Type & Properties of
Electroceramics
EBB 443 – Technical Ceramics
Dr. Sabar D. Hutagalung
School of Materials and Mineral Resources Engineering, Universiti
Sains Malaysia
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Ceramic insulators
High-k ceramic dielectrics
Piezoelectric ceramics
Ferroelectric ceramics
Magnetic ceramics
Superconductors
Photonic ceramics
Ceramic insulators
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The primary function of insulation in electrical circuits is
physical separation of conductors and regulation or
prevention of current flow between them.
Other functions are to provide mechanical support, heat
dissipation, and environmental protection for
conductors.
Ceramic materials which in use these functions are
classified as ceramic insulators.
They include most glasses, porcelains, and oxide and
nitride materials.
The advantage of ceramics as insulators is their
capability for high-temperature operation.
Insulation Resistance
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Conductivity
 = d/(R A)
and 1/  =  = (R A)/d
Or in terms of the material parameters
 = nq
where  is the electrical resistivity (m), R () the
sample resistance, A is area (m2), and d thickness (m).
If more than one type of charge carrier being present,
the resultant conductivity can be defined as the sum of
component conductivities (I) as follow
 = i ni (ez)i i = i i
Insulation Resistance
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Depending on which charge carriers predominate,
the solid may be classified as primarily an
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electronic (n or p type) or
ionic conductor.
However, mixed conduction is
 = electronic + ionic
Insulation Resistance
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For an ionic solid, mobility is related to the
diffusion coefficient D (cm2/sec) by the Einstein
relationship
 = ezD/kT
Diffusion and conductivity are related by the
Nernst-Einstein equation:
 = n(ez)2D/kT
Since both diffusion and N (number of defects
generated) are activated processes, where
N = n exp(-w/2kT)
Insulation Resistance
Then
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and
D = Do exp(- /kT)
 = o exp(-E/kT)
E = w/2 + 
Where w and  are activation energies for
defect generation and migration.
For extrinsic conduction w=0 and E=; that is,
the ionic mobility becomes the controlling
factor in the conduction.
Ionic Conduction
What is an ion?
 An ion is a positive or negative loaded atom
caused by electron deficiency or electron
excess.
 This electron deficiency/excess arises at the
reaction of two atoms (ionic connection).
 Positive loaded ions are called cations and
negative loaded ions are called anions.
 In ionic crystal, the individual lattice atoms
transfer electron between each other to form
positivily charged cations and negatively
charged anions.
Ionic Conduction
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The binding forces between ions are
electrostatic in nature and thus very strong.
The RT conductivity of ionic crystals is much
lower than the conductivity of typical metallic
conductors.
The large difference in conductivity can be
understood by realizing that the wide bandgap in
insulators allows only extremely few electrons to
become excited from the valence band into the
conduction band.
Ionic Conduction
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Ionic conduction is caused by the movement of some
negatively (or positively) charged ions which “hop” from
lattice site to lattice site under the influence of an
electric field.
This ionic conductivity:
 ion  N ion e  ion (1)
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Nion is the number of ions per unit volume that can
change their position under the influence of an
electric field
ion is the mobility of these ions.
Ionic Conduction
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In order for ions to move through a crystalline
solid, they must have sufficient energy to
pass over an “energy barrier” (see
schematic).
Thus, Nion in eq.(1) depends on the vacancy
concentration in the crystal (i.e., on the
number of Schottky defects).
Ionic Conduction
(b)
(a)
E
E
Q
d
distance
distance
Figure: Schematic representation of a potential barrier, which an ion (
) has to overcome to exchange its site with a vacancy ( ).
(a) Without an external electric field, (b) with an external electric field.
D = distance between two adjacent, equivalent lattice sites, Q =
activation energy.
Ionic Conduction
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The D varies with temperature; this dependence is
commonly expressed by an Arrhenius equation:
  Q 

D  Do exp  
  k BT 
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(2)
Where Q is the activation energy , Do is a preexponential factor that depends on the vibrational
frequency of the atoms and some structural
parameters.
Ionic Conduction
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Combining (1) through (2) yields,
N ion e 2 Do
  Q 

 ion 
exp  
k BT
  k BT  
(3)
Equation (3) is shortened by combining the preexponential constant:
  Q 

 ion   o exp  
  k BT 
Taking the natural logarithm yields:
Q1
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ln  ion  ln  o   
 kB  T
(4)
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Ionic Conduction
If plotted ln ion vs.
1/T, a straight line with
a negative slope
would result. (See
figure).
The slopes in
Arrhenius plots are
utilized to calculate
the activation energy,
Q or Ea.
Ionic Conduction
Slope = - Q/k
For SiO2 from graph:
Slope = (ln 10-7 – ln 10-14)/(1.5x10-3 – 2.55x10-3)
= [ln (10-7/10-14)]/(-1x10-3)
= ln 107/(-1x10-3) = - 1.612x104
From Slope = - Q/k
Q = (1.612x104)x(1.3806x10-23) = 2.225x10-19 J
Q = 1.39 eV
(1 eV = 1.6x10-19 J)
Ionic Conduction
800
600
400
T(oC)
ln 
Sometimes,
ln  vs. 1/T plot will
give us two (2) line
regions
representating of
two different Q
values.
1/T
Figure: Schematic representation
of ln  versus 1/T for Na+ ions in
NaCl. (Arrhenius plot).
Ionic Conduction
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At low T, the Q is small, the thermal energy is
just sufficient to allow the hopping of ions into
already existing vacancy sites. This T range is
commonly called the “extrinsic region”.
At high T, the thermal energy is large enough to
create additional vacancies.
The related Q is thus the sum of the Q for
vacancy creation and ion movement. This T
range is called the “intrinsic region”.
High Conducting Ceramics
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Ceramics are generally classified as electronic
conductors, ionic conductors, mixed
(electronic/ionic) conductors, and insulators.
The electronic conductors include superconductors,
and semiconductors.
Ionic conductors generally exhibit conductivities in
the range 10-1 to 100 S m-1 that increase
exponentially with temperature.
Insulators such as high-purity alumina are at the
lower extreme of the conductivity of 10 -13 S m-1.
Temperature Sensitive Resistor
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Some ceramic
resistors exhibit
high value of the
temperature
coefficient of
resistance (TCR)
and they may be
negative (NTC) or
positive (PTC).
Temperature Sensitive Resistor
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In a ceramic a large temperature coefficient of
resistivity can arise from 3 causes:
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The intrinsic characteristic.
A structure transition which accomponied by a change in
the conduction mechanism from semiconducting to
metallic.
A rapid change in dielectric properties in certain ceramics
which affects the electronic properties in the intergranular
region to give rise to a large increase in resistivity with
temperature over small temperature range.
The 3rd Mechanism has led to important TCR
devices.
Typical resistance-temperature response for various
sensor materials
NTC Thermistor
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The TCR of a semiconductor is expected to be
negative.
In each case the resistivity depends on temperature
according to
B
 (T )    exp  
T 
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where  is approximately independent of T and B is a
constant related to the energy required to active the
electron to conduct.
Differentiating this equation leads to TCR value R:
1 d
B
R 
 2
 dT
T
NTC Thermistor
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The most NTC materials are based on solid
solutions of oxides with spinel structure, e.g.
Fe3O4-ZnCr2O4 and Fe3O4-MgCr2O4.
A series that gives favourable combinations of
low resistivity and high coefficients is based on
Mn3O4 with a partial replacement of Mn by Ni,
Co and Cu.
PTC Thermistor
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PTC thermistors exhibit an increase in
resistance at a specified temperature.
PTC resistor could be classified as critical
temperature resistors because, in the case of
the most widely used type,
The positive coefficient is associated with the
ferroelectric Curie point.
PTC Thermistor
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Most PTC has the negative resistivity-temperature
characteristic up to about 100 oC and above about 200
oC.
While between these temperatures there is an increase
of several orders of magnitude in resistivity.
The PTC effect is exhibited by specially doped and
processed (eg. BaTiO3).
Application of PTC Thermistor
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The are two main groups:
 Applications such as temperature measurement,
temperature control, temperature
compensation and over-temperature
protection.
 The second group includes applications such as
over-current protection, liquid level detection
and time delay.
Voltage-dependent Resistors (Varistors)
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There are a number of situations in which it is valuable to have a
resistor which offers a high resistance at low voltages and a low
resistance at high voltages.
Such a devices can be used to protect a circuit from high-voltage
transients by providing a path across the power suply that
 takes only a small current under normal conditions but takes
large current if the voltage rises abnormally,
 thus preventing high-voltage pulses from reaching the circuit.
Schematic use of a VDR to protect a circuit against transients,
Source
VDR
Circuit to be
protected
Varistors-VDR
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Ceramics based on SiC and ZnO are two materials in
everyday use for VDR.
The VDR behaviour in ZnO varistors for example is
governed by electron states that are formed on the surfaces
of crystals as a consequence of the discontinuity.
These surface states act as acceptors for electrons from the
n-type semiconductor.
Electrons will be withdrawn from region near the surface
and replaced by a positive space charge.
Oppositely oriented Schottky barrier will be created at
surface of neihbouring crystals so that a high resistance will
be offered to electron flow in either direction.
Illustrations of actual microstructure of a varistor
Basic principles of Varistors-VDR
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At low applied fields small thermally activated currents pass over the
reverse biased junction.
At high fields tunneling through the junction will occur, accounting for the
low resistance.
The behaviour is similar in some respects to Zener diodes.
From varistor I-V characteristic, the linear part can be represented by the
relation,

I
I k U
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Where kI is a constant and  falls off at low voltages.
If I1 and I2 are currents at voltages that differ by factor of 10,
 I1 
  log10   ,
 I2 
I1  I 2
Basic principles of Varistors-VDR
U  kV I 
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Alternatively,
where
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The resistance at a given voltage is
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 1 /  and kV  k I1 / 
R  kV I
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Power dissipated is
 1
1  ( 1)
 U
kI
P  IU  k IU  1
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with  = 25, a 10 % increase in voltage would increase
the power dissipation by a factor about 2.5.