3 12.2 Ohm's Law: V = I R in most cases V = V = V 2 – V 1 voltage drop (volts)resistance (Ohms) current (amps) Resistivity, and Conductivity, : --geometry-independent.

3

• 12.2 Ohm's Law: V = I R in most cases V = V = V2 – V1

voltage drop (volts) resistance (Ohms)current (amps)

VIe-

A(cross sect. area)

L

• Resistivity, and Conductivity, :

--geometry-independent forms of Ohm's Law

VL

IA

E: electricfieldintensity

resistivity(Ohm-m)

J: current density

I

conductivity• Resistance:

R

LA

L

A

I. ELECTRICAL CONDUCTION

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12.6 Conduction in Terms of Band and Atomic Bonding Models

Metallic characterExcitation barrier is much smaller than heat (RT), noise or any background excitations. Practically anything excite electrons to the conduction band

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

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Scattering EventsElectric field drifts electrons in the opposite direction to the fieldb/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 = E

Ed

e

=

12.7 Electron Mobility

12.10 Intrinsic Semiconduction

II. SEMICONDUCTIVITYConductivity of semiconducting materials is lower than from metalsSensitive to minute concentrations of impuritiesIntrinsic: pure materialExtrinsic: doped with impurity atoms

Band structureSi (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

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n-type extrinsic semiconductor

nee

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p-type extrinsic semiconductor

peh

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p-type extrinsic semiconductor

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Intrinsic carrier increases rapidly with temperature

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n-type silicon1021/m3

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12.14 The Hall Effect

d

BIRV zxH

H

How we can determine the type of carriers?Use magnetic fieldsThe Hall voltage

The Hall coefficient

neRH

1

nee

He R

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p-n rectifying junction

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.

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The Junction Transistor

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The Junction Transistor

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The MOSFET

12.17 Electrical properties of polymers

Usually poor conductors of electricityMechanism not well-understoodConduction in polymers of high purity is electronic

Conducting PolymersConductivities of 1.5x107 (-m)-1

Even polyacetyleneDue to alternating single-double bonds

Dielectric Behavior

Dielectric materialElectric dipole structureCharge separation

V

QC

l

AC

or

Do = oE

Do = oE + P

o= permittivity of vacuum = 8.85x10-12 F/m

l

AC o

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12.19 Field vectors and polarization

p = qd

Surface charge density or dielectric displacement (C/m2)

Do = oE

For the dielectric caseD= E

P= o(r – 1)E

Do = oE + P where P is the polarization (C/m2)or total dipole moment per unit of volume of the dielectric

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Orientation polarization

Ionic polarization

Electronic Polarization

Response to alternating fields

12.21 Frequency Dependence of the dielectric constant

Reorientation time --- relaxation frequency

Substance Dielectric Strength (MV/m)

Air 3

Quartz 8

Strontium titanate 8

Neoprene rubber 12

Nylon 14

Pyrex glass 14

Silicone oil 15

Paper 16

Bakelite 24

Polystyrene 24

Teflon 60

12.22 Dielectric Strength

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Frequency dependence of the dielectric constant

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• 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).

SUMMARY