Dielectric Materials

Dielectric Materials

Aims

After completing this lecture, you should:

➢ Understand the meaning of terms dielectric constant, dielectric loss

and dielectric breakdown.
➢ Recognize that the properties of dielectrics are due to polarization and
understand how this polarization arises on the microscopic scale.
➢ Understand how material structure, temperature and frequency affect
the properties of dielectrics.
➢ Be aware of some practical applications of dielectric materials.
 Introduction
➢ A dielectric material is any material that supports charge without
conducting it to a significant degree.
➢ In principle all insulators are dielectric, although the capacity to
support charge varies greatly between different insulators.
➢ Dielectric materials are used in many applications, from simple
electrical insulation to sensors and circuit components.
 Electric dipoles
➢ A dielectric supports charge by acquiring a polarization in an electric
field, whereby one surface develops a net positive charge while the
opposite surface develops a net negative charge.
➢ This is made possible by the presence of electric dipoles – two
opposite charges separated by a certain distance – on a microscopic
scale.
➢ If two discrete charged particles of opposite charges are separated by
a certain distance, a dipole moment μ arises.
 Electric dipoles
➢ If the centre of positive charge within a given region and the centre of
negative charge within the same region are not in the same position,
a dipole moment μ arises.

For example, in the diagram below the centre of positive charge from the
8 cations shown is at X, while the centre of negative charge is located
some distance away on the anion.

Note that in the equation for

dipole moment, r is a vector
(the sign convention is that r
points from negative to
positive charge) therefore the
dipole moment μ is also a
vector.
 Electric dipoles
➢ The polarisation of a material is simply the total dipole moment for a
unit volume.

where V is the overall volume of the sample.

➢ Since Σμ is a vector sum, a material may contain dipoles without

having any net polarisation, since dipole moments can cancel out.
➢ When an electric field is applied, these dipoles align to the field,
causing a net dipole moment that affects the material properties.
 Polarisation mechanisms
➢ There are three main polarisation mechanisms that can occur within a
dielectric material:
• electronic polarisation,
• ionic polarisation (sometimes referred to as atomic polarisation)
• orientational polarisation.

The applied field causes the electron cloud to

Within each atom or ion there is a distort in one direction while the nucleus
positively charged nucleus surrounded moves in the other direction. Since the centre
by a negative electron cloud. of the electron cloud no longer coincides with
the nucleus, a dipole moment develops
 Polarisation mechanisms
➢ There are three main polarisation mechanisms that can occur within a
dielectric material:
• electronic polarisation,
• ionic polarisation (sometimes referred to as atomic polarisation)
• orientational polarisation.
 Polarisation mechanisms
➢ There are three main polarisation mechanisms that can occur within a
dielectric material:
• electronic polarisation,
• ionic polarisation (sometimes referred to as atomic polarisation)
• orientational polarisation.

To gain a more general The distortion of bonds caused by the electric

understanding of ionic polarisation, field leads to an off-centring of the cations with
we must consider many ions at once. respect to the anions (and vice versa). The centres
of positive and negative charge no longer coincide
and a net polarisation develops.
 Resistance and Capacitance

Current I

ℓ
ℓ

Capacitance Permittivity
Resistance
C=Q/V
R =V / I

Current I

A
C =
R=
A

10
 Parallel Plate Capacitor
A
C = e0 • Capacitance is the ability to store
ℓ charge across a potential difference.

❑ Capacitance definition
❑ Unit: Farad
❑ Capacitance is a device property
❑ From capacitance to material
property (dielectric constant)

A A A
C =e C = e = e re0
ℓ ℓ ℓ
e = e re0
permittivity of
e medium
er =
e0 permittivity of
a vacuum
dielectric constant
11
 Capacitors

➢ The capacitance is affected by various factors, such as the capacitor

geometry, however here we shall only deal with the effect of the
dielectric material chosen to occupy the space between the plates.
 Capacitors

Polarisation of the dielectric leads to a net

Here we have an empty parallel plate buildup of charge on the surfaces that are in
capacitor, with capacitance C = Q/V. contact with the capacitor plates. This partially
counteracts the electric field between the
plates, leading to a decrease in field strength.
This is observed as a fall in voltage
 The dielectric constant

Q and C depend on the geometry of the plates.

C = Q / V = 0 A / l
where the proportionality constant 0 is called permittivity of the vacuum.
The units of C are 1 Clb/V = 1 Farad (1 F).

Hence 0 = 8.85×10-12 F/m.

The equation above looks similar to Ohm’s Law:

R = V/I and 1/C = V/Q
So R of a resistor is to flowing charge I (Clb/s) what 1/C of a capacitor is to static
charge Q (Clb).
 The dielectric constant

When the space between the two plates of a capacitor is filled with a dielectric
material, experiments show that at constant applied voltage V, the charge Q' on
the plates is higher than the charge Q before:

In this case: C =  A / l = Q’/V

where  is the permittivity of the dielectric material.  can be written as
 = 0 r with r > 1
The factor r by which the capacitance has been increased due to the material
between the plates is called its dielectric constant.
 The dielectric constant

➢ The two definitions of the dielectric constant are illustrated by the

diagram below
Dielectric Constants for Materials

17
Frequency Dependence of Dielectric Constant

18
 Frequency Dependence of Dielectric Constant

The data for r in the table can be explained roughly in terms of the main
applicable polarization mechanism:

Mechanism Features Materials

Electronic small polarization, fast gases, non-polar

response liquids, polymers
Ionic medium polarization, ceramics, inorganic
medium response glasses
Orientational large polarization, slow polar liquids
response

The response time indicates how r depends on the frequency of the applied
field. If tp is a characteristic time for the polarization to change, then the
polarization cannot follow an applied electric field which changes in a time
shorter than tp, or which has a frequency higher than tp-1.
Variation of the dielectric constant in alternating fields

➢ a dielectric becomes polarised in an electric field.

➢ If the direction of the field is switched, the direction of the
polarisation will also switch in order to align with the new field.
➢ This cannot occur instantaneously: some time is needed for the
movement of charges or rotation of dipoles.
Variation of the dielectric constant in alternating fields
Variation of the dielectric constant in alternating fields
 Effect of structure on the dielectric constant

➢ Crystals with non-centrosymmetric structures such as barium titanate

have especially large spontaneous polarisations and so
correspondingly large dielectric constants.
➢ A polar gas tends to have smaller dipoles, and its low density also
means there is less to polarise, therefore polar gases have lower
dielectric constants than polar solids or liquids.
➢ The density argument also applies for non-polar gases when
compared with non-polar solids or liquids.
Effect of structure on the dielectric constant
 Effect of temperature on the dielectric constant

➢ For materials that possess permanent dipoles, there is a significant

variation of the dielectric constant with temperature.
➢ This is due to the effect of heat on orientational polarisation.
➢ As the temperature increases, the molecules have more thermal
energy and therefore the amplitude of random thermal motion is
greater.
➢ This means that the range of deviation from a perfect alignment with
the field is greater, therefore the molecules are less closely aligned
with each other, therefore the orientational polarisation of the
material - and hence the dielectric constant - is less.
 Effect of temperature on the dielectric constant

➢ However, this does not mean that the dielectric constant will increase
continually as temperature is lowered.
➢ There are several discontinuities in the dielectric constant as
temperature changes.
➢ First of all, the dielectric constant will change suddenly at phase
boundaries.
➢ This is because the structure changes in a phase change and the
dielectric constant is strongly dependent on the structure.
➢ Whether κ will increase or decrease at a given phase change depends
on the exact two phases involved.
 Effect of temperature on the dielectric constant

➢ In a crystalline solid, there are only certain orientations permitted by

the lattice.
➢ To switch between these different orientations, a molecule must
overcome a certain energy barrier ΔE.
 Effect of temperature on the dielectric constant

➢ At low temperature, the orientational mode cannot contribute to

polarization
 Loss in dielectrics
➢ An efficient dielectric supports a varying charge with minimal
dissipation of energy in the form of heat.
➢ There are two main forms of loss that may dissipate energy within a
dielectric.
➢ In conduction loss, a flow of charge through the material causes
energy dissipation.
➢ Dielectric loss is the dissipation of energy through the movement of
charges in an alternating electromagnetic field as polarisation
switches direction.
 Loss in dielectrics
➢ Dielectric loss is especially high around the relaxation or resonance
frequencies of the polarisation mechanisms as the polarisation lags
behind the applied field, causing an interaction between the field and
the dielectric’s polarisation that results in heating.
Loss in dielectrics
 Loss in dielectrics
➢ Dielectric loss tends to be higher in materials with higher dielectric
constants.
➢ Dielectric loss is utilised to heat food in a microwave oven:
➢ the frequency of the microwaves used is close to the relaxation
frequency of the orientational polarisation mechanism in water,
meaning that any water present absorbs a lot of energy that is then
dissipated as heat.
➢ The exact frequency used is slightly away from the frequency at which
maximum dielectric loss occurs in water to ensure that the
microwaves are not all absorbed by the first layer of water they
encounter, therefore allowing more even heating of the food.
 Dielectric breakdown
➢ At high electric fields, a material that is normally an electrical
insulator may begin to conduct electricity – i.e. it ceases to act as a
dielectric.
➢ This phenomenon is known as dielectric breakdown.
➢ The mechanism behind dielectric breakdown can best be understood
using band theory.
 Dielectric breakdown

➢ For each material, there is a characteristic field strength needed to

cause dielectric breakdown.
➢ This is referred to as the breakdown field or dielectric strength.
Typically values of the dielectric strength lie in the range 106 – 109
Vm-1.
➢ The exact value of the dielectric strength depends on many factors –
most obviously the size of the energy gap, but also the geometry and
microstructure of the sample and the conditions it is subjected to.
 Dielectric breakdown

➢ For each material, there is a characteristic field strength needed to

cause dielectric breakdown.
➢ This is referred to as the breakdown field or dielectric strength.
Typically values of the dielectric strength lie in the range 106 – 109
Vm-1.
➢ The exact value of the dielectric strength depends on many factors –
most obviously the size of the energy gap, but also the geometry and
microstructure of the sample and the conditions it is subjected to.
 Applications of dielectrics

➢ A major use of dielectrics is in fabricating capacitors.

➢ These have many uses including storage of energy in the electric field
between the plates, filtering out noise from signals as part of a
resonant circuit, and supplying a burst of power to another
component.
 Summary

➢ Dielectrics are electrical insulators that support charge.

➢ The properties of dielectrics are due to polarisation.
➢ There are three main mechanisms by which polarisation arises on the
microscopic scale: electronic (distortion of the electron cloud in an atom),
ionic (movement of ions) and orientational (rotation of permanent dipoles).
➢ A capacitor is a device that stores charge, usually with the aid of a dielectric
material. Its capacitance is defined by Q = C V
➢ The dielectric constant κ indicates the ability of the dielectric to polarise. It
can be defined as the ratio of the dielectric’s permittivity to the permittivity
of a vacuum.
➢ Each of the polarisation mechanisms has a characteristic relaxation or
resonance frequency. In an alternating field, at each of these (materials
dependent) frequencies, the dielectric constant will sharply drop.
 Applications of dielectrics

➢ The dielectric constant is also affected by structure, as this affects the ability
of the material to polarise.
➢ Polar dielectrics show a decrease in the dielectric constant as temperature
increases.
➢ Dielectric loss is the absorption of energy by movement of charges in an
alternating field, and is particularly high around the relaxation and
resonance frequencies of the polarisation mechanisms.
➢ Sufficiently high electric fields can cause a material to undergo dielectric
breakdown and become conducting.