What is an excition? What are key parameters to describe an exciton?
An exciton is a bound state of an electron and a hole in an insulator (or semiconductor), or in other words, a Coulomb correlated electron/hole pair. It is an elementary excitation of a solid. A vivid picture of exciton formation is as follows: a photon enters a semiconductor, exciting an electron from the valence band into the conduction band. The missing electron in the valence band leaves a hole behind, of opposite electric charge, to which it is attracted by the Coulomb force. The exciton results from the binding of the electron with its hole; as a result, the exciton has slightly less energy than the unbound electron and hole. The wavefunction of the bound state is hydrogenic (an "exotic atom" state akin to that of a hydrogen atom). However, the binding energy is much smaller and the size much bigger than a hydrogen atom because of the effects of screening and the effective mass of the constituents in the material. Excitons can be treated in two limiting cases, which depend on the properties of the material in question. In semiconductors, the dielectric constant is generally large, and as a result, screening tends to reduce the Coulomb interaction between electrons and holes. The result is a Mott-Wannier exciton, which has a radius much larger than the lattice spacing. As a result, the effect of the lattice potential can be incorporated into the effective masses of the electron and hole, and because of the lower masses and the screened Coulomb interaction, the binding energy is usually much less than a hydrogen atom, typically on the order of 0.1 eV. This type of exciton was named for Sir Nevill Francis Mott and Gregory Wannier. In insulators, excitons tend to be much smaller, of the same order as the unit cell, so the electron and hole sit on the same site. This is a Frenkel exciton, named after J. Frenkel. The probability of the electron falling into (annihilating with) the hole is...
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