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Module : 1 (Chapter /1)

Contents: Dielectric Materials

Polarization mechanism & Dielectric

constant

Behavior of polarization under impulse

an frequency switching

Piezoelectric effect

Application of Dielectric materials

Dielectric loss

Spontaneous polarization

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Why Dielectric Materials?

Insulators: Coolants for transformersEnergy storageand other applications in capacitors.Pulsed power and weaponsPower conditioning

Power factor correctionSuppression and couplingSignal coupling & DecouplingNoise filters andsnubbersMotor starters

Signal processingTuned circuitsSensingHazards and safety

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BASICS OF DIELECTRIC

MATERIALS

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section I: Basic Questions

What is a dielectric?

Can insulator be affected by electricfield?

Why there is any electrical effect if theinsulators are indeed insulators and donot conduct electricity?

Why should a field induce a dipolemoment in an atom if the atom is not aconducting sphere?

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What is a dielectric?

1. A material that can sustain an electric field but doesnot conduct electric current.

2. A nonconducting or insulating substance that resistspassage of electric current.

3. More or less a synonym for electrical insulator, amaterial with a low (compared with that of a metal)electrical conductivity.

4. Most generally, a dielectric is an insulator, a substance

that is highly resistant to flow of electric current.Layers of such substances are commonly inserted intocapacitors to improve their performance, and the termdielectric refers specifically to this application.

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Can insulator be affected byelectric field?

Till the time of Faraday people used to think; it cantbecause it does not conduct electricity.

Faradays experimental observation: Capacitance of acapacitor is increased when an insulator is placed

between the plates, the capacitance is increased by afactor if the insulator completely fills the spacebetween the plates.

depends only on the nature of the insulating materialand is called dielectric constant

Q: What should be the dielectric constant of vacuum?Q: Can we have a dielectric substance having dielectric

constant 0.9?

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Why there is any electrical effect if theinsulators are indeed insulators and do not

conduct electricity?

Now if we put a piece ofinsulating material like Lucite orglass between the plates, we find that the capacitanceis larger. That means, the voltage is lower for the same

charge.But voltage difference is the integral of the electric filedacross the capacitor, therefore we conclude, theelectric field is reduced even though the charges onthe plates remain unchanged.

.Q CV=

0A

Cd

=

Consider a parallel plate capacitor; Where

A= Area of plates,

d = Plate separation

C= Capacitance

Q= Charge on plate

V= Voltage difference

Capacitance

Charge

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Hence C, V & E:

C=q/V (1)

C=0A/d (2)

V=V0/ (3)

E=E0/ (4)

The capacitance of a set of charged parallel plates isincreased by the insertion of a dielectric material.

The capacitance is inversely proportional to the

electric field between the plates.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/pplate.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/pplate.html

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Why should a field induce a dipole moment in anatom if the atom is not a conducting sphere?

Consider a single atom. We have a positively charged nucleus and the electron

"cloud". For Spherically symmetric system; center of gravity of

negative charges (electron cloud) coincides exactlywith

the location of the nucleus. Ifwe now apply an electrical field, the centers of charge

(+ve and ve) will be separated. The electron cloudwill be pulled in the direction of the positive pole of thefield, the nucleus to the negative one.

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Section II: Review of Basics

Dipoles in solid dielectrics; Polarization. Dipole moment of the atom. Polarization is dipole moment per unit

volume: A relation between E & P: Connection between the Polarization P

and the Electrical Displacement D

Polarizability Relation between E, P, &

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Dipoles in solid dielectrics;Polarization

The dielectric constant of solids is an interestingmaterial parameter only if the material is exposedto an electric field. The effect ofelectrical fieldis

1. It induces electrical dipoles in the material and

tries to align them in the field direction.2. It tries to align existing dipoles.

* Of course we also may have a combination of botheffects: The electrical field may change the distribution ofexisting dipoles while trying to align them, and it may

generate new dipoles in addition.

The total effect of an electrical field on adielectric material is called the polarization ofthe material.

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Dipole moment of the atom

The center of the positive andnegative charges q (=z e) are

now separated by a distance ,and we thus induced a dipole

moment which is defined by = q

= q is a vectorbecause is a vector.The way we define it, its tip will alwayspoint towards the positive charge.

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Polarization is dipole moment perunit volume

For bulk materials - sum up all individual dipolemoments contained in the given volume of the materialand divide this sum by the volume V.

Polarization P;

P = /V = NVWhere =average vector dipole moment (C-m);

NV

=Number density of dipoles (per m3).

The physical dimension of the polarization thus isC/m2; (Coulomb per square meter). i.e. thepolarization has the dimension of an areacharge, andsince is a vector, Pis also a vector.

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More on polarization

Polarization P= 0 does notmean that the material does notcontain dipole moments, but only that the vector sum of all

dipole moments is zero.

This will always be the case if the dipole moment vectors

are randomly distributedwith respect to their directions. But it will also happen if there is an ordered distribution

with pairs of opposing dipole moments P has the dimension of C/m2, i.e. that of surface charge

density (Prove it.),

To see this, let us consider a simple plate capacitor orcondenser with a homogeneously polarized materialinside its plates. (isotropic dielectric slab) We have thefollowing idealized situation:

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all dipole moments have the same direction. the charge density inside a small probing volume, it is

clearly zero in the volume of the material (because there arejust as many positive as negative charges.)

We are thus left with the surfaces, means equal and oppositecharge (surface polarization charge) on surfaces separated bya distance ,

Thus surface "volume" VS = A

Hence P= v / V= s S / VS= . s q/ VS= . s q/ (. A)= s q/A

Therefore, surface charge density is equal to the

magnitude of polarization. pol=|P|=P=Nq

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linear relationship between the applied field E(Low)and P, i.e.

Where 0 =permittivity constant (of vacuum) = dielectric susceptibility ( Material parameter P/ 0

E ). Note that including 0 in the relation is a convention

which is useful in the SIsystem, to make dimensionless, P is proportional to E ( Linear relationship) for Low E. P is proportional to E2 or E3 (Non linear ) for High E.

A relation between Electric fieldE & Polarization P:

0P E =

r r

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Connection between the Polarization Pand the Electrical Displacement D

Inside materials, the electrical field strength Ewas (and stillis) replaced by a vector D called the electricaldisplacement or electrical flux density, which is definedas

D = r 0 E

Where r = (relative) dielectric constant (DK) of thematerial.

(the product r 0 is called the permittivity).

* Note that in the English literature often the abbreviation ("Kappa") is used; in proper microelectronics slang one than talksof "low materials" (pronounced "low khe" as in (O)K) when onactually means "low kappa" or "low epsilon relative".

D is supposed to give the "acting" fluxinside the material.

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The electric displacementD in a dielectric:

caused by some external field Eex is thedisplacement D0 in vacuum plus the polarizationP, i.e.

D = D0 + P = 0 E + P

= 0 E+ 0 E

= 0 (+1) E

Therefore, r = (+1)

Note:

1. Here we have used P=0 E , in which we have simply assumedthat P is parallel to E, which is only reasonable for isotropicmaterials .

2. In anisotropicmedia, e.g. non-cubic crystals, Pdoes not have tobe parallel to E, the scalar quantities r and then aretensors.

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Atomic Polarizability As an effect ofE, the plus charge shifted in one way and

the minus in the other.

So the atom has now a tiny dipole moment which pointsout in the same direction as E. which is proportional to thefield E (as long as E is reasonably weak):

=E The constant of proportionality is called the atomic

polarizability.

Ques.A primitive model of an atom

consists of a point nucleus (+q)

surrounded by a uniformly charged

spherical cloud (-q) of radius a. What will

be the atomic polarizability of such an

atom?

Note: we will discuss it in Electronic

polarization.

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A relation between E, P, & :

=EP = /V = N

V

Hence P = NV E

Or =P / NVE

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Section II : Summary

Dipoles in soliddielectrics; Polarization.

Dipole moment of theatom.

Polarization is dipole

moment per unitvolume:

A relation between E &P:

Connection between the

Polarization Pand theElectrical DisplacementD

Polarizability

= q

P = /V = N

V

Phas the dimension ofC/cm2, i.e. that ofsurface

charge density.

D = 0 (+1) E =E

0P E =r r

=P / NV

E

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Section III : PolarizationMechanisms

1. Types of Dielectrics Polar Non Polar

1. Electronic polarization:

2. Ionic polarization:

3. Orientation (Dipolar) polarization :

interface polarization

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Types of Dielectrics:

Polar dielectrics: Materials having permanent dipole moments Net dipole moment Not zero Many natural molecules are examples of

systems with a finite electric dipole moment(permanent dipole moment), since inmost types of molecules the centers ofgravity of the positive and negative chargedistributions do not coincide.

Ex. Water

Dipole moment ofwater molecule.

Non Polar dielectrics:Net dipole moment zero, (in the absence of E) centers of gravity of the positive and negative charge

distributions coincide with each other.

Ex. O2, N2 and Nobel gases

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Polarization Mechanisms

Dielectric Polarization is nothing but the displacement ofcharged particles under the action of the electric field towhich they are subjected.

Therefore this displacement of the electric charges resultsin the formation ofelectric dipole moment in atoms, ions

or molecules of the material. There are essentially three basic kinds of polarization

mechanisms:

1. Electronic polarization: also called

atomic polarization. An electric field will alwaysdisplace the center of charge of the electrons with respectto the nucleus and thus induce a dipole moment. e.gnoble gases.

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Polarization Mechanism----

2. Ionic polarization: In this case a (solid) material musthave some ionic character. It then automatically hasinternal dipoles, but net dipole moment is zero. Theexternal field then induces net dipoles by slightlydisplacing the ions from their rest position. Ex. simple

ionic crystals like NaCl.

3. Orientational polarization: Some time calledDipolar polarization; Here the (usually liquid orgaseous) material must have natural dipoles which can

rotate freely. In thermal equilibrium, the dipoles will berandomly oriented and thus carry no net polarization. Theexternal field aligns these dipoles to some extent and thusinduces a polarization of the material. Ex. is water, i.e.H

2O in its liquid form.

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NOTE: Some or all of these mechanisms may act simultaneously. Atomic polarization, e.g., is always present in any material and

thus becomes superimposed on whatever other mechanismthere might be.

All three mechanisms are essentialfor basic consideration andcalculations.

***********************************************************************************

However interface polarization isalso found in materials:

Surfaces, grain boundaries, interface boundaries may becharged, i.e. they contain dipoles which may become orientedto some degree in an external field and thus contribute to thepolarization of the material.

There is simply no generalway to calculate the chargeson interfaces nor their contribution to the totalpolarization of a material. Interface polarization istherefore often omitted from the discussion of dielectricproperties.