I. ELECTRICAL CONDUCTION • 12.2 Ohm's Law: V = I R in most cases V = DV = V2 – V1 voltage drop (volts) resistance (Ohms) current (amps) • Resistivity, r and Conductivity, s: --geometry-independent forms of Ohm's Law E: electric field intensity resistivity (Ohm-m) J: current density conductivity • Resistance: 3

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c12f05 12.6 Conduction in Terms of Band and Atomic Bonding Models Metallic character Excitation barrier is much smaller than heat (RT), noise or any background excitations. Practically anything excite electrons to the conduction band c12f05

An intrinsic semiconductor has a band gap or barrier for the electrons to get into the conduction band This barrier need a photon excitation, an external bias potential Usually RT cannot excite the electron to the conduction band. For instance, a photon of light ~4eV c12f06 c12f06

c12f07 12.7 Electron Mobility Scattering Events J = sE Electric field drifts electrons in the opposite direction to the field b/c electrons are –ve The actual speed of electrons is much higher than the drift velocity Scattering is due to the strike with the nuclei When the actual velocity of the electrons is similar to the drift velocity, the system is in the ballistic regime In the ballistic regime there is practically no barrier for the electrons Examples: in vacuum tubes, ~in carbon nanotubes (CNT), superconductors* J = sE c12f07

12.10 Intrinsic Semiconduction II. SEMICONDUCTIVITY Conductivity of semiconducting materials is lower than from metals Sensitive to minute concentrations of impurities Intrinsic: pure material Extrinsic: doped with impurity atoms 12.10 Intrinsic Semiconduction Band structure Si (1.1 eV) Ge (0.7 eV) GaAs (IIIA-VA) InSb (IIIA-VA) CdS (IIB-VIA) ZnTe (IIB-VIA) We have electrons as carriers in metals and “electrons” and ‘holes’ as carriers in semiconductors

c12f13 n-type extrinsic semiconductor c12f13

c12f14 p-type extrinsic semiconductor c12f14

c12f15 p-type extrinsic semiconductor c12f15

Intrinsic carrier increases rapidly with temperature c12f16 c12f16

c12f17 n-type silicon 1021/m3 c12f17

12.14 The Hall Effect c12f20 How we can determine the type of carriers? Use magnetic fields The Hall voltage The Hall coefficient c12f20

p-n rectifying junction c12f21 Flow of electrons in one direction only convert alternating current to direct current Processing: diffuse P into one side of a B-doped crystal. • Results: --No applied potential, no net current flow. --Forward bias: carriers flow through p-type and n-type regions; holes and electrons recombine at p-n junction; current flows. --Reverse bias: carrier flow away from p-n junction; carrier conc. greatly reduced at junction; little current flow. c12f21

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The Junction Transistor c12f24 c12f24

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c12f26 The MOSFET c12f26

c12eqf01 12.17 Electrical properties of polymers Usually poor conductors of electricity Mechanism not well-understood Conduction in polymers of high purity is electronic Conducting Polymers Conductivities of 1.5x107 (W-m)-1 Even polyacetylene Due to alternating single-double bonds

c12f28 Dielectric Behavior Do = eoE Do = eoE + P Dielectric material Electric dipole structure Charge separation Do = eoE c12f28 eo= permittivity of vacuum = 8.85x10-12 F/m Do = eoE + P Dielectric Behavior

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c12f29 p = qd Do = eoE D= e E 12.19 Field vectors and polarization Surface charge density or dielectric displacement (C/m2) Do = eoE For the dielectric case D= e E

c12f31 Do = eoE + P where P is the polarization (C/m2) P= eo(er – 1)E or total dipole moment per unit of volume of the dielectric c12f31 P= eo(er – 1)E

c12f32 Electronic Polarization Ionic polarization Orientation polarization

12.21 Frequency Dependence of the dielectric constant c12f33 Response to alternating fields Reorientation time --- relaxation frequency

12.22 Dielectric Strength Substance Dielectric Strength (MV/m) Air 3 Quartz 8 Strontium titanate Neoprene rubber 12 Nylon 14 Pyrex glass Silicone oil 15 Paper 16 Bakelite 24 Polystyrene Teflon 60

c12f34 Frequency dependence of the dielectric constant c12f34

SUMMARY --material parameters. • Electrical conductivity and resistivity are: --material parameters. --geometry independent but not at small scale (nano) • Electrical resistance is: --a geometry and material dependent parameter. • Conductors, semiconductors, and insulators... --different in whether there are accessible energy states for conductance electrons. • For metals, conductivity is increased by --reducing deformation --reducing imperfections --decreasing temperature. • For pure semiconductors, conductivity is increased by --increasing temperature --doping (e.g., adding B to Si (p-type) or P to Si (n-type). 15