dielectric properties of materialspioneer.netserv.chula.ac.th/~ksongpho/308/b.pdf · dielectric...

Dielectric Properties

B. Dielectric Properties of Materials

• Materials

– ceramics / polymers

– solids in which outer electrons are unable to move through structure

• Functions

– energy storage

– insulation

– new apps: capacitive sensing, …

• Objectives

– understand underlying energy storage mechanisms

– understand insulation breakdown mechanisms

– select proper dielectrics (from chips to high-power cables)

• Properties

– large C (freq dependent)

– high r, br

1

mostly organic (PET, PTFE, PP, PS …)strong covalent interchain, weak bonds intrachains

crystalline inorganic (Al2O3, BaTiO3, glasses …)strong ionic bond

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electronic ceramicsstructural ceramics (bricks…)

Reference: S.O. Kasap (4th Ed.) Chap. 7; RJD Tilley (Understanding solids, 2nd Ed) Chap. 11.

v.2020.JAN


Dielectric Materials

• introduction– relative permittivity (er), polarizability (a)

• polarization mechanisms– types: electronic, ionic, dipolar, interfacial

– frequency dependency

• br (electric field strength, breakdown field)

– gas, liquid, solid

• capacitors– ceramic, polymer, electrolytic

• nonlinear dielectrics– piezo-, ferro-, pyro-electricity

• special cases for EE– see brochure for EE ceramics (self-study)

re

( )e r

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7.1 Relative permittivity

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d

A

V

QC oo

o

e==

- dielectric is the working material (active component) in capacitors. The simplest structure is the

parallel plate capacitor (Fig. 7.1). Without the dielectric (a), the stored charge is Qo. With the

dielectric (c), the stored charge increase to Q, or by a factor of er , the relative permittivity.

- under electric field E, the constituents of the dielectric (ions, atoms, molecules) become polarized

(Fig. 11.3). Internal electric dipole moment (p) induced by E, resulting in observable

polarization (P).

re also called “dielectric constant”

22

1 2 VQCVU ==Potential Energy:

* i(t) is a displacement current, not conduction current.

oo

ror

C

C

Q

Q

d

AC === e

ee;


A. dipole moment: separation of –ve and +ve charges (equal magnitude, charge balance)

The origin of electronic polarization.

(a) A neutral atom in E = 0. (b) Induced dipole moment in a field

Electron cloud

Atomicnucleus

pinduced

E

Center of negativecharge

xC O

B. electronic polarization (all atoms)

(a: polarizability)

(ae: electronic polarizability)

aeinducedp =

00

0=

=

=p

a

Qnet 00

0

=p

a

Qnet

p can interacts with external

Ex. H+-Cl−, p ~ 3.6×10−30 C.m

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(unit: C·m)

( unit: C·m = [F·m2][V/m] )

- electric dipole moment (p) or dipole moment (or just dipole) is charge balanced, see A

- a mechanism that gives rise to such dipole is electronic polarization, see B

- the resulting dipole is proportional to the electric field strength E, the proportionality constant is

termed (electronic) polarizability, see C

- the relative permittivity (er) is related to the polarizability (a) of materials, see D


10

30

1

0.1

ae

fo

x1015 Hz

x10-40 F m2

1 10Atomic number Z

100

ae

fo

He

Ne

Ar Kr

XeRn

ae ~ Z0.99

Electronic polarizability and its resonance frequency vs. the

number of electrons in the atom (Z). The dashed line is the best

fit line.

Z → large electron cloud

→ further from nucleus →

can be shifted easily → a

2

2

2/1

oe

e

e

o

m

Ze

Zm

a

=

~constant

( )

22eZ

xZeQap

xZe

e ===

=

simple harmonic equation:

with electric field

without

2

2

2

0

2

2

2

2

1

dt

xd

dt

xdZmx

dt

xdZmx

e

e

==

=

Hook’s

(restoring force)

5

eaC. polarizability

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Key message: The heavier the element ( Z ), the higher the electronic polarizability (ae)

,


Area = A ptotal

P-QP +QP

(c)

-QP +QP

Bound polarizationcharges on the surfaces

(b)

d

+QE

-Q

V(a)

(a) When a dilectric is placed in an electric field, bound polarization

charges appear on the opposite surfaces. (b) The origin of these

polarization charges is the polarization of the molecules of the

medium. (c) We can represent the whole dielectric in terms of its

surface polarization charges +QP and -QP.

free

charges

bound

charges

note: ae is atomic-level , er ismaterial-level parameters

Before insertion: Qo

After insertion: Qp

e

e

AQ

A

Q

dC

Q

d

V

oo

o

o

o

o

=

→===

( )

( ) a ANQ

d

AdNp

d

pQ

dQp

ep

inducedtotalp

ptotal

=

==

→=

*

6

er ae &

microscopic macroscopic

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* ptot = (p / molecule) × (molecule / volume) × (volume)

D.

o

e

o

p

o

r

po

N

Q

Q

Q

Q

QQQ

e

ae +=+=

+=

11

More detail analysis (solid polarized by a local

electric field) yields Clausius-Mossotti relation:

or

r N

e

a

e

e

32

1=

+

−

- solid must be homogeneous isotropic (no

permanent dipoles, dipolar molecules)

− a includes other polarization mechanisms

Dielectric Properties 72102308

Polarization P (C/cm2)

Area = A ptotal

P-QP +QP

(c)

-QP +QP


(b)

d

+QE

-Q

V(a)






A

Q

Ad

dQp pp===

volume

volume

moment dipole totalon Polarizati

total

( ) eea )1( −=== roe

pN

A

QP

as a function of external electric field

definition

Area = A ptotal

P-QP +QP

(c)

-QP +QP


(b)

d

+QE

-Q

V(a)






re

excite

material responds

polarizability(atomic/molecular)

density

surface charge (storage)


Ex. 7.2

The electronic polarizability of the Ar atom is ae = 1.710-40 F m2. What is the static dielectric

constant er of solid Ar (below 84K) if its density is 1.8 g/cm3 and atomic mass is 39.95.

8

Origin of charge/energy storage:

material develops polarization (P) pinduced (=a) binds or draws more charges (Qp)

to the electrodes. These charges can be released to do work.

(Think of stretched strings)

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(a) Valence electrons in covalent bonds in the absence of an applied field. (b) When an electric field is applied

to a covalent solid, the valence electrons in the covalent bonds are shifted very easily with respect to the

positive ionic cores. The whole solid becomes polarized due to the collective shift in the negative charge

distribution of the valence electrons.

7.2 (electronic) polarization in covalent solids (semiconductors)

• to shift electrons in ionic cores need ~ 10 eV (difficult)

• to shift electrons in covalent bonds need ~ 1-2 eV (easy)

• stronger bonds (EG ↑) smaller shifts (x, ae, er)

erEG(eV)

Ge 16 0.67

Si 11.9 1.12

C 5.7 5.5

GaAs ? 1.43

SiO2 3.9 9.00

valenceecoreee

o

er

N

−− +

+=

aaa

e

ae

:

1

= 13.1, but why?

9

✓ ✓

Q) why concern with er of “semiconductors”?

A1) (device) In depletion layer of p-n junctions, dielectric property (er) is more important than electrical property (s ).A2) (circuit & system) er C CR BW

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p+

p-

x

p'+

p'-

E

ClÐ

Na+

(a)

(b)

(a) NaCl chain in the NaCl crystal without an applied field. Average or net dipole moment per ion = 0. (b) In the

presence of an applied field the ions become slightly displaced which leads to a net average dipole moment per ion.

7.3 Polarization Mechanisms

ei

r

roi

N

aa

e

eea

10usually

2

13

+

−=

7.3.0 Electronic polarization: (for all neutral atoms) displacement of electrons

7.3.1 Ionic polarization: (for charged ions) displacement of ions. Example: NaCl (below)

Qap == a

large

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Clausius-Mossotti relation:


- certain molecule has “permanent” dipole moment due to bonding (see Examples in Box)

- similar to ionic but |p+| |p-| for each molecule

- under electric fields, molecules are re-oriented such that p align along E as much as possible

(atoms/molecules in liquid/solid phase are not free to move)

kT

p

Qap

od

o

3

2

=

=

a

note strong

temperature

dependency

Examples (materials):

Polar liquids – water (),

acetone, alcohol, electrolyte

Polar gases – steam,

gaseous HCl ()

Polar solids – glasses

Examples (values):

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p ~ 6.2×10−30 C.m

p ~ 3.6×10−30 C.m

7.3.2 Orientational polarization (or dipolar polarization): re-orienting of molecules

with permanent dipole moments.


7.3.3 Interfacial polarization (or space charge polarization): build-up of mobile

charges

- certain dielectric has mobile charges (electrons, holes, ions)

- though they move under electric fields, they cannot leave dielectrics, but pile-up at grain

boundaries (polycrystals), at equilibrium, internal field block further charge movement

− aif not significant in most cases, except at low frequencies


7.3.4 Total polarization

die aaaa ++ (average)

(aif is location specific)

dipolar

7.3.0 7.3.1 7.3.2

7.3.3

1. semiconductor: concerned with parasitic capacitance

2. insulator: more concerned with breakdown field (br)

1

2

Dipolar solid

die aaa general trend:

except those related to valence electrons


- capacitors are used in applications throughout the frequency spectrum: from low, power line

frequencies (50/60 Hz), to high, communications frequencies (MHz/GHz)

- dielectric materials may or maynot have time to respond to the excitation (ac frequency), this

depends on the dominant polarization mechanism(s) and the ac frequency

- generally, the mechanisms which involves heavy masses are slowest, light are fastest (Fig. 11.5)

− aif (charge switch positions at grain boundaries), upto 106 Hz

− ad (dipoles of molecules rotate in medium), upto 109 Hz

− ai (ions stretch/compress), upto 1012 Hz

− ae (electron cloud shifts around nucleus), upto 1016-1017 Hz (see slide #5)

- frequency dependency of polarisability:

7.4 Frequency dependency of polarisability and relative permittivity

( )

aa

aaaaa

j

dc

eidiftotal

+=

+++=

1


- when dipoles respond to electric field, there’s a delay (in the case of step function, Fig. 7.12) or

phase lag (sinusoidal function) because:

1. ions/molecules have to rotate in a viscous material (liquids, polymers, solids), this transfers

energy to medium (working principle of microwave oven, 2.45 GHz), causing energy loss

2. thermal agitation tries to randomize dipole orientation

- the dielectric response to electric field (delay, loss) is best described using a complex dielectric

function (): the real part (☺) signifies energy storage, the imaginary part () signifies loss.

Datasheet for dielectric usually state loss tangent () at frequencies of interest

- frequency dependency of complex relative permittivity in materials with

Case A: one polarization mechanism (simplest)

Case B: four polarization mechanisms (complex, hypothetical)

rrr jeee −=

r

r

e

e

=tan

☺


v = Vosint

P = Posin(t - )

E = Eosint

(a)

er''

er'

er

(0)

1

1/10/

100/0.01/

0.1/

er' and er''

(b)

(a) An ac field is applied to a dipolar medium. The polarization P (P = Np) is

out of phase with the ac field. The relative permittivity is a complex number

with real (er') and imaginary (er'') parts that exhibit frequency dependence.

out of phase

Dielectric resonance:

• energy storage by field () =

• energy transfer to random

collisions (1/)

fromo

r

N

e

ae +=1

rrr jeee −=

storage (C)

loss (G)

16

case A: material has one polarization mechanism

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and the frequency dependency of real and imaginary parts

of the relative permittivity follows curves in (b)

( )

aa

j

dc

+=

1


102 104 106 108 1010 1012 1014 1016ƒ

Orientational,

Dipolar

Interfacial and

space charge

Ionic

Electronic

er'

er''

er' = 1

1102

Radio Infrared Ultraviolet light

The frequency dependence of the real and imaginary parts of thedielectric constant in the presence of interfacial, orientational, ionicand electronic polarization mechanisms.

storage

loss

iaea

daifa

17

case B: material has many polarization mechanisms

In practice: one mechanism dominates at operating frequency

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from ( )

aaaaaaa

e

a

e

e

j

N dceidiftotal

or

r

+=+++==

+

−

1;;

32

1


Admittance of a parallel plate capacitor:

ideal capacitor (lossless):

real capacitor (lossy): GCj

Cj

+

v = Vosint

P = Posin(t -)

C

Conductance = Gp

= 1/Rp

v = Vosint

re

re

d

AεG

d

AC

GCjd

A

d

Aj

d

AjY

roro

rorojro rrr

=

=

+=

+

⎯⎯⎯ →⎯−=

eee

eeeeee eee

; where

quantity DC ac

I/V, i/v conductance (G) admittance (Y)

V/I, v/i resistance (R) impedance (Z)

quantity real imaginary

Y = conductance (G) + susceptance (jB)

Z = resistance (R) + reactance (jX)

18

PR

VGVW

22 ==

ee tan2

rovoldA

WW ===

tan2VC

WWcap ===

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EE basic definitions:

- the storage and loss characters of dielectric (in parallel plates) appear in the equivalent circuit ()

as an ideal (lossless) capacitor of capacitance C (☺) in parallel with a conductance G ()

- this can be derived from the basic definition of admittance ()

- important design parameters are loss per unit volume () and loss per unit capacitance ()

☺


Ex. 7.6-7.7

At a given voltage, which dielectric will have the lowest power dissipation per unit capacitance at 60Hz? Is this also true at 1MHz?

Calculate the heat generated per second due to dielectric losses per cm3 of XLPE (power cable insulator) and Al2O3 at 60Hz and

1MHz at a field of 100kV/cm.

(from Kasap 3rd Ed., table 7.4 p.611)

19

f = 60 Hz f = 1 MHz

Material er' tan Loss/Volume

(mW cm-3

)er' tan

Loss/Volume

(W cm-3

)k (W cm

-1K

-1)

XLPE 2.3 3 x 10-4

0.230 2.3 4 x 10-4

5.12 0.005

Alumina 8.5 1 x 10-3

2.84 8.5 1 x 10-3

47.3 0.33

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7.6 Dielectric strength and breakdown7.6.1 Dielectric strength

• dielectric materials used as insulator between two conductors at different voltages to prevent

the ionization of air

• at high fields, all dielectrics fail (breakdown, become conducting)

• critical field is called dielectric strength (br)

Types of pole insulators:

- glass

- ceramic

- glass-ceramic

corona discharge

arcing


The nature of breakdown:

• breakdowns in liquid and gaseous dielectrics are temporary; in solids, permanent(conducting channels physically created)

• dielectric strength (br) depends on frequency: different for DC and AC fields

• br depends on molecular structure, impurities, defects (esp. voids), geometry, T,

humidity, ...

(@ 1 atm)

Dielectric strength (br) of typical insulators

gas

liquid

solid

glass

polymer

Key: air (N2/O2, lower limit), glass (SiO2, upper limit)


Corona and Partial Discharges: (a) The field is greatest on thesurface of the cylindrical conductor facing the ground. If the voltageis sufficiently large this field gives rise to a corona discharge. (b) Thefield in a void within a solid can easily cause partial discharge. (c)The field in the crack at the solid-metal interface can also lead to apartial discharge.

High voltage conductor

Gas

Ground

(a)

Void in dielectric

(b)

Crack (or defect) at dielectric-

electrode interface

(c)

7.6.2 Dielectric breakdown in gases

2e1e

Mechanisms:

* corona discharge -- partial breakdown of air around curved electrodes, see fig. (a)

* partial discharge -- see figs. (b,c)

Partial Discharge(does not connect the electrodes)

Gauss: e11 = e22→ voids & cracks reduce br

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Mechanism (physical origin): electron avalanche effect

(similar to reverse biassed p-n junction [2102385, C5])

• always a few free electrons (due to cosmic rays)

• under high fields, these electrons can accelerate and

impact ionize neutral gas atoms, giving electrons and

ions which conduct

• process repeat → avalanche

Remedies:

* increase conductor spacing d (decrease electric

field, E = V/d)

* increase air pressure: pressure → mfp & mft

→ average kinetic energy → breakdown

* replace dielectric: air → SF6

“Spacing” matter:


7.6.3 Dielectric breakdown in liquids

7.6.4 Dielectric breakdown in solids

• mechanisms not clear, but probably due to:

• conductive particles bridging electrodes (in impure liquids)

• gas bubbles in liquids (after partial discharge → local temperature → bubble size )

• electrode injection (see next slide)

Caused by intrinsic properties of dielectrics and environmental factors. Five main mechanisms:

1. Intrinsic (electronic) breakdown (by avalanche)

• initial electrons:

- pre-exist in CB of dielectrics

- electrode injection (see next slide)

• under br, electron move a distance l gains an energy of ebrl

• ebrl > EG → impact ionization (break valence bond)

• Ex: EG ~ 5 eV, l = 50nm → br ~ 1 MV/cm

• upper theoretical limits: occur only in high purity dielectric—e.g., SiO2 in MOSFET

242102308


Vo

e-

x = 0 x = xF

EF

(b)

E

Cathode

Grid or Anode

HV V

(c)

PE(x)

x

EF

+ eff

xF

Metal Vacuum

EF

00

(a)

Electrode Injection

= Enormous increase in the injected electrons from metal electrodes

Mechanism: electron tunnelling through thin potential barrier (Fowler-Nordheim)

Possible at: metal-air, metal-liquid, metal-solid interfaces

(dielectric)

25

(a) Field emission is the tunneling of an electron at an energy EFthrough the narrow PE barrier induced by a large applied field. (b)For simplicity we take the barrier to be rectangular. (c) A sharp pointcathode has the maximumfield at the tip where the field-emission ofelectrons occurs.

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An exaggerated schematic illustration of a soft dielectric mediumexperiencing strong compressive forces due to the applied voltage.

+Q

d

F F

V

Q

Thermal breakdown

• e.g., in ceramics and glasses

• Two heat sources:

1. s. finite conduction @ LF (Joules heat = s2)

2. er. dielectric loss @ HF (V2 tan )

• Positive feedback: T → (1,2) thermal runaway

(Metals, r T. Insulators, s T)

Two indicators/signatures of thermal breakdown

1. br depends on field duration due to heat capacity

(thermal lag)

Example: Pyrex @ 70C

- pulse 1ms → br = 9 MV/cm

- cont. @ 30s → br = 2.5 MV/cm

2. br depends on temperature:

Electromechanical breakdown

• e.g., in polyethylene and polyisobutylene

• Positive feedback:

F → d → C → Q → F mechanical runaway

• End results:

- plastic flow (viscous deformation)

- cracks (electrofracture)

- thermal breakdown (since )

===

2

21

d

QQkFCVQ

d

AC

e

d

V=polyethylene-based

polymeric insulation

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(a) A schematic illustration of electrical treeing breakdown in a high voltage coaxial cable which was initiated

by a partial discharge in the void at the inner conductor - dielectric interface. (b) A schematic diagram of a

typical high voltage coaxial cable with semiconducting polymer layers around the inner conductor and around

the outer surface of the dielectric.

Internal discharge

Origin

• microvoids (manufacturing defects) → partial discharge (see 7.6.2) → erosion of local,

internal surfaces, then …

• voids propagate → tree branches (see next slide)

(hollow volumes in which gaseous discharge takes place and forms a conducting channel)

Remedy: prevent microvoids by improving manufacturing process

Example: Power Coax

• semi-PE surface has no

microvoids due to

manufacturing (extrusion

process draws sheaths and

PE at the same time)

• semiconducting →

equipotential (V)→

reduce local high field

regions () → no tree

branches

27

PE

PVC

Two types of dielectric:

1. PE, polyethylene, to maximize voltage

2. PVC, polyvinyl chloride, to protect cable

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M-I-MM-S-I-S-M

polymer


Insulation ageing

Sources:

* physical: temp and mechanical stress variations → structural defects such as microcracks

* chemical: radiation, ambient, oxidation → deteriorate chemical structure

* electrical: dc fields dissociate & transport ion → structural change

ac fields → treeing

• in moist environment → microscopic voids containing water (or aqueous electrolyte)

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10

100

10

Ebr

1 kV cm-1

1 ns 1 µs 1 ms 1 s 1 hr1 min 1 day 1 mo1 yr10 yrs

Water trees

Internal discharges

and electrical treesThermal

Electro-

mechanical

Intrinsic

Electronic

Time to breakdown

1 MV cm-1

Time to breakdown and the field at breakdown, br, are interrelated and depend on the mechanism that causes

the insulation breakdown. External discharges have been excluded (based on L.A. Dissado and J.C. Fothergill,

Electrical Degradation and Breakdown in Polymers, Peter Peregrinus Ltd. for IEE, UK, © 1992, p. 63)

• Breakdown mechanism can change, depending on

operating conditions

• It is not possible to clearly identify a specific

breakdown mechanism for a material

302102308

SiO2, dc

Air, 60 Hz


7.7 Dielectric Materials• selection criteria: C, f, max. volt, acceptable loss

• large C more easily obtained at low frequency (interface & dipolar polarizations)

31

Fundamental trade-offs:

C-Vmax

freq-loss

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electrolytic

ceramic

polymer

ceramic

polymer

electrolytic


source: Wiki

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Metal termination

Metal electrode

CeramicEpoxy

Leads

(b) Multilayer ceramic capacitor

(stacked ceramic layers)(a) Single layer ceramic capacitor(e.g. disk capacitors)

Single and multilayer dielectric capacitors

Ceramic capacitors (high-er)

pFC

cmA

md

885

1

10

2

=→

=

=

FCA 100→

10=re

33

MLCC status

2005: 100s F, 1,400 layers

2013: d = 0.5 m

Class 1 (low loss)

resonant, tuning

Class 2 (volume efficiency)

buffer, coupling

ferroelectric (doped)

BaTiO3 (er ~ 100s – 1,000s)

source: Wiki

Non-polar

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(b)

Al metallization

Polymer film

(a)

Two polymer tapes in (a) each with a metallized film electrode on thesurface (offset from each other) can be rolled together (like a Swiss roll-cake) to obtain a polymer film capacitor as in (b). As the two separatemetal films are lined at oppose edges, electroding is done over the wholeside surface.

Polymer film capacitors (low-er)

slightly offset to provide

means for connections

Polymers: low er but wide frequency response (low tan )32−re

34

Polymers

Market share:

50%

40%

source: Wiki

er @ 1 kHz:

(PP) 2.2

(PET) 3.3

(PEN) 3.0

(PPS) 2.0

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(a)

Al case

Al foils

Al2O3

Anode Cathode

(b)

Electrolyte

Al Al

Epoxy

Silver paint

Ta

Lads

(a) (b)

Ta

Ta2O

5

M nO2

Graphite

Silver paste

Solid electrolyte tantalum capacitor. (a) A cross section withoutfine detail. (b) An enlarged section through the Ta capacitor.

Electrolytic capacitors: (high-C)

Liquids Solids

solid electrolyte

Polarity is important because Al/Al2O3 and Ta/Ta2O5 are

rectifying contacts → need to be reverse biased; otherwise,

the structures conduct! (no longer insulate / store energy)

Capacitive behaviour due to

Al/Al2O3/electrolyte

grown electrolytically,

thin (0.1m),

responsible for large C

* paper-soaked

* conducting

* makes good

contact with Al2O3

etched to make surface porous

(A) before forming Al2O3

50

-10

0

m

: liquids dry

9re28=re

Ag paste

35

electrolyte: ionic conducting liquid/solid

by electrolysis

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Comparison of dielectrics for capacitor applications

7.7.2Capacitor name Polypropylene Polyester Mica Aluminum,

electrolytic

Tantalum,

electrolytic,

solid

High-K ceramic

Dielectric Polymer film Polymer film Mica Anodized Al2O3

film

Anodized

Ta2O5 film

X7R

BaTiO3 base

er 2.2 – 2.3 3.2 – 3.3 6.9 8.5 27 2000

tan 4 10-4 4 10-3 2 10-4 0.05 - 0.1 0.01 0.01

Ebr (kV mm-1) DC 100 - 350 100 - 300 50 - 300 400 - 1000 300 - 600 10

d (typical minimum) 3 - 4 µm 1 µm 2 - 3 µm 0.1 µm 0.1 m 10 µm

Cvol (µF cm-3) 2 30 15 7,500a 24,000a 180

Rp = 1/Gp; C = 1 F;

1000 Hz

400 kW 40 kW 800 kW 1.5 - 3 kW 16 kW 16 kW

Evol (mJ cm-3)b 10 15 8 1000 1200 100

Polarization Electronic Electronic and

Dipolar

Ionic Ionic Ionic Large ionic

displacement

Volume efficiency:

Capacitance per unit volume

low Chigh frequency

high Clow-medium frequency

(ferroelectric)

(see 7.8.3)

36

(C3H6)n (C10H8O4)n KAl3Si3O10(OH)2

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Max energy per

unit volume


dielectric

piezo

372102308

7.8 Nonlinear dielectrics

pyro

ferro

- normal dielectric materials are polarized

(polarization P) under electric fields (field

strength E): zero E, zero P (see )

- some dielectrics have non-zero P even at zero E

due to pressure (piezoelectric, ), or heat

(pyroelectric, )

- some (pyro & ferroelectric) even have

permanent or spontaneous polarization Ps (no

fields, pressure, heat required, )

- the direction of Ps in pyro cannot be switched

(), in ferro can be switched () by E

mat

eria

ls r

esp

on

d t

o:

-el

ectr

ic f

ield

-p

ress

ure

-h

eat

7.8.1

7.8.3

7.8.2


V(d)

Force

P V(b)

V(c)P = 0(a)

The piezoelectric effect. (a) A piezoelectric crystal with noapplied stress or field. (b) The crystal is strained by an appliedforce which induces polarization in the crystal and generatessurface charges. (c) An applied field causes the crystal to becomestrained. In this case the field compresses the crystal. (d) Thestrain changes direction when the field is reversed, and now thecrystal is extended. The dashed rectangle is the original samplesize in (a).

converse piezoelectric effect

iijj EdS =

dij: piezoelectric coefficient

(or piezoelectric modulus)

Pi = induced polarization along i Sj = induced mechanical strain

Tj = applied mechanical stress along j Ei = applied electric field

(direct) piezoelectric effect

jiji TdP =

382102308

A

FT = stress l

lS

=strain

- Piezoelectricity comprises a direct and a converse effect (Fig. 7.40)

- piezoelectric crystals must be non-centro symmetric (Figs. 11.7, 7.42)

7.8.1 Piezoelectricity


- of the possible 32 point groups (Appendix), only 20 are non-centrosymmetric (Fig. 11.7)

- when centrosymmetric crystals are under pressure, the dipole changes cancel out (Fig. 7.41)

- when non-centrosymmetric crystals are under pressure, the dipole changes do not cancel,

resulting in net polarization P (Fig. 7.42)

- non-centrosymmetric requirements → only piezo crystals, not polycrystals or amorphous

- examples of piezo crystals and associated coefficients (Table 7.8)

- applications: (Fig. 7.43) direct and converse piezoelectric effects are complementary and

often used together in a transducer


P

(b)

A'

B'

P = 0O

(a)

A

B

y

x

P = 0

P

(c)

A''

B''

P = 0O

(a)

Force

P = 0

(b)

A cubic unit cell has a center of symmetry.(a) In the absence of an applied force the centers of mass for positiveand negative ions coincide. (b) This situation does not change whenthe crystal is strained by an applied force.

Centrosymmetric crystals:

CoM of –ve & +ve charges coincide,

even with external forces

Non-centrosymmetric crystals:

* CoM of –ve & +ve charges shifted

under stress → P

* Direction of P can be different from

those of applied force


PbZrO3 + PbTiO3

0. standard piezo crystals (large d but ceramics cannot be bent)

1. most widely used: a quartz (Figs. 11.9-11.10)

2. light/flexible: polymers (Fig. 11.12)

0

1

2


a quartz

- chemically SiO2; structurally, not amorphous, not single crystal, but ...

− a helix: helices () of distorted corner connected SiO4 tetrahedra (Fig. 11.10a)

- tetrahedral unit (Fig. 11.9): internal dipoles cancel, but when force F applied, net dipole p results

- quartz unit cell (Fig. 11.10): internal dipoles cancel, but when force F applied, net dipole p results

helix double helix

a helix


polymers

- rely on permanent dipoles on polymer chains: strong polar bonds (C—F, C—Cl, C—N), H-bonds

- example units, chains: PVF (Fig. 11.12a, c); PVDF (Fig. 11.12b, d)—to form isotactic chains

(maximum dipoles) the polymers must be poled during cooldown

- without poling, polymer crystallizes into centrosymmetric form (Fig. 11.14a), thus nonpiezoelectric

- with poling, polymer crystallizes into non-centrosymmetric form (Fig. 11.14b), thus piezoelectric

432102308


A B

Oscillator

Elastic

waves in the

solid

Oscilloscope

Mechanical

vibrations

Piezoelectric

transducer

Applications involve (electrical mechanical): ultrasonic transducer, microphone, oscillator,...

Applications

442102308

Seiko Astron 35SQ

World's first Quartz watch

December 1969


F

F

Piezoelectric

Piezoelectric

A

F

F

PiezoelectricL V

(a) (b)

The piezoelectric spark generator

Ex. 7.13

Given piezoelectric coefficient d = 25010-12 m/V and er = 1000, piezoelectric cylinder has a

length of 10mm and diameter of 3mm. Spark gap is in air and has a breakdown voltage of about

3.5kV. What is the force required to spark the gap? Is the force realistic?

note: J = W.s = N.m

soln

( ) ( )

=

⎯⎯ →⎯⎯⎯ →⎯

==

==

F

VQP

A

FddTP

CVQAPQ

452102308


7.8.2 Ferroelectric

- ferroelectric crystals have spontaneous or permanent polarization (even without applied field)

- example: perovskite BaTiO3 where small cation (Ti4+) displaced from the center of unit cell, thus

internal dipole, results in increased overall stability (Fig. 7.46, next slide)

- origin of ferroelectricity comes from long-range dipolar interactions (vs short-range chemical

bonds between atoms). If the interaction results in parallel internal dipoles, we have ferroelectric

(Fig. 11.5), but if antiparallel we have antiferroelectric materials (Fig. 11.10), Table 11.2

- the long-range dipolar interactions (resulting polarization) is reduced by increasing temperature.

At the Curie temperature TC, the dipole orientations are random and the material becomes

paraelectric (Fig. 11.21)

- ferroelectric is a subset of piezoelectric: it responds to external force F which causes change of

polarization P (Fig. 7.47)

- ferroelectric is a subset of dielectric: it responds to electric field E which causes change of

polarization P. The P-E characteristic is hysteresis (Fig. 18.35). (hysteresis = “to lag bebind”)

- “ferro-” in analogy to ferromagnetic (such as Fe) that posses permanent magnetization

- ferroelectric, ferromagnetic are ferroic materials (that exhibit hysteresis and domain structure)


Perovskite (ABO3)think of cubic lattice with

Ba at corners of cube (sc)

O at every face center (fcc)

Ti at body center (bcc)

BaTiO3 (Curie temperature = 130C)

- practical ceramic ferroelectrics are polycrystalline; internal dipoles in different domains sum to zero, hence

no ferroelectricity unless they are poled

- Poling: manufacturing process whereby electric field is applied during crystal cooling which leads to well-

defined polarization direction at T < TCurie

c/a = 1.01

a = 4Å

For BaTiO3: er along

a axis = 4,100

c axis = 160


ferroelectric antiferroelectric

ferroelectric paraelectric


P

P

y

x

502102308

©2003 B

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isio

n o

f T

ho

mso

n L

earn

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T

ho

mso

n

Lea

rnin

g™

is a

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dem

ark u

sed h

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n u

nder

lic

ense

.

( )10 −=

=

=

r

P

P

eea

a

a

P

P Np

p = a

field (V/m)

polarizability (F.m2)

dipole moment (C.m)

molecules/volume (/m3)

polarization (C/m2)

Figure 18.35 Ferroelectric hysteresis loops

Ferroelectric ⊆ Piezoelectric

P-E characteristic

Ferroelectric ⊆ Dielectric


Heat

P V

Temperature change = T

512102308

7.8.3 Pyroelectricity“Pyro” = fire, heat

- pyroelectric crystals must be noncentro-symmetric + have unique polar axis (internal dipoles

spontaneously lie parallel to this axis)

- Examples i) BaTiO3 under heat yields measurable voltage proportional to heat (Fig. 7.48), due

to T→ Ti4+ shifted → Ps. ii) LiTaO3 operates similarly (above). iii) wurtzite ZnS (Fig. 11.8)

- the sensitivity of pyroelectric crystals is reflected by the pyroelectric coefficient p: the ratio

between the change in permanent polarization Ps to the change in temperature T

Tp s

=

P

LiTaO3 pyroelectric heat detector


pyroelectric material used in human/animal intruder detector systems

Ex. For PZT, how much voltage is generated over a 0.1mm gap when the temperature change is 1mK?

522102308


self-study

https://th.mouser.com/new/Kemet-

Electronics/kemet-pyroelectric-sensor-modules/

https://th.mouser.com/new/Kemet-Electronics/kemet-pyroelectric-sensor-modules/

dielectric properties of materialspioneer.netserv.chula.ac.th/~ksongpho/308/b.pdf · dielectric...

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