Bonding in Solids Metals, Insulators, and Semiconductors

Bonding in Solids Metals, Insulators, and Semiconductors Models of Metallic Bonding Band Theory and Conductivity Semiconductors... 

Band theory (8.3) Description of chemical bonding in solids in terms of bands of orbitals. Used to explain the electrical properties of metals, insulators, and semiconductors. 

Bonding in solids may be described in terms of bands of molecular orbitals. In metals, the conduction bands are incompletely filled orbitals that allow electrons to flow. In insulators, the valence bands are full and the large band gap prevents promotion of electrons to empty orbitals. In semiconductors, empty levels are close in energy to filled levels. 

Irradiation of all kinds of solids (metals, semiconductors, insulators) is known to produce pairs of the point Frenkel defects - vacancies, v, and interstitial atoms, i, which are most often spatially well-correlated [1-9]. In many ionic crystals these Frenkel defects form the so-called F and H centres (anion vacancy with trapped electron and interstitial halide atom X° forming the chemical bonding in a form of quasimolecule X2 with some of the nearest regular anions, X-) - Fig. 3.1. In metals the analog of the latter is called the dumbbell interstitial. 

The sp hybridization results in the formation of four energetically degenerate bonds arranged tetrahedrally with each containing one electron. This allows an atom to bond to four other atoms simultaneously. The interactions and overlap of the wave functions of many atoms or ions in a solid give rise to energy bands. If the outermost bands are not filled, the electrons are said to be delocalized and the solid is considered to be a metal. If the bands are separated from each other by a band gap, the solid is considered a semiconductor or insulator depending on the size of that gap. 

As outlined before, once a low-energy positive muon has been deposited in the sample of interest, it slows down to thermal velocities in a time of order 10 s (for solids), with no loss of original polarization. It may emerge from thermalization as an apparently bare (in metals) or in a muonium-like state (sometimes, in semiconductors and insulators). Muonium-like states will not be discussed further here. A bare muon in a metal is in contact hyperfine interaction with the conduction electron density at its location, which results in a muonic Knight shift (usually small in nonmagnetic materials). A bare x+ in an insulator is a diamagnetic center, and is quite likely to be bonded to the most electronegative species present. 

This leads to independent-particle equations for the noninteracting system that can be considered exactly soluble (in practice by numerical means) with all the difficult many-body terms incorporated into an exchange-correlation functional of the electron density. The Kohn-Sham approach has indeed led to very useful approximations that are now the basis of most calculations that attempt to make ab initio predictions for the properties of solids and large molecular system. The approach is remarkably accurate, most notably for wide-band systems, such as the group IV and 11-V semiconductors, the sp bonded metals like sodium and aluminum, insulators like diamond, sodium chloride, and molecules with covalent and ionic bonds. It also appears to be successful in many cases in which the electrons have stronger effects of correlation, such as in transition metals. 

COVALENT-NETWORK SOLIDS (SECTION 12.7) Covalent-network solids consist of atoms held together in large networks by covalent bonds. These solids are much harder and have higher melting points than molecular solids. Important examples include diamond, where the carbons are tetrahedrally coordinated to each other, and graphite, where the sp -hybridized carbon atoms form hexagonal layers. Semiconductors are solids that do conduct electricity, but to a far lesser extent than metals. Insulators do not conduct electricity at all. 

Owing to the fact that valence electrons determine bonds, the electrical properties of a material are related to the bond type. In conductors such as metals, alloys, and intermetallics, the atoms are bound to each other primarily by metallic bonds, and metals such as tungsten or aluminum are good conductors of electrons or heat. Covalent bonds occur in insulators such as diamond and silicon carbide and in semiconductors such as silicon or gallium arsenide. Complexes and salts have ions that are bound with electrostatic forces. Ionic conductors can be used as solid electrolytes for fuel cells because solids with ionic bonds may have mobile ions. Most polymers have covalent bonds in their chains but the mechanical... 

The LCAO-MO model is the most popular one in the description of covalent bonding in atomic lattices of metals, semiconductors, and insulators. As in the case of the MO model for molecules, the atomic orbitals on the atoms in a solid can be combined into molecular orbitals by linear combination. As many molecular orbitals can be made out of atomic orbitals as there are atomic orbitals for them. In solids that number is very high and the many molecular orbitals made from one atomic orbital on each atom form continuous bands. The number of nodal planes in the molecular orbitals increases with their energy. 

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