Formation of electron energy bands

Most metal oxides are ionic crystals and belong to either the class of semiconductors or insulators, in which the valence band mainly comprises the frontier orbitals of oxide ions and the conduction band contains the frontier orbitals of metal ions. In forming an ionic metal oxide ciTstal from metal ions and oxide ions, as shown in Fig. 2-21, the crystalline field shifts the frontier electron level of metal ions to higher energies to form an antibonding band (the conduction 

For ionic crystals, the band gap, e, appears to be a linear function of the bond energy as shown in Eqn. 2-34 and in Fig. 2-25  

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Fig. 2-3. Formation of electron energy bands in constructing a solid crystal X from atoms of X ro = stable atom-atom distance in crystal BB = bonding band ABB = antibonding band e, = band gap.

Fig. 2-21. Formation of electron energy bands in metal oxides from isolated metal ions and oxide ions.

Fig. 2-29. Formation of electron energy bands and surface danj ing states of silicon crystals DL-B = dangling level in bonding DL-AB = dangling level in antibonding.

The photoluminescence properties of Tl[Au(CN)2] (103) and related cona-plexes have been extensively studied by Nagle, Patterson, and co-workers [175]. Covalent Tl-Au interactions in 103 have been suggested and supported by electronic structure calculations. Yeisin and co-wo-kers also report the pressure dependence emissive behavior of M[Au(CN)2] [M K (10applied hydrostatic pressure is increased from 0 to 30 kbar [176]. This observation has been related to the quasi-one-dimensional metal-metal interactions and the quasi-two-dimensional formation of electronic energy bands. 

One further effect of the formation of bands of electron energy in solids is that the effective mass of elecuons is dependent on the shape of the E-k curve. If dris is the parabolic shape of the classical free electron tlreoty, the effective mass is the same as tire mass of the free electron in space, but as tlris departs from the parabolic shape the effective mass varies, depending on the curvature of tire E-k curve. From the dehnition of E in terms of k, it follows that the mass is related to the second derivative of E widr respect to k tlrus... 

Fig. 2-12. Electron energy band formation of silicon crystals from atomic frontier orbitals number of silicon atoms in crystal r = distance between atoms rg = stable atom-atom distance in crystals, sp B8 = bonding band (valence band) of sp hybrid orbitals sp ABB = antibonding band (conduction band) of sp hybrid orbitals.

The decomposing ionization will take place preferentially by way ofthe electron-hole pair formation, if the formation energy of the electron-hole pair, e, is smaller than the formation energy of the cation-emion vacancy pair, Hv(ab>, and vice versa. In general, compound semiconductors, in which the band gap is small (e,< Jfv(AB>), will prefer the formation of electron-hole pairs whereas, compound insulators such as sodium chloride, in which the band gap is great (e(>Hv(AB>), will prefer the formation of cation-anion vacancy pairs [Fumi-Tosi, 1964]. 

As shown in Fig. 3.4b, when a semiconductor electrode is illuminated with photons having an energy hv equal to or larger than the semiconductor handgap the result is formation of electronic charge carriers, electrons in the conduction band and holes in the valence band, see equation (3.2.1). 

Figure 4.3 Formation of electronic bands in a hypothetical array of hydrogen atoms, (a) Two H atoms, infinitely far apart, (b) Two H atoms interacting (as in the actual H2 molecule), (c) Four, (d) eight, and (e) a very large number of H atoms interacting. The dots or (in the band) shading represent the occupancy of the energy levels by the electrons, in the absence of thermal excitation. (/) Percentage distribution of the electron population in a band at a nonzero temperature.

Our results clearly show that modification of the electronic state of titanium oxide by metal ion implantation is closely associated with the strong and longdistance interaction which arises between the titanium oxide and the metal ions implanted, as shown in Fig. 13, and not by the formation of impurity energy levels within the band gap of the titanium oxides resulting from the formation of impurity oxide clusters which are often observed in the chemical doping of metal ions, as shown in Figs. 6 and 13. 

When a semiconductor electrode is in contact with an electrolyte solution, thermodynamic equilibration takes place at the interface. This may result in the formation of a space charge layer within a thin surface region of the semiconductor, in which the electronic energy bands are generally bent upwards or downwards, respectively, in the cases of n- and p-type semiconductors. Fig. 2.3... 

It is possible that partially decrease of selected energy of EAi+ = 0,3 keV. Possibly, the a E) drop is connected with the formation of Cd-C complexes, which create the deep traps for capture of free electrons. The appearance of such traps in energy range of HOMO-LUMO confirms in the formation of the new bands of the emission of excitons for the Cd-C6o mixture... 

It should be noted that this view does not exclude conformational and configurational changes upon radical anion or radical cation formation, which have clearly been established for small organic radical anions and radical cations (see Sect. 1). These are not evidenced, however, by the absorption spectra of the ionic species because the spectra reflect the electronic energy band scheme, after occurrence of the geometric relaxation. 

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