uctivity of a material can be controlled by (i) controlling number of charge carriers, n or (ii) controlling the mobility of the carriers, μ. Mobility is important for metals or electrical conductors, whereas number of carriers is important for semi-conductors and insulators. Electrons are charge carriers in metals. In ionic materials (for example ionic ceramics), conduction is result of net movement of charged particles (cations and anions) in addition to any electron motion. However, both electrons and holes are charge carriers in semiconductors and in doped conductive polymers. Thus equation 7 can be written as follows: for metals : σ = ne. q e. μe (8) for semiconductors : σ = n. q. μn + n. q. μ p..(9) for ionic materials : σ total = σ electronic + σ ionic.(10) In all conductors, semiconductors, and many insulating materials, only electronic conduction exists i.e. electrons are the only charge carriers. Ionic conduction results because of net motion of charged ions. Movement different particles in various materials depend on more than one parameter. These include: atomic bonding, imperfections, microstructure, ionic compounds, diffusion rates and temperature. Because of these, electrical conductivity of materials varies tremendously. In metals not all electrons will accelerate in the presence of an electric field. Instead the number of charge carriers is dependent on the arrangement of electron states/levels with respect to energy, and the manner in which these states are occupied by electrons. Electrons in metals are arranged into shells and sub-shells in accordance with Pauli exclusion principle. Each of these shells / sub-shells is distinguished from every other by their energy state/level. Basic existence of metals is dependent on metallic bond where large groups of atoms come together and share valence electrons in what is called metallic bond. Thus there are N atoms in the lattice with N atomic orbitals and N
4 molecular orbitals, many of which are of same energy. This leads to bands of electrons. The electrons 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 ma