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CONDUCTING MATERIALS-BASICS
- 1. Silicon atomic structureFig.1TheSI unit of electric current is ampere (A)The SI unit of resistance is ohm (Ω)Introduction<br />All the substances are broadly classified into two groups, namely conductors and insulators. As you know that a substance is made up of atoms and electrons revolve around the nucleus of an atom in different orbits. In some substances, some electrons from the outermost shell of an atom get detached very easily and move freely in whole of the substance. Such a substance is called a metal.(The other substance from which an electron cannot get detached from the atom is called non-metal.)<br />Thus, a conductor (metal) is a collection of positive ions fixed at their position and a large number of free electrons moving freely here and there in the conductor. The free electrons follow a zigzag path inside a conductor. Note that these free electrons cannot come out of the conductor but are free to move anywhere in the conductor.<br />Consider a conductor placed in a region. Initially, there is no electric field and the conduction electrons are almost uniformly distributed within the conductor. (Shown by dots in fig.1)<br />Electric Current<br />The electric current is defined as the rate of flow of electric charge i.e., quantity of charge flowing per unit time. Suppose ‘q’ is the amount of charge that passes through the surface in a time‘t’. The current is given by<br />I = amount of chargetime = qt <br />Ohm’s law and Resistance<br />“The electric current I flowing through a conductor is directly proportional to the potential difference across the two ends of the conductor”.<br />Mathematically, V ∝ I<br />OrV = I R <br />Where R is a “constant” and is called the resistance of the conductor.<br />A wire or an electrical device which offers resistance to the flow of current is called a resistor. The resistance of a conductor is<br />i). directly proportional to the length of the conductor.<br />R ∝ L<br />ii).inversely proportional to the cross-sectional area of the conductors.<br />R ∝ 1A<br /> <br />The SI unit of resistivity or specific resistance is ohm meter (Ωm). Conductor I A Fig.2The SI unit of current density is ampere-meter−2 (A-m−2)The SI unit of electric field is volt-meter−1 (V-m−1)Electrical conductivity σ = JEThe SI unit of electrical conductivity is mho−1-m−1 (Ω−1-m−1)From above, R ∝ LA<br />Or R = ρ LA<br />Where ρ is a constant and is called the resistivity or specific resistance of the material.<br />Current density (J) <br />Current density is defined as the current per unit area of cross-section of an imaginary plane held normal to the direction of flow of current in a current carrying conductor.<br />If ‘I’ is the current and ‘A’ is the area of cross-section (as shown in fig.2), then current density is given by<br />J = IA<br />Electric Field (E)<br />The electric field E, of a conductor of uniform cross-section is defined as the potential Difference (voltage) V per unit length.<br />E = VL<br />Electrical Conductivity<br />From ohm’s law <br />V = IR<br />We knowR = LρA<br />∴ V = I LρA<br /> = ILAσ <br />(Resistivity ρ = 1σ and<br /> σ is a conductivity)<br />IA = σ VL<br />J = σ E {J =IA and E = VL}<br />Orσ = JE<br />Thus electrical conductivity can be defined as, the rate of charge flow across a unit area per unit potential gradient with in a conductor.<br />Velocity = DistancetimeDrift velocity is defined as the average velocity gained by the charge carriers in the presence of an electric field.Mobility of the charge carrier is defined as the drift velocity per unit electric field.µ = vdEThe SI unit of mobility is m2 V−1 s−1 The relation between current density and mobility<br />Electric current I = amount of chargetime = qt <br />If ‘n’ is the charge carrier density in a conductor of length ‘L’ with area of cross-section ‘A’ then, the current flow through the conductor in time ‘t’ is given by<br /> I=n e A Lt<br />=n e A vd<br />Where vd=Lt and is called drift velocity. Drift velocity is defined as the average velocity gained by the charge carriers in the presence of an electric field.<br />We know the current density<br />J = IA<br />I value substitute in the equation <br />J = n e A vdA<br />J=n e vd<br />We know the conductivity<br />σ = JE<br />=n e vdE<br />=n e vdE<br />σ=n e µ<br />Where µ = vdE is called mobility of the charge carrier. Mobility of the charge carrier is defined as the drift velocity per unit electric field.<br />