h the voltage is applied. Units for ρ are ohm-meters (Ω-m). Reciprocal of the electrical resistivity, known as electrical conductivity (σ), is used to express the electrical behavior of a material, which is indicative of the ease with which a material allows of flow of electrons. 1 σ = = ρ l RA....(3) Electrical conductivity has the following units: (Ω-m) -1 or mho/meter. Resistivity or conductivity does not depend on the dimensions of the material. These properties are microstructure-sensitive instead, like many other intrinsic properties, for example yield strength. Thus either of it (usually conductivity) allows us to compare different materials. Solid engineering materials exhibit very wide range of electrical conductivity (about 27 orders of variation). Hence the materials for electrical applications are classified according to their electrical conductivity as: conductors, semiconductors and insulators/dielectrics. Metals are conductors having conductivities in range of 10 7 (Ω-m) -1, while semiconductors have conductivities in range from 10-6 to 10 4 (Ω-m) -1, and materials with conductivity lower than (Ω-m) -1 are termed as insulators. In components designed to conduct electrical energy, minimizing losses is important to conserve energy as well as minimize heating. The electric power (P) lost when a current flows through a material is given by: P = VI = I 2 R..(4) Electrical losses are also known as Joule heating losses. Second form of Ohm s law can be obtained by combining the equations (3) and (4) to give: I A V = σ J = σe (5) l where J current density (A/cm 2 ), E electric field strength (V/cm).
3 Current density can be defined in different terms as J = n. q. v..(6) where n number of charge carriers (1/cm 3 ), q charge on each carrier (1.6x10-19 C), v - average drift velocity (cm/s), which occurs as a result of an applied electric or magnetic field. The term v /E is called mobility, μ (cm 2 /V.s) of the carriers, thus σ = n.q.μ.(7) From the above equation, the following can be concluded: electrical conductivity 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 el