[Physics Class Notes] on Exciton Pdf for Exam

Essentially, when an electron and a positive hole (an empty electron particle in valence band) combine and are able to move freely through a non-metallic crystal as a unit, then the combination of these two particles is called an exciton. It shall be noted that the electron and the positive hole carry opposite charges. Thus they cancel each other’s charges, and there is no electrical charge in the exciton. Owing to this property, detecting an exciton can be challenging at times. Now there are different characteristics of excitons, and they are generally classified in two limiting cases – first, the one has a small dielectric constant and the other, which has a large dielectric constant. 

Frenkel Exciton

Yakov Frenkel was the first one who proposed the concept of exciton when he stated about the excitation of atoms in a lattice of a certain excitonic insulator. The Frenkel exciton has a relatively small dielectric constant, and its binding energy is on the order of 0.1 to 1 eV. This takes place because, at times, the Coulomb interaction between the hole and an electron may be forceful and strong. Owing to this extra force, the exciton tends to be small; thus, they carry less dielectric constant. EEX = -e₂/∈crystals are a general source where Frenkel excitons are found. Further, they can also be located in organic molecular crystals like anthracene and tetracene.

Wannier–Mott Exciton

The dielectric constant is generally large in semiconductors; owing to this, the electric field screen reduces the interaction which takes place in Coulomb between the particles. Through this process, a Wannier-Mott exciton is formed. The said exciton has a radius that is way larger than the lattice spacing. Large exciton radii are favoured greatly by small masses of electrons which are typical of semiconductors. Through this, the said lattice potential can be put into the masses of electron and hole, which forms an exciton polariton. The binding energy in these is quite low, and it is generally in the order of 0.01 eV. These excitons are typically found in semiconductor crystals and liquids such as xenon. 

Charge-Transfer Exciton

There can be an intermediate case between Frenkel and Wannier exciton, and this case has been termed as charge transfer exciton (CT). These generally come to existence when the electron and the hole are present in the adjacent molecules. They occur typically in molecular and organic crystals. Unlike the other two, they have a property to show a static electric dipole. CT excitons may also be present in transition metal oxides. Their concept is always in proximity with a transfer of charge, which mainly occurs from one atomic site to another, this transfer of charge aids in spreading the wave-function around lattice sites. 

Exciton in 2D Semiconductors

In two dimensional objects and materials, the whole systematic process is quantum-confined, and the direction of the same is perpendicular to the normal plane of the said object or material. This reduction in the dimensions of the object greatly manipulates the energies and radii of Warrier excitons; generally, the exciton b exciton effect amplifies in such restricted systems. In most excitons in 2d materials semiconductors, the Rytova–Keldysh provides a good approximation which is indicative of the exciton interaction. The said equation is given below. 

V(r) = [frac{pi}{2r_{0}}] [[H_{0}(frac{kr}{r_{0}})] – [Y_{0}(frac{kr}{r_{0}})]]

Self-Trapping of Excitons

In crystals, the phonons and excitons interact; there is lattice vibration. If the coupling between the two is not cohesive in a semiconductor, then excitons generally get dissipated by phonos. On the other hand, if the coupling between the two is strong, owing to great cohesion, then, in such a situation, excitons can be self-trapped. In the case where interlayer exciton is self-trapped, they get surrounded by a dense cover of clouds made up of virtual phonos. This dressing greatly hinders the ability of the excitons to move across the crystal itself. Essentially, there is a local deformation of the lattice which surrounds the exciton. Self-trapping is quite similar to forming strong polarons which strongly couple together.