1. Lecture 26: Dielectric materials
ENGR-1600
Materials Science for Engineers
Lecture 26: Dielectric materials

2. Dielectric Materials
A dielectric material is an insulator which contains electric dipoles, that is where positive and negative charge are separated on an atomic or molecular level
When an electric field is applied, these dipoles align to the field, causing a net dipole moment that affects the material properties.
dipole moment:
p = d q
dipole “p” d

3. Resistance and Capacitance
Current I ℓ ℓ
Capacitance
C=Q/V
Permittivity
Current I

4. Parallel Plate Capacitor
Capacitance is the ability to store charge across a potential difference.
Capacitance definition
Unit: Farad
Capacitance is a device property
From capacitance to material property (dielectric constant)
permittivity of medium
permittivity of a vacuum
dielectric constant

5. Dielectrics or Insulators
Q and C depend on the geometry of the plates.
C = Q / V = e0 A / l
where the proportionality constant e0 is called permittivity of the vacuum.
The units of C are 1 Clb/V = 1 Farad (1 F).
Hence e0 = 8.85×10-12 F/m.
The equation above looks similar to Ohm’s Law:
R = V/I and 1/C = V/Q
So R of a resistor is to flowing charge I (Clb/s) what 1/C of a capacitor is to static charge Q (Clb).

6. Dielectrics or Insulators
When the space between the two plates of a capacitor is filled with a dielectric material, experiments show that at constant applied voltage V, the charge Q' on the plates is higher than the charge Q before:
In this case: C = e A / l = Q’/V
where e is the permittivity of the dielectric material. e can be written as
e = e0 er with er > 1
The factor er by which the capacitance has been increased due to the material between the plates is called its dielectric constant.

7. Dielectric Constants for Materials

8. From Whence Dielectric? Dipole Moment and Polarization
Alignment of Dipole
p = q d

9. Remember Weak Secondary Bonding?
Temporary
Time Average
Temporary
VdW δ+ δ− δ− δ+
Time Average
dipole δ− δ+ O H H O H H
H-bond O H

10. Dielectric Medium in a Capacitor

11. Team Problem
Consider a parallel-plate capacitor having an area of 6.65 x 10-4 m2 and a plate separation of 2 x 10-3 m across which a potential of 10 V is applied. If a material having a dielectric constant of 6.0 is positioned within the region between the plates, compute the following:
The capacitance
The magnitude of the charge stored on each plate
The dielectric displacement
The polarization

12. Origins of Polarization
Electronic Polarization
Electronic Polarization: Displacement of negative electron “clouds” with respect to positive nucleus. Requires applied electric field. Occurs in all materials.
Ionic Polarization: In ionic materials, applied electric field displaces cations and anions in opposite directions
Orientation Polarization: Some materials possess permanent electric dipoles, due to distribution of charge in their unit cells. In absence of electric field, dipoles are randomly oriented. Applying electric field aligns these dipoles, causing net (large) dipole moment.
Ionic Polarization
Orientation Polarization

13. Frequency Dependence of Dielectric Constant

14. Dielectrics or Insulators
The data for er in the table can be explained roughly in terms of the main applicable polarization mechanism:
Mechanism
Features
Materials
Electronic
small polarization, fast response
gases, non-polar liquids, polymers
Ionic
medium polarization, medium response
ceramics, inorganic glasses
Orientational
large polarization, slow response
polar liquids
The response time indicates how er depends on the frequency of the applied field. If tp is a characteristic time for the polarization to change, then the polarization cannot follow an applied electric field which changes in a time shorter than tp, or which has a frequency higher than tp-1.

15. Dielectrics or Insulators
What happens physically to the dielectric is that the applied voltage (or electric field) polarizes the material. This polarization is caused by internal charges being moved slightly off of their normal equilibrium positions.
Material er
Vacuum
1.0000
Dry air
1.0006
Methane
1.7
Chlorine
2.0
Gasoline
HDPE
2.3
PTFE
Olive Oil
3.0
PMMA
2.9
PVC
3.1
Quartz
4.7
fused SiO2
3.8
Pyrex glass 5
Diamond
5.0
NaCl
5.9
MgO
9.6
Ethanol 24
Water 80
SrTiO3
300
BaTiO3
1500

16. Dielectrics or Insulators
SrTiO3 and BaTiO3 are “ferroelectric”: very large er is due to permanent internal polarization.
SrTiO3 and BaTiO3 are are also “piezoelectric”: polarization changes when mechanically strained. Conversely, if a voltage is applied, the materal expands or contracts.
This piezoelectric effect is useful for making electro- mechanical sensors, actuators, and transducers.
The material used most often in such applications is lead zirconate titanate (abbreviated PZT), a mixture of PbTiO3 and PbZrO3.
PZT can be doped to adjust its piezoelectric and dielectric parameters.

17. BaTiO4 has a permanent electrical dipole at the unit cell level
Ferroelectrics
BaTiO4 has a permanent electrical dipole at the unit cell level
This effect vanishes above a critical temp (Curie Temp), where the crystal structure converts to cubic

18. Piezoelectrics
In these materials, polarization can be induced by mechanical force
Broad Application
sensors
actuators
imaging
microphones
speakers
Compression  (+) electric field
Tension  (-) electric field

19. Sustainable Energy on the Dance Floor

20. Dielectrics or Insulators
Optical properties
Insulators are optically transparent in single-crystal or amorphous form.
Polycrystals may cause light scattering.
Wide bandgap insulators
Light excites e- from VB to CB when the energy of the photon matches (or exceeds) the Eg
electronic and optical properties are intimately related concepts

21. Dielectrics or Insulators
Quantum properties of light
A light wave of frequency n and wavelength l consists of small energy packets called photons. A photon with frequency n has an energy Eph of
Eph = hn
where h is Planck's constant (numerical value: 6.63×10-34 Js).
In addition, you should recall that the frequency n and wavelength l of light are related to each other by the equation
n × l = c
where c is the speed of light (numerical value: 3x108 m/s).

22. Dielectrics or Insulators
Absorption/transmission of light
If a photon with frequency n impinges on a material, it can give its energy to an electron in the VB, thus creating an electron-hole pair, if hn > Eg.
On the other hand, if hn < Eg, no excitation can take place and the material is transparent.
The threshold condition for absorption is
Eg = hn = hc/l Þ l = hc/Eg
Material
Eg (eV)
l = hc/Eg Ge
0.67
1.85 µm Si
1.1
1.13 µm
GaAs
1.4
0.88 µm

23. Is there such a thing as a transparent metal?
Team Problem
Is there such a thing as a transparent metal?
Is such a thing theoretically possible?
Why or why not?

24. Solar Cells
6.4×1019 J = annual worldwide electricity consumption (2008)
5.5×1024 J = total energy from the Sun that hits the Earth each year