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Chương 6 Tính chất điện-điện môi

Định luật Ohm

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• Ohm's Law: V = I R voltage drop (volts = J/C)

C = Coulomb

resistance (Ohms) current (amps = C/s)

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• Conductivity,

• Resistivity, :

-- a material property that is independent of sample size and

geometry

RA

l

surface area

of current flow

current flow

path length

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Which will have the greater resistance?

Analogous to flow of water in a pipe

Resistance depends on sample geometry and

size.

D

2D

R1 2

D

2

2

8

D2

2

R2

2D

2

2

D2

R1

8

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Further definitions

J = E <= another way to state Ohm’s law

J current density

E electric field potential = V/

flux a like area surface

current

A

I

Electron flux conductivity voltage gradient

J = (V/ )

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• Room temperature values (Ohm-m)-1 = ( m)-1= S m-1

CONDUCTIVITY: COMPARISON

Silver 6.8 x 10 7

Copper 6.0 x 10 7

Iron 1.0 x 10 7

METALS conductors

Silicon 4 x 10 -4

Germanium 2 x 10 0

GaAs 10 -6

SEMICONDUCTORS

semiconductors

Polystyrene <10 -14

Polyethylene 10 -15 -10 -17

Soda-lime glass 10

Concrete 10 -9

Aluminum oxide <10 -13

CERAMICS

POLYMERS

insulators

-10 -10 -11

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What is the minimum diameter (D) of the wire so that V < 1.5 V?

(=6.07 x 107 (Ohm-m)-1)

EXAMPLE:

Cu wire I = 2.5 A - +

V

Solve to get D > 1.87 mm

< 1.5 V

2.5 A

6.07 x 107 (Ohm-m)-1

100 m

I

V

AR

4

2D

100 m

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Energy levels of an isolated atom

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ELECTRON ENERGY BAND STRUCTURES

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BAND STRUCTURE REPRESENTATION

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Metals Insulators Semiconductors

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CONDUCTION & ELECTRON TRANSPORT

• Metals (Conductors): -- for metals empty energy states are adjacent to filled states.

-- two types of band

structures for metals

-- thermal energy

excites electrons

into empty higher

energy states.

- partially filled band

- empty band that

overlaps filled band

filled band

Energy

partly filled band

empty band

GAP

fille

d s

tate

s

Partially filled band

Energy

filled

band

filled band

empty band

fille

d s

tate

s

Overlapping bands

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• Insulators: -- wide band gap (> 4 eV)

-- few electrons excited

across band gap

Energy

filled band

filled valence band

fille

d s

tate

s

GAP

empty

band conduction

• Semiconductors: -- narrow band gap (< 4 eV)

-- more electrons excited

across band gap

Energy

filled band

filled valence band

fille

d s

tate

s

GAP ?

empty

band conduction

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where, E is the electron energy, Ef is the Fermi energy, and T

is the absolute temperature. Its physical meaning is that: f(E)

is the probability of occupancy for an electron energy

state at energy E by an electron. That is, the probability

that this state is occupied by an electron is f(E), and the

probability that it is vacant is 1 - f(E).

The Fermi energy is the maximum energy occupied by

an electron at 0K.

Fermi function

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CHARGE CARRIERS IN INSULATORS AND SEMICONDUCTORS

Two types of electronic charge carriers:

Free Electron

– negative charge

– in conduction band

Hole

– positive charge – in valence band

Move at different speeds - drift velocities

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INTRINSIC SEMICONDUCTORS

Pure material semiconductors: e.g., silicon &

germanium

Group IVA materials

Compound semiconductors

– III-V compounds

• Ex: GaAs & InSb

– II-VI compounds

• Ex: CdS & ZnTe

– The wider the electronegativity difference between

the elements the wider the energy gap.

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INTRINSIC SEMICONDUCTION IN TERMS OF

ELECTRON AND HOLE MIGRATION

electric field electric field electric field

• Electrical Conductivity given by:

# electrons/m3 electron mobility

# holes/m3

hole mobility he epen

Concept of electrons and holes:

+ -

electron hole pair creation

+ -

no applied applied

valence electron Si atom

applied

electron hole pair migration

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NUMBER OF CHARGE CARRIERS

Intrinsic Conductivity

)s/Vm 45.085.0)(C10x6.1(

m)(10219

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hei

en

For GaAs ni = 4.8 x 1024 m-3

For Si ni = 1.3 x 1016 m-3

• Ex: GaAs

he epen

• for intrinsic semiconductor n = p = ni

= ni|e|(e + h)

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INTRINSIC SEMICONDUCTORS:

CONDUCTIVITY VS T

• Data for Pure Silicon: -- increases with T

-- opposite to metals

material

Si

Ge

GaP

CdS

band gap (eV)

1.11

0.67

2.25

2.40

Selected values from Table 18.3,

Callister & Rethwisch 8e.

ni eEgap /kT

ni e e h

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Intrinsic semiconductor - A semiconductor in

which properties are controlled by the

element or compound that makes the

semiconductor and not by dopants or

impurities.

Extrinsic semiconductor - A semiconductor

prepared by adding dopants, which determine

the number and type of charge carriers.

Doping - Deliberate addition of controlled

amounts of other elements to increase the

number of charge carriers in a semiconductor.

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Extrinsic semiconductor

(doped with an electron donor)

Without thermal

excitation

With thermal

excitation

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Energy bands

Intrinsic

semiconductor

Extrinsic semiconductor

(doped with an electron

donor)

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Extrinsic semiconductor

(doped with an electron acceptor)

Without thermal

excitation

With thermal

excitation

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Energy bands

Intrinsic

semiconductor

Extrinsic semiconductor

(doped with an electron

acceptor)

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Defect semiconductor

(excess semiconductor Zn1+xO)

Zn+ ion serves as an electron donor.

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Energy bands of Zn1+xO

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Defect semiconductor

(deficit semiconductor Ni1-xO)

Ni3+ ion serves as an electron acceptor.

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Energy bands of Ni1-xO

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Temperature Effect - When the temperature of a

metal increases, thermal energy causes the

atoms to vibrate

Effect of Atomic Level Defects - Imperfections in

crystal structures scatter electrons, reducing

the mobility and conductivity of the metal

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T

where = temperature coefficient of

electrical resistivity

Change of resistivity with temperature

for a metal

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= q n

For a metal, σ decreases with increasing

temperature because μ decreases with

increasing temperature.

For a semiconductor, σ increases with

increasing temperature because n and/or

p increases with increasing temperature.

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where Eg = energy band gap between conduction and

valence bands,

k = Boltzmann's constant,

and T = temperature in K.

The factor of 2 in the exponent is because the

excitation of an electron across Eg produces an

intrinsic conduction electron and an intrinsic hole.

,en/2kTEg

For a semiconductor

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Taking natural logarithms,

Changing the natural logarithms to

logarithms of base 10,

.eσσ/2kTE

og

.2kT

Eσlnσln

g

o

.(2.3)2kT

Eσlogσlog

g

o

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Conductivity of an ionic solid

, )A + C(n q = An q + Cn q =

where n = number of Schottky defects

per unit volume

C = mobility of cations,

A = mobility of anions.

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,nnn ei

where n = total concentration of conduction

electrons,

ni = concentration of intrinsic conduction

electrons,

ne = concentration of extrinsic conduction

electrons.

An n-type semiconductor

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,eDD

, +N = n De

. e nkT2/Eg-

i

. e n/kTE- D

e

. < < nn ei

.pp i

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However

,

.pp i

No extrinsic holes, thus

pi = ni

Thus,

p = ni

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enn

. 0 p

. qp + qn = pn

nqn

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, p + p = p ei

where p = total concentration of

conduction holes

pi = concentration of intrinsic holes,

pe = concentration of extrinsic holes.

A p-type semiconductor

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, A-

e-

+A

, h+

+ A-

A

, N = p Ae

, e pkT2/Eg-

i

. e-

p/kTEA

e

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p < < p ei

.nn i

. p =n i

p p e

. 0n

. qp + qn = pn qn p

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THE MASS-ACTION LAW

Product of n and p is a constant

for a particular semiconductor

at a particular temperature

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.ppnn ii

.nnp 2i

Siforcm101.5n 310i

.Geforcm102.5n 313

i

Intrinsic semiconductor

This equation applies

whether the semiconductor

is doped or not.

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De Nnn

DD NN

.Nn D

. N

n =

n

n = p

D

2i

2i

Consider an n-type semiconductor.

(Donor exhaustion)

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ANpp e

A-A NN

.Np A

. N

n =

n =

2i

2i

Apn

Consider an p-type semiconductor.

(Donor exhaustion)

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Conducting polymers

THE NOBEL PRIZE IN CHEMISTRY, 2000:

CONDUCTIVE POLYMERS

Professor Alan J. Heeger at the University of California at Santa Barbara, USA

Professor Alan G. MacDiarmid at the University of Pennsylvania, USA and

Professor Hideki Shirakawa at the University of Tsukuba, Japan

rewarded the Nobel Prize in Chemistry for 2000 “for the discovery and development of electrically conductive polymers”.

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of other materials, from quartz (insulator) to copper

(conductor).

Polymers may also have conductivities

corresponding to those of semiconductors.

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Chemical structures of some conductive polymers. From top left

clockwise: polyacetylene; polyphenylene vinylene; polypyrrole (X = NH)

and polythiophene (X = S); and polyaniline (X = NH/N) and

polyphenylene sulfide (X = S).

A key property of a conductive polymer is the presence of conjugated

double bonds along the backbone of the polymer. In conjugation, the

bonds between the carbon atoms are alternately single and double.

The presence of C5 makes

it impossible for the π

electrons of the C6-C7 pi

bond to join the conjugated

system on the first four

carbons.

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Conjugation is not enough to make the polymer

material conductive. In addition – and this is what the

dopant does – charge carriers in the form of extra

electrons or ”holes” have to be injected into the

material.

The “doped” form of polyacetylene had a conductivity of

105 Siemens per meter, which was higher than that of any

previously known polymer. As a comparison, Teflon has a

conductivity of 10–16 S.m–1and silver and copper 108 S.m–1.

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• The halogen doping that transforms

polyacetylene to a good conductor of electricity is

oxidation (or p-doping).

• Reductive doping (called n-doping) is also

possible using, e.g., an alkali metal.

The doped polymer is thus a salt. However, it is not the counter

ions, I3– or Na+, but the charges on the polymer that are the

mobile charge carriers.

Mechanism of polymer conductivity – role

of doping

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Ferroelectric - A material that shows spontaneous

and reversible dielectric polarization.

Piezoelectric – A material that develops voltage upon

the application of a stress and develops strain when

an electric field is applied.

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The (a) direct and (b) converse piezoelectric effect.

In the direct piezoelectric effect, applied stress

causes a voltage to appear.

In the converse effect (b), an applied voltage

leads to development of strain.

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