Bonding in metals and semiconductors

Most of the known chemical elements are metals, and many of these combine with each other to form a large number of intermetallic compounds. The special properties of metals - their bright, lustrous appearance, their high electrical and thermal conductivities, and their malleability - suggest that these substances are bound together in a very special way. 

The fact that the metallic elements are found on the left side of the periodic table gives us two important preliminary clues to the nature of their bonding. 

These points lead us to the simplest picture of metals, which regards them as a lattice 

This view is really an oversimplification that fails to explain metals in a quantitative way, nor can it account for the differences in the properties of individual metals. A more detailed treatment, known as the bond theory of metals, applies the idea of resonance hybrids to metallic lattices. In the case of an alkali metal, for example, this would involve a large number of hybrid structures in which a given Na atom shares its electron with its various neighbors. 

In Li4 we begin to see a trend in which the lower (mostly bonding) MO s are filled and the upper (mostly antibonding) ones are empty. 

If we consider the various structure types adopted by metals and then try to provide a model for localized metal-metal bonding, we run into a problem there are not enough valence shell orbitals or electrons for each metal atom to form two-centre two-electron bonds with all its neighbours. For example, an alkali metal has eight near-neighbours (Table 5.2), but only one valence electron. We must therefore use a bonding model with multi-centre orbitals (see Sections 

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We now introduce some simple models for bonding in metals and semiconductors such as jellium and hydridization and at the same time assess our theoretical tool of choice, DFT, at predicting some of the central cohesive properties of solids. 

This technique is useful for studying conduction electrons in metals and semiconductors as well as bonding of transition metal ions and other paramagnetic species. In general, it is more suitable for determination of environment than for identification of elements and measurement of concentration. Sensitivity varies with the para-... 

This section will outline the simplest models for the spectra of both metal and semiconductor nanocrystals. The work described here has illustrated that, in order to achieve quantitative agreement between theory and experiment, a more detailed view of the molecular character of clusters must be incoriDorated. The nature and bonding of the surface, in particular, is often of crucial importance in modelling nanocrystal optical properties. Wlrile this section addresses the linear optical properties of nanocrystals, both nonlinear optical properties and the photophysics of these systems are also of great interest. The reader is referred to the many excellent review articles for more in-depth discussions of these and other aspects of nanocrystal optical properties [147, 148, 149, 150, 151, 152, 153 and 1541. 

The development of molecular orbital theory (MO theory) in the late 1920s overcame these difficulties. It explains why the electron pair is so important for bond formation and predicts that oxygen is paramagnetic. It accommodates electron-deficient compounds such as the boranes just as naturally as it deals with methane and water. Furthermore, molecular orbital theory can be extended to account for the structures and properties of metals and semiconductors. It can also be used to account for the electronic spectra of molecules, which arise when an electron makes a transition from an occupied molecular orbital to a vacant molecular orbital. 

In this chapter, we develop a model of bonding that can be applied to molecules as simple as H2 or as complex as chlorophyll. We begin with a description of bonding based on the idea of overlapping atomic orbitals. We then extend the model to include the molecular shapes described in Chapter 9. Next we apply the model to molecules with double and triple bonds. Then we present variations on the orbital overlap model that encompass electrons distributed across three, four, or more atoms, including the extended systems of molecules such as chlorophyll. Finally, we show how to generalize the model to describe the electronic structures of metals and semiconductors. 

The first successful first-principle theoretical studies of the electronic structure of solid surfaces were conducted by Appelbaum and Hamann on Na (1972) and A1 (1973). Within a few years, first-principles calculations for a number of important materials, from nearly free-electron metals to f-band metals and semiconductors, were published, as summarized in the first review article by Appelbaum and Hamann (1976). Extensive reviews of the first-principles calculations for metal surfaces (Inglesfeld, 1982) and semiconductors (Lieske, 1984) are published. A current interest is the reconstruction of surfaces. Because of the refinement of the calculation of total energy of surfaces, tiny differences of the energies of different reconstructions can be assessed accurately. As examples, there are the study of bonding and reconstruction of the W(OOl) surface by Singh and Krakauer (1988), and the study of the surface reconstruction of Ag(llO) by Fu and Ho (1989). 

In contrast to metals and semiconductors, the valence electrons in polymers are localized in covalent bonds.The small current that flows through polymers upon the application of an electric field arises mainly from structural defects and impurities. Additives, such as fillers, antioxidants, plasticizers, and processing aids of flame retardants, cause an increase of charge carriers, which results in a decrease of their volume resistivity. In radiation cross-linking electrons may produce radiation defects in the material the higher the absorbed dose, the greater the number of defects. As a result, the resistivity of a radiation cross-linked polymer may decrease. Volume resistivities and dielectric constants of some polymers used as insulations are in Table 8.3. It can be seen that the values of dielectric constants of cross-linked polymers are slightly lower than those of polymers not cross-linked. 

In this chapter, we ll look at both metals and solid-state materials. We ll examine the natural sources of the metallic elements, the methods used to obtain metals from their ores, and the models used to describe the bonding in metals. We ll also look at the structure, bonding, properties, and applications of semiconductors, superconductors, ceramics, and composites. 

It s important to know how many electrons one has in one s molecule. Fe(II) has a different chemistry from Fe(III), and CR3+ carbocations are different from CRj radicals and CR3 anions. In the case of Re2Cl82, the archetypical quadruple bond, we have formally Re(III), d4, i.e., a total of eight electrons to put into the frontier orbitals of the dimer level scheme, 17. They fill the a, two x, and the 6 level for the explicit quadruple bond. What about the [PtHj2] polymer 12 Each monomer is d8. If there are Avogadro s number of unit cells, there will be Avogadro s number of levels in each bond. And each level has a place for two electrons. So the first four bands are filled, the xy, xz, yz, z2 bands. The Fermi level, the highest occupied molecular orbital (HOMO), is at the very top of the z2 band. (Strictly speaking, there is another thermodynamic definition of the Fermi level, appropriate both to metals and semiconductors,9 but here we will use the simple equivalence of the Fermi level with the HOMO.)... 

METALS AND SEMICONDUCTORS exhibit significant differences in their chemical and physical characteristics consistent with the corresponding differences between the metallic bond and the covalent or ionic bond. Research and development on metals centers about their electrical, thermal, and particularly about their mechanical properties. Basic and applied studies of semiconductors, on the other hand, center about their electronic properties because the concentration of their mobile carriers is orders of magnitude smaller than in metals and can be varied at will within wide limits. 

Unraveling the relationship between the atomic surface structure and other physical and chemical properties is probably one of the most important achievements of surface science. Because of the mixed ionic and covalent bonding in metal oxide systems, the surface structure has an even stronger influence on local surface chemistry as compared to metals or elemental semiconductors [1]. A vast amount of work has been performed on Ti02 over the years, and this is certainly the best-understood surface of all the metal oxide systems. 

Now we come to another important distinction between metals and semiconductors in that two types of electronic carriers are possible in the latter. Consider the thermal excitation of an electron from VB to CB. This gives rise to a free electron in the CB and a vacancy or hole in the VB. A localized chemical picture for the case of Si shows that the hole may be regarded as a missing electron in a chemical bond (Figure 3). There is a crude chemical analogy here with the dissociation of a solvent such as water into H3O+ and OH. In either case, equal numbers of oppositely charged species are produced. Thus, Eq. 1 becomes... 

Questions that had been of fundamental importance to quantum chemistry for many decades were addressed. When the existence of bond alternation in trans-polyacetylene was been demonstrated [14,15], a fundamental issue that dates to the beginnings of quantum chemistry was resolved. The relative importance of the electron-electron and electron-lattice interactions in Ti-electron macromolecules quickly emerged as an issue and continues to be vigorously debated even today. Aspects of the theory of one-dimensional electronic structures were applied to these real systems. The important role of disorder on the electronic structure and properties of these low dimensional metals and semiconductors was immediately evident. The importance of structural relaxation in the excited state (solitons, polarons and bipolarons) quickly emerged. 

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