Dielectric Materials

1
Dielectric Materials

• Chapter 10 of Solymar

2
Introduction

• Dielectrics are insulators
• No distinction between semiconductors and
  dielectrics in terms of band structure
• Dielectrics have larger band gap (gt3 eV)

3
Macroscopic Approach

• Under an electric field, there is no charge
  carriers moving from one end to the other end
  no conduction
• Charges respond to electric field - displacement
• Dielectric displacement
• Electric field E
• Dielectric constant e ereo
• Permittivity of free space eo
• Relative dielectric constant er

4
Capacitor

• A capacitor consists of two conductive plates,
  separated by an insulator (Fig. 10.1)
• Charge accumulates on the plates with voltage
• If the insulator is vacuum, the surface charge
  density on one of the plates is
• If a dielectric is inserted between plates,
  surface charge density increases
• The increase in surface charge density
• Dielectric susceptibility

5
Microscopic Approach

• How atoms react to an external electric field
• The centers of positive and negative charges
  coincide with no electric field
• With an electric field, there is a shift in
  negative charge center (electrons are easily
  moved with respect to nucleus)
• If the separation between centers is d and the
  total charge is q, the atom has an induced dipole
  moment m qd

6
Surface Charge Density

• The amount of charge on the dielectric surface is
  AdNmq
• Area A, charge per atom q, and number of atoms
  per unit volume Nm
• Surface charge density is dNmq
• This is the amount of charge on dielectric
  surface
• It is equal to the increase in surface charge
  density on metal surface
• This is the relationship between macroscopic and
  microscopic quantities
• For low electric fields, m aE
• Polarizability a
• Local electric field E

7
Types of Polarization

• Electronic
• All atoms are made of ions surrounded by electron
  clouds
• Electrons are light, and they rapidly respond to
  field changes
• Molecular
• Ionic bonds are stretched by electric field
• Electric field changes the separation, thus
  changing the dipole moment

8
Orientational Polarization

• In liquids and gases, molecules with dipole
  moments align with the electric field
• The alignment is not perfect at finite
  temperatures, since the number of molecules with
  energy E is proportional to exp(-E/kT)
• Energy of a dipole in an electric field (Fig.
  10.4)
• E is the energy and (E) is the electric field
• The number of dipoles in a solid angle dW

9
Average Dipole Moment

• The average dipole moment in an electric field is
  the net moment of the assembly divided by the
  total number of dipoles
• Solution
• Langevin function L(a)
• For small a
• It is inversely proportional to temperature

10
Dielectric Constant/Refractive Index

• The dielectric constant has real and imaginary
  parts
• From Maxwell equation
• dc current sE and ac (displacement) current iweE
• Complex dielectric constant e is/w
• Usual expression e eeo and s/w eeo
• The loss tangent tan d e/e
• The refractive index
• Permeability m
• Vacuum velocity of light c
• Velocity of light in the material v
• Both dielectric constant and refractive index are
  measures of polarizability of a material

11
Applications in Optics

• Alternate layers of transparent materials with
  refractive indices n1 and n2 (Fig. 10.5)
• Reflection and transmission at each interface
• The reflection coefficient at interface a is
• At interface b
• If each layer is l/4 thick (actual thickness
  n1l/4 and n2l/4), reflection from b is p radius
  out of phase with reflection from a
• The - sign gives another p radius
• Total phase difference is 2p, i.e. they are in
  phase
• A large number of these layers makes a excellent
  mirror
• If each layer is l/2 thick, successive
  reflections are out of phase
• It becomes a reflectionless coating

12
Frequency Response

• Three types of polarization
• Each has a different frequency response (Fig.
  10.7)
• Electronic polarization has the highest response
  frequency
• Molecular polarization the next
• Orientational polarization the lowest
• To measure, say, electronic contribution to the
  dielectric constant
• We can measure the refractive index n at optical
  frequencies
• For water, n 1.3, n2 1.7, but e 80
• Electronic contribution to dielectric constant is
  1.7
• 80 1.7 78 is due to molecular and
  orientational contributions

13
Polar Nonpolar Materials

• A nonpolar material has no permanent dipoles
• Si, Ge, C, all have pure covalent bonds and the
  atoms are the same
• All polarization is electronic
• Polar materials
• Compound semiconductors with mixed covalent and
  ionic bonds
• Some atoms are more negatively charged and some
  more positively charged
• When an electric field is applied, the moments
  change
• Another type of polar materials
• Symmetric molecules
• C6H6 has permanent dipoles in their bonds, but
  the net dipole moment is zero
• Third type of polar materials
• They have permanent dipole moments, which are
  determined by their orientational polarizability

14
Examples

• Dielectric constant and refractive index of
  materials (Table 10.1)
• For nonpolar materials
• For most transparent dielectrics, n 1.4 1.6
• Why?

15
Dielectric Breakdown

• Dielectric breakdown important
• Breakdown is a sudden increase in current when
  the voltage exceeds a critical value Vb (Fig.
  10.11)
• In a capacitor, the energy (charge) stored is
  eE2/2
• Three mechanisms
• Intrinsic breakdown
• When few electrons gain sufficient energy through
  accelaration in a high field, they ionize lattice
  atoms by knocking out valence electrons and
  exciting them into the conduction band
• The knocked out electrons accelerate and knock
  out more electrons
• It is avalanche

16
Dielectric Breakdown

• Thermal breakdown
• When the frequency of an ac field is comparable
  with the reciprocal of the relaxation time, the
  field heats the lattice
• The heated lattice atoms are more easily ionized
  by accelerated free electrons, and the breakdown
  field becomes lower than the intrinsic breakdown
  field
• Discharge breakdown
• In porous dielectrics, the gas trapped ionizes
  often before the solid breaks down
• The gas ions cause surface damage and accelerate
  breakdown

17
Piezoelectricity

• A mechanical strain produces dielectric
  polarization and vice versa, an applied electric
  field causes mechanical strain
• Materials which lack a center of symmetry are
  piezoelectric
• In a symmetric cubic crystal (Fig. 10.12)
• If a mechanical force is applied, all the dipole
  moments change
• But the centers of positive and negative charges
  still coincide
• No dipole moment is created
• In a crystal with no center of symmetry (Fig.
  10.13)
• When a force is applied, the separation between
  centers of positive and negative charges is
  changed
• A dipole moment is created

18
Optical Fibers

• They are purified silica (SiO2)
• Diameter 5 50 mm
• Covered with lower refractive index cladding
• The light going into a fiber is contained within
  the fiber by total internal reflection
• Low attenuation coefficient critical
• For a length of 1,000 m in decibels (db/km)
• Attenuation coefficient has decreased by 4 orders
  of magnitude in last 4 decades (Fig. 10.19)
• Today A 0.2 db/km for l 1.5 1.7 mm, making
  optical communication possible

19
Liquid Crystals

• They contain long rod-like molecules with strong
  dipole moments and easily polarizable (Fig.
  10.21)
• Molecules on the two opposite surfaces are at
  right angles
• Molecules between the two surfaces orient
  randomly from one surface to the other
• With two polarizers at right angle, light can
  easily pass through
• When an electric field is applied, molecules will
  align in parallel with the field
• No light is transmitted

20
HW Assignment

• 10.3, 10.8, 10.11