Part I Dielectric MaterialsDefinition: is the material that does not conduct electricity

readily, i.e., an insulator

Applications: range from power engineering to microelectronics

Lecture StructureReview of basic electrostatic theoryCapacitorComplex permittivityPolarisation processesElectrets

Basic Electrostatic TheoryCoulomb's lawExperiments on electrically-charged bodies yield the following observations-Like charges repel and opposite charges attract each other;-The force between the charges is inversely proportional to the square of the distance between themdependent on the medium in which they are embeddedacts along the line joining the chargesproportional to the product of the charge magnitudes.

041

0 221

221 rrF

r

QQr

QQor

k pi==

F= force of one charge on the other, newtons (N)Q1 and Q2 = charge quantities, coulombs (C)r= distance between charges, metres (m)k=constant of proportionalityr= relative permittivity of the dielectric0=8.85x10-12F/m, permittivity of free space or vacuum

Electric fieldAn electric field is region where forces actThe resulting force per unit charge is defined as the electric field intensity E

An equivalent unit for the electric field intensity is the volt per metre (Vm-1)The total or resultant electric field at a point is the vector sum of the individual component fields at the point.

104

1

221

== NCQ rQ

orr

FE pi

Electric flux densityThe electric field --forces on charge

-- magnitude of the charges

For dielectric materials, the electric flux density with a symbol D is defined as

ED ro=

Electric potential and potential differenceElectric field is inconvenient to work with (vector).Any system of charges at rest is unstable. The inverse square law causes charges of unlike sign to collide and charges of like sign to separate unless the charges are held in position by force which are not electrostatic.Work has to be done to assemble systems of charges and this work can be recovered when they are released. The systems possess potential energyelectric potential.

We often are interested in the change of electric potentialelectric potential difference. It is defined as the work done when unit positive charge is moved from one point to the other. Consider the figureThe force on the charge is E.The work done on the chargeby the external force when it is moved through a small distance dl is the product of the external force and the distance moved in the direction of that force, ie

+ dl

unit charge

= lE ddV

The potential difference between two points A and B can be calculated by integrating along a suitable path between them.

The potential difference depends only on the starting and finishing points, not on the path which taken between them.

Consider a charge is moved from A to B in the field of another charge Q at O

==B

A

B

AdlEdVV AB coslE

The potential difference froma small movement of dl of a unit charge at P is

Therefore

Using the principle of superposition the conclusion can be extended to the field of any combination of charge.

Q

dlE

BA

r

P

rArB

dlrdlE == 204 r

QdVpi

)11(44

4

02

0

20

AB

B

A

AB

rr

Qdrr

Qr

QVV

==

==

pipi

pidlrdlE

B

A

B

A

CapacitorDefinition: a device for storing electric charge and, hence, electric energy. It consists of two conductors separated by an insulating medium.Capacitance is defined as the ratio of the stored charge to the voltage applied.

Its unit is Coulombs/Volt=farads.The capacitance is independent of the charge and voltage. Thus, an increase in applied voltage increases the charge stored, but the ration of charge to voltage remains the same.

VQC =

Energy stored in a capacitorIt requires work to charge a capacitor energy is stored by a charged capacitor.Consider a capacitor of capacitance C charged to a potential difference V (Q=CV)The potential is work per charge. In terms of infinitesimals it is the infinitesimal work dW per infinitesimal charge dq, i.e.

Therefore, the energy stored in a capacitor:

W vdqqC

dqQC

CV QVQQ

= = = = =00

221

212

12

VdWdq

=

Imperfect dielectrics & Complex permittivity

Ideal dielectric no loss

Defects and impurities lead to various charge carriers in dielectrics. Under the influence of electric field, current flows through the dielectrics

VI

C0 V

I=jC0

V

I

VCIR 0"=

VCIC 0'=0*CC =

IC

IR

VCjVCjI

0

=

=

VCjjVCjVC

jIIVCjI CR

0

00

0

)"'('"

*

=

+=

+==

"'* j=* is called complex permittivity

From the equivalent circuit:

0'CC p =0"

1C

Rp =

The physical meaning of complex permittivity

Real part is the same as permittivityImaginary part represents the resistance in parallel with capacitor

is an important angle. In practice, it often appears in terms of tan

'

"

'

"

tan0

0

===VCVC

II

C

R

PolarisationWhat happens when an insulating material is inserted between the plates of a capacitor?Experimental evidence

+

+

+

+

-

-

-

-

-

-

-

-

++++++++

-

-

-

-

-

-

++++

+

+

-

-

-

-

E

+Q0C

C0 -Q+Q-Q0

Ei(t)

(a) (c)(b)

Die

lect

ricV VV

According to , the capacitance has been increased due to the insertion of a dielectric between the plates.Why?Electrons in an insulator are bound to the atoms and are not free to wander through the material under the action of an electric field.

VQC =

+E=0 E0

_

This leads to dipole oriented along the electric field. Inside the material manyatoms overlap no noticeableeffect (positive and negative cancel each other) At the edges of the material surface layers of charge appear.Much the same as if there were free charges in the material, but the amount of surface charge is always less in an insulating material than in a conductor.

- - - - - - - - - - -

-- - - - - - - - - -

+ + + + + + + + + + + + + + + + + + + + +

-q

+q

Let Q be the charge on the metal plates and q the induced charge on the insulators surfaceThe electric field between theplates is now due to Q and q.

p.d. is

capacitance

is called the relative permittivity of the insulating material

-q

+q

+Q

-Q

E=? d

S

SqQE

0

=

dSqQEdlV

0

==

dS

dS

qQQ

VQC r 00

=

==

qQQ

r

=

q is proportional to the applied field E, i.e.

E is proportional to E(Q-q)

e is called the electric susceptibility which is a constant

The capacitance is increased by inserting an insulating material

Eq

)( qQq e =

111 >+=

+=

+=

= er qQq

qQqqQ

qQQ

The product of 0 and r is called the absolute permittivity, represented by

q is bound to atoms (cant move within the material) -- bound chargeQ comes from power source -- free chargeThe total charge (Q-q) contributes to EFrom the definition of D,

(Q-q) is proportional to E D only depends on the free charge Q

0 r=

qQQ

ED

r

== 00

Imagine that the electric flux density in a dielectric is due to two courses:(i) the flux density set up by an applied field and(ii) the polarisation of the dielectric resulting from the electric field

Therefore

Polarisation is related to permittivity of the dielectric.

PED += 0

EEEEDP rr )1(0000 ===

Mechanisms of polarisationPermittivity is a macroscopic description of the dielectric properties. How is it linked with atomic and molecular processes taken place in the dielectric?

There are four polarisation mechanisms responsible for frequency characteristics of and and they are(i) electronic (optical)(ii) ionic(iii) dipolar (orientational) and(iv) interfacial

Dipole and dipole momentDipole and dipole moment

Polarisation

ppppP Nvol N

=+++= )(1 21

dp qm =)(-q +q

d

PolarisationMicroscopic LevelA polarised atom of dielectric material based on Classical Atom Model

d

+ -

E=0 E0

m=edElectron cloud

The dipole moment of the atom

-- the polarisability and El the local field

If there are n polarisable atoms per unit volume then the polarisation

lEm =

lEP n=

Since the above dipole moment is created under the influence of an electric field it is called the induced dipole moment.Many molecules contain dipole moments for examples

ClH

H

HO

Electronic polarisation (e)When a field is applied to an atom electron clouds are displaced slightly with respect to the positive charge

d

+ -

E=0 E0

m=edElectron cloud

The induced dipole moment

e-- the electronic polarisabilityd

If there are n polarisable atoms per unit volume then the polarisation

lEm e=

lEP en=

Ionic polarisation (i)This type of polarisation occurs in ionic crystals such NaCl, KCl and so forth.

The ionic crystal has distinctly identifiable ions located at well-defined lattice sites. Each pair of oppositely charged neighbouring ions has a dipole moment.

In the absence of an electric field, the solid has no net polarisation as the dipole moments of equal magnitude are lined up head to head and tail to tail, so that the net dipole moment is zero.

In the presence of a field along the x direction, Cl-ions pushed in x direction and the Na+ ions in +x direction about their equilibrium positions. Consequently, p+ increases and p- decreases.

0==+ pppnet

0>=+ pppnet

Based on electronic polarisation, we can write

Ni number of ion pairs/voli ionic polarisiability

lii ENP =

Dipolar polarisation (d)Certain molecules posses permanent dipole moments, such as HCl and H2O.

In the absence of electric field, these dipoles are randomly oriented due to thermal agitation.

Pnet = 0When a field E is applied, E tries to align the dipoles parallel to itsself.

Pnet > 0

If all the molecules were simply rotated and aligned with the E, the polarisation of the material would be

Pnet = Np0N number of molecules/vol. p0 permanent dipole moment of moleculeDue to their thermal energy, the molecules move around randomly and collide with each other which destroy the dipole alignments. The higher the temperature, the lower the polarisation P.

0pNP d=

Interfacial polarisation (m-w)All materials will have defects (lattice vacancies, impurity ions and free electrons). Under the influence of the applied field, migration will occur

Frequency DependenceAny or all of the mechanisms of polarisation may be operative in any material, i.e.

total=e+i+d+m-wHow identify the important ones for a given material?

Polarisation will tend to follow direction of the field.AC field a continuous reversal of polarisation in sympathy with the field.

What happens if frequency increases?

Example---polar dipolesAs frequency increases, the inertia of dipoles will make it more and more difficult for the dipoles to follow the field, resulting in a lag of the polarisation behind the field.

This appears as an apparent reduction in permittivity of the material.

At a critical frequency, dipoles will be unable to follow the field virtually no polarisation of the dielectric

The process is termed as relaxation and the frequency of transition is called relaxation frequency.Different polarisation mechanisms will have different relaxation frequencies!

ElectretsDefinition: Electrets are quasi-permanently charged dielectrics, i.e. dielectrics whose charge arrangement persists much longer than the time period over which it is studied.

Materials used for electrets (i) Wax

(ii) Polymers--Highly insulating substances e.g.

Polytetrafluoroethylene (PTFE), Fluoroethylene-propylene (FEP)

--Polar substances e.g.Polyvinylidene flouride (PVDF)

Forming methodsThermal method

H e a t i n gc h a m b e r

P o l y m e r ( m e t a l i s e do r n o n - m e t a l i s e d

V o l t a g e p r o f i l e

T e m p e r a t u r ep r o f i l e

t i m e

T

a

n

d

V

Corona discharge method

Needleelectrode

Wire mesh

polymer

metalisation

Liquid contact method

Clothelectrode

(wet)motion

polymer

metalisation

Electron beam method

Scanning ordefocusing

polymer

metalisation

Electron beam

Electron source

Vacuumchamber

Charge measurement methodsCapacitive probe method

Electrostatic voltmeters

In this voltage following device, the output of the integrator drives a high voltage amplifier circuit to replicate the voltage on the test surface. The amplified voltage is then applied to the sensor thus nullifying the electric field between the tested surface and the sensing electrode. Potential on the electrode follows the potential on the surface. In this case there is no threat of the eventual discharge between the probe and the surface under test, even at close spacing. This ability of following the voltage makes the electrostatic voltmeter measurement independent of the distance D0 at least within a certain range of D0. If the span between the surface and sensor is too big, the probe becomes influenced by other electric fields present in the vicinity.

The charge stability is reflected by the change in surface potential of the sample under test.

Pulsed electroacoustic method

Fig.3 Schematic diagram of PEA system

Vs(t)

transducer Vdc

Vp(t)

Sample

Vs(t) d

p(t)

electrode

electrode Detecting

(x) 1 2

Electret Applications1 Transducer--Microphone

Advantages(i) Compact and light weight

(ii) Insensitive to mechanical vibration & shock

(iii) Insensitive to electromagnetic pickup

2 Filters

Advantages(i) Spread into a broad web

(ii) Able to capture both charged or neutral particles

(iii) Capable of capturing different sizes of particles