Transcript Document

Dielectric properties of ceramics
Polarization mechanisms
After application of an electric field, the center of gravity of positive and negative charges does not
correspond anymore
f
Electronic polarization: deformation of the
electronic shell.
Electronic
Atomic or ionic polarization: displacement of
negative and positive ions in relation to one
another
Ionic
Dipolar
Orientation
Space charge
or diffusional
Dipolar and orientation polarization
•Alignement of dipolar molecules in a liquid
•Spontaneous alignement of dipoles in a polar
solid (ferroelectricity)
•Ion jump polarization occurs when two or more
lattice positions are available for a ion or lattice
defect
•Reorientation of dipolar defects
Space charge polarization occurs when
charges accumulate at interfaces: composite
materials, insulating surface skin, electrode
polarization effects
Polarization, capacitance and dielectric constant
h
A
p
p
Dipoles and surface charges in a polarized dielectric
Dipole moment
Polarization
  Qd
P  N
(dipole moment per unit volume)
Dielectric displacement D   E  P (0 is the vacuum permittivity)
0
Surface charge density
T  0E  P
For a linear dielectric
P  e 0 E
Capacitance
Permittivity
C
 T  1  e  0 E
(e is the electric susceptibility)
QT  T A  T A
A
A
A


 1   e  0 ;  C     r  0
U
U
Eh
h
h
h
   0 1  e 
Relative permittivity (or dielectric constant)

 r   1   e 
0
Polarization, capacitance and dielectric constant
Polarizability ()
  E
Clausius-Mosotti relationship
More generally  r  1 
(induced dipole moment per unit field)
 r  1  Ni i

r  2
3 0
N
1    N  
i
0
i
i
i
N  
i i
i
1
than
 is the local field constant
i
“Polarization catastroph”
If
Electronic
polarizabilities
are
rather
independent of crystal environment and high
frequency dielectric constant can be predicted
r  
The local field produced by polarization can
increase more rapidly than the restoring force thus
stabilizing the polarization further  possibility of
spontaneous polarization (ferroelectric instability)
  e  ion  dip   sc
P  N
 r 1 
P
 0 E0
for a linear dielectric
Dielectric losses
IC: 90° in
advance of U
Current
Angular frequency
=2f = 2/T
Il: in phase with U
Voltage
Ideal capacitor: 90° phase
difference between I and U,
no dissipation
Real capacitor: <90° phase difference between
I and U.
Ic: charging current (capacitative component)
Il: loss current, dissipative comp., power loss
1
1 2
P

U
I
tan


U 0 C tan 
Power dissipated per unit time W
0 c
2
2
Dissipated power density
PW 1 2
 E 0 0 r tan 
V
2
PW 1 2
 E 0  ac
V
2
Dielectric or ac conductivity
 ac  0 r tan
tan: “dissipation factor”
or “loss tangent”
rtan: “loss factor”
By analogy with dc current
PW
 E 2
V
Complex permittivity
The behaviour of ac circuits can be conveniently analysed using complex quantities
exp(i )  cos  i sin 
i  1
90° in advance
Real part
Imaginary part
Im
Complex sinusoidal voltage
U  U0 expit 

Re
Vacuum capacitor
U  iU0 expit   iU
I  Q  UC0  iCoU
Capacitor with a lossy dielectric
 r*   r'  i r''
Ic
I  i r' C0U   r''C0U
I C  i 0 r' E
Il
 r''
tan  '
r
 r''   r' tan
I l  0 r'' E   ac E
By analogy with
Ohm’s law:
I =U/R or J =  E
"loss factor"
Resonance effects in dielectrics
E
Charged particle in a
harmonic potential well
Equation of motion
mx  mx  m02  qE  E0 exp(it )
0: natural vibration frequency
: damping factor
Q: charge
m: mass
E: local field
This behaviour is generally observed for the
electronic and ionic polarization processes,
where the charges/dipoles move around the
equilibrium positions and final polarization is
almost instantaneously achieved. Resonant
frequencies are of the order of 1013 and 1015
s-1, respectively, and fall in the optical range.
Relaxation effects in dielectrics – migration & orientation polarization
Dipolar and space charge polarization is generally accompanied by the diffusional
movement of charge and dipoles over several atomic distances and surmounting energy
barriers of different high. These polarization processes are relatively slow and strongly
temperature dependent (thermally activated). If the transient polarization is described by a
simple exponential function, the dipolar relaxation is described by the Debye equation.
Debye relaxation
Reorientation of dipolar defects (defects pairs)
CaCl2 KCl
 CaK  2ClCl  VK'
CaK  VK'  (CaK VK' ) x
Fe2O3  2 BaO BaTiO
3  2 BaBa  2 FeTi'  5OO  VO
FeTi

FeTi'  VO  FeTi' VO
VO
Electrostatic potential in a glass or defective oxide


dP Pf  P

dt

'
'



 r*   r' ,  r , s r ,
1  i
'
'



 r'   r' ,  r , s 2 r ,2
1  
'
'



 r''   r , s 2 r ,2
1  
'
'



 ac   2 r , s 2 r ,2
1  

1
r
Relaxation time
’r
’r,s
Debye relaxation
’r,
’’r
Frequency dispersion region
½(’r,s- ’r,)
’’r
<< r: ions
follow the field
low losses
(’r,s- ’r,)/
=1
Maximum loss occurs when the
field frequency is equal to the
jump frequency , =1
>> r: ions
do not jump
low losses
 Ea 

   0 exp 
 k BT 
Ea takes values typical of
ionic conduction processes
(0.7 eV), giving a loss peak in
the range 103 – 106 Hz.
Relaxation effects in dielectrics – migration polarization
Debye relaxation holds when the transient
polarization is described by a simple exponential
with a single relaxation time. In most materials,
including single crystals, a distribution of relaxation
times exists and permittivity dispersion is observed
over a wider frequency range. This is related to
variations of the ionic environment and thermal
fluctuations with distance and existence of lattice
defects. The extreme case is represented by
glasses and amorphous materials.
 r'
 r''
100
 r' ,s   r' ,
Dielectric relaxation is better described by the
equation (Cole&Cole)
 
*
r
'
r ,
 r' ,s   r' ,

1  i 
which takes into account that the the motion of ions
responsible for relaxation can be of cooperative type.
 = 0.2-0.3 for glasses.  = 1: Debye
Dielectric dispersion in silicate glasses
Relaxation effects in dielectrics – effect of temperature and frequency
Electronic and ionic polarization resonance occurs at f>1010 Hz which is above the limit of
normal uses. The effect of temperature is small.
Contribution from ion and defect migration as well as dc conductivity determine a sharp rise
of permittivity with increasing temperature and decreasing frequency. Increasing
concentration of charge carriers in turn leads to space charge effects.
Dielectric constant of single crystal Al2O3
Dielectric constant of soda-lime silica glass
Relaxation effects in dielectrics - Space charge polarization
Polycrystalline and polyphase ceramics exhibit interface or
space charge polarization (also called Maxwell-Wagner
polarization) arising from different conductivity of the various
phases. The most important occurrence of this phenomenon
is in semiconducting ceramic oxides with resistive (oxidized)
grain boundaries (magnetic ferrites, titanates, niobates) , in
which the low frequency permittivity can be several orders of
magnitude higher than the high frequency dielectric constant
and is dominated by the contribution of grain boundaries.
(1)
(2)
d1
d2
Brick-wall model
If x = d1/d2 << 1, 1 >> 2 and ’r,1= ’r,2
  2
 r'    r' 2
  '   0 r' 2
0  x1  1
x12  22
'
'
 r0   r2
2


x



1
2
1  2
x1   2
Special relationships involving permittivity
RF & MW
IR
UV-Vis
P  N
  E0
 r'  1 
P
 0 E0
At optical frequencies, electronic polarization
is the main contribution to permittivity. If n is
the index of refraction
 r' ,  n2
BaTiO3 single crystal
For ferroelectric materials in the
paraelectric regime (T > TC)
 r' 
C
T  T0
C: Curie constant
T0: Curie-Weiss temperature
TC =120°C
Properties and applications of
dielectric ceramics of commercial
interest
Dielectric losses
 ac
tan 
2f r'  0
For alumina ceramics,  = 10-12 ohm cm, ’r = 10, tan = 2x10-4 at 1 kHz
MW region
Properties of ceramics with low permittivity and low losses
Typical properties of dielectric ceramics
Material
Applications
Steatite
Porcelain insulators
Cordierite
Applications requiring good thermal shock resistance. Supports for high-power
wire-wound resistors.
Alumina
Best compromise of dielectric losses, high mechanical strength, high thermal
conductivity. Reliable metal-ceramic joining technoloy (MolyMn) available.
Beryllia
Good properties, very high thermal conductivity, expensive and difficult
processing. Insulating parts in high-power electromagnetic energy generation
(klynstrons and magnetotrons).
AlN
High thermal conductivity and TEC close to that of silicon. Substrate for power
electronic circuits and chips.
Glass & glass-ceramics
Cheap material and easy processing. Low thermal conductivity
Properties of ceramics with low permittivity and low losses
Typical properties of alumina ceramics
Spark plugs
Microstructure of alumina ceramics
99.9% Al2O3
96% Al2O3
Tan of 99.9% alumina ceramics
Insulating parts in high-power
electromagnetic generation. Windows
for high-power microwave generators.
Substrates for electronic circuits.
Cheap packaging.
Electronic substrates and chip
packaging
Power electronic substrates
The role of the substrate in power electronics is to provide the interconnections to form an
electric circuit (like a printed circuit board), and to cool the components. Compared to materials
and techniques used in lower power microelectronics, these substrates must carry higher
currents and provide a higher voltage isolation (up to several thousand volts). They also must
operate over a wide temperature range (up to 150 or 200°C).
Direct bonded copper (DBC) substrates are commonly used in power
modules, because of their very good thermal conductivity. They are
composed of a ceramic tile (commonly alumina) with a sheet of
copper bonded to one or both sides by a high-temperature oxidation
process. The top copper layer can be preformed prior to firing or
chemically etched using printed circuit board technology to form an
electrical circuit, while the bottom copper layer is usually kept plain.
The substrate is attached to a heat spreader by soldering the bottom
copper layer to it. Ceramic materials used in DBC include Al2O3, AlN
and BeO.
Dual in-line package (DIP)
Ceramic (EPROM)
Plastic
Ceramic (Intel 8080)
Pin grid array packaging (PGA)
Celeron (top)
Pentium (bottom)
Socket PGA (AMD)