ENGR-1600Materials Science for Engineers

Lecture 26: Dielectric materials

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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 “p”dipole moment:

p = d qd

Resistance and Capacitance

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RA

A

C

Current I

Resistance

/R V I

Current I

ℓ ℓ

CapacitanceC=Q/V

Permittivity

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Parallel Plate Capacitor

Capacitance definition Unit: Farad Capacitance is a device property From capacitance to material property (dielectric constant)

• Capacitance is the ability to store charge across a potential difference.

permittivity of medium

permittivity of a vacuum

dielectric constant

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).

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.

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Dielectric Constants for Materials

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From Whence Dielectric?Dipole Moment and Polarization

Alignment of DipoleElectric Dipole Moment

p = q d

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Remember Weak Secondary Bonding?

δ− δ+

Time Average

δ− δ+δ+ δ−

Time Average TemporaryTemporary

OHH O

H

H

O

H

H

VdW

dipole

H-bond

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Dielectric Medium in a Capacitor

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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:

1) The capacitance2) The magnitude of the charge stored on each plate3) The dielectric displacement4) The polarization

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– 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.

Origins of PolarizationElectronic Polarization

Ionic Polarization

Orientation Polarization

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Frequency Dependence of Dielectric Constant

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.

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 erMaterial er

Vacuum 1.0000 Dry air 1.0006

Methane 1.7 Chlorine 2.0

Gasoline 2.0 HDPE 2.3

PTFE 2.0 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

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.

FerroelectricsBaTiO4 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

PiezoelectricsIn these materials, polarization can be induced by mechanical force

Compression (+) electric field Tension (-) electric field

Broad Application• sensors• actuators• imaging• microphones• speakers

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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

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).

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

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Team Problem

Is there such a thing as a transparent metal?Is such a thing theoretically possible?

Why or why not?

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