WannierMott

Wannier-Mott excitons are bound electron-hole pairs in semiconductors characterized by a spatial extent much larger than the lattice spacing. They are named after Gregory Wannier, who described the effective-mass hydrogenic model for excitons, and N. F. Mott, who contributed to the understanding of density-driven ionization. In typical semiconductors with moderate dielectric screening, the Coulomb attraction between an itinerant electron in the conduction band and a hole in the valence band is screened enough that the bound state extends over many lattice constants, forming a hydrogenic series of energy levels E_n ≈ -R* / n^2, where R* is the effective Rydberg energy, μ is the reduced effective mass, and ε_r is the dielectric constant. The effective Bohr radius a_B* ≈ 4π ε0 ε_r ħ^2/(μ e^2) sets the spatial scale. In bulk semiconductors, a_B* is usually a few nanometers and binding energies are on the order of tens of meV, though values vary with material.

In two-dimensional systems, screening and confinement modify the interaction, often increasing the binding energy and altering the Rydberg series. Two-dimensional Wannier-Mott excitons in quantum wells and layered materials can still be described within a modified hydrogenic framework, but with deviations from the simple 1/n^2 law.

Experimentally, Wannier-Mott excitons appear as sharp absorption or photoluminescence features close to the band edge and can be tuned by temperature, strain, and the dielectric environment. They play a key role in optoelectronic devices, photovoltaics, and light-emitting materials.

At high carrier density, excitons may dissociate into a conducting electron-hole plasma when the Mott density is reached, marking the Mott transition.