Valence band theory

The first reliable energy band theories were based on a powerfiil approximation, call the pseudopotential approximation. Within this approximation, the all-electron potential corresponding to interaction of a valence electron with the iimer, core electrons and the nucleus is replaced by a pseudopotential. The pseudopotential reproduces only the properties of the outer electrons. There are rigorous theorems such as the Phillips-Kleinman cancellation theorem that can be used to justify the pseudopotential model [2, 3, 26]. The Phillips-Kleimnan cancellation theorem states that the orthogonality requirement of the valence states to the core states can be described by an effective repulsive... 

In Chapter 9, we considered a simple picture of metallic bonding, the electron-sea model The molecular orbital approach leads to a refinement of this model known as band theory. Here, a crystal of a metal is considered to be one huge molecule. Valence electrons of the metal are fed into delocalized molecular orbitals, formed in the usual way from atomic... 

Therefore, there could exist rich defects in Ba3BP30i2, BaBPOs and Ba3BP07 powders. From the point of energy-band theory, these defects will create defect energy levels in the band gap. It can be suggested that the electrons and holes introduced by X-ray excitation in the host might be mobile and lead to transitions within the conduction band, acceptor levels, donor levels and valence band. Consequently, some X-ray-excited luminescence bands may come into being. 

All these properties of metals are consistent with a bonding description that places the valence electrons in delocalized orbitals. This section describes the band theory of solids, an extension of the delocalized orbital ideas... 

A pure transition metal is best described by the band theory of solids, as introduced in Chapter 10. In this model, the valence s and d electrons form extended bands of orbitals that are delocalized over the entire network of metal atoms. These valence electrons are easily removed, so most elements In the d block react readily to form compounds oxides such as Fc2 O3, sulfides such as ZnS, and mineral salts such as zircon, ZrSi O4. ... 

Further studies were carried out on the Pd/Mo(l 1 0), Pd/Ru(0001), and Cu/Mo(l 10) systems. The shifts in core-level binding energies indicate that adatoms in a monolayer of Cu or Pd are electronically perturbed with respect to surface atoms of Cu(lOO) or Pd(lOO). By comparing these results with those previously presented in the literature for adlayers of Pd or Cu, a simple theory is developed that explains the nature of electron donor-electron acceptor interactions in metal overlayer formation of surface metal-metal bonds leads to a gain in electrons by the element initially having the larger fraction of empty states in its valence band. This behavior indicates that the electro-negativities of the surface atoms are substantially different from those of the bulk [65]. 

In order to explain the changing optical properties of AIROFs several models were proposed. The UPS investigations of the valence band of the emersed film support band theory models by Gottesfeld [94] and by Mozota and Conway [79, 88]. The assumption of nonstoichiometry and electron hopping in the model proposed by Burke et al. [87] is not necessary. Recent electroreflectance measurements on anodic iridium oxide films performed by Gutierrez et al. [95] showed a shift of optical absorption bands to lower photon energies with increasing anodic electrode potentials, which is probably due to a shift of the Fermi level with respect to the t2g band [67]. 

With the absorption of a quantum with an energy of more than 3.05 eV resp. 3.29 eV, an electron is lifted out of the valence band and into the conduction band, thereby forming an exciton (Fig. 5). This interpretation is also supported by the molecular orbital theory and the crystal field theory regarding the bonding conditions in the TiC lattice. 

According to the electronic theory, a particle chemisorbed on the surface of a semiconductor has a definite affinity for a free electron or, depending on its nature, for a free hole in the lattice. In the first case the chemisorbed particle is presented in the energy spectrum of the lattice as an acceptor and in the second as a donor surface local level situated in the forbidden zone between the valency band and the conduction band. In the general case, one and the same particle may possess an affinity both for an electron and a hole. In this case two alternative local levels, an acceptor and a donor, will correspond to it. 

Chemical bonds are defined by their frontier orbitals. That is, by the highest molecular orbital that is occupied by electrons (HOMO), and the lowest unoccupied molecular orbital (LUMO). These are analogous with the top of the valence band and the bottom of the conduction band in electron band theory. However, since kinks are localized and non-periodic, band theory is not appropriate for this discussion. 

The Schottky-Mott theory predicts a current / = (4 7t e m kB2/h3) T2 exp (—e A/kB 7) exp (e n V/kB T)— 1], where e is the electronic charge, m is the effective mass of the carrier, kB is Boltzmann s constant, T is the absolute temperature, n is a filling factor, A is the Schottky barrier height (see Fig. 1), and V is the applied voltage [31]. In Schottky-Mott theory, A should be the difference between the Fermi level of the metal and the conduction band minimum (for an n-type semiconductor-to-metal interface) or the valence band maximum (for a p-type semiconductor-metal interface) [32, 33]. Certain experimentally observed variations of A were for decades ascribed to pinning of states, but can now be attributed to local inhomogeneities of the interface, so the Schottky-Mott theory is secure. The opposite of a Schottky barrier is an ohmic contact, where there is only an added electrical resistance at the junction, typically between two metals. 

The electronic properties of solids can be described by various theories which complement each other. For example band theory is suited for the analysis of the effect of a crystal lattice on the energy of the electrons. When the isolated atoms, which are characterized by filled or vacant orbitals, are assembled into a lattice containing ca. 5 x 1022 atoms cm 3, new molecular orbitals form (Bard, 1980). These orbitals are so closely spaced that they form essentially continuous bands the filled bonding orbitals form the valence band (vb) and the vacant antibonding orbitals form the conduction band (cb) (Fig. 10.5). These bands are separated by a forbidden region or band gap of energy Eg (eV). 

According to band theory, the electrons inside a metal populate the valence band up to the highest occupied molecular orbital, which is called the Fermi level. The potential applied to a metallic electrode governs the energy of its electrons according to Figure 5. 

In conclusion, photoelectron spectroscopy evidences only a weak 5 f character in the valence band of UO2, substantially in agreement with theory. The alleged much stronger 6 d character of the valence band, especially at its bottom, has not yet been demonstrated by this method. 

---