From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005) Sinai University Faculty of Engineering Science Department of Basic sciences 4/24/2020 1

Course name: Electrical materials Code: ELE163

Text references

1- Principles of Electronic Materials and Devices, 3 rd 2- Kittel, Introduction to Solid State Physics 3-College Physics , Serway, 7 th edition 4-Lecture notes (power points) 5- Internet sites edition Prepared by

Pr Ahmed Mohamed El-lawindy

From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

[email protected]

Faculty site: www.engineering.su.edu.eg

2

These PowerPoint color diagrams can only be used by instructors if the 3 rd Edition has been adopted for his/her course. Permission is given to individuals who have purchased a copy of the third edition with CD-ROM Electronic Materials and Devices to use these slides in seminar, symposium and conference presentations provided that the book title, author and © McGraw-Hill are displayed under each diagram.

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Ch 7 Dielectric materials and insulators

Where

 0

is the absolute C

 

o A d permittivi ty

,

A is the area of the plate

,

d is the separation dista

tan

ce If a dielectric material is inserted between the plates

,

then the capaci

tan

ce

,

increases by a the ch

arg

e factor



r Where



r is the dielectric storage ability consta nt or per unit relative voltage permittivi ty

.

Fig 7.28

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Consequences

• • • • •

-Storage capacity increases -Insulation between plates increases -Electric losses, like I

2

R in resistors, appears -Power dissipation of capacitors is frequency dependent -Dielectric strength increases

Fig 7.28

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

7. 1 Material polarization and relative permittivity Definition of Capacitance

C

o



Q

o

V

C o

= capacitance of a parallel plate capacitor in free space

Q o

= charge on the plates V = voltage From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

C o



Q o V C



Q V

(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



r



Q Q o



C C o



r

= relative permittivity, Q = charge on the plates with a dielectric medium, Q

o

= charge on the plates with free space between the plates, C = capacitance with a dielectric medium, C

o

= capacitance of a parallel plate capacitor in free space From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

7.1.2 Dipole moment and electronic polarization E interacts with other E and E

ext

Fig 7.28

Definition of Dipole Moment

p = Qa

p = electric dipole moment, Q = charge, a = vector from the negative to the positive charge From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Fig 7.3

The origin of electronic polarization.

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Definition of Polarizability

p

induced

=

 E

p

induced = induced dipole moment,  = polarizability, E = electric field

Electronic Polarization

p e

 (

Ze

)

x

   

Z 2 e 2 β

   E

p e

= 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 (© McGraw-Hill, 2005)

Similar behavior

+ Fig 7.28

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Fig 7.28

F r

  

x restoring At ZeE equilibriu m

 

x force x



ZeE

 

p e

 (

Ze

)

x

   

Z 2 e 2 β

   E

F



mass x accelerati on

  

x x where

   0 2

x

0

d x Zm e

2 cos

d t

  0

is the oscillatio n of frequency of electron cloud about the nucleus

,

the center of mass OR the electronic polarizati on resonance frequency

 

e



Ze

2

m e

 0 2 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Example 7.1

From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

Static Electronic Polarizability



e



Ze

2

m e



o

2 

e

= electronic polarizability Z = total number of electrons around the nucleus

m e

= mass of the electron in free space 

o

= natural oscillation frequency From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)



o

   

Zm e

  1 / 2 

e



Ze

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)

Fig 7.5

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 +Q

P

and -Q

P

.

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, p 1 , p 2 , ..., p

N

molecules in the volume are the dipole moments induced at N

Definition of Polarization Vector P

=

N

p

av

p

av = 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 (© McGraw-Hill, 2005)

Polarization and Bound Surface Charge Density

p total



Q p d P



p total



Q p d



Q p

 

p Volume Ad A

P = polarization, 

p

= polarization charge density on the surface

For P

normal

any sample

 

p

shape

Polarization charge density on the surface of a polarized medium is related to the normal component of the polarization vector.

From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

Definition of Electronic Susceptibility

P = polarization, 

e P =

 = electric susceptibility,

e



o



o

E = permittivity of free space, E = electric field 

e

Electric Susceptibility and Polarization

= electric susceptibility, 

e

 1 

o N



e



o

= permittivity of free space, N = number of molecules per unit volume, 

e

= electronic polarizability

Relative Permittivity and Electronic Susceptibility



r =

1 +



e



r

= relative permittivity, 

e

= electric susceptibility From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

Relative Permittivity and Polarizability



r

 1 

N

 

o



r

= relative permittivity

e

N = number of molecules per unit volume 

e

= electronic polarizability 

o

= permittivity of free space Assumption: Only electronic polarization is present

Assignment: 1- Write a report about one of Semiconductor electronic devices

From Principles of Electronic

2- Derive the above equation

Edition, S.O. Kasap (© McGraw-Hill, 2005)

7.1.4 Local field and Clausius-Mossotti equation 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)

Local Field in Dielectrics

E loc  E  1 3 

o P

E loc = local field, E = electric field, 

o

= permittivity of free space, P = polarization

Clausius-Mossotti Equation



r



r

 1  2 

N

 3 

o e



r

= relative permittivity, N = number of molecules per unit volume, 

e

From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005) polarizability, 

o

= permittivity of free space = electronic

7.2 Electronic polarization: covalent solids

1-2 eV is the Energy involved to free covalence electron in a crystal 10 eV Energy involved to free an electron from its ionic core (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 mechanisms

7.3.1 Ionic polarization (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 p dipole moment per molecule.

0

.

(b) In the absence of a field, thermal agitation of the molecules results in zero net average (c) A dipole such as HCl placed in a field experiences a torque that tries to rotate it to align p

0

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

p

av  1 3

p o

2 E

kT p

av = average dipole moment, p

o

= permanent dipole moment, = Boltzmann constant, T = temperature E = electric field, k

Dipolar Orientational Polarizability



d

 1 3

p o

2

kT



d

= dipolar orientational polarizability, p

o

= permanent dipole moment From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005)

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 (© McGraw-Hill, 2005)

Total Induced Dipole Moment

p

av

=



e

E

loc

+



i

E

loc

+



d

E

loc

p

av = average dipole moment, E loc polarizability, 

i

= local electric field, 

e

= ionic polarizability, 

d

= electronic = dipolar (orientational) polarizability

Clausius-Mossotti Equation

 

r r

 1  2  1 3 

o

(

N e



e



N i



i

) 

r

= dielectric constant, 

o

ions per unit volume, From Principles of Electronic

Materials and Devices, Third

Edition, S.O. Kasap (© McGraw-Hill, 2005) 

e

= permittivity of free space, N

e

= electronic polarizability, N

i

unit volume , 

i

= ionic polarizability = number of atoms or = number of ion pairs per