Excitons Wannier

The small and weakly time-dependent CPG that persisLs at longer delays can be explained by the slower diffusion of excitons approaching the localization edge [15]. An alternative and intriguing explanation is, however, field-induced on-chain dissociation, a process that does not depend on the local environment but on the nature of the intrachain state. The one-dimensional Wannier exciton model describes the excited state [44]. Dissociation occurs because the electric field reduces the Coulomb barrier, thus enhancing the escape probability. This picture is interesting, but so far we do not have any clear proof of its validity. 

Shinozuka Y, Matsuura M (1983) Wannier exciton in quantum wells. Phys Rev B 28 4878 1881... 

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

These two types of exciton are schematically illustrated in Figure 4.13. The Mott-Wannier excitons have a large radius in comparison to the interatomic distances (Figure 4.13(a)) and so they correspond to delocalized states. These excitons can move freely throughout the crystal. On the other hand, the Frenkel excitons are localized in the vicinity of an atomic site, and have a much smaller radius than the Mott-Wannier excitons. We will now describe the main characteristics of these two types of exciton separately. 

Thus, Mott-Wannier excitons can give rise to a number of absorption peaks in the pre-edge spectral region according to the different states = 1, 2, 3,... As a relevant example. Figure 4.14 shows the low-temperature absorption spectrum of cuprous oxide, CU2O, where some of those hydrogen-like peaks of the excitons are clearly observed. These peaks correspond to different excitons states denoted by the quantum numbers = 2, 3, 4, and 5. 

Crystal (Mott-Wannier excitons) Eg (eV) Eg (meV) Crystal (Frenkel excitons) Eg (eV) Ei (meV)... 

For weakly bound (Mott-Wannier) excitons (mainly observed in semiconductors), the binding energies are in the meV range, as can be appreciated from Table 4.4. Inspection of this table also shows a general trend Ei, tends to increase as increases. 

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. 

Weiser G (1992) Stark-effect of one-dimensional Wannier excitons in polydiacetylene single-crystals. Phys Rev B 45 14076... 

Blossey DF (1970) Wannier exciton in an electric field. I. Optical absorption by bound and continuum states. Phys Rev B 2 3976... 

Beside, the above-mentioned asymmetry of size-depended shifts of electron and hole levels for light-produced Wannier excitons can lead to the photo-induced mutual charging of SC nanoparticles with different sizes in composite film with high SC content. Such process for SC nanoparticles of different electron structure has been noticed in work [29]. It has been shown that the photo-induced mutual charging of SC nanoparticles can increase their photocatalytic activity [29]. 

InSe and GaSe crystals are characterized with a weak interaction of 3D Wannier excitons with homopolar optical A -phonons [18, 19]. Therefore, when calculating the exciton absorption spectra, we took into consideration effects of broadening the exciton states using the standard convolution procedure (see in [18]) for theoretical values of a(7jco) the absorption coefficient in the Elliott s model [20] with y /io>) — 77 [n(E 2+/ 2)] the Lorentzian function in the Toyozawa s model [21], where r is the half-width at half-maximum which is usually associated with the lifetime tl/2r. 

Mobile defects are Frenkel78 excitons, Mott-Wannier excitons, polarons, bipolarons, polaritons, and solitons. 

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. 

The prevailing view of excitations in solids is based on the two extreme approximations—the Frenkel and Wannier excitons—but more realistic exciton wave functions are intermediate of these two and are linear combinations of various singly-excited (or higher-order) configurations with the same k. CIS and TDHF offer exactly such wave functions for extended systems in a size-correct fashion. Figure 2-2 shows the performance of CIS and HF for describing these three... 

Two complementary models can be developed to describe the features mentioned above. Both models consider the electron-electron interaction and the exciton-lattice interaction. Although both models have different starting points, they yield satisfying interpretations of the experimental findings. The one model is the model of Wannier excitons which ensues directly from the one-electron band model discussed above. The other one starts from the many electron states of the [Pt(CN)4]2 ion and takes into account the coupling between neighbouring complex ions. 

The conduction-band minima and valence-band maxima are studied in terms of the k p method, which relates the effective masses to the oscillator strengths discussed in Chapter 4. Wannier excitons and impurity states are also understandable in this context. 

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. 

Dynamics. Cluster dynamics constitutes a rich held, which focused on nuclear dynamics on the time scale of nuclear motion—for example, dissociahon dynamics [181], transihon state spectroscopy [177, 181, 182], and vibrahonal energy redistribuhon [182]. Recent developments pertained to cluster electron dynamics [183], which involved electron-hole coherence of Wannier excitons and exciton wavepacket dynamics in semiconductor clusters and quantum dots [183], ultrafast electron-surface scattering in metallic clusters [184], and the dissipahon of plasmons into compression nuclear modes in metal clusters [185]. Another interesting facet of electron dynamics focused on nanoplasma formation and response in extremely highly ionized molecular clusters coupled to an... 

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