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Lecture 15

# Lecture 15 - Electrical Properties Electrical Properties...

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1 Electrical Properties ISSUES TO ADDRESS. .. • How are electrical conductance and resistance characterized? • What are the physical phenomena that distinguish conductors, semiconductors, and insulators? • For metals, how is conductivity affected by imperfections, T , and deformation? • For semiconductors, how is conductivity affected by impurities (doping) and T ? Electrical Properties

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2 • Scanning electron microscope images of an IC: • A dot map showing location of Si (a semiconductor): -- Si shows up as light regions. • A dot map showing location of Al (a conductor): -- Al shows up as light regions. Fig. (a), (b), (c) from Fig. 18.0, Callister 7e . Fig. (d) from Fig. 18.27 (a), Callister 7e . (Fig. 18.27 is courtesy Nick Gonzales, National Semiconductor Corp., West Jordan, UT.) (b) (c) View of an Integrated Circuit 0.5mm (a) (d) 45 μ m Al Si (doped) (d) Electrical Conduction Resistivity, ρ and Conductivity, σ : -- geometry-independent forms of Ohm's Law E : electric field intensity resistivity (Ohm-m) J : current density conductivity -- Resistivity is a material property & is independent of sample ρ = Δ A I L V σ= 1 ρ • Resistance: σ = ρ = A L A L R Ohm's Law: Δ V = I R voltage drop (volts = J/C) C = Coulomb resistance (Ohms) current (amps = C/s) I e - A (cross sect. area) Δ L
3 Electrical Properties • Which will conduct more electricity? • Analogous to flow of water in a pipe • So resistance depends on sample geometry, etc. D 2 D λ λ I VA RA = = ρ Definitions Further definitions J = σ ε <= another way to state Ohm’s law J current density ε electric field potential = V / λ or ( Δ V / Δλ ) flux a like area surface current A I = = Current carriers • electrons in most solids • ions can also carry (particularly in liquid solutions) Electron flux conductivity voltage gradient J = σ ( Δ V / Δλ )

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4 • Room T values (Ohm-m) -1 Selected values from Tables 18.1, 18.3, and 18.4, Callister 7e . Conductivity: Comparison Silver 6.8 x 10 7 Copper 6.0 x 10 7 Iron 1.0 x 10 7 METALS conductors Silicon 4 x 10 -4 Germanium 2 x 10 0 GaAs 10 -6 SEMICONDUCTORS semiconductors = ( Ω -m) -1 Polystyrene <10 -14 Polyethylene 10 -15 -10 -17 Soda-lime glass 10 Concrete 10 -9 Aluminum oxide <10 -13 CERAMICS POLYMERS insulators -10 -10 -11 What is the minimum diameter ( D ) of the wire so that Δ V < 1.5 V? Example: Conductivity Problem 100m Cu wire I = 2.5A - + e - Δ V Solve to get D > 1.87 mm < 1.5V 2.5A 6.07 x 10 (Ohm-m) 7- 1 100m I V A L R Δ = σ = 4 2 D π
5 Electronic Band Structures Adapted from Fig. 18.2, Callister 7e .

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Lecture 15 - Electrical Properties Electrical Properties...

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