Excitons radii

At the crossing point k = ko (for S > 0) we have Aa(ko) 2 = 1/2 and the FE oscillator strength is equally distributed between the two hybrid states. For the hybrid exciton radii the opposite relation holds. Calculating the expectation value of the exciton radius squared f2 in the state a, k) we obtain... 

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. 

A Mott-Wannier exciton is a neutral quasi-particle, consisting of an excited bound-state electron and its associated "Coulomb hole" in a high-dielectric constant solid, that can also travel throughout the lattice without transporting net charge since the exciton radius is several lattice constants, its binding energy is as low as 0.01 eV it thus tends to be more "delocalized" than the Frenkel exciton. 

A possible interpretation of these observations can be done taking into account features of optical absorption for this system described earlier [4]. A key point of the absorption spectra in the visible range was shown to be the excitonic maxima, which are characteristic for tellurides and their solid solutions after the heat treatment. Occurrence of excitons is more probable in tellurides and Te-rich solid solutions possessing a smaller Bohr exciton radius than in selenides. The heating promotes phase transitions in nanoparticles (chalcopyrite-sphalerite). In the selenides the transition can appear at higher temperatures. Thus, the appearance of PL maxima we can associate with excitons in the nanoparticles. 

In a quantum dot, which is also often called an artificial atom, the excitons are confined in all three spatial dimensions. In a bulk semiconductor, an electron-hole pair is bound within the Bohr exciton radius, which is characteristic for each type of semiconductor. A quantum dot is smaller than the Bohr exciton radius, which causes the appearance of discrete energy levels. The bandgap, AE, between the valance and conduction band of the semiconductor is a function of the nanocrystaTs size and shape. Q-dots feature slightly lower luminescence quantum yields than traditional organic fluorophors but... 

The exciton radius is, at around 5 nm, larger than in Ti02 (on account of a smaller effective mass), and may lead to quantum confinement effects in nanocrystalline films [18, 65, 67]. These affect the ease of transport between particles, leading to barriers between large and small particles for polydisperse particle size distributions. 

Inorganic QCNs specifically refer to those semiconducting nanocrystals whose physical dimensions are less than the Bohr exciton radius of the corresponding bulk semiconductor. They can be of different shapes viz. spherical (also called QDs) [39], elongated (also called rods, tubes, wires) [40,41], multipodal (e.g., tripodal, tetrapodal, or hyperbranched structures) [42,43] as can be seen in the representative transmission electron microscopy (TEM) images (Figure 3.3). 

Quantum confinement exhibits novel spectroscopic effects in senuconductors and quantum dots, where the carriers are pinched into a dimension smaller than the Bohr exciton radius. As Zych has pointed out [192], the situation is different in insulators where electronic states are strongly localized. Nevertheless, there have been reports in the literature of quantum confinement effects of Ln " doped into sesqiuoxides, as evidenced by excitation or emission spectra. The spectroscopic effects are very minor so that other causes due to impurities, phase changes, or physical effects such as scattering, certainly play an important role. In particular, combustion syntheses produce variable spectroscopic results, particularly when non-stoichiometric ratios are employed [193]. Zych has ruled out quantum confinement effects for insulators doped with lanthanide ions, at least down to 6 nm. 

Semiconductor nanoparticles exhibit size-dependent unique optical and electronic properties that are different from their bulk counterpart due to quantum confinement. Bulk semiconductor crystal is considered as one large molecule, and electronic excitation of semiconductor crystals generates an electron-hole pair. The size of the delocalization area of this electron-hole pair is generally many times larger than the lattice constant. Decrease in the size of a semiconductor crystal down to a size comparable with the delocalization area of the electron-hole pair or to that of the Bohr excitonic radius of those materials modifies the electronic structure of the nanocrystals. When the particle radius decreases below the Bohr excitonic radius, there is widening in the energy band gap, which results in a blue shift in the excitonic absorption band of a semiconductor crystal. For example, in CdS semiconductor material, the blue shift of the excitonic absorption band is observed to begin at a crystal size of 5-6 nm [138-141]. 

Nano-composite materials with fine semiconductor particles dispersed in the matrix have attracted considerable interest because the properties of the particles are much different from their bulks when the diameters are l s than the Bohr exciton radius. Such particles, which are generally named as nano-particles, are characterized by non-stoichiometric surface structure and quantum size effect 2). These properties would lead to new phenomena, new theoretical insights, and new materials and devices. 

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