Energy band, containing electrons

The outer electrons from the atoms are then placed in the bands in a similar way to molecular orbital theory. This electronic arrangement leads to different properties, depending on the level of filling of the bands. The highest energy band containing electrons is referred to as the valence band as it contains the outer (valence) electrons. The lowest energy empty band above the valence band is called the conduction band The separation between the valence and conduction bands dictates the overall electronic properties. 

The description of the formation of energy bands contained in (2.28) and illustrated in Fig.2.7 constitutes a scaling principle according to which the unhybridised band structure of any close-packed solid of a given crystal structure may be synthesised from the same canonical bands. Hence, the unhybridised energy bands of all elemental metals with, for instance, fee structure may be obtained from the fee canonical bands shown in Fig.2.4 once their one-electron potentials (or potential parameters) are known. 

Figure 7.1 Band structure of an intrinsic semiconductor. At T = 0 the valence band is completely filled and the conduction band is empty. At higher temperatures the conduction band contains a low concentration of electrons, the valence band an equal concentration of holes. Bands with a lower energy, one of which is shown, are always completely filled.

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). 

The empirical approach [7] was by far the most fruitful first attempt. The idea was to fit a few Fourier coefficients or form factors of the potential. This approach assumed that the pseudopotential could be represented accurately with around three Fourier form factors for each element and that the potential contained both the electron-core and electron-electron interactions. The form factors were generally fit to optical properties. This approach, called the Empirical Pseudopotential Method (EPM), gave [7] extremely accurate energy band structures and wave functions, and applications were made to a large number of solids, especially semiconductors. [8] In fact, it is probably fair to say that the electronic band structure problem and optical properties in the visible and UV for the standard semiconductors was solved in the 1960s and 1970s by the EPM. Before the EPM, even the electronic structure of Si, which was and is the prototype semiconductor, was only partially known. 

In this section, we write down the explicit forms for the one-electron TDAN equations of motion for the situation where the Coulomb repulsion integral is set equal to zero. Also, we consider only the case where the band energy levels contain 2n electrons and the valence orbital of the scattered atom is initially empty. It will be obvious how to modify the equations to deal with other possible cases mostly this will involve just a change in the initial conditions. 

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... 

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