ELECTRICAL CONDUCTION

(1)

Learning

Objectives...

Chapter 12:

Electrical Properties

• 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, deformation,

and temperature?

F i d h i d i i ff d b i f i i i i (d i )

• For semiconductors, how is conductivity affected by imperfections, impurities (doping) and Temperature?

•

Pages 483-541

Relevant Reading for this Lecture...

1

•

Ohm's

Law:



V = I R

voltage

drop

(volts)

resistance

(Ohms)

current

(amps)

A



V

L



I

A



ELECTRICAL

CONDUCTION



I

V

e-A (cross sect. area) L

Cross‐sectional Area

•

Resistivity,



and

Conductivity,



:

these

terms

are

independent

of

sample

geometry

or

shape

this

equation

is

another

form

of

Ohm's

Law

(recall

normalization

with



)

RA





•

Resistance:

R





L

A



L

A



 

I



conductivity

(Ohm‐m)

‐1 e e e

q

n







More about this later

resistivity

(Ohm

‐

m)





L

(2)

Electrical Properties

• Which will have the greater resistance?

D

R



2







8







2

D

2

D



R

₁





D

2













2





D

2





R

₂









2

D

2













2









D

2



R

₁

8

Chapter 12 - 3

• Analogous to flow of water in a pipe

• Resistance depends on sample geometry and

size.

3

Electrical

Conductivity

Electrical

Conductivity

:

Comparison

(at room temperature!)

• Ceramics

10

-10

Soda lime glass

Material

(Ohm‐m)‐1

• Metals

Silver

6.8 x 10

7

Material

(Ohm‐m)‐1

Alumina (Al

2

O

3

)

10

Soda-lime glass

10

-9

Concrete

10

-13

Aluminum

Silver

6.8 x 10

Copper

6.0 x 10

7

Iron

1.0 x 10

7

3.8 x 10

7 conductors

• Semiconductors

Silicon

4.0 x 10

-4

• Polymers

<10

-13

Polystyrene

Silicon

4.0 x 10

Germanium

2.2 x 10

0

GaAs

1.0 x 10

-6 semiconductors

Polyethylene

10

Polystyrene

10

-15

– 10

-17 insulators

(3)

100m

Cu wire- e- I = 2.5A +

EX:

CONDUCTIVITY

PROBLEM

EX:

CONDUCTIVITY

PROBLEM

What

is

the

minimum

diameter

(D)

of

the

Cu

wire

so

that



V

<

1.5V?

V

R

L



V

<

1.5V

100m

R



A





I

2.5A

6.07

x

10

7

(Ohm

‐

m)

‐1



D

2

4

Solve

to

get

D

>

1.88

mm

5

Pauli

Exclusion

Principle

gives

rise

to

energy

bands

Figure 12.2 in Callister

Quantum Mechanics

states that no two

electrons can occupy the

same state Electrons not accompanying h same state http://www.aps.org/p ublications/apsnews/2 00701/images/Wolfga ng_Pauli_1.jpg

Energy‐level diagram for a hypothetical Nɑ4 molecule. The four shared, outer orbital

electrons are “split” into four slightly different energy levels (the Pauli exclusion principle). the same state

(4)

Metals are good conductors since their valence band is

only partially filled.

Adapted from Fig. 12.3,

Callister & Rethwisch 4e.

7 Metal e.g., Cu Metal e.g., Mg Insulator Semiconductor Know this! >2eV <2eV

Adapted from Fig. 12.4,

Callister & Rethwisch 4e.

Ef= Fermi energy.

This is the boundary between the filled and unfilled energy levels. For electrons to conduct, they must move to where there are unfilled energy levels.

(5)

•

Metals:

‐‐

Thermal

energy

puts

many

electrons

into

a higher energy state.

+

-net e- flow

CONDUCTION

&

ELECTRON

TRANSPORT

CONDUCTION

&

ELECTRON

TRANSPORT

e e e

q

n







ne= # of e‐per m3 qe= Charge of e‐ e= e‐mobility

a

higher

energy

state.

net e flow

•

Energy

States:

the

cases

at

right

for

metals

show

that

nearby

energy

states

are

accessible

by

th

l fl t ti

Energy

filled empty band

s

Energy

partly filled empty band

GAP

‘My level’ – highest filled state Cu is like this. Mg is like this.

thermal

fluctuations

filled band filled valence band

filled state

s

filled band filled valence band

filled states

Fermi

http://www.bayarea.net/~kins/ AboutMe/GIFs/Fermi_2.jpg

Only

those

e

‐

that

can

get

into

the

empty

energy

levels

can

“conduct”

9

•

Insulators:

‐

Higher

energy

states

are

not

accessible

due

to

band

gap.

•

Semiconductors:

‐

Higher

energy

states

separated

by

a

smaller

gap.

ENERGY

STATES:

INSULATORS

AND

SEMICONDUCTORS

g p

Energy

filled valence empty band

a

tes

GAP

Energy

filled

valence

empty

band

es

GAP

?

Engineered material: Gaps are tunable – more to come…

filled

band

filled st

a

filled

band

valence

band

filled stat

wide band gap (> 2 eV)

narrow band gap (< 2 eV) 10

(6)

Insulators:

A parallel‐plate capacitor involves an insulator, or dielectric, between

two metal electrodes. The charge density buildup at the capacitor surface is related to

the dielectric constant of the material

kE

D



E, Electric field strength (V/m)

A

kE

D





o D, charge

density (C/m2₎

oelectric permittivity in vacuum, constant, 8.9x10‐12_C/(Vm) k, dielectric constant (material property)

l

constant, 8.9x 0 C/(Vm)

k

o





electric permittivity = C = Q/V→C=A/l

l

A

C

V

Q

C









Capacitance charge

voltage Note your text uses rfor k

11

Dielectric

Constants

&

Strength

• Ceramics

Titanate ceramics

--

15 – 10,000

Dielectric constant



_r

60 Hz 1 MHz

Dielectric strength

(V/mil)*

50 – 300

Soda-lime glass 6.9

Titanate ceramics

15 10,000

Mica --

5.4 – 8.7

Porcelain 6.0

6.0

6.9

• Polymers

2.6

Polystyrene

500 – 700

40 – 400

250

1000 – 2000

50 300

Polyethylene

2.6 2.6

Polystyrene

2.3 2.3

450 – 500

500 700

* 0.001 in = 1 mil

(7)

•

Imperfections

increase

resistivity

‐

grain

boundaries

‐

dislocations

‐

impurity

atoms

These act to scatter electrons so that they

take a less direct path, thus



.

METALS:

RESISTIVITY

VS

T,

IMPURITIES

‐

vacancies

Cu +

3.3

2 at

%Ni

Cu +

2.16

at%

Ni

defo

rme

d Cu

+ 1.

12 a

t%N

i

2

3

4

5

6

R

esistivity,



0

-8

Ohm-m)

1 12

at%

Ni

•

Resistivity

)]

(

1

[

rt o



a

T



T





a is temperature coefficient of

resistivity, ois intrinsic (no impurity) resistivity

T (°C)

-200 -100

0

d

1

2

R

(1

0

Cu +

1.1

“Pur

e” Cu

•

Resistivity

increases

with:

‐

temperature

‐

wt% impurity

‐

%Cold Work

Adapted from Fig. 18.8, Callister 6e. (Fig. 18.8 adapted from J.O. Linde,

Ann. Physik5, p. 219 (1932); and C.A. Wert and R.M. Thomson, Physics of

Solids, 2nd ed., McGraw‐Hill Book Company, New York, 1970.)

Why????

13

Variation

in

electrical

resistivity

with

composition

for

various

copper

alloys

with

small

levels

of

elemental

additions

(at

T

=

20

°

C).



i



i

c

Ac





1



A – composition independent constant

c

ii

– concentration of impurities

p

14

(8)

• Data for Pure Silicon:

‐



increases

with

T

‐

opposite

to

metals

Energy empty band GAP ? electrons

PURE

SEMICONDUCTORS:

CONDUCTIVITY

VS

T

l t i l d ti it filled band filled valence band filled states can cross gap at higher T

material band gap (eV) electrical conductivity,  (Ohm-m)-1 100 101 102 103 104 pure Si Ge GaP CdS 1.11 0.67 2.25 2.40 Adapted from Fig. 19.15, Callister 5e. (Fig. 19.15 adapted

from G.L. Pearson and J. Bardeen, Phys. Rev. 75, p. 865,

1949.)

Selected values from Table

18.2, Callister 6e. 50 100 1000 10-2 10-1 10 p (undoped) T(K) 15

CONDUCTION

IN

TERMS

OF

ELECTRON

AND

HOLE

MIGRATION

Light (shown), heat,

some input of energy

• Electrical Conductivity given by:

# holes/m

3 some input of energy

is required to excite

e‐from valence band

to conduction band

leaving a positively

charged hole behind. Conduction can be either by negative carriers, h e

p

q

n









# electrons/m

3

electron mobility

#

holes/m

3

hole

mobility

y g ,

electrons (n‐type) and/or positive carriers, holes (p‐type).

Electrons move towards (+) potential and holes

(9)

In class problem

What fraction of the conductivity of intrinsic silicon at room temperature is due to

(a) electrons and (b) holes?

h e

p

q

n













n

e

q

e



e ne= # of e‐per m3 qe= Charge of e‐ From Table 12.3, =0.736 _e= e‐mobility Here n = p From Table 12.3, = 0.263 17

kT

Eg

o

e

2







Arrhenius equation; Why 2?Produce two

charge carriers – electron and hole

mx B y T k E e g o T k E o g      1 2 ln ln 1 2



Determining the activation energy for conduction

(10)

•

Intrinsic

semiconductors:

#

of

thermally

generated

electrons

=

#

of

holes

(broken

bonds)

•

Extrinsic semiconductors: Impurities are added to the

INTRINSIC

VS

EXTRINSIC

CONDUCTION

•

Extrinsic

semiconductors:

Impurities

are

added

to

the

semiconductor

that

contribute

additional

electrons

or

holes.

Doping

=

intentional

impurities

•

Si

is

the

primary

material

in

semiconductors

– Large band gap (1.1 eV); allows Si to operate at warmer temperatures (150o_C) – Can form a native oxide, SiO2, for insulating barriers (important in fabrication)

•

Si

can

be

made

into

large

(12

inch

dia.),

high

purity,

single

crystal

ingots.

•

Doping

of

Si

– Si has 4 outer shell electrons (group IV)

– n‐type: Phosphorous, arsenic (group V), donate extra electron – p‐type: boron (group III) for Si

19

n

‐

type

4 valence electrons of As allow it to bond like Si, but the fifth electron is left orbiting As

site – the energy to release the fifth electron into the CB is small

(11)

p

‐

type

• Boron has only 3 valance electrons. When it substitutes for a Si atoms, one of its bonds

has a missing electron (hole)

• Hole tunnels around, and can be liberated by thermal vibration of Si atoms, from the B

site into the VB.

 

p e



h

21 p‐type n‐type ?‐type ?‐type 22

(12)

Arrhenius plot of electrical

conductivity for an n‐type

semiconductor over a wide

temperature range. At low

temperatures (high 1/T), the

material is extrinsic. At high

temperatures (low 1/T), the

material is intrinsic. In

between is the exhaustion

range, in which all “extra

electrons” have been promoted

to the Why the

increase?

Why 2?Produce two charge carriers – electron and hole

to the

why?

23

In class problem

Calculate the conductivity for the saturation range of silica doped with 10‐ppb boron.

The calculated density of B atoms/m3_is_also_the_density_of_electron_holes_in_this

p‐type semiconductor at saturation. 10/109

= 10‐8 Hence solve for n

h d h d f bl ( h d f l amu B n = 10‐8 6.02x10 23_atoms_B 10.81 g B 2.33x10 6_g/m3 _Si₌_1.30_x1021 X X Density of Si Hence solve for n

Using this equation σ=nqµhand the data from Table 12.3: (q is the magnitude of electron charge which equals 0.16 x 10‐18 _C)

σ

=

nqµ

_h

(13)

Compound

Semiconductors

Group III‐V and II‐V compounds nominally have

the Zinc Blend structure and are intrinsic

the inc lend structure and are intrinsic semiconductors. Can be doped, like Si, to change

conduction (extrinsic)

MX Compounds: Group III 3+ valence, Group V

5+ valence – avg. of 4+ valence per atom //

Group II 2+ valence, Group VI 6+ valence – avg.

4+ valence per atom

Applications:

•Solar cells

•Light emitting diodes (occurs with

electron‐hole recombination)

•Higher operation speeds, etc.

25

•

Allows

flow

of

electrons

in

one

direction

only

(e.g., useful

to convert alternating current to direct current).

•

Results:

+

p-type

n-type

IC

DEVICES:

P

‐

N

RECTIFYING

JUNCTION

‐

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

+

+ +

+

--

-

-p ty-pe

n type

+

-

-p-type

n-type

+

-14

p‐n junction; current flows.

‐

Reverse bias: carriers

flow away from p‐n junction;

carrier conc. greatly reduced

at junction; little current flow.

+

--

-

-p-type

n-type

-

+

26

(14)

P

‐

N

Rectifying

Junction

27

Light

Emitting

Diode

(LED)

http://electronics.howstuffworks.com/led.htm/printable

http://spie.org/Images/Graphics/Newsroom/Importe Band gap determines

(15)

Compare three light bulbs.

Conventional incandescent (tungsten filament)

Bulb is hot to the touch, most of the electricity is lost as heat. Short life (few months?)

Compact fluorescent (CFL’s)

Bulb is warm, but not hot, less heat loss Longer life (many months – 2 years)

LED’s

E t l ffi i t littl i f l t i it t h t

Extremely efficient, little or no conversion of electricity to heat.

Very long life – decades. Many LED’s made in the 70’s & 80’s are still working!

29

The

Transistor

•

Invented by Shockley, Bardeen, and

Brattain in 1948. Nobel prize in 1956.

•

A three terminal device that acts like a

simple “on‐off” switch (logic control).

–

The basis of Integrated Circuits (IC)

Circa 1948

technology

–

Computers, cell phones,

automotive control, etc.

today

•When voltage (potential) is applied

to the “gate”, current flows between

the “source” and the “drain”. On/off

switch –logic switch, go/no go

(16)

•

Electrical

conductivity

and

resistivity

are:

‐

material

parameters,

i.e.

properties.

‐

independent of

geometry.

•

Electrical

resistance

is:

SUMMARY

‐

a

geometry

and

material

dependent parameter.

•

Conductors,

semiconductors,

and

insulators...

‐

each

is

different,

depending

on

whether

there

are

accessible

energy

states

for

conducting

electrons.

•

For

metals,

conductivity

is

increased

by

‐

reducing

deformation

reducing imperfections

‐

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).



Transistors

are

logic

based

devices

31

Metals:

Influence

of

Temperature

and

Impurities

on

Resistivity

• Presence of imperfections increases resistivity

-- grain boundaries

-- dislocations

-- impurity atoms

These act to scatter

electrons so that they

t k

l

di

t

th

-- vacancies

take a less direct path.

• Resistivity

increases with:

3

4

5

6

e

sistivity

,



0

-8

Ohm-m)

d

%

CW

-- wt% impurity

-- temperature



=

Adapted from Fig. 12.8, Callister & Rethwisch 4e.(Fig. 12.8 adapted from J.O. Linde, Ann. Physik 5, p. 219 (1932); and C.A.

T(°C)

-200

-100

0

1

2

R

e

(1

0

-- %

CW

+



_deformation i +



impurity t



thermal