Introduction to Engineering Materials ENGR2000...

69
Introduction to Engineering Materials ENGR2000 Chapter 18: Electrical Properties Chapter 18: Electrical Properties Dr.Coates

Transcript of Introduction to Engineering Materials ENGR2000...

Introduction to Engineering Materials

ENGR2000

Chapter 18: Electrical PropertiesChapter 18: Electrical Properties

Dr.Coates

18.2 Ohm’s Law

current. theis and voltage theis

material, theof resistance theis R where

lR

IV

IRV

=

section.-cross of area theis

andspecimen theoflength theis

material, theofy resistivit theis where

A

l

A

lR

A

lR

ρ

ρ=⇒

Measurement of Electrical

Resistivity

Recall from Physics 2211

• What are units for I, V, R?

Does voltage flow through a

material? Why/why not?

Units of ρ?

Does shape of cross-section

affect ρ?

18.3 Electrical Conductivity

• The ease with which a material is capable of

conducting an electrical current.

1σ =

material. theofty conductivi electrical theis where

1

σ

ρσ =

Units of σ?

Ohm’s law in a different form

I

J

J

Ε

Ε=

intensity. field electric theis

anddensity current theis where

σ

l

V

A

IJ

=

Prove equivalence

to V = IR for Class

work!

Energy levels in atoms (Review)

• In a single isolated atom only certain discrete

electron energy levels are allowed

18.5 Energy Band Structures in Solids

• As atoms are brought close together, the electrons

are perturbed by the electrons and nuclei of

adjacent atoms.

• Each atomic state is split into a series of closely• Each atomic state is split into a series of closely

spaced electron states in the solid – electron

energy band

Energy bands in solids

• The energy band structure as a function of the inter-

atomic separation distance

wider energy band

wid

eren

ergy

ban

d

Energy bands in solids

• For large separation distances the electrons associated

with any atom are independent of those of the other

atoms.

Energy bands in solids

• There is an energy gap Eg known as a band gap when the

energy levels do not overlap.

Energy bands in solids

• Energy levels overlap to form an extended energy band.

Four Types of Energy Bands

• Valence band – the highest energy band that is at least

partially occupied (eg. Fig 18.4c)

• Core bands – all the bands below the valence band

• Conduction band – the energy band above the valence• Conduction band – the energy band above the valence

band

• Band gap or energy gap – forbidden energy range

between the valence and conduction bands

Fermi energy

• The energy corresponding to the highest filled

state at 0 K is called the Fermi energy, Ef.

Classification of solid materials based on

electrical conductivity

• Conductors

• Semiconductors

• Insulators• Insulators

What are conductivity ranges for

each? See sec. 18.3!

18.6 Conduction in terms of band and atomic

bonding models

• Free electrons

– For an electron to become free it must be excited orpromoted into one of the empty and available electronstates above Efstates above Ef

– Only electrons with energies >Ef may be accelerated inthe presence of an electric field and participate in theconduction process.

• Holes

– Electronic entity found in semiconductors andinsulators, have energies < Ef

Metals

• Band structures in Figs. 18.5a, 18.5b

• Very little energy is required to promote the• Very little energy is required to promote the

electrons into the empty states…because?

For a metal, occupancy of electron states

before and after an electron excitation

Free

electron

Fermi

energy

electron

Insulators and Semiconductors

• Electrons must be promoted across the energy

band gap into the empty states to become free…

• Excitation energy is most often in the form of a

non-electrical source such as heat or lightnon-electrical source such as heat or light

For an insulator or semiconductor, occupancy

of electron states before and after an electron

excitation from the valence band into the

conduction band

Insulators and semiconductors

• Energy band gap > 2 eV

• Ionic or covalent bonding

• Valence electrons are

tightly bound to individual

• Energy band gap < 2 eV

• Covalent bonding

• Valence electrons are not

as strongly bound to thetightly bound to individual

atoms

as strongly bound to the

atoms

• Electrons are easily made

free by thermal excitation

Energy bands and charge carriers

• Electrical conduction requires the presence of

empty energy levels that are not too different in

energy levels currently occupied by the electrons.

Energy bands and charge carriers

• An electron jumping from a filled level into a nearby

empty level

• An empty level or a hole is located near the bottom of the

band.band.

Energy bands and charge carriers

• Transition can be viewed as either 13 electrons each

moving up one energy level or the empty level moving

down 13 levels.

18.7 Electron Mobility

• The ease with which the free electrons movethrough the solid in response to an electric field.

• Electric field => force on electron

• Why doesn’t electron continually accelerate?• Why doesn’t electron continually accelerate?

Frictional forces-scattering of electrons due to

imperfections in crystal lattice, impurity

atoms,vacancies, interstitial atoms, dislocations, thermal

vibrations

Drift velocity

- Average electron velocity in the direction of

the force imposed by the electric field.

v

:velocity Drift

ed Ε= µ

electron. an on charge electrical the is C101.6e and

volume unit per electrons free of number the is n where

en

:tyconductivi Electrical

events). g scatterinof (frequencymobility electron the is where

v

e

e

ed

19−×=

=

Ε=

µσ

µ

µ

18.8 Electrical conductivity of metals

• Electron mobility (or the electrical conductivity)

depends on…

– the nature of the charge carriers (the smaller size of

electrons permits them to move easily through theelectrons permits them to move easily through the

solid)

– temperature

– Defects in the crystal structure

Model of an electron moving through

a crystal structure

citydrift velo theis where v

tavd =

constant acceleration

.collisionsbetween

mean time theis

&onaccelerati theis

citydrift velo theis where d

t

a

v

Influence of temperature

• As temperature is increased…

– atoms gain thermal and kinetic energy

– mean time between collisions decreases

– decrease in electron mobility– decrease in electron mobility

– Decrease in electrical conductivity

metalparticularforconsa

aTt

.,0

0

=

+=

ρ

ρρ

Influence of impurities

• In the presence of impurities…

– mean time between collisions is decreased

– decrease in electron mobility

– Decrease in electrical conductivity– Decrease in electrical conductivity

( )( )

.

100/%

1

constindependenncompositioA

atonconcetratiimpurityc

cAc

i

iii

−=

=

−=ρ

• For a two-phase alloy

ρρρρ ++=

.resindividual

fractionvolumeV

VV

s

s

i

=

=

+=

ρ

ρρρ ββαα

• For a metal, the total

rulesenMattthiess

dtitotal

'

ρρρρ ++=• For a metal, the total

electrical resistivity

equals the sum of

thermal, impurity and

deformation

contributions

• See Figure 18.8

Semiconductors

• Intrinsic

semiconductors

– Electrical behavior is

based on the electronic

• Extrinsic

semiconductors

– Electrical behavior is

dictated by impuritybased on the electronic

structure inherent to

the pure material.

– Elemental Si, Ge

dictated by impurity

(external) atoms.

Intrinsic

• Characterized by band structure 18.4b

• At 0K, completely filled valence band

• Band gap < 2eV

• Groups III-V compounds, ex. Gallium Arsenide

(GaA)

• Groups IIB-VIA ex. Cadmium Suplhide (Cds)

For these compounds, how might wider separation in electronegativity influence the type of bond and band gap energy?

Which of ZnS and CdSe will have a larger band gap energy, Eg? why?

Concept of a hole

• For every electron excited into the conduction

band, there is left behind a missing electron in one

of the covalent bonds.

• This missing electron is treated as a positively• This missing electron is treated as a positively

charged particle called a hole.

• A hole has the same magnitude of charge as that

of an electron.

18.10 Intrinsic Semiconduction

Electron bonding model of electrical

conduction in intrinsic silicon

- before excitation

Electron bonding model of electrical

conduction in intrinsic silicon

- after excitation

Intrinsic conductivity

he

p

epenσ

µ

µµ +=

mobility. hole theis and

meter cubicper holes ofnumber theis where

:tyconductivi Electrical

( )hei

i

i

h

enσ

n

npn

µµ

µ

+=

==

:tyconductivi electrical theHence,

ion.concentratcarrier intrinsic theis where

:torssemiconduc intrinsicFor

mobility. hole theis and

Example 18.1

• For intrinsic gallium arsenide, the room

temperature electrical conductivity is 10-6 (Ωm)-1;

the electron and hole mobilities are 0.85 and 0.04

m2/Vs respectively. Compute the intrinsic carrierm2/Vs respectively. Compute the intrinsic carrier

concentration ni at room temperature.

( )

i

h

e

n

Vsm

Vsm

µ

µ

=

=

=

Ω=−−

:Theory

torsemiconduc intrinsic -

?

/04.0

/85.0

10

:statement Problem

2

2

16

:Solution

( )hei

i

he

enσ

npn

epenσ

µµ

µµ

+=

==

+=

:tyconductivi electrical theHence,

:torssemiconduc intrinsicFor

:Theory

( )312100.7

:Solution

−×=

+=

m

e

σn

he

iµµ

18.11 Extrinsic Semiconductors

- n-type extrinsic semiconduction

• The addition of a Group V atom, such as P into a

Si crystal…

n-type extrinsic semiconduction

• The addition of a Group V atom, such as P into a

Si crystal…

donor

level

Extrinsic n-type semiconduction using

electron bonding model

- before excitation

Extrinsic n-type semiconduction using

electron bonding model

- after excitation

Energy band for a donor impurity level

Extrinsic n-type conductivity

he epenσ µµ +=

tors,semiconduc type-n extrinsicFor

:tyconductivi Electrical

eenσ

pn

µ≅

>>

>>

:tyconductivi electrical theHence,

:band valencein the holes of # band conduction in the electrons of #

tors,semiconduc type-n extrinsicFor

18.11 Extrinsic Semiconductors

- p-type extrinsic semiconduction

• The addition of a Group III atom, such as B into a

Si crystal…

p-type extrinsic semiconduction

• The addition of a Group III atom, such as B into a

Si crystal…

acceptor level

Extrinsic p-type semiconduction using

electron bonding model

Energy band for an acceptor impurity level

Extrinsic p-type conductivity

he epenσ µµ +=

tors,semiconduc type-p extrinsicFor

:tyconductivi Electrical

hepσ

pn

µ≅

<<

<<

:tyconductivi electrical theHence,

:band valencein the holes of # band conduction in the electrons of #

tors,semiconduc type-p extrinsicFor

Doping

• Extrinsic semiconductors are produced from

materials that are initially extremely pure.

• Controlled concentrations of specific donors or

acceptors are added.acceptors are added.

Temperature Dependence of Carrier

Concentration

How would band gap affect carrier concentration? Ge vs Si?

Why concentrations increase with temperature for intrinsic?

Temperature Dependence of Carrier

Concentration

Why concentrations constant with temperature

in extrinsic region?

As dopant level is increased would you expect

the temperature at which a semiconductor becomes in

trinsic to increase, to remain essentially the

same, or to decrease? Why?

Temperature Dependence of Carrier Mobility

Example 18.2

• Calculate the electrical conductivity of intrinsic

silicon at 423 K.

epenσ

KT

σ

µµ +=

=

=

:Theory

silicon intrinsic -

423

?

:statement Problem

( )hei

i

he

enσ

npn

epenσ

µµ

µµ

+=

==

+=

:tyconductivi electrical theHence,

:torssemiconduc intrinsicFor

( ) 319104423

:Solution

−×= mKni

( )

( )

( )

( ) 1

2

2

52.0

:K 423at Si intrinsic ofty conductivi Electrical

/022.0423

/06.0423

−Ω=

+=

=

=

m

enσ

VsmK

VsmK

hei

h

e

µµ

µ

µ

Example 18.3

• To high-purity silicon is added 1023 m-3 arsenic

atoms.

– Is this material n-type or p-type semiconductor?

– Calculate the room temperature electrical conductivity– Calculate the room temperature electrical conductivity

of this material.

– Compute the conductivity at 100 C.

Arsenic is a Group V element

- n-type semiconductor

( )KT

mn

σ

=

=

=−

:Theory

torsemiconduc extrinsic type-n -

re temperaturoom298

10

?

:statement Problem

323

e

he

enσ

pn

epenσ

µ

µµ

>>

+=

:tyconductivi electrical theHence,

:torssemiconduc extrinsic type-nFor

:Theory

( )( ) 1

2323

1120

/07.010

:Solution

Ω==

=

men

Vsmm

e

e

µσ

µ

KT

mn

σ

=

=

=−

:Theory

torsemiconduc extrinsic type-n -

373

10

?

:statement Problem

323

e

he

enσ

pn

epenσ

µ

µµ

>>

+=

:tyconductivi electrical theHence,

:torssemiconduc extrinsic type-nFor

:Theory

( )

( ) 1

2

640

:tyconductivi Electrical

/04.0373

:Solution

−Ω==

=

menσ

VsmK

e

e

µ

µ