What are excitons ? Also give their type.

What are excitons ? Also give their type.

Ans. The excitons are defined as the bound states of photo-excited and Coulomb-correlated electron-hole pairs, produced momentarily by light Incident Photon illumination of energy greater than the band gap of the material concerned. The electron-hole pairs, thus

produced, will orbit around each other, having equal and opposite charges. (see fig. 1.39). These electron-hole pairs are elementary excitation, or a quasi-particle of a solid and combine in a short time giving off a flash of light. As the exciton results from the binding of the electron with its hole, the exciton has slightly less energy than the unbound electron and hole. The wave function of the bound state is hydrogenise. However, the binding energy is much smaller and the size is much bigger than a hydrogen atom because of the effects of screenino and the effective mass of the constituents in the material. Also unlike in the hydrogen atom, where the nucleus is assumed to be stationary and electrons circle around the nucleus, in the case of excitons, the electron-hole pairs Circle around each other with respect to their centre of mass.

The Schrodinger equation should contain terms involving both electron and hole. Hence the equation will look like in Cartesian coordinate.

Schematic Diagram of  the formation of an exciton

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Depending on the materials, there are two types of excitons that can exist. In semiconductors, the dielectric constant is generally large, and due to this, screening tends to reduce the Coulomb interaction between electrons and holes. This results in the formation of

Mott-Wannier excitou, which has a radius much larger than the lattice spacing. As a: result, the effect of the lattice potential can be incorporated into the effective masses of the electron and the

hole, and because of the lower masses and the screened Coulomb interaction the binding energy is usually much less than a hydrogen atom, typically of the order 0.1 eV. On the other hand, when the dielectric constant of the material is very small, the Coulomb interaction between the electron and the hole becomes very strong and the excitons tend tn be much smaller, of the same order as the unit cell, so the electron and the hole sit on the same cell. This type of excitons are called Frenkel excitons, whose binding energy is typically of the order of 1.0 eV.

 

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