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Electronic Materials and
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From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
Chapter Objectives
• 1- Study the properties of capacitors
• 2- Demonstrate the effect of dielectric media
on the capacitance
• 3- Discuss the polarization phenomena
• 4- Formulate the relation between electric
permittivity and polarizability
Fig 7.28
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
Definition of Capacitance
Co =
Qo
V
= e0
A
d
Co = capacitance of a parallel plate capacitor in free space
Qo = charge on the plates
V = voltage
e0 =absolute permittivity
A = capacitor plate area
d =distance between plates
Dielectric strength
WHY?
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
7-1 Matter polarization and relative permittivity
(a) Parallel plate capacitor with free space between the plates.
(b) As a slab of insulating material is inserted between the plates, there is an external current
flow indicating that more charge is stored on the plates.
(c) The capacitance has been increased due to the insertion of a medium between the plates.
Fig 7.1
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
7-1-1 Definition of Relative Permittivity
C =
Q
V
Co =
C
=
Co
C =
= em
Qo
V
Q
= e0
=
Qo
Q
V
= em
A
d
A
d
em
eo
A
d
= er
= e oe r
A
d
er = relative permittivity, Q = charge on the plates with a dielectric
medium, Qo = charge on the plates with free space between the plates, C
= capacitance with a dielectric medium, Co = capacitance of a parallel
plate capacitor in free space
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
7-1-2 Dipole moment and electronic polarization
7-1-2 Definition of Dipole Moment
p = Qa
p = electric dipole moment, Q = charge, a = vector from
the negative to the positive charge
Fig 7.2
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
The origin of electronic polarization.
Fig 7.3
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
Definition of Polarizability
pinduced = E
pinduced = induced dipole moment, , E = electric field
 = polarizability, Electronic, ionic polarization, Orientational polarization
Fr =   x
Electronic Polarization
ZeE =  x
 Z 2e 2
p e = ( Ze ) x = 
 β

 E

Proof
pe = magnitude of the induced electronic dipole moment, Z = number of electrons orbiting
the nucleus of the atom, x = distance between the nucleus and the center of negative
charge,  = constant, E = electric field
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
Static Electronic Polarizability
e =
Ze
2
m e o
Proof
2
e = electronic polarizability
Z = total number of electrons around the nucleus
me = mass of the electron in free space
o = natural oscillation frequency
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
Example 7-1
0= 2pf0
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
 
 o = 
 Zm e
e =
Ze




1/ 2
2
m e o
2
Electronic polarizability and its resonance frequency versus the number of electrons in the
atom (Z). The dashed line is the best-fit line.
Fig 7.4
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
7-1-3 Polarization vector P
(a) When a dilectric is placed in
an electric field, bound
polarization charges appear on
the opposite surfaces.
(b) The origin of these
polarization charges is the
polarization of the molecules of
the medium.
(c) We can represent the whole
dielectric in terms of its surface
polarization charges +QP and QP.
Fig 7.5
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
Definition of Polarization Vector
P =
1
Volume
[p 1 + p 2 + ... + p N ]
P = Polarization vector, p1, p2, ..., pN are the dipole moments induced at N
molecules in the volume
Definition of Polarization Vector
P = Npav
pav = the average dipole moment per molecule
P = polarization vector, N = number of molecules per unit volume
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
Polarization and Bound Surface Charge Density
Ptot =Qp d
P=Ptot/ Volume=Qpd/Ad= Qp/A=p
P = polarization, p = polarization charge density on the surface
Definition of Electronic Susceptibility
P = eeoE
P = polarization, e = electric susceptibility, eo = permittivity of free space, E = electric field
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
Polarization charge density on the surface of a polarized medium is related to the normal
component of the polarization vector.
Fig 7.6
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
Electric Susceptibility and Polarization
e =
1
eo
N e
e = electric susceptibility, eo = permittivity of free space, N = number of molecules per unit
volume, e = electronic polarizability
Relative Permittivity and Electronic Susceptibility
er = 1 + e
er = relative permittivity, e = electric susceptibility
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
Relative Permittivity and Polarizability
er = 1
N e
eo
Proof
er = relative permittivity
N = number of molecules per unit volume
e = electronic polarizability
eo = permittivity of free space
Assumption: Only electronic polarization is present
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
The electric field inside a polarized dielectric at the atomic scale is not uniform. The
local field is the actual field that acts on a molecules. It can be calculated by
removing that molecules and evaluating the field at that point from the charges on
the plates and the dipoles surrounding the point.
Fig 7.7
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
7-1-4 Local Field in Dielectrics
E loc = E 
1
3e o
P
For cubic structure materials, or a liquids
Eloc = local field, E = electric field, eo = permittivity of free space, P = polarization
Pinduced= e Elocal
P = eeoE
Clausius-Mossotti Equation
er  1
er  2
=
N e
3 eo
er = relative permittivity, N = number of molecules per unit volume, e = electronic
polarizability, eo = permittivity of free space
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
7.2 Electronic polarization: Covalent solids
(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.
Fig 7.8
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
7-3 Polarization mechanism
7-3-1 Ionic polarization
Pav= i Elocal
er 1
er  2
=
N i
3e o
(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.
Fig 7.9
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
7-3-2 Orientational (dipolar) polarization
(a) A HCl molecule possesses a permanent dipole moment p0.
(b) In the absence of a field, thermal agitation of the molecules results in zero net average
dipole moment per molecule.
(c) A dipole such as HCl placed in a field experiences a torque that tries to rotate it to align p0
with the field E.
(d) In the presence of an applied field, the dipoles try to rotate to align with the field against
thermal agitation. There is now a net average dipole moment per molecule along the field.
Fig 7.10
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
Average Dipole Moment in Orientational Polarization
2
p av =
1 po E
Proof
3 kT
pav = average dipole moment, po = permanent dipole moment, E = electric field, k
= Boltzmann constant, T = temperature
Dipolar Orientational Polarizability
d =
1 po
2
3 kT
d = dipolar orientational polarizability, po = permanent dipole moment
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
7-3-3 Interfacial polarization
(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.
Fig 7.11
From Principles of Electronic Materials and
Devices, Third Edition, S.O. Kasap (©
McGraw-Hill, 2005)
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
7-3-4 Total Induced Dipole Moment
pav = e Eloc + i Eloc + d Eloc
pav = average dipole moment, Eloc = local electric field, e = electronic
polarizability, i = ionic polarizability, d = dipolar (orientational) polarizability
Clausius-Mossotti Equation
er 1
er  2
=
1
3e o
( N e e  N i i )
er = dielectric constant, eo = permittivity of free space, Ne = number of atoms or
ions per unit volume, e = electronic polarizability, Ni = number of ion pairs per
unit volume , i = ionic polarizability
From Principles of Electronic
Materials and Devices, Third
Edition, S.O. Kasap (©
Solve the following problems
• 7-1, 2, 3