Band theory semiconductors

Large numbers of nonmetal or metalloid atoms can also combine to form bands of MOs. Metals conduct a current well (conductors), whereas most non-metals do not (insulators), and the conductivity of metalloids lies somewhere in between (semiconductors). Band theory explains these differences in terms of the size of the energy gaps between the valence and conduction bands, as shown in Figure 12.36 ... 

Simply put, a conductive organic polymer, or for that matter any organic polymer, is not a metal, although many of the theories used to explain the electrical nature of ICPs are based on our understanding of conduction mechanisms in metals and semiconductors. Band theory, polarons, bipolarons, thermopower, etc., are but a few examples of the models borrowed from solid-state chemistry and physics to explain the observed electronic behavior of these materials. Lattice distortions that... 

Baker-Venkataraman synthesis, 2, 76 Balsoxin, 6, 232 Bamicetin isolation, 3, 147 Band theory semiconductors, 1, 355 Ban thine... 

The beginnings of the enormous field of solid-state physics were concisely set out in a fascinating series of recollections by some of the pioneers at a Royal Society Symposium (Mott 1980), with the participation of a number of professional historians of science, and in much greater detail in a large, impressive book by a number of historians (Hoddeson et al. 1992), dealing in depth with such histories as the roots of solid-state physics in the years before quantum mechanics, the quantum theory of metals and band theory, point defects and colour centres, magnetism, mechanical behaviour of solids, semiconductor physics and critical statistical theory. 

The recognition of the existence of semiconductors and their interpretation in terms of band theory will be treated in Chapter 7, Section 7.2.1. Pippard, in his chapter, includes an outline account of the early researches on semiconductors. 

The high electrical conductivity of metals as well as the high electron (and hole) mobility of inorganic covalently bound semiconductors have both been clarified by the band theory [I9, which slates that the discrele energy levels of individual atoms widen in the solid stale into alternatively allowed and forbidden bands. The... 

It is important to realize that each of the electronic-structure methods discussed above displays certain shortcomings in reproducing the correct band structure of the host crystal and consequently the positions of defect levels. Hartree-Fock methods severely overestimate the semiconductor band gap, sometimes by several electron volts (Estreicher, 1988). In semi-empirical methods, the situation is usually even worse, and the band structure may not be reliably represented (Deak and Snyder, 1987 Besson et al., 1988). Density-functional theory, on the other hand, provides a quite accurate description of the band structure, except for an underestimation of the band gap (by up to 50%). Indeed, density-functional theory predicts conduction bands and hence conduction-band-derived energy levels to be too low. This problem has been studied in great detail, and its origins are well understood (see, e.g., Hybertsen and Louie, 1986). To solve it, however, requires techniques of many-body theory and carrying out a quasi-particle calculation. Such calculational schemes are presently prohibitively complex and too computationally demanding to apply to defect calculations. 

In the case of elemental semiconductors such as Si, which are also well described in band theory terms, the equation for the conductivity is composed of an electron and hole component so that ... 

A hopping semiconductor such as an oxide is often best described by Eq. (7.1) rather than by classical band theory. In these materials the conductivity increases with temperature because of the exponential term, which is due to an increase in the successful number of jumps, that is, the mobility, as the temperature rises. Moreover, the concentration of charge carriers increases as the degree of nonstoichiometry increases. 

A comparison of the relevant equations for metals, band theory semiconductors, and hopping semiconductors is given in Table 7.1. These equations can be used in a diagnostic fashion to separate one material type from another. In practice, it is not quite so easy to distinguish between the different conductivity mechanisms. 

Note that the above model is for a simple system in which there is only one defect and one type of mobile charge carrier. In semiconductors both holes and electrons contribute to the conductivity. In materials where this analysis applies, both holes and electrons contribute to the value of the Seebeck coefficient. If there are equal numbers of mobile electrons and holes, the value of the Seebeck coefficient will be zero (or close to it). Derivation of formulas for the Seebeck coefficient for band theory semiconductors such as Si and Ge, or metals, takes us beyond the scope of this book. 

This book systematically summarizes the researches on electrochemistry of sulphide flotation in our group. The various electrochemical measurements, especially electrochemical corrosive method, electrochemical equilibrium calculations, surface analysis and semiconductor energy band theory, practically, molecular orbital theory, have been used in our studies and introduced in this book. The collectorless and collector-induced flotation behavior of sulphide minerals and the mechanism in various flotation systems have been discussed. The electrochemical corrosive mechanism, mechano-electrochemical behavior and the molecular orbital approach of flotation of sulphide minerals will provide much new information to the researchers in this area. The example of electrochemical flotation separation of sulphide ores listed in this book will demonstrate the good future of flotation electrochemistry of sulphide minerals in industrial applications. 

It is well known that the flotation of sulphides is an electrochemical process, and the adsorption of collectors on the surface of mineral results from the electrons transfer between the mineral surface and the oxidation-reduction composition in the pulp. According to the electrochemical principles and the semiconductor energy band theories, we know that this kind of electron transfer process is decided by electronic structure of the mineral surface and oxidation-reduction activity of the reagent. In this chapter, the flotation mechanism and electron transferring mechanism between a mineral and a reagent will be discussed in the light of the quantum chemistry calculation and the density fimction theory (DFT) as tools. 

The results of the electron theory as developed for semiconductors are fully applicable to dielectrics. They cannot, however, be automatically applied to metals. Contrary to the case of semiconductors, the application of the band theory of solids to metals cannot be considered as theoretically well justified as the present time. This is especially true for the transition metals and for chemical processes on metal surfaces. The theory of chemisorption and catalysis on metals (as well as the electron theory of metals in general) must be based essentially on the many-electron approach. However, these problems have not been treated in any detail as yet. 

Chapter 4 discussed semiconductivity in terms of band theory. An intrinsic semiconductor has an empty conduction band lying close above the filled valence band. Electrons can be promoted into this conduction band by heating, leaving positive holes in the valence band the current is carried by both the electrons in the conduction band and by the positive holes in the valence band. Semiconductors, such as silicon, can also be doped with impurities to enhance their conductivity. For instance, if a small amount of phosphorus is incorporated into the lattice the extra electrons form impurity levels near the empty conduction band and are easily excited into it. The current is now carried by the electrons in the conduction band and the semiconductor is known as fl-type n for negative). Correspondingly, doping with Ga increases the conductivity by creating positive holes in the valence band and such semiconductors are called / -type (p for positive). 

Chapter 2 introduces the band theory of solids. The main approach is via the tight binding model, seen as an extension of the molecular orbital theory familiar to chemists. Physicists more often develop the band model via the free electron theory, which is included here for completeness. This chapter also discusses electronic condnctivity in solids and in particular properties and applications of semiconductors. 

An important aspect of semiconductor films in general with regard to electronic properties is the effect of intrabandgap states, and particularly surface states, on these properties. Surface states are electronic states in the forbidden gap that exist because the perfect periodicity of the semiconductor crystal, on which band theory is based, is broken at the surface. Change of chemistry due to bonding of various adsorbates at the surface is often an important factor in this respect. For CD semiconductor films, which are usually nanocrystalline, the surface-to-volume ratio may be very high (several tens of percent of all the atoms may be situated at the surface for 5 mn crystals), and the effects of such surface states are expected to be particularly high. Some aspects of surface states probed by photoluminescence studies are discussed in the previous section. 

For many years, during and after the development of the modem band theory of electronic conduction in crystalline solids, it was not considered that amorphous materials could behave as semiconductors. The occurrence of bands of allowed electronic energy states, separated by forbidden ranges of energy, to become firmly identified with the interaction of an electronic waveform with a periodic lattice. Thus, it proved difficult for physicists to contemplate the existence of similar features in materials lacking such long-range order. 

The energy states of gaseous atoms split because of the overlap between electron clouds. Obviously, therefore, atoms must come much closer before the clouds of the core electrons begin to overlap compared with the distance at which the clouds of outer (or valence) electrons overlap (Fig. 6.119). Hence, at the equilibrium interatomic distances, the energy levels of the core electrons (in contrast to the valence electrons) do not show any band structure and therefore will be neglected in the following discussion. This simplified picture of the band theory of solids will now be used to explain the differences in conductivity of metals, semiconductors, and insulators. 

---