exciton

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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).

History

The concept of the exciton was proposed by Soviet scientist Yakov Frenkel in 1931 while studying how light converts into heat in crystals. Later, in the 1930s, Gregory Wannier and Nevill Mott described another type of exciton existing in many semiconductors.

How it works

An exciton is born when light is absorbed by the semiconductor. An electron jumps to a higher energy level, leaving a hole. Their electrical attraction keeps the pair together. The exciton travels through the crystal, carrying energy but not charge (because the net charge of the pair is zero). After some time, the electron and hole meet again and annihilate, emitting light.

💡 Excitons can exist in liquid helium and even form a Bose-Einstein condensate at ultralow temperatures, exhibiting quantum properties at the macroscopic level.

An exciton is an elementary excitation of the electronic system of a crystal, described as a bound state of an electron from the conduction band and a hole from the valence band. Within the effective mass approximation, the problem reduces to the Schrödinger equation for two particles with a Coulomb potential screened by the dielectric constant ε of the medium. The energy spectrum resembles the Lyman series for the hydrogen atom, but with anisotropy of effective masses taken into account. At low densities, excitons can be treated as bosons, allowing for Bose condensation. In semiconductor nanostructures (quantum wells, wires, dots), size quantization enhances the binding energy and makes excitonic effects stable at room temperature, which is exploited in exciton-polariton lasers and electroluminescent devices.

History

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.

How it works

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.

E_1 = - \frac{\mu e^4}{2 (4 \pi \varepsilon \varepsilon_0)^2 \hbar^2}

μ — reduced effective mass of electron and hole, e — elementary charge (≈ 1.60×10⁻¹⁹ C), ε — dielectric constant of the material (dimensionless), ε₀ — electric constant (≈ 8.85×10⁻¹² F/m), ħ — reduced Planck constant (≈ 1.055×10⁻³⁴ J·s). The minus sign indicates a bound state; the absolute value is the binding energy.

Open problems & fun facts

Achieving room-temperature Bose condensation of excitons in solids; Controllable creation and detection of single excitons for quantum computing; Suppression of blinking of exciton luminescence in colloidal quantum dots

💡 In indirect-bandgap semiconductors like silicon, excitons have a long lifetime (up to milliseconds) due to the need for phonon participation in recombination, making silicon light detectors sensitive to long-wavelength radiation.

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exciton

History

How it works

History

How it works

History

How it works

Open problems & fun facts

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