ectrons not involved in bonding remain in what is called the core band, whereas the valence electrons that form the electron gas enter into the valence band. The remaining un-filled orbitals form higher-energy bands, called conduction band. It is the conduction band that gives metals and alloys the ability to freely conduct electrons. Four different types of band structures are possible at 0 K: (1) Where one outermost band is only partially filled with electrons. The energy corresponding to the highest filled state at 0 K is called the Fermi energy, E f. (2) There is overlap of an empty band and a filled band. (3) and (4) One filled band (valence band) and an empty band (conduction band) are separated by an energy band gap which lies between them. These are schematically shown in the figure Figure 14-1: Possible electron band structures. Band structures (1) and (2) are found in metals / conductors. Band structures (3) and (4) are distinguished by the size of energy band gap. Narrower energy band gap i.e. size < 2 ev, is found in semiconductors, while the broader energy band gap i.e. size > 4 ev, is found in insulators. Fermi energy for these two band structures lies within the band gap near its center. Metals have high conductivities because of the large number of free electrons that have been excited into empty states above the Fermi energy. If the metal crystal lattices were perfect and there are no lattice vibrations, the electrons would pass through the lattice unscattered, encountering no resistance. However, lattice vibrations and phonon scattering play a role in disrupting the mean free path of electrons. In addition, crystalline defects and impurity atom affect the conductivity. These scattering mechanisms act independently on one another. Thus the effective resistivity of metals can be represented as follows:
5 ρ = ρ thermal + ρ residual...(11) Equation 11 is some times known as Mathiessen s rule. With increase of temperature, thermal vibrations increase so the resistivity, and vice versa. In the same manner, with increase of either defects or impurities, resistivity increases. Thus, in general, for pure metals, the resistivity approaches zero at absolute zero temperature. Some metals, however, such as Pb, lose all resistivity abruptly and completely at some low temperatures. This phenomenon is called superconductivity, and the materials that exhibit it are called superconductors. The temperature at which the resistivity vanishes is called the critical transition temperature, T c. Many elemental metals, solid-solution alloys, some ceramics and intermetallic compounds exhibit superconductivity. For example: Ti, V, Zn, W, Al, Hg, NbTi, Nb 3 Sn, MgB 2, La-Sr-Cu oxide, YBa 2 Cu 3 O 7-x, carbon nanotubes, etc. BCS (Bardeen, Cooper and Schrieffer) theory explains that the super conductivity is caused by electron-lattice interaction and that the superconducting electrons consist of paired ordinary electrons called a Cooper pair Semiconductivity Conductivity of semiconductors is not as high as metals / conductors. However, their electrical properties are unique, in the sense that their electrical properties are extremely sensitive to even minute concentrations of impurities. For intrinsic semiconductors, their electrical behavior is based on inherent electronic structure of the pure material. On the other hand, if the electrical properties are dominated by impurities, they are called extrinsic semiconductors. Intrinsic semiconduction: Energy band gap between the valence and conduction bands can be used to classify materials as conductors, insulators, and semiconductors. The magnitude of the band gap is characteristic of the lattice alone, and varies widely for different crystals. In semiconductors, the valence and conduction bands do not overlap as in metals, but they possess enough electrons in the valence band those can be promoted to the conduction band at a certain temperature. Promotion of electrons leaves behind positively charged holes in the valence band which maintain the charge neutrality. These holes can be r