The Energy Band Picture

In semiconductors, the valence band is full and the conduction band is empty, but the energy gap between these two bands is very small. At very low temperatures, close to T = 0, the conductivity of the semiconductors is zero and the energy-band picture looks like that of an insulator (Fig. 7.3). As temperature increases, however, the tail of the Fermi distribution brings some electrons into the conduction band and conductivity increases (Fig. 7.5). That is, as temperature increases, some electrons obtain enough energy to cross over to the... 

The energy band picture and density of states, Figure 5, is now reminiscent of that of a semiconductor indeed, for polyacetylene an energy gap of 1.4 eV is measured and a conductivity at room temperature of 10 (ohm-cm) is known [5]. These values are similar to those of the semiconductor silicon. Doping of polyacetylene with anions such as 13 and CIO and cations such as Na+ leads to an increase in conductivity to nearly metallic values as illustrated in Figure 8. 

The simple picture of the MOS capacitor presented in the last section is complicated by two factors, work function differences between the metal and semiconductor and excess charge in the oxide. The difference in work functions, the energies required to remove an electron from a metal or semiconductor, is 0ms = —25 meV for an aluminum metal plate over a 50-nm thermally grown oxide on -type silicon with n = 1016 cm-3. This work function difference leads to a misalignment of energy bands in the metal and semiconductor which has to be compensated by a variation of the energy band with distance. When there is no misalignment the flat-band condition results. 

In metals beyond Group IA, the picture becomes more complicated as both the s and p orbitals are used to form the band of MOs, which then contains many more orbitals than the number of electron pairs available. The criterion for electrical conductivity, a property associated with metals, is that the energy band be only partially filled. 

The picture that emerges is remarkable and applies to all tetrahedral semiconductors. The principal peak in the optical absorption comes at an energy determined by matrix elements between p orbitals, rather than between hybrids. To be sure, the s orbitals are necessary for any reasonable description of the energy bands or for calculating the full absorption spectrum, but the strongest features in X2(< ) and, by Eq. (4-4), in Xi(w), and perhaps in all dielectric properties, are dominated by p orbitals. 

For solids with heavy atoms, relativistic shifts may affect the bonding properties, and also optical properties may be influenced. The relativistic shifts of the 5d bands relative to the s-p bands in gold change the main inter band edge more than 1 eV. Already Pyykko and Desclaux mentioned [1] that the fact that gold is yellow is a result of relativistic effects. These are indirect [2] (see also the introduction. Sect. 1), and the picture was confirmed by relativistic band structure calculations [3,4]. Also the optical properties of semiconductors are influenced by relativistic shifts which affect the gap between occupied and empty states, see for example Ref. [5]. Two additional examples may be mentioned where relativistic shifts in the energy band structure drastically influence the physical properties. First,... 

From the entries in Table 4.1 and (3.50,4.16,18) it is simple to establish the overall picture of the energy bands of chromium presented in Fig.4.1. In this connection one should note the following points. 

Light-induced processes are described quite differently in molecular photochemistry and solid-state photophysics. In photochemistry one is used to an atomistic picture in which the arrangement of the atoms in the structure of a single molecule determines the electronic levels and thus the photochemical behavior. In contrast, the electronic levels of a solid are determined by the infinite periodicity of the atomic sequence in the crystal lattice. This leads to a basic concept according to which the solid can be treated as a dielectric continuum. Atomistic irregularities in the crystalline structure, such as lattice defects or impurities, are treated as perturbations of the spatially independent states in the energy bands. 

The simplest band picture of a semiconductor is drawn in Figure 13.7. The energy gap between the top of the valence band, Ey, and the bottom of the... 

The simplest band picture of a p-n junction is shown in Figure 13.15. In separated materials, the Fermi energies are unequal (Figures 13.15a and 13.15b). When a p-type region abuts an n-type... 

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