Dielectric studies of functional materials

1. Dielectrics
Prof. V. Krishnakumar
Professor and Head
Department of Physics
Periyar University
Salem – 636 011

2. Introduction
• Dielectric materials: high electrical resistivities, but
an efficient supporter of electrostatic fields.
• Can store energy/charge.
• Able to support an electrostatic field while
dissipating minimal energy in the form of heat.
• The lower the dielectric loss (proportion of energy
lost as heat), the more effective is a dielectric
material.
• Another consideration is the dielectric constant,
the extent to which a substance concentrates the
electrostatic lines of flux.

3. Capacitance
• Two electrodes separated by a gap
define a capacitor.
• When a bias is applied across the
capacitor plates, one charges positively,
the other negatively.
• The amount of charge that the capacitor
can store (Q) is proportional to the bias
(V) times how good the capacitor is, the
‘capacitance’ (C).
• The capacitance is related to the area of
the plates (A), their separation (d), and
the Dielectric Constant (εεo) of the
dielectric between the plates
• Dielectric constant of vacuum; εo =
8.85x10-12 F/m=55.2 Me/(V*m)
d
A
C o


e
 o  *
V 
e
 m
m
V
d
A
Q V m
* 2
 *

4. Why does charge built up?
There is generally not a built-in electric field between the
plates of an unbiased capacitor.
When an electric field is applied, any charged carriers or
species within the material will respond.
For a conductor or semiconductor, e- will flow to the +
plate, and possibly also holes will flow to the - plate.
Current is carried=no charge buildup.
For an insulator, there aren’t a significant number of free
carriers. There are highly ionic species, however, but they
aren’t very mobile at low temperatures. No appreciable
current is carried=charge buildup.

5. Polarization in Insulators
Positively charged species in insulators shift/rotate/align toward the
negative electrode and negatively charged species shift/rotate/align
towards the positive electrode; creating dipoles. The dipole moment
density is termed the Polarization (P) and has the units of C/m2.
Electron Cloud Electron Cloud
+
+
-
E
Electronic polarization, occurs
in all insulators
-
- -
+ - +
-
+ +
+ +
E
Ionic polarization occurs
in all ionic solids: NaCl,
MgO…
-
-
-
+ +
E
Molecular polarization, occurs
in all insulating molecules;
oils, polymers, H2O…
Electric Dipole Moment
p  q x
Polarization
q
A
p
P  
V

6. Dielectric Effects
Metal plates
Dielectric
A
d
C


What makes  different from 0?
POLARIZATION
 
 
  1


0
r
r
In electrostatics, the CONSTITUITIVE RELATION is
D E E P
   
 Polarization
P E
0
0


Susceptibility

7. Dielectric Effects
POLARIZATION arises from charge shifts in the material—
there is a macroscopic separation of positive charge (e.g., the
ions) and negative charge (e.g., the BONDING ELECTRONS).
Induced DIPOLE MOMENT
POLARIZATION is then
di  q  x0
There are many sources of dipoles.
Amount of charge shift
P  Ndipolesdi

8. Definitions
•Permittivity is a physical quantity
that describes how an electric field
affects and is affected by a dielectric
medium and is determined by the
ability of a material to polarize in
response to an applied electric field,
and thereby to cancel, partially, the
field inside the material. Permittivity
relates therefore to a material's ability
to transmit (or "permit") an electric
field…The permittivity of a material
is usually given relative to that of
vacuum, as a relative permittivity,
(also called dielectric constant in
some cases)….- Wikipedia
Dk
Df
 '

"
r r

9. Permittivity and Permeability Definitions
(Dielectric Constant)
' "

Permittivity
    

0
r r r   j
•interaction of a material in the
presence of an external electric
field.

10. Permittivity and Permeability Definitions
(Dielectric Constant)
' "

Permittivity
    

0
r r r   j
•interaction of a material in the
presence of an external electric
field.
Dk

11. Permittivity and Permeability Definitions

    '  "
' "


0
r r r   j
•interaction of a material in the
presence of an external electric
field.
   
0
r jr

interaction of a material in the
presence of an external magnetic field.
Permittivity
(Dielectric Constant)
Permeability
Dk

12. Permittivity and Permeability Definitions

    '  "
' "


0
r r r   j
•interaction of a material in the
presence of an external electric
field.
   
0
r jr

interaction of a material in the
presence of an external magnetic field.
Permittivity
(Dielectric Constant)
Permeability
Dk

13. STORAGE
Electric Magnetic
Fields Fields
Permittivity Permeability
' "
Electromagnetic Field Interaction
MUT
r r  jr ' "
 r  r  j r
STORAGE

14. STORAGE
Electric Magnetic
Fields Fields
LOSS
Permittivity Permeability
' "
Electromagnetic Field Interaction
MUT
r r  jr ' "
 r  r  j r
STORAGE
LOSS

15. Loss Tangent
"

r

'
tan
r
 
r 
'
r 
''
r 
Energy Lost perCycle
Energy Stored perCycle
1
 D  
Q
tan
Dissipation Factor D Quality Factor Q
Df

16. Relaxation Constant t
t = Time required
for 1/e of an aligned
system to return to
equilibrium or
random state, in
seconds.
1 1
c fc
t
2
 
100
1
1
10
Water at 20o C
10 100
f,
GHz
most energy is lost at 1/t
'
r 
"
 r
 
t
  
j
s


  
 1
Debye equation : ( )

17. Dielectric Effects
 s  static
   optical
0 ln() 
P LO
30-50 meV 10-15 eV
visible
infrared
Major source of POLARIZATION
is distortion of the bonding
electrons around atoms. This
leads to the normal
semiconductor dielectric
constant.
In POLAR materials, like
GaAs and SiC, the different
charge on the A and B atoms
can be polarized as well,
leading to a difference
between the optical and the
static dielectric constants.
In Appendix C, the two values for GaAs are reversed!

20. Definition:
A photonic crystal is a periodic arrangement
of a dielectric material
that exhibits strong interaction with light

23. Piezoelectric Effect
In materials with NO REFLECTION SYMMETRY (like GaAs or
many molecular species) the applied electric field produces a
DISTORTION OF THE LATTICE (size change) and vice versa.
FORCE
ELECTRIC FIELD
A common piezoelectric is Poly-Vinylidene Flouride, which is
used in a variety of stereo headsets. The most common is
crystalline quartz used as frequency control crystals—pressure
applied to the quartz has a resonance which can be used in a
feedback loop to create a highly-stable oscillator—the quartz
crystal oscillator.

26. Phase sensitive multimeter interfaced
with impendence analyzer for dielectric
measurements