Tightly Bound Frenkel Excitons

In tightly bound (Frenkel) excitons, the observed peaks do not respond to the hy-drogenic equation (4.39), because the excitation is localized in the close proximity of a single atom. Thus, the exciton radius is comparable to the interatomic spacing and, consequently, we cannot consider a continuous medium with a relative dielectric constant as we did in the case of Mott-Wannier excitons. 

Frenkel excitons are also observed in many organic crystals and in noble gas crystals (Ne, Ar, Kr, and Xe). However, for the latter crystals the band gap lies out 

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Figure 4.13 The schemes of (a) a weakly bound (Mott-Wannier) exciton and (b) a tightly bound (Frenkel) exciton.

The spectra may also be described in the language of solid state theory. The atomic excited states are the same as the excitons that were described, for semiconductors, at the close of Chapter 6. They are electrons in the conduction band that are bound to the valence-band hole thus they form an excitation that cannot carry current. The difference between atomic excited states and excitons is merely that of different extremes the weakly bound exciton found in the semiconductor is frequently called a Mott-Wannier exciton-, the tightly bound cxciton found in the inert-gas solid is called a Frenkel exciton. The important point is that thecxcitonic absorption that is so prominent in the spectra for inert-gas solids does not produce free carriers and therefore it docs not give a measure of the band gap but of a smaller energy. Values for the exciton energy are given in Table 12-4. 

We know that, in semiconductors or insulators, valence and conduction bands are separated by some finite energy gap characteristic of the material. When an electron from the valence band gets sufficient energy to overcome the energy gap may be by thermal excitation or absorption of photons, and it goes to conduction band, a hole is left behind. The electron-hole pair so formed is a quasi-particle called exciton. An exciton can move in the crystal whose centre of mass motion is quantized. Different kinds of excitons can be identified in a variety of materials. If the electron-hole bound pair is tightly-bound with distance of electron-hole pair comparable to lattice constant, then it is called Frenkel exciton. On the other hand, one may have an exciton with electron-hole separation... 

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