dielectric materials

MT-201A MATERIALS SCIENCE
Electrical and Electronic Materials

Module 7

Dielelctric Materials

Compiled by
Dr. Vikram Dabhade
Dept. 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
l
where 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.

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

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

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 Permittivity
Consider 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]
Volume
Where 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.

dielectric materials

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