Sinai University Faculty of Engineering Science Department of Basic sciences 5/20/2015 1 From Principles of Electronic Materials and Devices, Third Edition,

Sinai University Faculty of Engineering Science Department of Basic sciences

04/18/231

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

Course name: Electrical materials

Code: ELE163

Text references1- Principles of Electronic Materials and Devices, 3rd edition2- Kittel, Introduction to Solid State Physics3-College Physics , Serway, 7th edition4-Lecture notes (power points)5- Internet sites

Prepared byPr Ahmed Mohamed El-lawindy

[email protected] site: Faculty site:

www.engineering.su.edu.egwww.engineering.su.edu.eg04/18/23

2

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)

These PowerPoint color diagrams can only be used by instructors if the 3rd 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.

Ch 7 Dielectric materials and insulators

Fig 7.28From Principles of Electronic Materials and

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

.

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AC

r

r

o

Consequences

Fig 7.28From Principles of Electronic Materials and

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

• -Storage capacity increases• -Insulation between plates increases• -Electric losses, like I2R in resistors, appears• -Power dissipation of capacitors is frequency

dependent• -Dielectric strength increases

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

7. 1 Material polarization and relative permittivityDefinition of Capacitance

Co = capacitance of a parallel plate capacitor in free space

Qo = charge on the plates

V = voltage

V

QC o

o

Fig 7.1From Principles of Electronic Materials and

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

(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.

V

QC o

o V

QC

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

7.1.1 Definition of Relative Permittivity

r = 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

r Q

Qo

C

Co

7.1.2 Dipole moment and electronic polarization

Fig 7.28From Principles of Electronic Materials and

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

E interacts with other E and Eext

Definition of Dipole Moment

p = Qa

p = electric dipole moment, Q = charge, a = vector from the negative to the positive charge

Fig 7.3From Principles of Electronic Materials and

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

The origin of electronic polarization.

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

Definition of Polarizability

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

pinduced = E

Electronic Polarization

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

E

β

eZxZep

22

e )(

Fig 7.28From Principles of Electronic Materials and

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

Similar behavior

+

Fig 7.28From Principles of Electronic Materials and

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

E

β

eZxZep

ZeEx

xZeE

mequilibriuAt

forcerestoringxF

22

e

r

)(

20

2

0

00

2

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,

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m

Ze

frequencyresonanceonpolarizatielectronictheOR

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massofcentertheoffrequencynoscillatiotheiswhere

txtx

td

xdZmx

onacceleratixmassF

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 = electronic polarizability

Z = total number of electrons around the nucleus

me = mass of the electron in free space

o = natural oscillation frequency

e Ze2

me o2

Fig 7.4From Principles of Electronic Materials and

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

e Ze2

me o2

2/1

eo Zm

Electronic polarizability and its resonance frequency versus the number of electrons in theatom (Z). The dashed line is the best-fit line.

Fig 7.5From Principles of Electronic Materials and

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

(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.

7.1.3 polarization vector P

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

Definition of Polarization Vector

P = Polarization vector, p1, p2, ..., pN are the dipole moments induced at N molecules in the volume

P = 1

Volume [p1 + p2 +... + pN ]

Definition of Polarization Vector

pav = the average dipole moment per molecule

P = polarization vector, N = number of molecules per unit volume

P = Npav

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

Polarization and Bound Surface Charge Density

P = polarization, p = polarization charge density on the surface

ppptotal

ptotal

A

Q

Ad

dQ

Volume

pP

dQp

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

pnormalP

shapesampleanyFor

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

Electric Susceptibility and Polarization

e = electric susceptibility, o = permittivity of free space, N = number of molecules per unit volume, e = electronic polarizability

e 1

o

N e

Relative Permittivity and Electronic Susceptibility

r = relative permittivity, e = electric susceptibility

r = 1 + e

P = polarization, e = electric susceptibility, o = permittivity of free space, E = electric field

Definition of Electronic Susceptibility

P = eoE

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

Relative Permittivity and Polarizability

r = relative permittivity

N = number of molecules per unit volume

e = electronic polarizability

o = permittivity of free space

Assumption: Only electronic polarization is present

r 1N e

o

Assignment:1- Write a report about one of Semiconductor electronic devices2- Derive the above equation

Fig 7.7From Principles of Electronic Materials and

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

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.

7.1.4 Local field and Clausius-Mossotti equation

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

Local Field in Dielectrics

Eloc = local field, E = electric field, o = permittivity of free space, P = polarization

Po3

1loc EE

Clausius-Mossotti Equation

r = relative permittivity, N = number of molecules per unit volume, e = electronic polarizability, o = permittivity of free space

r 1

r 2

N e

3o

Fig 7.8From Principles of Electronic Materials and

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

(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.

7.2 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

Fig 7.9From Principles of Electronic Materials and

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

(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.

7.3 Polarization mechanisms7.3.1 Ionic polarization

Fig 7.10From Principles of Electronic Materials and

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

(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 averagedipole 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.

7.3.2 Orientational (dipolar) polarization

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

Average Dipole Moment in Orientational Polarization

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

kT

pp o E

2

av 3

1

Dipolar Orientational Polarizability

d = dipolar orientational polarizability, po = permanent dipole moment

d 1

3

po2

kT

Fig 7.11From Principles of Electronic Materials and

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

(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 negativecharges and positive charges in the dielectric. The dielectric therefore exhibits interfacialpolarization.(c) Grain boundaries and interfaces between different materials frequently give rise to Interfacial polarization.

7.3.3 Interfacial polarization

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

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

r = dielectric constant, o = 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

)(3

1

2

1iiee

or

r NN