kwang kim yonsei university kbkim@yonsei.ac.kr

Kwang Kim Yonsei University

kbkim@yonsei.ac.kr

Foundations of Materials Science and Engineering

Lecture Note 11(Electrical Properties of Materials)

June 3, 2013

39Y

88.91

8O

16.00

53I

126.9

34Se

78.96

7N

14.01

Electrical Properties

ISSUES TO ADDRESS...• 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, temperature, and deformation?

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

Electric Conduction – classical model

• Metallic bonds make free movement of valence electrons possible.

• Outer valence electrons are completely free to move between posi-tive ion cores.

• Positive ion cores vibrate with greater amplitude with increasing temperature.

• The motion of electrons are random and restricted in absence of elec-tric field.

• In presence of electric field,

electrons attain directed drift

velocity.

Electric Conduction

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

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

1

• Conductivity,

• Resistivity, : -- a material property that is independent of sample size and geometry

RAl

surface area of current flow

current flow path length

Electrical Properties

• 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

D2

2

8D2

2

R2

2D2

2

D2

R1

8

Definitions

Further definitions

J = <= another way to state Ohm’s law

J current density

electric field potential = V/

flux a like area surface

currentAI

Electron flux conductivity voltage gradient

J = (V/ )

ARI V

JAI

Conductivity: Comparison

Example: Conductivity Problem

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

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

IV

AR

4

2D

100 m

Electron Energy Band Structures

Band Structure

• Valence band – (filled) highest occupied energy levels• Conduction band – (empty) lowest unoccupied energy

levels

Valence band

Conductionband

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 st

ates

Partially filled band

Energy

filled band

filled band

empty band

fille

d st

ates

Overlapping bands

Energy Band Structures: Insulators & Semiconductors

• Insulators: -- wide band gap (> 2 eV) -- few electrons excited across band gap

Energy

filled band

filled valence band

fille

d st

ates

GAP

empty

bandconduction

• Semiconductors: -- narrow band gap (< 2 eV) -- more electrons excited across band gap

Energy

filled band

filled valence band

fille

d st

ates

GAP?

empty

bandconduction

Charge Carriers

Two types of electronic charge carriers:

Free Electron – negative charge – in conduction band

Hole – positive charge

– vacant electron state in the valence band

Metals: Resistivity vs. T, Impurities

• Presence of imperfections increases resistivity -- grain boundaries -- dislocations -- impurity atoms -- vacancies

These act to scatterelectrons so that theytake a less direct path.

• Resistivity increases with:

=

deformed Cu + 1.12 at%Ni

T (ºC)-200 -100 0

123456

Res

istiv

ity,

(1

0-8

Ohm

-m)

0

Cu + 1.12 at%Ni

“Pure” Cu

d -- %CW

+ deformation

i

-- wt% impurity

+ impurity

t

-- temperature

thermal

Cu + 3.32 at%Ni

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.

Conduction: Electron and Hole Migration

electric field electric field electric field

• Electrical Conductivity given by:

# electrons/m3 electron mobility

# holes/m3

hole mobilityhe epen

• Concept of electrons and holes:

+-

electron hole pair creation

+-

no applied applied

valence electron Si atom

applied

electron hole pair migration

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

ni e Egap / kT

ni e e h

Intrinsic vs. Extrinsic Conduction

• Intrinsic: -- case for pure Si -- # electrons = # holes (n = p)• Extrinsic: -- electrical behavior is determined by presence of impurities that introduce excess electrons or holes -- n ≠ p

3+

• p-type Extrinsic: (p >> n)

no applied electric field

Boron atom

4+ 4+ 4+ 4+

4+

4+4+4+4+

4+ 4+ hep

hole

• n-type Extrinsic: (n >> p)

no applied electric field

5+

4+ 4+ 4+ 4+

4+

4+4+4+4+

4+ 4+

Phosphorus atom

valence electron

Si atom

conductionelectron

een

Electrical Properties

HOMO : Highest Occupied Molecular Orbital

LUMO : Lowest Unoccupied Molecular Orbital

Extrinsic Semiconductors : Conductivity vs. T

• Data for Doped Silicon: -- increases doping -- reason: imperfection sites lower the activation energy to produce mobile electrons.

• Comparison: intrinsic vs extrinsic conduction... -- extrinsic doping level: 1021/m3 of a n-type donor impurity (such as P). -- for T < 100 K: "freeze-out“, thermal energy insufficient to excite electrons. -- for 150 K < T < 450 K: "extrinsic" -- for T >> 450 K: "intrinsic"

Con

duct

ion

elec

tron

conc

entra

tion

(1021

/m3 )

T (K)6004002000

0

1

2

3

freez

e-ou

t

extri

nsic

intri

nsic

doped

undoped

EF

EV

EC

n-type Si

p-type Si

p-n Rectifying Junction

• Allows flow of electrons in one direction only (e.g., useful to convert alternating current to direct current).• Processing: diffuse P into one side of a B-doped crystal.

-- 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: carriers flow away from p-n junction; junction region depleted of carriers; little current flow.

++

+ ++

- ---

-p-type n-type

+ -

++ +

++

--

--

-

p-type n-type

+++

+

+

---

--

p-type n-type- +

Energy Band Bending

LED from p-n Rectifying Junction

Properties of Rectifying Junction

Junction Transistor

MOSFET Transistor Integrated Circuit Device

• Integrated circuits - state of the art ca. 50 nm line width– ~ 1,000,000,000 components on chip– chips formed one layer at a time

Fig. 18.26, Callister & Rethwisch 8e.

• MOSFET (metal oxide semiconductor field effect transistor)

Electrical Properties of Ceramics

• Basic properties of dielectric: Dielectric constant:- Q = CVQ = ChargeV = VoltageC = CapacitanceC = ε0A/d ε0 = permeability of free space = 8.854 x 10-12 F/m

• When the medium is not free space C = Kε0A/d Where K is dielectric constant of the material between the

plates

Dielectric Strength and Loss Factor

• Dielectric strength is measure of ability of material to hold energy at high voltage.

Defined as voltage gradient at which failure occurs.

Measured in volts/mil.• Dielectric loss factor: Current leads voltage by 90

degrees when a loss free dielectric is between plates of capacitor.

• When real dielectric is used, current leads voltage by 900 – δ where δ is dielectric loss angle.

• Dielectric loss factor = K tan δ measure of electric energy lost.

Ferroelectric Ceramics

• Experience spontaneous polarization

BaTiO3 -- ferroelectric below its Curie temperature (120ºC)

If cooling takes place in electric field, dipoles align in the direction of the field.

Piezoelectric Materials

stress-free with applied stress

Piezoelectricity – application of stress induces voltage – application of voltage induces dimensional change

Mechanicalforce

Electricresponse