1. 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 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.

2. 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)

3. Definition of Capacitance C o = capacitance of a parallel plate capacitor in free space Q o = charge on the plates V = voltage    absolute permittivity A = capacitor plate area d =distance between plates Dielectric strength WHY?

4. Fig 7.1 From 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. 7-1 Matter polarization and relative permittivity

5. 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, 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

6. Fig 7.2 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) 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

7. Fig 7.3 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) The origin of electronic polarization.

8. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Definition of Polarizability p induced = induced dipole moment,, E = electric field  = polarizability, Electronic, ionic polarization, Orientational polarization p induced =  E Electronic Polarization 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 Proof

9. 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 m e = mass of the electron in free space  o = natural oscillation frequency Proof

10. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Example 7-1   = 2  f 0

11. Fig 7.4 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Electronic polarizability and its resonance frequency versus the number of electrons in the atom (Z). The dashed line is the best-fit line.

12. Fig 7.5 From 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 +Q P and - Q P. 7-1-3 Polarization vector P

13. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Definition of Polarization Vector P = Polarization vector, p 1, p 2,..., p N are the dipole moments induced at N molecules in the volume Definition of Polarization Vector p av = the average dipole moment per molecule P = polarization vector, N = number of molecules per unit volume P = Np av

14. 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 P tot =Q p d Definition of Electronic Susceptibility P = polarization,  e = electric susceptibility,  o = permittivity of free space, E = electric field P =  e  o E P=P tot / Volume=Q p d/Ad= Q p /A=  p

15. Fig 7.6 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Polarization charge density on the surface of a polarized medium is related to the normal component of the polarization vector.

16. 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 Relative Permittivity and Electronic Susceptibility  r = relative permittivity,  e = electric susceptibility  r = 1 +  e

17. 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 Proof

18. Fig 7.7 From 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.

19. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) 7-1-4 Local Field in Dielectrics For cubic structure materials, or a liquids E loc = local field, E = electric field,  o = permittivity of free space, P = polarization P induced =  e E local Clausius-Mossotti Equation  r = relative permittivity, N = number of molecules per unit volume,  e = electronic polarizability,  o = permittivity of free space P =  e  o E

20. Fig 7.8 From 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

21. Fig 7.9 From 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 mechanism 7-3-1 Ionic polarization P av =  i E local

22. Fig 7.10 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) (a) A HCl molecule possesses a permanent dipole moment p 0. (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 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. 7-3-2 Orientational (dipolar) polarization

23. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Average Dipole Moment in Orientational Polarization p av = average dipole moment, p o = permanent dipole moment, E = electric field, k = Boltzmann constant, T = temperature Dipolar Orientational Polarizability  d = dipolar orientational polarizability, p o = permanent dipole moment Proof

24. Fig 7.11 From 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 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. 7-3-3 Interfacial polarization

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

26. 7-3-4 Total Induced Dipole Moment p av =  e E loc +  i E loc +  d E loc p av = average dipole moment, E loc = local electric field,  e = electronic polarizability,  i = ionic polarizability,  d = dipolar (orientational) polarizability Clausius-Mossotti Equation  r = dielectric constant,  o = permittivity of free space, N e = number of atoms or ions per unit volume,  e = electronic polarizability, N i = number of ion pairs per unit volume,  i = ionic polarizability

27. Solve the following problems 7-1, 2, 3