Resistance and Resistivity A l RA V IR but resistance is not a material property because it depends on the sample geometry Resistivity units m is the material property that describes a material s resistance to the passage of electric current independent of size and geometry Conductivity and are inversely related 1 1 Materials consist of many atoms in close proximity The Pauli exclusion principle dictates that only two electrons may reside at a given energy level Therefore rather than reside at specific discrete energy levels the electrons inhabit energy bands 2 Conductors Insulators Semiconductors Charge carriers in conductors e g most metals do not need to overcome an energy barrier to participate in electrical conduction as do semiconductors and insulators For semiconductors and insulators electrons in the valence band are associated with a particular atom while electrons in the conduction band may move from atom to atom conducting electricity 3 Metals lots of charge carriers Copper 2 10 8 m Semiconductors few charge carriers Silicon 2500 m Insulators essentially no charge carriers 10 Zirconium Oxide 1 10 m 4 Charge Carrier e g electrons Mobility V E V is the applied potential E is the applied electric field Electrons drift in the opposite direction of the applied electric field 5 Electrons do not move in a straight line they are scattered by lattice vibrations vacancies dislocations and localized strain fields The net movement is opposite the direction of the applied electric field Drift Velocity vd v d eE E is the magnitude of the electric field driving force e is the mobility It depends on the scattering frequency 6 Influence of Temperature Alloying and Deformation Temperature C 7 Resistivity vs Composition for a Ni Cu Alloy Copper 2 10 8 m Nickel 9 5 10 8 m 8 The resistivity of two phase alloys follow a simple rule of mixtures i V V Where V is the volume fraction of each phase The resistivity of single phase alloys e g solid solutions depends on the degree of scattering caused by lattice strain associated with the different atomic radii of the alloying elements Lattice strain scatters electrons decreasing their mobility thereby increasing resistivity In Callister i Ac i 1 c i 9 10 Intensity XRD Pattern of a 55 wt Cu 45 wt Ni alloy Constantan Two Theta 11 Resistivity vs Composition for a Ni Cu Alloy Copper 2 10 8 m Nickel 9 5 10 8 m 12 Intrinsic Semiconductor 13 The carrier concentration and conductivity increase with increasing temperature However generally we would prefer that conductivity displays little or no temperature dependence 14 Extrinsic Semiconductor n type 15 Extrinsic Semiconductor n type 16 Extrinsic Semiconductor p type 17 Extrinsic Semiconductor p type 18 By precise control over the dopant concentration we can control the electrical conductivity and decrease the temperature dependence of conductivity 19 21 22 p n junction In forward bias the majority carriers move towards the junction In reverse bias the majority carriers move away from the junction 23 The result is a device with easy current flow in forward bias but limited current flow in reverse bias 24 Which in turn lead to devices like this rectifier that converts AC current to DC 25
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