1. CHAPTER 7: Dielectrics …
What is a capacitor ?
a passive two-terminal electrical component used to store energy in an electric field

2. Capacitors What is a dielectric material ?
an electrical insulator that can be polarized by an applied electric field
What are the ways of increasing capacitance? C o + Q E V D i e l c t r ( )

3. Polarization Polarization … polar molecules vs. non-polar molecules
Can non-polar molecules become polar ?
Electric Dipole Moment,

4. Polarization
How do dielectrics increase the capacitance of a capacitor ? + Q E V A r e a = p t o l P d ( c ) B u n i z h g s f C o + Q E V D i e l c t r ( )
Polarization,

5. Polarization
Susceptibility, Χe: A proportionality constant that indicates the degree of polarization of a dielectric material in response to an applied electric field. (dimesnionless)
Permittivity: A measure of how an electric field affects, and is affected by, a dielectric medium. (F/m)
polarizability … dielectric constant … are material properties.
In a way they are equivalent to what mobility is for conductors and semiconductors.

6. Polarization Mechanism
Dependence of ε’r & ε”r frequency depends on polarization mechanism:
Electronic
Ionic
Interfacial
Orientational

7. POLARIZATION MECHANISMS
Ionic:
polarization caused by relative displacements between positive and negative ions in ionic crystals
(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.

8. POLARIZATION MECHANISMS
Electronic:
the stretching of atoms/electronic clouds under an applied E-field (in 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.

9. POLARIZATION MECHANISMS
Interfacial:
charge accumulation at defective interfaces (2 material or 2 regions of same material) leads to the formation of a net polarization vector

10. POLARIZATION MECHANISMS
Orientational (Dipolar):
in “rigid polarized molecule” materials, an applied field aligns the permanent dipoles to yield a net polarization vector C l H + p o ( a ) b v = q Q F E t c d

11. POLARIZATION MECHANISMS

12. DIELECTRIC LOSS The dielectric constant is frequency dependent … why ?
The polarization process is not instantaneous … i.e. it takes a finite amount of time for the molecules to align themselves.
If the applied field is changing so fast that the molecules cannot respond to it at all … then the polarization is … zero!
Therefore ε is frequency dependent …

13. DIELECTRIC LOSS
The imaginary part represents dielectric “losses” due to “slow” polarization.

14. Dielectric Loss per unit volume,

15. DIELECTRIC LOSS
For the dielectric material as in the figure, calculate the loss tangent at 10 MHz frequency.
If the parallel plate capacitor is formed with the material, where the separation is 1mm, plate area is 1mm2 and 1V is applied across…
Calculate the value of resistance and capacitance.
Calculate the power loss per unit volume.
=0.5
=1.8x106 ohm
=1.7x10-14 F
=556 Wcm-3

16. Matter Polarization & Permittivity
Electric Dipole Moment,
Spring action
Induced Electric Dipole Moment,

17. Matter Polarization & Permittivity
Induced Electric Dipole Moment,
Removal of applied E field cause the vibration with a resonant frequency…
F=ma
Electronic Polarizability
Electronic polarization resonance frequency

18. Permittivity: Electronic Polarization
Total Polarization
Total Polarization
=surface polarization charge density!
Also, total polarization

19. Permittivity: Electronic Polarization
before insertion of dielectric medium
free surface charge density
after insertion of dielectric medium
dividing by the area, A

20. Permittivity: Electronic Polarization
Substitution for surface charge density
Relative permittivity
Relation between polarization mechanism to relative permittivity

21. Clausius-Mossotti Equation
The bulk electric field assumption is not valid in the atomic level
Lorentz Field
Relation between polarization mechanism to relative permittivity
Clausius-Mossotti Equation
For electronic polarization

22. Total Polarization Clausius-Mossotti Equation For ionic polarization
Relative permittivity due to ionic and electronic polarization

23. Total Polarization under dc operation under optical frequency
7.9 Electronic and ionic polarization in KCl
KCl has the FCC crystal structure. Lattice parameter is nm.
The ionic polarizability per ion pair (per K+-Cl- ion) is 4.58 F m2.
The electronic polarizability of K+ is  F m2 and Cl- is  F m2. Calculate the dielectric constant under dc operation and at optical frequencies.
Experimental values are 4.84 and 2.19.
FCC… 4 KCl ion pairs per unit cell. The number of ion pairs, or individual ions, per unit volume (N) is:
=  1028 m-3
under dc operation
under optical frequency
r(op) = 2.18
Example 7.2, 7.3