Exciton

An exciton is a bound state of an electron and an imaginary particle called an electron hole in an insulator (or semiconductor), or in other words, a Coulomb correlated electron-hole pair. It is an elementary excitation, or a quasiparticle 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. 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 are thus the main mechanism for light emission in semiconductors at low temperatures (T being less than the exciton binding energy), replacing the free electron-hole recombination at higher temperatures.

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. When a material's dieletric 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, so the electron and hole sit on the same cell. This is a Frenkel exciton, named after J. Frenkel.

The probability of the hole disappearing (the electron occupying the hole) is limited by the difficulty of losing the excess energy, and as a result excitons can have a relatively long lifetime. (Lifetimes of up to several milliseconds have been observed in copper (I) oxide) Another limiting factor in the recombination probability is the spatial overlap of the electron and hole wavefunctions (roughly the probability for the electron to run into the hole). This overlap is smaller for lighter electrons and holes and for highly excited hydrogenic states.

The existence of exciton states may be inferred from the absorption of light associated with their excitation. Typically, excitons are observed just below the band gap. Alternatively, an exciton may be thought of as an excited state of an atom or ion, the excitation wandering from one cell of the lattice to another.

Provided the interaction is attractive, an exciton can bind with other excitons to form a "biexciton", analogous to a hydrogen molecule. If a large density of excitons is created in a material, they can interact with one another to form an electron-hole liquid, a state observed in k-space indirect semiconductors.

Additionally, excitons are integer-spin particles obeying Bose statistics in the low-density limit. In some systems, where the interactions are repulsive, a Bose-Einstein condensed state is predicted to be the ground state, but has yet to be observed due to the influence of factors such as material disorder, short exciton lifetimes (less than the re-thermalization times) and low exciton densities.