Dielectric properties of ceramics. Polarization mechanisms Electronic polarization: deformation of...
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Transcript of Dielectric properties of ceramics. Polarization mechanisms Electronic polarization: deformation of...
Dielectric properties of ceramics
Polarization mechanisms
Electronic polarization: deformation of the electronic shell.
Atomic or ionic polarization: displacement of negative and positive ions in relation to one another
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
After application of an electric field, the center of gravity of positive and negative charges does not correspond anymore
Electronic
Ionic
DipolarOrientation
Space charge or diffusional
f
Dipole moment
Polarization (dipole moment per unit volume)
Dielectric displacement (0 is the vacuum permittivity)
Surface charge density
For a linear dielectric
Capacitance
Permittivity
Relative permittivity (or dielectric constant)
dQ
NP
PET 0
EP e 0 EeT 01
PED 0
h
A
p
Dipoles and surface charges in a polarized dielectric
p
h
A
h
AC
h
A
Eh
A
U
A
U
QC re
TTT00 ;1
e 10 er 10
Polarization, capacitance and dielectric constant
(e is the electric susceptibility)
Polarizability () (induced dipole moment per unit field)
Clausius-Mosotti relationship
E
032
1
ii
r
rN
iii
iir N
N
1
10
is the local field constantMore generally
scdipione
Electronic polarizabilities are rather independent of crystal environment and high frequency dielectric constant can be predicted
1 iiiN rIf than
“Polarization catastroph” 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)
Polarization, capacitance and dielectric constant
00
1E
Pr for a linear dielectric
NP
Dielectric losses
tan2
1tan
2
1 2
00CUIUP cW Power dissipated per unit time
Dielectric or ac conductivity tan0 rac
Ideal capacitor: 90° phase difference between I and U, no dissipation
Voltage
Cu
rre
nt Angular frequency
=2f = 2/T
Real capacitor: <90° phase difference between I and U.Ic: charging current (capacitative component)Il: loss current, dissipative comp., power loss
Il: in phase with U
IC: 90° in advance of U
Dissipated power density tan2
10
2
0 rW EV
P
tan: “dissipation factor” or “loss tangent”rtan: “loss factor”
acW EV
P 202
1
By analogy with dc current 2EV
PW
Complex permittivity
The behaviour of ac circuits can be conveniently analysed using complex quantities
1sincos)exp( iii
Vacuum capacitor UCiCUQI o 0
Complex sinusoidal voltage
UitiUiUtiUU expexp 00
90° in advance
Capacitor with a lossy dielectric'''*rrr i
'
''
''0
'0
0''
0'
tanr
r
acrlrC
rr
EEIEiI
UCUCiI
Ic
Il
Real partImaginary part
Im
Re
By analogy with Ohm’s law:I =U/R or J = E
""tan''' factorlossrr
Resonance effects in dielectrics
Charged particle in a harmonic potential well
E )exp(020 tiEqEmxmxm Equation of motion
0: natural vibration frequency: damping factorQ: chargem: massE: 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.
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.
Relaxation effects in dielectrics – migration & orientation polarization
Electrostatic potential in a glass or defective oxide
Debye relaxation
r
rsrac
rsrr
rsrrr
rsrrr i
11
1
1
1
22
',
',2
22
',
',''
22
',
','
,'
',
','
,*
Relaxation time
Reorientation of dipolar defects (defects pairs)
OTiOTiOOTiBaBaTiO
xKKKKKClK
KCl
VFeVFeVOFeBaBaOOFe
VCaVCaVClCaCaCl
'''32
'''2
5222
)(2
3
FeTi VO
PP
dt
dP f
’r
’’ r
’
’ r’r,s
’r,
½(’r,s- ’r,)
(’r,s- ’r,)/
=1
Frequency dispersion region
Debye relaxation
Tk
E
B
aexp0
Ea takes values typical of ionic conduction processes (0.7 eV), giving a loss peak in the range 103 – 106 Hz.
<< r: ions follow the field low losses
>> r: ions do not jump low losses
Maximum loss occurs when the field frequency is equal to the jump frequency , =1
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.
Relaxation effects in dielectrics – migration polarization
Dielectric relaxation is better described by the equation (Cole&Cole)
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
i
rsrrr
1
',
','
,*
Dielectric dispersion in silicate glasses
'r
100',
',
''
rsr
r
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.
If x = d1/d2 << 1, 1 >> 2 and ’r,1= ’r,2
1102 x
221
22
21'
2'0
'2
'
x
xrrrr
21
21'20'
xr
d1
d2
(1)
(2)
Brick-wall model
Special relationships involving permittivity
At optical frequencies, electronic polarization is the main contribution to permittivity. If n is the index of refraction
2', nr
BaTiO3 single crystal
TC =120°C
UV-VisIRRF & MW
For ferroelectric materials in the paraelectric regime (T > TC)
0
'
TT
Cr
C: Curie constantT0: Curie-Weiss temperature
00
' 1E
Pr
0E
NP
Properties and applications of dielectric ceramics of commercial
interest
Dielectric losses
0'2
tan
r
ac
f 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
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
Typical properties of dielectric ceramics
Typical properties of alumina ceramics
Properties of ceramics with low permittivity and low losses
Spark plugs
Insulating parts in high-power electromagnetic generation. Windows for high-power microwave generators. Substrates for electronic circuits. Cheap packaging.
Tan of 99.9% alumina ceramics
99.9% Al2O3 96% Al2O3
Microstructure of alumina ceramics
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)
Plastic Ceramic (Intel 8080)
Ceramic (EPROM)
Pin grid array packaging (PGA)
Celeron (top) Pentium (bottom)Socket PGA (AMD)