lecture 2 105

8/7/2019 Lecture 2 105

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Module : 1 (Chapter /1)

Contents: Dielectric Materials� Polarization mechanism & Dielectric

constant

� Behavior of polarization under impulse

and frequency switching

� Spontaneous polarization (ferroelectric)

� Piezoelectric effect

� Application of Dielectric materials

� Dielectric loss

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Why Dielectric Materials?

�Insulators: Coolants for transformers

�Energy storage and other applications in capacitors.

�Pulsed power and weapons

� Power conditioning�Power factor correction

�Suppression and coupling

�Signal coupling & Decoupling

�Noise filters and snubbers Motor starters

� Signal processing�Tuned circuits

�Sensing Hazards 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 electric field?

� Why there is any electrical effect if the

insulators are indeed insulators and do not

conduct electricity?

� Why should a field induce a dipole moment

in an atom if the atom is not a conductingsphere?

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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 , a

material with a low (compared with that of a metal)electrical conductivity.

4. Most generally, a dielectric is an insulator, asubstance that is highly resistant to flow of electric

current. Layers of such substances are commonlyinserted into capacitors to improve their performance,and the term dielectric refers specifically to thisapplication.

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Why there is any electrical effect if the

insulators are indeed insulators and do not

conduct electricity?

Now if we put a piece of insulating material like Lucite or glass

between the plates, we find that the capacitance is larger . That

means, the voltage is lower for the same charge.

But voltage difference is the integral of the electric filed across the

capacitor, therefore we conclude, the electric field is reduced

even though the charges on the plates remain unchanged.

.Q CV !

0 A

C d

I !

Consider a parallel plate capacitor; Where

A= Area of plates,

d = Plate separation

C= Capacitance

Q= Charge on plateV= Voltage difference

Capacitance

Charge

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Hence C, V & E:

C=q/V (1)

C=I0 A/d (2)

V=V0/O (3)E=E0 /O (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.

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Why should a field induce a dipole moment in an

atom 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 exactly withthe location of the nucleus.

� If we now apply an electrical field, the centers of charge(+ve and ±ve) will be separated. The electron cloud willbe pulled in the direction of the positive pole of the field,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 µE¶, µP¶, µ¶ & µ¶

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Dipoles in solid dielectrics; Polarization

The dielectric constant of solids is an interestingmaterial parameter only if the material is exposed to anelectric field. The effect of electrical field is

1. It induces electrical dipoles in the material and tries toalign 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 distributionof existing dipoles while trying to align them, and it may

generate new dipoles in addition.

The total effect of an electrical field on a dielectricmaterial is called the polarization of the 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 dipolemoment Q which is defined

by Q = q ·

Q = q · � Q is a v ector because is a vector.The way we define it, its tip will always point towards the positi v e charge.

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Polarization is dipole moment per

unit volume� For bulk materials - sum up all indi v idual dipolemoments contained in the given volume of the materialand divide this sum by the volume V .

� Polarization P;

P = 7 Q V = Q" · N VWhere Q" = average vector dipole moment (C-m);

N V = Number density of dipoles (per m3).

The physical dimension of the polarization thus isC/

m2

;(Coulomb per square meter). i.e. the polarization has thedimension of charge per area, and since Q is a vector, P is also a vector.

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More on polarization� Polarization P = 0, does not mean that the material does

not contain dipole moments, but only that the vector sumof all dipole moments is zero.

± This will always be the case if the dipole momentvectors are randomly distributed with respect to their directions.

± But it will also happen if there is an ordered distributionwith pairs of opposing dipole moments

� P has the dimension of C/m2, i.e. that of surface chargedensity (Prove it.),

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

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� all dipole moments have the same direction.

� the charge density V inside a small probing volume, it isclearly zero in the volume of the material (because there

are just as many positive as negative charges.)� We are thus left with the surfaces, means equal and opposite charge ( surface polarization charge) on surfacesseparated by a distance ,

� Thus surface "volume" V S = A ·

� Hence P = �v

/ V = �s

S

/ V S

= . �s

q / V S

= . �s q / (. A)= �s q /A

� Therefore, ³surface 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)

± G = dielectric susceptibility ( Material parameter´P/ 0 E´ ).

� Note that including 0 in the relation is a convention whichis useful in the SI system, to make G 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 field µE¶ &

Polarization µP¶:

0 P E I G

r r

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Connection between the Polarization P and the

Electrical Displacement D

� I nside materials, the electrical field strength E was (andstill is) 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 O ("Kappa")is used; in proper microelectronics slang one than talks of "low Omaterials" (pronounced "low khe" as in (O)K) when on actually means"low kappa" or "low epsilon relative".

� D is supposed to give the "acting" flux inside the material.

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� The el ectric displacement D in a dielectric:

caused by some external field E ex is the

displacement D0 in vacuum plus the polarizationP , i.e.

D = D0 + P = 0 E + P

= 0 E + 0 GE

= 0

(G+1) E

Therefore, r = (G+1)

Note:

1. Here we have used P =0 GE , in which we have simply

assumed that P is parallel to E , which is only reasonablefor isotropic materials .

2. In anisotropic media, e.g. non-cubic crystals, P does nothave to be parallel to E , the scalar quantities r and G thenare tensors.

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Atomic Polarizability� As an effect of E, the plus charge shifted in one way and

the minus in the other.� So the atom has now a tiny dipole moment Q which

points out in the same direction as E. which isproportional to the field E (as long as E is reasonably

weak): Q =EE

� The constant of proportionality µE¶ is called the atomicpolarizability.

Q u es. A primiti v e 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 E lectronic

polarization.

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A relation between µE¶, µP¶, µ¶ & µ¶ :

Q =EE

P = 7Q V = Q" · N V

Hence P = N V EE

Or E =P / N V E

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Section II : Summary

� Dipoles in solid dielectrics;

Polarization.

� Dipole moment of the

atom.� Polarization is dipole

moment per unit volume:

� A relation between E & P:

�C

onnection between thePolarization P and the

Electrical Displacement D

� Polarizability

Q = q ·

P = 7Q V = Q" · N VP has the dimension of C/cm2, i.e.

that of surface charge density.

D = 0 (G+1) E

Q =EE

0 P E I !

r r

E =P / N V E

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Section III : Polarization

Mechanisms1. Types of Dielectrics

� Polar

� Non Polar 2. Electronic polarization:

3. Ionic polarization:

4. 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 dipol e moment ), since in mosttypes of molecules the centers of gravity of the

positive and negative charge distributions do

not coincide.

± Ex.Water

Dipole moment of

water 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 of charged particles under the action of the electric field towhich they are subjected.

� Therefore this displacement of the electric charges resultsin the formation of electric dipole moment in atoms, ions or molecules of the material.

± There are essentially three basic kinds of polarizationmechanisms:

1. E l ectronic polari zation: also called atomicpolarization. An electric field will always displace the

center of charge of the electrons with respect to thenucleus and thus induce a dipole moment. e.g noblegases.

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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. simpleionic crystals like NaCl.

3. Orientational polarization: Some time called³Dipolar polarization´; Here the (usually liquid or gaseous) material must have natural dipoles which canrotate freely. In thermal equilibrium, the dipoles will be

randomly oriented and thus carry no net polarization.The external field aligns these dipoles to some extentand thus induces a polarization of the material. Ex. iswater, i.e. H2O 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 thusbecomes superimposed on whatever other mechanism there might be.

� All three mechanisms are essential for basic consideration andcalculations.

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

However interf ace polari zation is also found in materials:

Surfaces, grain boundaries, interface boundaries may be charged , i.e.they contain dipoles which may become oriented to some degree in anexternal field and thus contribute to the polarization of the material.

± There is simply no general way to calculate the charges oninterf aces nor their contribution to the total polarization of amaterial. Interface polarization is therefore often omitted from thediscussion of dielectric properties.

lecture 2 105

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