An exciton is a bound electron-hole pair that forms in semiconductors and insulators, influencing optical properties.An exciton is a quasiparticle (collective excitation) representing a bound state of an electron and a hole in a semiconductor or insulator. The Coulomb attraction between them leads to the formation of hydrogen-like energy levels. The binding energy of an exciton ranges from a few meV to tens of meV, comparable to thermal energy at room temperature, but in wide-bandgap materials it can reach ~0.1 eV. Excitons come in two types: Wannier-Mott (weakly bound, radius of tens of nanometers) and Frenkel (tightly bound, on the order of the unit cell size).
The concept of an exciton was introduced by Yakov Frenkel in 1931 to explain photoconductivity in dielectrics. He proposed that an absorbed photon does not immediately create free charge carriers but transfers an electron to an excited state that remains bound to a hole. In 1937, Gregory Wannier and Nevill Mott developed a model for semiconductors with high dielectric constant, where the exciton radius spans many atomic layers (Wannier-Mott excitons). In the 1950s, experimental confirmation came from absorption spectroscopy of semiconductor crystals. Later, with the advent of nanotechnology, excitons became a key object in the physics of quantum dots and two-dimensional materials.
When a photon with energy exceeding the band gap is absorbed, an electron transitions from the valence band to the conduction band, leaving a hole. According to Coulomb's law, an attraction arises between them with potential V(r) = -e²/(4πεε₀r). The quantum mechanical solution of this problem in the effective mass approximation yields a hydrogen-like spectrum of binding energies: E_n = -R*/n², where R* = μe⁴/(2(4πεε₀)²ħ²) is the effective Rydberg constant. The exciton can move freely through the crystal as a whole, carrying energy. Recombination of the electron and hole results in the emission of a photon, often with energy less than the band gap by the binding energy. In low-dimensional systems (quantum wells, dots), the role of Coulomb interaction increases, stabilizing excitons.
Excitons determine the emission color of LEDs and the efficiency of light absorption in solar cells.
Excitons can exist in liquid helium and even form a Bose-Einstein condensate at ultralow temperatures, exhibiting quantum properties at the macroscopic level.



















