Formative, 297 Wannier excitons

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. 

In the last decade the Wannier exciton emission from direct band gap soniconductors was reconsidered for high count-rate and coincidence-detection scintillation applications and Cul, Hglj, Pbl2, ZnO Ga, and CdS In compounds in powder form were studied (Derenzo et al. 2002). In direct gap semiconductors a favorable combination of a smaller gap and an UV-VIS emission center based on Wannier exciton can provide high scintillation efficiency and subnanosecond radiative lifetimes due to microscopic superradiance effect (Niki 2006, Wilkinson et al. 2004). On the other hand, the Stokes shift of such emission centers is necessarily low (typically below 0.1 eV) and it prevents their usage in the bulk form due to enhanced reabsorption effect, see Figure 4.4. The ZnO Ga has shown the best combination of subnanosecond decay time and emission intensity... 

For simplicity, however, we prefer to denote all excitons formed from bound states of conduction band electrons and valence band holes as Mott-Wannier excitons, recognizing that this term includes both small and large radius excitons. We call this limit the weak-coupling limit, as the starting point in the construction of the exciton basis is the noninteracting band limit. As we will see, a real space description of a Mott-Wannier exciton is of a hole in a valence band Wannier orbital bound to an electron in a conduction band Wannier orbital. 

At = 0.1 there are both Mott-Hubbard and Mott-Wannier excitons, forming two inter-related families of essential states. In general, the B states are linear superpositions of eqns (6.22) and (6.30), while the states are linear superpositions of eqns (6.23) and (6.31). As the bond dimerization decreases the spin-density-wave component of the state increases (Mukhopadhyay et al. 1995). Figure 6.10(c) shows the l H, 2 A+, and 4 H states, predominately forming the Mott-Wannier family of excitons, while Fig. 6.10(d) shows the l B, ... 

The EMA is a quasi-particle theory, which treats the hole created in the valence band and electron excited to the conduction band, as free particles whose effective masses are determined by a quadratic fit to the curvature at the band minima (maxima) of the conduction (valence) band (Fig. 1). If we add the coulumbic attraction of an electron and hole to this picture, we can have a theoretically simple manifestation of an exciton. The electron and hole are bound together by a screened coulomb interaction to form a so-called Mott-Wannier exciton [29],This exciton presents an energy spectrum analogous to a hydrogen atom (i.e. with radial and angular quantum number) but it is further complicated by the fact that it is coupled to a thermal bath of phonons and that the mass of an exciton is energy dependent. 

D translational invariance of the system, we classify the excitons by their inplane wavevector k. Supposing that for some bands of Frenkel excitons in the OQW and Wannier-Mott excitons in the IQW the energy separation is much less than the distance to other exciton bands we take into account only the hybridization between these two bands. We choose as a basis set the pure Frenkel and Wannier states, i.e. the state (denoted by F,k)) when the OQW is excited, while the IQW is in its ground state, and vice versa (denoted by W, k)), their energies being Ep(k) and W(k). We seek the new hybrid states in the form... 

More generally, there are two kinds of exciton when the electron and hole are completely delocalised from any specific atomic site and form bound states, one has a Wannier-Mott exciton. When both the electron and hole are localised on or near a specific atomic site in the solid, so that the exciton is formed from atomic or molecular states perturbed by the crystalline environment, one has a FVenkel-Peierls exciton 102. ... 

In conclusion, we have discussed the excitation spectra arising from the interaction of Frenkel, Wannier-Mott, and intermediate type excitons with conduction electrons to form bound states at low temperatures such conducting states are appropriate to occur in molecular crystals, semiconductors and rare-gas solids, respectively. We hope that the present discussions will stimulate experimental interest on the spectroscopic properties of electron-exciton complexes and their transport properties as well. 

Let us turn now to the case where the excitation is not in a single atom or molecule but is much more delocalized. Considering a crystal which has the valence band filled and the conduction band empty in the ground state, Wannier /2/ has developed exciton energy levels that have the form of a hydrogen atomic series in this type of system. 

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