kwang kim yonsei university [email protected]

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Kwang Kim Yonsei University [email protected] Foundations of Materials Science and Engineering Lecture Note 11 (Electrical Properties of Materials) June 3, 2013 39 Y 88.91 8 O 16.00 53 I 126.9 34 Se 78.96 7 N 14.01

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Foundations of Materials Science and Engineering Lecture Note 11 (Electrical Properties of Materials ) June 3, 2013. Kwang Kim Yonsei University [email protected]. 8 O 16.00. 7 N 14.01. 34 Se 78.96. 53 I 126.9. 39 Y 88.91. Electrical Properties. ISSUES TO ADDRESS. - PowerPoint PPT Presentation

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Page 1: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

Kwang Kim Yonsei University

[email protected]

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

Page 2: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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?

Page 3: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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.

Page 4: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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

Page 5: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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

Page 6: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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

Page 7: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

Conductivity: Comparison

Page 8: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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

Page 9: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

Electron Energy Band Structures

Page 10: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

Band Structure

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

levels

Valence band

Conductionband

Page 11: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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

Page 12: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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

Page 13: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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

Page 14: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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

Page 15: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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.

Page 16: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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

Page 17: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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

Page 18: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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

Page 19: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

Electrical Properties

HOMO : Highest Occupied Molecular Orbital

LUMO : Lowest Unoccupied Molecular Orbital

Page 20: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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

Page 21: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

n-type Si

Page 22: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

p-type Si

Page 23: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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- +

Page 24: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

Energy Band Bending

Page 25: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

LED from p-n Rectifying Junction

Page 26: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

Properties of Rectifying Junction

Page 27: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

Junction Transistor

Page 28: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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)

Page 29: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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

Page 30: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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.

Page 31: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

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.

Page 32: Kwang Kim  Yonsei University  kbkim@yonsei.ac.kr

Piezoelectric Materials

stress-free with applied stress

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

Mechanicalforce

Electricresponse