Chapter10 Electrical Properties

8/3/2019 Chapter10 Electrical Properties

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Chapter 10 Electrical Properties

Preet M. Singh

(404) 894-6641

[email protected]

MSE 2001

Chapter 10 Electrical Properties

Electrical Conduction

Charge per carrier

Mobility

Energy bands and number of charge carriers

Conductors, semiconductors and insulators

Ionic conduction

Conducting polymers

Superconductivity Semiconductors

Intrinsic and extrinsic conduction

Role of defects

Simple devices

Microelectronics


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Electrical Conduction

V = IR

Ohms Law

Positive

potential

Negative

potential

AR

L

1

Resistivity conductivity

Electrical conductivities for a variety of materials at rootemperature

Metals and alloys [( -cm)-1]Al 3.8 x 10

5

Ag 6.3 x 105

Au 4.3 x 105

Co 1.6 x 105

Cr 7.8 x 104

Cu 6.0 x 105

Fe 1.0 x 105

Mg 2.2 x 105

Ni 1.5 x 105

Pd 9.2 x 104

Pb 4.8 x 104

Pt 9.4 x 104

Sn 9.1 x 104

Ta 8.0 x 104

Zn 1.7 x 105

Zr 2.5 x 104

Plain carbon steel (1020) 1.0 x 105

Stainless steel (304) 1.4 x 104

Gray cast iron 1.5 x 104


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Electrical conductivities for a variety of

materials at room temperature

Ceramics [(-cm)-1]ReO3 5.0 x 10

5

CrO2 3.3 x 104

SiC 1.0 x 10-1

Fe3O4 1.0 x 102

SiO2


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Conductivity Depends on

The number of mobile charge carriers per

unit volume (N with units of m-3)

Charge per Carrier, q (units of C)

The mobility of the charge,, with unitsm2/(V-s)

Nq

Charge Carriers

Electrons (metals and some covalent bonds), q

Ions (ionic solids), then q = qe * Z

Z is the valence of the ion


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Collisions

Charge Mobility, Same as diffusion driven by charge gradient

Charge Mobility

E

vor

,

mobilityelectronisWhere

strengthfieldelectrictoalproportionis

fieldappliedtodueonacceleratiofmagnitudeSince

Ev

or

Ev

tavVelocityDrift


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Charge

Mobility

Thermal vibrations

Foreign atomsVacancies

0

T

0

dN

The Influence of Alloying on Conductivity


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The Influence of Cold Work on Conductivity

Increasing electronegativity,increased tendency to add electrons

Increasingatomicradius

Alkalimetals

Alkalineearth

metals

Halogens

Noble

gases

6C

14Si

32Ge

sp3 hybridized orbitals


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Energy,eV

Energy-level diagram for the orbital electrons in a 12C atom.

Primary Bonds

Na

Na+

rNa = 0.186nm

rCl = 0.107nm

rNa = 0.098nm+

rCl = 0.181nm-

Cl

Cl-Ionization

potential

Electron

affinity

Energy required: 5.14 eV Energy released: 4.02 eV


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Metallic Bond

Ion cores of

2+ charge

Delocalized cloud

of valence electrons

Schematic of metallic bonds in solid magnesium

Atomic Structure

Energy

Principal quantum number, n1 2 3 4 5 6 7

s

ps

ps

ps

ps

ps

ps

d

d

d

d

df

f

f

Schematic representation of

the relative energies of the

electrons for the various shellsand subshells.


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Energy Bands in Solids

The permissible energy levels

are a function of separation

distance. Discrete energy levels in the

isolated atoms spread intobands in the solid.

Outermost atoms no longerspatially localized to a particularatom.

The energy bands becomewider as the amount of overlapincreases.

The higher the energy level, thewider the corresponding energyband.

The number of energy levels inan energy band equals thenumber of atoms in the solidmultiplied by the number ofdiscrete energy states in anisolated atom.



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Electron Distributions in an Energy Band

N = 2 N = 0 N = 2

Sparsely filled Nearly filledCompletely filled

Electron Distribution in a Sparsely Filled Energy BandOriginalemptyResulting hole

after jump


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Electron Distribution in a Partially Filled Band as

a Function of Temperature

T = 0K T1 > 0K T2 > T1

Fermi-Dirac Statistics

1

exp 1f

f EE E

kT


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Effect of Temperature on theDistribution of Electrons in aPartially Filled Electron Band

Permissible by Fermi-Diracbut not allowed since in

band gap N = 0

Energy Distribution for Solids with a Band Gap


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Permissible byboth Fermi-Dirac

and band structure

Charge carrier

Hole invalence

band

Charge carrier


kT

E

oe

g

NN2

expNumber of Electrons in Conduction Band


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Energy Band Diagram for Three Classes of

Electrical Materials At 0K

Conductor Semiconductor Insulator

Electron Band Structure for Solid Sodium


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Electron Band Structure for Solid Magnesium

Reference

ConductorTemperature

(C) o(-cm) e (C-1)Al 20 2.65 x 10-6 0.0043

Ag 20 1.59 x 10-6

0.0041

Au 20 2.35 x 10-6 0.0040

Co 20 6.24 x 10-6 0.0060

Cr 0 1.29 x 10-5 0.0030

Cu 20 1.67 x 10-6 0.0068

Fe 20 9.71 x 10-6 0.0065

Mg 20 4.45 x 10-6 0.0065

Ni 20 6.84 x 10-6 0.0069Pd 20 1.08 x 10

-50.0038

Pb 20 2.06 x 10-5

0.0034

Pt 20 1.06 x 10-5 0.0039

Sn 0 1.10 x 10-5 0.0047

Ta 25 1.25 x 10-5 0.0038

Zn 20 5.92 x 10-6 0.0042

Zr 20 4.00 x 10-5 0.0044

TTeo 1)(

Resistivity at Temp (T)

o= Resistivity at a

Reference Temperature

e= Temp. Coefficient of

Resistivity

T = T-T Reference

Effect of Temperature on Electrical Resistivities of selected conductors


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Temperature Measurement by a Thermocouple

SemiconductorsIntrinsic and Extrinsic Conductivities


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Intrinsic Conductivity of Semiconductor

hheee NNq

Conductivity of Semiconductors (when Ionic Conduction in Negligible)

heee qN or

kT

E

oe

g

NN2

expFor band gap materials

kT

E

heeo

g

qN2

exp

kT

E

o

g

2exp heeoo qN Where

Tk

Ego

1

2lnln or

Intrinsic Conductivity of Semiconductor


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Effect of Doping

Effect of Doping


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Effect of Doping

Effect of Defects


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Superconductivity


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Homework Assignment(Not to be turned-in)

2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 18, 19,23, 24, 25, 34, 36, 37, 38, 39, 43, 46, 47, 54,& 57.

Chapter10 Electrical Properties

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