Molecular orbital theory semiconductors

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. 

Use molecular orbital theory to account for the differences between metals, insulators, and semiconductors (Sections 3.13 and 3.14). 

Molecular orbitals, in organic semiconductors, 22 211 Molecular orbital theory, 16 737 Molecular orientation, in linear low density polyethylene, 20 188-189 Molecular oxygen, 17 746. See also Oxygen (0)... 

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. 

Extensions of this model in which the atomic nuclei and core electrons are included by representing them by a potential function, V, in Equation (4.1) (plane wave methods) can account for the density of states in Figure 4.3 and can be used for semiconductors and insulators as well. We shall however use a different model to describe these solids, one based on the molecular orbital theory of molecules. We describe this in the next section. We end this section by using our simple model to explain the electrical conductivity of metals. 

We know that not all solids conduct electricity, and the simple free electron model discussed previously does not explain this. To understand semiconductors and insulators, we turn to another description of solids, molecular orbital theory. In the molecular orbital approach to bonding in solids, we regard solids as a very large collection of atoms bonded together and try to solve the Schrodinger equation for a periodically repeating system. For chemists, this has the advantage that solids are not treated as very different species from small molecules. 

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. 

Our results will be based on the one electron energy band theory of solids (13) that forms the basis for the present-day understanding of metal and semiconductor physics. It is the counterpart of the chemist s molecular orbital theory, and we shall try to relate our results back to the underlying atomic structure. 

Electronic band structures were calculated for several polymeric chains structurally analogous to polyacetylene (-CH-CH) and carbyne (-CbC). Ihe present calculations use the Extended Huckel molecular orbital theory within the tight binding approximation, and values of the calculated band gaps E and band widths BW were used to assess the potential applic ilitf of these materials as electrical semiconductors. Substitution of F or Cl atoms for H atoms in polyacetylene tended to decrease both the E and BW values (relative to that for polyacetylene). Rotation about rhe backbone bonds in the chains away from the planar conformations led to sharp increases in E and decreases in BW. Substitution of -SiH or -Si(CH,) groups for H in polyacetylene invaribly led to an increase in E and a decrease in BW, as was generally the case for insertion of Y ... 

The band structure of a three-dimensional solid, such as a semiconductor crystal, can be obtained in a similar fashion to that of a polyene. Localized molecular orbitals are constructed based on an appropriate set of valence atomic orbitals, and the effects of delocalization are then incorporated into the molecnlar orbital as the number of repeat units in the crystal lattice is increased to infinity. This process is widely known to the chemical conununity as extended Hiickel theory (see Extended Hiickel Molecular Orbital Theory). It is also called tight binding theory by physicists who apply these methods to calcnlate the band structures of semiconducting and metallic solids. 

B. Smith et al. extended the basic Anderson-Newns model introduced in the previous section to electron transfer reactions at semiconductor-liquid interfaces, related them to molecular orbital theory, and addressed certain inherent energy dependencies in them [23]. These authors also performed for the first time electronic structure calculations coupled to molecular dynamics simulations, i.e. they carried out first principle" molecular dynamic calculations. Their principal approach is as follows. 

In Section 11.6 we saw that the ability of metals to condnct heat and electricity can be explained with molecular orbital theory. To gain a better nnderstanding of the conductivity properties of metals we must also apply our knowledge of qnantnm mechanics. The model we will use to study metallic bonding is band theory, so called becanse it states that delocalized electrons move freely through bands formed by overlapping molecular orbitals. We will also apply band theory to certain elements that are semiconductors. 

Figure 12.23 shows that, in small molecules, electrons occupy discrete molecular orbitals whereas in macroscale solids the electrons occupy delocalized bands. At what point does a molecule get so large that it starts behaving as though it has delocalized bands rather than localized molecular orbitals For semiconductors, both theory and experiment tell us that the answer is roughly at 1 to 10 nm (about 10—100 atoms across). The exact number depends on the specific semiconductor material. The equations of quantum mechanics that were used for electrons in atoms can be applied to electrons (and holes) in semiconductors to estimate the size where materials undergo a crossover from molecular orbitals to bands. Because these effects become important at 1 to 10 nm, semiconductor particles with diameters in this size range are called quantum dots. 

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