Energy bands in metals

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

It should be noted that such a local view is entirely inappropriate for covalent semiconductors such as silicon, in which the electrons are completely delocalized over the material. This local vs. delocalized view is a key feature that distinguishes metal oxide semiconductors from their covalently bonded counterparts. The local character of the energy bands in metal oxides sometimes leads to ambiguous interpretatiOTis. For example, free electrons in Ti02 are sometimes distinguished from Ti species. While such a distinction may be realistic at the surface of a material, where the electronic structure is distorted due to a disruption of the lattice symmetry, it is not obvious in the bulk in which the conduction band is mainly composed of Ti 3d orbitals. 

Figure 25.15 Energy bands in metals (conductors), semiconductors, and insulators.

The reciprocal lattice is useful in defining some of the electronic properties of solids. That is, when we have a semi-conductor (or even a conductor like a metal), we find that the electrons are confined in a band, defined by the reciprocal lattice. This has important effects upon the conductivity of any solid and is known as the "band theory" of solids. It turns out that the reciprocal lattice is also the site of the Brillouin zones, i.e.- the "allowed" electron energy bands in the solid. How this originates is explciined as follows. 

We have shown the least complicated one which turns out to be the simple cubic lattice. Such bands are called "Brilluoin" zones and, as we have said, are the allowed energy bands of electrons in any given crystalline latttice. A number of metals and simple compounds have heen studied and their Brilluoin structure determined. However, when one gives a representation of the energy bands in a solid, a "band-model is usually presented. The following diagram shows three band models ... 

The occupation of the energy levels of the conduction band in metals is described by the Fermi function... 

Figure 4.6 The filling of energy bands in a metal (sodium) and in an insulator (sodium chloride).

As shown by Ruderman and Kittel (77) and Bloembergen and Rowland (78), Aij in a solid is dependent on the nature of the energy bands in the solid. For metals A is proportional to the product of the square of the electron density of Fermi surface electrons at the nucleus and the effective mass, and decreases as the inverse cube of the internuclear distance. Insulators have been treated by the energy band method (78) and by a molecular method (79) where each atom is considered to be bonded to its nearest neighbors. Unfortunately, both of these methods involve approximations in the evaluation of An which are quite crude at present. 

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. 

Understanding the behavior of a MOS capacitor is useful in understanding the operation of a MOS transistor. When a negative voltage is applied to the conductor or metal, the energy bands in the p-type semiconductor... 

Conduction bands in metals represent at the moment the most interesting problems. Fig. 8 shows a spectrum obtained of the low energy range of gold. The small intensity-s-band 30) extending to the Fermi level (EF) is clearly visible. The spectrum itself is in good agreement with predictions by relativistic... 

For metallic materials, charges are conducted by electrons or holes because most of the energy bands of metals are partially filled. A common equation for the electrical conductivity of metals can be derived from the following simple model. Applying Newton s second law to an electron in a crystal, it yields... 

Here 1 labels the electronic states of the SWCNT with the chiral index (p,0), which are described by a simple two-band k p model based on an effective mass approximation [4], p being equal to 3M + v with integer M and v = 0( 1) for metallic (semiconducting) SWCNTs. The energy bands in Eq.(3) are given by... 

We are not going here to discuss the rf-likc energy bands of metallic transition elements except for two pioneer studies (237,238) and an important demonstration (239) that palladium-silver alloys behave as if individual I(Pd4d) and I(Ag4d) remain distinct. Watson and Perlman discuss gold and its alloys in great detail in the present volume. Many authors (240—245) have studied the valence region of... 

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