linker
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