Quantum amorphous materials

Amorphous materials exliibit speeial quantum properties with respeet to their eleetronie states. The loss of periodieify renders Bloeh s theorem invalid k is no longer a good quantum number. In erystals, stnietural features in the refleetivify ean be assoeiated with eritieal points in the joint density of states. Sinee amorphous materials eaimot be deseribed by k-states, seleetion niles assoeiated with k are no longer appropriate. Refleetivify speetra and assoeiated speetra are often featureless, or they may eonespond to highly smoothed versions of the erystalline speetra. 

The terms nanocrystals and quantum dots are often used interchangeably. Quantum dots, as used here, are invariably nanocrystals (amorphous materials could, in principle, also exhibit quantum size effects as long as some electronic separation between different particles occurs) that show quantum effects, while nanocrystals may or may not be small enough to exhibit such effects. 

In an imperfect crystal or amorphous material the wavenumber k is not a good quantum number, and if Ak/k becomes comparable to unity then the concept of a Fermi surface has little meaning. Nevertheless, at zero temperature a sharp Fermi energy must still exist. 

The theory predicts a strong dependence of photogeneration efficiencies on the field and it approaches unity at high field. The temperature sensitivity decreases with the increase in field. The theory has found satisfactory explanations in the photogeneration process in many organic disordered systems, such as PVK (Scheme la) [25], and triphenylamine doped in polycarbonate [26], Figure 4 shows an example of the field dependence of c() calculated from Eq. (22) (the solid lines) to fit the quantum efficiency data at room temperature for hole and electron generation in an amorphous material. The material consists of a sexithiophene covalently linked with a methine dye molecule (compound 1) (Scheme 2). 

So far, most of the quantum-chemical computations of solid compounds have assumed a free molecular model that is the intermolecular effects are initially not considered. Although these second-order effects are minor in many cases and do not cause much disagreement with solid-state NMR measurements, they might become significant and should not be neglected. Recently a series of publications has addressed this problem, based on a supercell technique.38-41 The appealing feature of this new method is that it can deal not only with free molecules but also with crystals, amorphous materials or materials with defects. 

Above we had in mind that the wavevector k is a good quantum number and thus that all exciton states are coherent. In the opposite case, which can occur, for example, as a result of exciton-phonon scattering or scattering by lattice defects, the exciton energy bands are not characterized by the k value. In this case incoherent localized states can appear, for which the translation symmetry of the crystal is not important and which are similar, for example, to excitations in amorphous materials. In some solids the coexistence of coherent and incoherent excitations can also be possible. 

Several methods have been developed for generating models of the structure of amorphous materials at the atomic level. These include random network models (which may be made by hand or, as discussed later, generated on a computer), energy minimization (or relaxation) methods, Monte Carlo (MC), Molecular Dynamics (MD), Reverse Monte Carlo (RMC), and Quantum Mechanical (QM) methods. The aim of this chapter is to discuss the generation of models for amorphous solids mainly using the most widely used and successful MD and RMC techniques, giving examples from the literature. 

Exceptions from the rule usually show up as quantum-chemical effects which lower the total energies by also lowering the structural symmetries (see Section 3.4). On the other hand, we should add that there is a whole universe of amorphous structures which are deliberately excluded from the discussion if we follow Pauling s fifth rule but, admittedly, these refer to thennod)mami-cally metastable states in practically all cases. Indeed, the study of solid-state materials that do not exhibit translational invariance albeit chemical, local order - ordinary window glass is an ubiquitous example - has not been particularly excessive when compared with "normal" (that is, crystalline) solid-state materials, simply because the characterization of such matter is much more difficult for amorphous materials, ordinary X-ray or neutron diffraction loses its enormous analytical power. Thus, our atomistic knowledge of amorphous materials is far from being satisfactory, and Pauling s fifth rule should probably be taken with a pinch of salt. 

The prototype molecule (or cluster) approach to the quantum chemical treatment of relevant portions of extended systems is an important tool in the study of localized phenomena. For example, in solid state quantum chemistry this method offers a convenient way of treating surfaces or adsorbed molecules interacting with surfaces [177], crystal impurities, [178, 179], amorphous materials [180], and so on. 

Another parameter of relevance to some device appHcations is the absorption characteristics of the films. Because the k quantum is no longer vaUd for amorphous semiconductors, i -Si H exhibits a direct band gap (- 1.70 eV) in contrast to the indirect band gap nature in crystalline Si. Therefore, i -Si H possesses a high absorption coefficient such that to fully absorb the visible portion of the sun s spectmm only 1 p.m is required in comparison with >100 fim for crystalline Si Further improvements in the material are expected to result from a better understanding of the relationship between the processing conditions and the specific chemical reactions taking place in the plasma and at the surfaces which promote film growth. 

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