MT-201A MATERIALS SCIENCEElectrical and Electronic Materials

Module 7

Dielelctric Materials

Compiled by Dr. Vikram DabhadeDept. of Metallurgical and Materials Engineering,Indian Institute of Technology Roorkee,Roorkee-247667, Uttrakhand.

INTRODUCTION

• Dielectric material: is one that is electrically insulating (non-metallic) and exhibits or may be made to exhibit an electric dipole structure; that is, there is a separation of positive and negative electrically charged entities on a molecular or atomic level.

• While insulating materials are used to resist the flow of current, dielectric materials are used to store electrical energy.

Capacitance

• When a voltage is applied across a capacitor, one plate becomes positively charged, the other negatively charged, with the corresponding electric field directed from the positive to the negative. The capacitance C is related to the quantity of charge stored on either plate Q by

C = Q / V

where V is the voltage applied across the capacitor. The units of capacitance are coulombs per volt, or farads (F).

• Now, consider a parallel-plate capacitor with a vacuum in the region between the plates. The capacitance may be computed from the relationship C = εo A

lwhere A represents the area of the plates and l is the distance between them.

• The parameter εo is called the permittivity of a vacuum, is a universal constant having the value of 8.86 x 10-12 F/m.

If a dielectric material is inserted into the region within the plates then

C = ε A

l

where ε is the permittivity of this dielectric medium, which will be greater in magnitude than εo. The relative permittivity εr often called the dielectric

constant, is equal to the ratio

εr =

ε εo

which is greater than unity and represents the increase in charge storing capacity by insertion of the dielectric medium between the plates. The dielectric constant is one material property that is of prime consideration for capacitor design.

Dielectric Constant (Permittivity)

As explained above, dielectric constant or permittivity of a material is defined as the “ratio of capacitance of a capacitor with that material as dielectric between the conducting plates, to the capacitance of the same capacitor with vacuum as dielectric medium.” εr = ε / εo or εr = c / co

The relative permittivity of vacuum is 1.00 and that of air is 1.00058 which is taken as unity. Gases have a relative permittivity slightly higher than unity, while polar liquids and ionic solids have high values of permittivity.

Dielectric Strength (breakdown voltage)

• Dielectric strength of an insulating material is the maximum electric field strength that it can withstand intrinsically without breaking down, i.e., without experiencing failure of its insulating properties or it is the minimum electric field that produces breakdown in a given configuration of dielectric material.

• The dielectric strength is also know as the breakdown voltage i.e. the voltage below which the dielectric material remains stable but above which it results in the destruction of insulating properties.

• The theoretical dielectric strength of a material is an intrinsic property of the bulk material and is dependent on the configuration of the material on which the field is applied.

• At breakdown, the electric field frees bound electrons. If the applied electric field is sufficiently high, free electrons may become accelerated to velocities that can liberate additional electrons during collisions with neutral atoms or molecules in a process called avalanche breakdown.

• Breakdown occurs quite abruptly (typically in nanoseconds)., resulting in the formation of an electrically conductive path and a disruptive discharge through the material. For solid materials, a breakdown event severely degrades, or even destroys, its insulating capability.

• Factors affecting dielectric strength

1. It increases with the increase in thickness of the specimen. (Directly proportional)

2. It decreases with the increase in operating temperature. (Inversely proportional)

3. It decreases with the increase in frequency. (Inversely proportional)4. It decreases with the increase in humidity. (Inversely proportional)

The field strength at which break down occurs in a given case is dependent on the respective geometries of the dielectric (insulator) and the electrodes with which the electric field is applied, as well as the rate of increase at which the electric field is applied. Because dielectric materials usually contain minute defects, the practical dielectric strength will be a fraction of the intrinsic dielectric strength seen for ideal, defect free, material.

Substance Dielectric Strength (MV/m)

Helium 0.15

Air 3.0 (depends on pressure)

Alumina 13.4

Window glass 9.8 - 13.8

Silicone oil, Mineral oil 10 - 15

Benzene 16

Polystyrene 19.7

Polyethylene 18.9 - 21.7

Neoprene rubber 15.7 - 27.6

Ultra pure Water 30

High Vacuum (field emission limited) ] 20 - 40 (depends on electrode shape)

Fused silica 25 - 40

Waxed paper 40 - 60

PTFE (Teflon) 60

Mica [11] 20 - 70

Thin films of SiO2 in ICs > 1000

Table: Dielectric strength (in MV/m) of various common materials:

Dielectric Loss

• The dielectric material separating two electrodes / conductors / plates is stressed when subjected to a potential. When the potential is reversed, the stress is also reversed.

• This change of stress involves molecular rearrangement within the dielectric. This involves energy loss with each reversal. This is because the molecules have to overcome a certain amount of internal friction in the process of alignment. The energy expended in the process is released as heat in the dielectric.

“The loss appearing in the form of heat due to reversal of electric stresses compelling molecular rearrangement is known as dielectric loss”

• The dielectric loss is not appreciable at ordinary frequency of 50 Hz, but in communication systems where frequencies of mega hertz are used, the heat released will be very high and can be observed by the increase in the temperature of the dielectric material.

Dielectric Polarization

• A material is made up of atoms; each atom consists of a cloud of negative charge (electrons) bound to and surrounding a positive point charge at its center. Because of the comparatively huge distance between them, none of the atoms in the dielectric material interact with one another. • In the presence of an electric field the charge cloud is distorted, as shown in the top right of the figure.• This can be reduced to a simple dipole using the superposition principle. A dipole is characterized by its dipole moment, a vector quantity shown in the figure as the blue arrow labeled M. It is the relationship between the electric field and the dipole moment that gives rise to the behavior of the dielectric

Figure: Electric field interaction with an atom under the classical dielectric model

Polar and Non-Polar Dielectrics

Polar Dielectrics• Like water, alcohol, CO2, NH3, HCl etc. are

made of polar atoms/molecules. • In polar molecules when no electric field is applied centre of positive charges does not coincide with the centre of negative charges.

• A polar molecule has permanent electric dipole moment in the absence of electric field also. But a polar dielectric has net dipole moment is zero in the absence of electric field because polar molecules are randomly oriented as shown in figure.

• In the presence of electric field polar molecules tends to line up in the direction of electric field, and the substance has finite dipole moment.

Non - Polar Dielectrics

• Like N2, O2, Benzene, Methane etc. are made of non-polar atoms/molecules.

In non-polar molecules, when no electric field is applied the centre of positive charge coincides with the centre of negative charge in the molecule. Each molecule has zero dipole moment in its normal state.

• When electric field is applied, positive charge experiences a force in the direction of electric field and negative charge experiences a force in the direction opposite to the field i.e., molecules becomes induced electric dipole.

7.1 Matter Polarization and Relative Permittivity

Relative PermittivityConsider a parallel plate capacitor with vacuum as the dielectric medium between the plates (Fig.(a)). The plates are connected to a constant voltage supply V. Let Qo be the charge on the plates. The capacitance Co of the

parallel plate capacitor in free space is defined by Co = Qo / V

Co = capacitance of a parallel plate capacitor in free space

Qo = charge on the plates

V = voltage

When a dielectric slab (slab of non-conducting material) is inserted into this parallel plate capacitor (Fig.b & c) with V kept the same. Now due to the insertion of the dielectric slab, there is an external current flow that indicates that there is additional charge being stored on the plates. The charge on the electrodes increases from Qo to Q. Because now there is greater amount of

charge stored on the plates, the capacitance of the system in Fig.(a) is larger than that in Fig.(b) by the ratio Q to Qo.

The relative permittivity (or the dielectric constant) εr is defined to reflect this

increase in the capacitance or the charge storage capacity by virtue of having a dielectric medium. If C is the capacitance with the dielectric medium (Fig.(c)) then: εr = Q/Qo = C/Co

The increase in the stored charge is due to the polarization of the dielectric by the applied field.

Dipole Moment and Electronic Polarization

An electrical dipole moment is simply a separation between a negative and positive charge of equal magnitude Q in a system of charges. In the simple case of two point charges, one with charge + q and one with charge − q, the electric dipole moment p is: p = Qa

where a is the displacement vector pointing from the negative charge to the positive charge (a in the scalar form is the bond length in the molecule which has got polarized)

• The net charge within a neutral atom is zero. In the absence of an electric field the center of negative charge of the electrons coincides with the positive nuclear charge, means that the atom has no net dipole moment (Fig.7.3(a)).

• With an application of electric field induced dipole moment will take place causing electrons being much lighter than the positive nucleus to get displaced by the field. This results in the separation of the negative charge center from the positive charge center as shown in Fig.7.3(b).

• This separation of negative and positive charges and the resulting induced dipole moment are termed polarization. An atom is said to be polarized if it possesses an effective dipole moment, that is, if there is a separation between the centers of negative and positive charge distributions.

• The induced dipole moment depends on the electric field causing it. We define a quantity called the polarizability α to relate the induced dipole moment pinduced to the field E causing it, pinduced = αE

where α is a coefficient called the polarizability of the atom. Since the polarization of a neutral atom involves the displacement of electrons α is generally called electronic polarization denoted as αe.

Polarization Vector P

• When a material is placed in an electric field, the atoms and molecules of the material become polarized, so we have a distribution of dipole moments in the material. We can visualize this effect with the insertion of a dielectric slab into the parallel plate capacitor as shown in Fig.(a).

• The placement of the dielectric slab into an electric field polarizes the molecules in the material. The induced dipole moments all point in the direction of the field.

• Consider a polarized medium alone, as shown in Fig.(b) in which every positive charge has a negative charge next to it and vice versa. There is therefore no net charge within the bulk. But the positive charges of the dipoles appearing at the right hand face are not canceled by negative charges of any dipoles at this face. There is therefore a surface charge +Qp on the right hand face that results from the polarization of the medium.

• Similarly, there is a negative charge -Qp with the same magnitude appearing on the left hand face due to the negative charges of the dipoles at this face. These charges are bound and are a direct result of the polarization of the molecules. They are termed surface polarization charges.

• Fig(c) emphasizes this aspect of dielectric behavior in an electric field by showing the dielectric and its polarization charges only.

• We represent the polarization of a medium by a quantity called polarization P, which is defined as the total dipole moment per unit volume, P = 1 [p1 + p2 + ……+ pN] VolumeWhere p1, p2,….pN are the dipole moments induced at N molecules in the volume.

• If pav is the average dipole moment per molecule, then an equivalent definition of P is P = Npav

• To calculate the polarization P for the polarized dielectric we need to sum all the dipoles in the medium and divide by the volume Ad as in eqn.1. However the polarized medium can be simply represented as in Fig.(c) in terms of surface charge +QP and -QP, which are separated by the thickness distance d.

• We can view this arrangement as one big dipole moment per unit volume, the magnitude of P is P = ptotal / volume = Qpd / Ad = Qp / A

But Qp / A is the surface polarization charge density σp,

so P = σp• Polarization is a vector and the above equation only gives its magnitude. For the rectangular slab in Fig.7.5., the direction of P is normal to the surface. For +σp (right face), it comes out from the surface and for -σp (left face), it is

directed into the surface. If Pnormal is the component of P normal to the surface

where the polarization charge density is σp, as shown in Fig.7.6, then,

Pnormal = σp

Local Field Eloc

• The electronic polarizability αe is related to relative permittivity εr by the

relation εr = 1 + Nαe / εo. Relative permittivity εr is a macroscopic property

while electronic polarizability αe is related to microscopic polarization

mechanisms. This equation assumes that the field acting on an individual atom or molecule is the field E, which is assumed to be uniform within the dielectric.

• However the induced polarization depends on the actual field experienced by the molecule. But there are polarized molecules within the dielectic with their negative and positive charges separated so that the field is not constant on the atomic scale as we move through the dielectric. This is depicted in Fig.7.7.

• The field experienced by an individual molecule is actually different than E, which represents the average field in the dielectric. As soon as the dielectric becomes polarized, the field at some arbitrary point depends not only on the charges on the plates (Q) but also on the orientations of all the other dipoles around this point in the dielectric. When averaged over some distance, say a thousand molecules, this field becomes E, as shown in Fig.7.7.

• The actual field experienced by a molecule in a dielectric is defined as the local field and denoted by Eloc. It depends not only on the free charges on the

plates but also on the arrangement of all the polarized molecules around this point. In evaluating Eloc we simply remove the molecule from this point and

calculate the field at this point coming from all sources, including neighbouring polarized molecules as shown in Fig.7.7.

7.2 Electronic Polarization: Covalent Solids

• When a field is applied to a solid substance, the constituent atoms or molecules become polarized as shown in Fig.7.8. The electron clouds within each atom becomes shifted by the field, and this gives rise to electronic polarization.

• This type of electronic polarization within an atom, however, is quite small compared with the polarization due to the valence electrons in the covalent bonds within the solid.

• For example, in crystalline silicon, there are electrons shared with neighboring Si atoms in covalent bonds as shown in Fig.7.8. These valence electrons form bonds (i.e. become shared) between the Si atoms because they are already loosely bound to their parent atoms. Thus, they readily respond to an applied field and become displaced.

• This type of electronic polarization, due to the displacement of electrons in covalent bonds is responsible for the large dielectric constants of covalent crystals.

(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.

7.3 Polarization Mechanisms

In addition to electronic polarization, there are a number of other polarization mechanisms such as:

1. Ionic polarization

2. Orientational (Dipolar) Polarization

3. Interfacial Polarization and

4. Total Polarization (which is the sum of electronic, ionic and dipolar)

Ionic Polarization

• This type of polarization occurs in ionic crystals such as NaCl, KCl and LiBr. Ionic crystals have distinctly identifiable ions, ex, Na+ and Cl-, located at well defined lattice sites, so each pair of oppositely charged neighboring ions has a diple moment.

• As an example, we consider the one-dimensional NaCl crystal depicted as a chain of alternating Na+ and Cl- ions as shown in Fig.7.9a. In the absence of and applied field, the solid has no net polarization because the dipole moments of equal magnitude are lined up head to head and tail to tail so that the net dipole moment is zero. The dipole moment p+ in the positive direction has the same magnitude as p- in the negative x direction, so the net dipole moment pnet is zero.

• In the presence of a field E along the x direction, however, the Cl- ions are pushed in the –x direction and the Na+ ions in the +x direction about their equilibrium positions. Consequently, the dipole moment p+ in the +x direction increases to p'+ and the dipole moment p- decreases to p'- as shown in Fig.7.9b. The net dipole moment, or the average dipole moment, per ion pair is now (p'+ - p'-), which depends on the electric field E.

(a) A NaCl chain in the NaCl crystal without an applied field. Average or net dipole moment per ion is zero.

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

Orientational (Dipolar) Polarization

• Certain molecules exhibit permanent dipole moments as discussed earlier. For example HCl molecule shown in Fig.7.10a has a permanent dipole moment po

from the Cl- ion to the H+ ion.

• In the liquid or gas phases, these molecules, in the absence of an electric field, are randomly oriented as a result of thermal agitation as shown in Fig.7.10b.

• When a electric field E is applied E tries to align the dipoles parallel to itself, as depicted in Fig.7.10c. The Cl- and H+ charges experience forces in opposite directions. But the nearly rigid bond between Cl- and H+ holds them together, which means that the molecule experiences a troque τ about its center of mass.

• This torque acts to rotate the molecule to align po with E. If all the molecules

were to simply rotate and align with the field, the polarization of the solid would be P = Npo

Where N is the number of molecules per unit volume.

• However, due to their thermal energy, the molecules move around randomly and collide with each other and with the walls of the container. These collisions destroy the dipole alignments. Thus the thermal energy tries to randomize the orientations of the dipole moments.

• A snapshot of the dipoles in the material in the presence of a field can be pictured in Fig.7.10d in which the dipoles have different orientations. There is, never less, a net average dipole moment per molecule Pav that is finite and directed along the field. Thus the material exhibits net polarization, which leads to a dielectric constant that is determined by this orientational polarization.

Interfacial Polarization

• Interfacial polarization occurs whenever there is accumulation of charge at an interface between two materials or between two regions within a material. The simplest example is interfacial polarization due to the accumulation of charges in the dielectric near one of the electrodes, as shown in Fig.7.11a and b.

• Invariably all materials, however perfect, contain crystal defects, impurities, and various mobile charge carriers such as electrons, holes, or ionized host or impurity ions.

• Consider a material which has equal number of positive ions and negative ions, but the positive ions are more mobile because they are relatively smaller then the negative ions. Under the presence of an applied field, these positive ions migrate to the negative electrode. The positive ions, however cannot leave the dielectric and enter the crystal structure of the metal electrode. They therefore simply pile up at the interface and give rise to a positive space charge near the electrode.

• These positive charges at the interface attract more electrons to the negative electrode. This additional charge on the electrode, of course, appears as an increase in the dielectric constant.

• The term interfacial polarization arises because the positive charges accumulating at the interface and the remainder of negative charges in the bulk together constitute dipole moments that appear in the polarization vector P.

• Grain boundaries frequently lead to interfacial polarization as they can trap charges migrating under the influence of an applied field, as indicated in Fig.7.11c. Dipoles between the trapped charges increase the polarization vector.

(a) A crystal with equal number of mobile positive ions and fixed negative ions. In the absence of a field, there is no net separation between all the positive charges and all the negative charges.

(b) In the presence of an applied field, the mobile positive ions migrate toward the negative charges and positive charges in the dielectric. The dielectric therefore exhibits interfacial polarization.

(c) Grain boundaries and interfaces between different materials frequently give rise to interfacial polarization.

Total Polarization

• In the presence of electronic, ionic, and dipolar polarization mechanisms, the average induced dipole moment per molecule will be the sum of all the contributions in terms of the local field,

Pav = αeEloc + αiEloc + αdEloc

• Each effect adds linearly to the net dipole moment per molecule. Interfacial polarization cannot be simply added to the above equation as it occurs at interfaces and cannot be put into an average polarization per molecule in the bulk.