Excitons

An exciton is a bound state of an electron in the conduction band and a hole in the valence band of a crystal, held together by Coulomb attraction. It is a quasiparticle that can transport energy without net charge transport. Excitons are created when a material absorbs a photon with energy above the bandgap or by electrical excitation.

Two main classes exist: Frenkel excitons and Wannier-Mott (or Wannier) excitons. Frenkel excitons are tightly bound and localized on a single lattice site or molecule, with radii on the order of a lattice constant and binding energies around 0.1–1 eV; they dominate in organic molecular crystals and some insulators. Wannier-Mott excitons have much larger radii, extending over many unit cells, with binding energies in the meV range and are common in inorganic semiconductors with high dielectric screening, such as GaAs, CdS, and transition-metal dichalcogenides.

The effective-mass hydrogenic model describes Wannier-Mott excitons, with binding energy E1 = μ e^4 /(2 (4π ε0 ε)^2 ħ^2) and radius aX ≈ ε ħ^2 /(μ e^2), where μ is the reduced effective mass and ε the dielectric constant. In practice, screening and band structure modify these values.

Excitons influence optical properties by producing sharp absorption and emission features near the band edge. They can diffuse through a crystal over a characteristic exciton diffusion length and recombine radiatively, emitting photons. In some systems, strong coupling between excitons and photons leads to exciton-polaritons in microcavities; these can show Bose-Einstein-like condensation at elevated temperatures under suitable conditions.

In devices, excitons are central to the operation of light-emitting diodes, solar cells, and certain sensors; their dissociation into free carriers is critical for photovoltaic performance, while their recombination determines emission efficiency.