Exciton: Difference between revisions

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(→‎Wannier–Mott exciton: add new section on the Wannier binding energies in 2D materials, and re-patch some stuff.)
==Wannier–Mott exciton==
In semiconductors, the dielectric constant is generally large. Consequently, [[electric field screening]] tends to reduce the Coulomb interaction between electrons and holes. The result is a ''Wannier-Mott exciton'',<ref>{{cite journal|doi=10.1103/PhysRev.52.191|title=The Structure of Electronic Excitation Levels in Insulating Crystals|year=1937|last1=Wannier|first1=Gregory|journal=Physical Review|volume=52|page=191|bibcode = 1937PhRv...52..191W|issue=3 }}</ref> which has a radius larger than the lattice spacing. Small effective mass of electrons that is typical of semiconductors also favors large exciton radii. As a result, the effect of the lattice potential can be incorporated into the effective masses of the electron and hole. Likewise, because of the lower masses and the screened Coulomb interaction, the binding energy is usually much less than that of a hydrogen atom, typically on the order of {{gaps|0.01|eV}}. This type of exciton was named for [[Gregory Wannier]] and [[Nevill Francis Mott]]. Wannier-Mott excitons are typically found in semiconductor crystals with small energy gaps and high dielectric constants, but have also been identified in liquids, such as liquid [[xenon]]. They are also known as ''large excitons''.
In single-wall [[carbon nanotubes]], excitons have both Wannier-Mott and Frenkel character. This is due to the nature of the Coulomb interaction between electrons and holes in one-dimension. The dielectric function of the nanotube itself is large enough to allow for the spatial extent of the [[wave function]] to extend over a few to several nanometers along the tube axis, while poor screening in the vacuum or dielectric environment outside of the nanotube allows for large (0.4 to {{gaps|1.0|eV}}) binding energies.