Ferroelectric ceramics
Important events in the history of ferroelectrics
1824
Pyroelectricity in Rochelle salt NaKC4H4O6*4H2O (Brewster)
1880
Piezoelectricity in quartz and Rochelle salt (Jacques & Pierre Curie – quartz balance)
1912
Ferroelectricity proposed as a property of solids
1921
Ferroelectricity in Rochelle salt (Valasek)
1935
Ferroelectricity in KH2PO4
1941
High dielectric constant in BaTiO3
1944
Ferroelectricity in BaTiO3 (von Hippel, Wul & Goldman)
1945
BaTiO3 ceramics for piezoelectric transducers (electrical poling)
1949
Theory of ferroelectricity in BaTiO3 (Devonshire)
1949
Ferroelectricity in LiNbO3 and LiTaO3
1952
Phase diagram of Pb(Zr,Ti)O3 – PZT established
1954
PZT reported as a useful piezo transducer
1955
Ferroelectricity in alkali niobates
1961
PbMg1/3Nb2/3O3-PMN reported as ferroelectric relaxor
1969
Optical transparency achieved in hot pressed PLZT
1971
Useful electrooptical properties reported for PLZT
1980
Electrostrictive PMN devices developed
1992
New types of PZT piezo actuators developed
1993
Integration of FE films on silicon technology - FERAMs
1997
Ultrahigh piezoelectric coefficients in PMN-PT and PZN-PT
2002
High polarization and magnetoelectric coupling in BiFeO3 films
2004
High-performance lead free KNN piezoceramics (KxNa1-xNbO3)
Important events in the history of ferroelectrics
Fundamental steps in the understanding and application of ferroelectric and
piezoelectric ceramics
(1) The discovery of unusually high dielectric constant of BaTiO3 ( multilayer
ceramic capacitors - MLCCs).
(2) The discovery that the origin of the high dielectric constant in BaTiO3 is its
ferroelectric nature, thus disclosing an entire new class of piezoelectric/ferroelectric
materials –ABO3 perovskites with BO6 octahedra. Ferroelectricity no longer related
to hydrogen bonds.
(3) The discovery of the electrical poling process to align the electrical dipoles of
the grains/domains within the ceramics obtaining properties similar to those of
single crystals (large scale production and application of piezoelectric transducers
and actuators).
Piezoelectricity and ferroelectricity in solids
21 noncentrosymmetric crystal classes
Optical activity
(Circular Dichroism)
1
Enantiomorphism
5
5
1
Polar crystals
(Pyroelectricity)
2
3
3
current
1
T
Piezoelectricity
Second-Harmonic Generation (SHG)
Piezoelectricity and ferroelectricity in solids
7 Crystal systems - 32 Symmetry Point Groups
21 Noncentrosymmetric
11 Centrosymmetric
(Non-piezoelectric)
20 Piezoelectric
Polarized under stress
10 Pyroelectric/Polar
Spontaneously polarized
Subgroup Ferroelectric
Spontaneously polarized
Polarization reversible
Tungsten bronze
PbNb2O6
Oxygen octahedra
ABO3
Layered structures
Bi4Ti3O12
Pyrochlores
Cd2Nb2O7
Na1/2Bi1/2TiO3
Perovskites
BaTiO3
PbTiO3
PT
Pb(Zr,Ti)O3
PZT
(Pb,La)(Zr,Ti)O3
PLZT
PbMg1/3Nb2/3O3
PMN
BiFeO3
(Na,K)NbO3
Pyroelectricity and ferroelectricity
Pyroelectric or polar materials exhibit an electrical dipole even in the absence of an
external electric field. The polarization associated to this electrical dipoles is called
spontaneous polarization, Ps (C/m2). The variation of Ps with temperature
determines a variation of the surface charge density and originates a pyroelectric
current.
i
dPS  dPS  dT 



dt  dT  dt 
Ferroelectric crystals are polar crystals in which there are at least two equilibrium
orientations of the spontaneous polarization vector in the absence of an external
electric field, and in which the spontaneous polarization vector may be switched
between those orientations by an electric field.
“Fingerprints” of ferroelectric behaviour are:
- very high dielectric constant (r>100, often >1000);
- sharp peak or anomaly of r around a critical temperature TC;
- permittivity obeys the Curie-Weiss law above TC;
- hysteresis loop for polarization;
-Ps
+Ps
Not all polar crystals are ferroelectrics, examples are tourmaline and hexagonal CdS.
Quartz is only piezoelectric; polarization is induced by the electric field. Antiparallel
alignment of elementary dipoles can lead to antiferroelectricity.
The paraelectric to ferroelectric phase transition
In some perovskites containing Ti or Nb on the B site (BaTiO3, PbTiO3, KNbO3), a phase
transition from a paraelectric cubic structure to a lower symmetry phase (tetragonal) with
appearance of spontaneous polarization occurs at a critical temperature TC (Curie temperature).
Ba
Δz
Centrosymmetric
T<TC, Polar, noncentrosymmetric
Spontaneous strain: (cT-aT)/aC  cT/ac - 1
Compound
TC
(°C)
PS
(μC/cm2)
Qc-t
(J/mol)
cT/aT-1
Δz(Ti)
(pm)
BaTiO3
125
26
197
1%
120
PbZr0.5Ti0.5O3 (PZT)
380
40-50
-
2.5%
-
PbTiO3
495
81
4815
6.5%
300
KNbO3
435
30
796
-
-
TC = 2x104 (Δz)2
The paraelectric to ferroelectric phase transition
 r' 
C
T  T0
1/’r
For T>TC:
Curie-Weiss law
6 orientations
Polarization and order of transition
Continuous decrease of Ps:
2° order transition
Polarization:
order parameter
of transition
Discontinuity of Ps at
Tc: 1° order transition
Ferroelectric hysteresis loop and polarization switching
PS: saturation (spontaneous) polarization
PR: remanent polarization
EC: coercive field
The slope of the initial polarization curve
gives the dielectric constant
Ideally +PR = -PR and +EC = -EC
-Pr
The paraelectric to ferroelectric phase transition
The Landau-Ginsburg-Devonshire thermodynamic theory
strain
electric field
3
Free energy of a crystal subjected to external stresses
and electric field.
dG  SdT   xi dXi  E  dP
i 1
stress
polarization
For centrosymmetric crystals above TC, the function G can be expanded in even powers of
polarization. As the polar phases can be regarded as slightly distorted variants of the non polar
cubic phase, the same thermodynamic function can be used for all ferroelectric phases (BT,
PZT, NaNbO3).
For a tetragonal crystal (P1 = P2 = 0; P3 >0) :
G  1 P32  11 P34  111 P36



1
1
 S12 X 12  X 22  X 32  S12  X 1 X 2  X 2 X 3  X 3 X 1   S 44 X 42  X 52  X 62
2
2
 Q11 X 3 P32  Q12 X 1P32  X 2 P32  Q44  X 4 P3  X 5 P3 

G  1P32  11P34  111P36


Free energy for zero stress conditions (P = PS)
The relevant physical properties (Ps, P, x, ε, etc.) can be determined by minimizing G.
The paraelectric to ferroelectric phase transition
First order transition (TC > T0)
Second order transition (TC = T0)
T0
TC
T1
T2
In BaTiO3 : T0 = TC-12
T0
Phase transitions in barium titanate
Lattice parameters
(001)C
TC
Polarization orientation
(110)C
C
C
T
(111)C
O
T
R
O
R
TC
TC
Dielectric constant
O/T
O/T
R/O
R/O
Spontaneous polarization
Phase transitions in ferroelectric perovskites
CUBIC
NO POLARIZATION
Polymorphic phase transition (PPT) in ferroelectrics are determined by:
- temperature change;
- external electric field;
- external stress;
The paraelectric to ferroelectric phase transition
1st order transition
TC > T0
T > Tm
C
 
T  T0
'
r
Non-linear, hysteretic
2nd order transition
TC = T0
Relaxor ferroelectric
T(max, )  TC
T > Tm
r 
C'
T  Tm 2
Non-linear, non-hysteretic
Ferroelectric domains
Non poled FE crystals spontaneously split in domains. A domain is a region with a uniform
orientation of polarization. Domains are separated by domain walls. Ferroelectric domains form
to minimize the electrostatic energy and the elastic energy associated with mechanical
constraints to which the ferroelectric material is subjected as it is cooled through the Curie
temperature.
Domains with perpendicular orientation of
polarization (90° walls) minimize the elastic energy
and reduce the depolarizing field (Ed) associated to
the surface charges. Formation of 90° domain walls
is determined by mechanical stresses. These domain
walls differ for both the orientation of polarization
(ferroelectric domains) and the orientation of
spontaneous strain (ferroelastic domains)
Domains with oppositely oriented polarization (180°
walls) minimize the depolarizing field (Ed)
associated to the surface charges and are purely
ferroelectric domains.
FE domains in tetragonal BaTiO3
In tetragonal BaTiO3 ceramics formation of complex domain structures with both 180° and 90°
walls is observed due to the distribution of stresses and electrostatic boundary conditions to
which each grain is subjected.
Ferroelectric domains
180° and 90° domain walls
1-10nm
c/a = 1.01
<90°
dw 10 mJ/m2
Domain walls can easily move under the influence of mechanical stresses (90° walls) and
electric field (90° and 180° walls) unless pinned by electrically charged defects. Defects such
as oxygen vacancies, trapped electrons and (acceptor ion-oxygen vacancy) pairs can have a
strong effect on domain movement.
Ferroelectric domains
Structure of 90° ferroelastic domain walls in PbTiO3
W = (1.0 ±0.3) nm
(001)
(101)C
<90°
c
(100)
c/a = 1.06
(101)
P
c
P
P
a
Ferroelectric domains
Domain wall configurations
The number of possible orientations of Ps as well as the number of domain wall configurations
increase with decreasing the crystal symmetry.
90 and 180° domain walls
60, 90, 120 and 180° domain walls
71, 109 and 180° domain walls
CUBIC
NO POLARIZATION
Ferroelectric domains
The “no bound space charges” principle ( div P = 4Q = 0 in the bulk ) rules the formation of
domain structures.
180° domain walls
FE domains in single crystal BaTiO3.
Combinations of 90° and 180° domain walls
FE domains in BaTiO3 ceramics
180°
90°
“harring bone”
domain structure
90° domain walls
180° domain walls
FE domains in BaTiO3 ceramics
Fine grained ceramics (0.5-few m) show a simpler domain structure with 90° domain walls.
The domains disappear above TC
P
Heat-to-tail
arrangement of
domain walls
Influence of grain size on the dielectric constant of ferroelectric BaTiO3 ceramics
g
g
d
g
Model of a cubic grain of
size g with 90° domain walls
Equilibrium energy density
Single 90° dws
Complex domains
domain 2D arrang. 3D arrangement
0.3-0.5 μm
5 μm
Domain-wall contribution to the properties of ferroelectric materials
Movement of domain walls (vibration, bending, jump) at weak to moderate fields (subswitching
fields) is one of the most important so-called extrinsic (nonlattice) contributions to the dielectric,
elastic and piezoelectric properties of ferroelectric materials and may be comparable to the
intrinsic effect of the lattice.
• Movement of all types of DWs affect polarization and permittivity
• Movement of non-180° DWs affect polarization and piezoelectric properties (strain)
The dielectric constant of BaTiO3 ceramics decreases with decreasing grain
size down to a grain size of about 1 μm. This is ascribed to the increasing
density of 90° DWs with decreasing grain size. Similar behaviour observed
in PZT ceramics.
1

'
'
'
'
2
g: grain size
r
r ,lattice
r ,dw
r ,lattice
 


 Ag
d  k  90 g 
1/ 2
Thickness of domain
walls as a function of
grain size
σ90: domain wall energy
FE domains walls as interfaces: conducting domain walls in La:BiFeO3
BiFeO3 thin film with 109° stripe domains
PFM amplitude
PFM phase
C-AFM current
3D current plot
Origin: domain wall doping by oxygen vacancies
Oxygen vacancies segregate at domain walls (strain
gradient, formation of dipoles) and determine a
localized increase of the electron concentration.
1
OO  VO  2e' O2
2
FE domain walls as interfaces: free-electron gas at charged domain walls in
insulating BaTiO3
25 µm
tail-to-tail dw
head-to-head dw
charged dws
Charge compensation of polarization
charge by free carriers forming a
q2DEG at the dw
Influence of grain size on the dielectric constant of ferroelectric BaTiO3 ceramics
Arlt et al., HPS
Frey & Payne, IP
Randall et al., CSM
Randall et al., HPS
Takeuchi et al., SPS
Zhao et al., SPS
Buscaglia et al., SPS
Deng at al., SPS
Zhu et al., SPS
Wang, 2SS
Relative dielectric constant
6000
5000
4000
3000
2000
1000
0
10
100
1000
10000
Grain size (nm)
Dilution effect of the non
ferroelectric grain
boundaries (“dead” layer)
Domain size
and mobility
effect
Poling of ferroelectric ceramics
If the direction of the spontaneous polarization through the ceramic is random or distributed in
such a way as to lead to zero net polarization, the pyroelectric and piezoelectric effects of
individual domains will cancel and such material is neither pyroelectric nor piezoelectric.
Polycrystalline ferroelectric materials may be brought into a polar state by applying a strong
electric field (10–100 kV/cm), usually at elevated temperatures. This process, called poling,
cannot orient grains, but can reorient domains within individual grains in the direction of the field.
A poled polycrystalline ferroelectric exhibits pyroelectric and piezoelectric properties, even if
many domain walls are still present. Poling is only possible in FE ceramics. Ceramics of purely
piezoelectric compounds do not exhibit ferroelectric properties (examples: quartz).
Before poling, PR = 0
Due to the random orientation of the crystallites, the
maximum polarization attainable in a ceramic (PR) is
always smaller than in a single crystal and dependent
on the number of available domain states:
PR = 0.83 PS in tetragonal BT
PR = 0.87 PS in rhombohedral BT
PR = 0.91 PS in orthorhombic BT
In practice PR is much smaller (less than 0.5PS in
tetragonal BT) because switching of 90° domain walls
is hindered by the large mechanical stress exerted on
each grain by the adjacent grains. Only displacement
of the 90° domain walls is observed.
After poling, PR  0
Ferroelectric hysteresis loop and polarization switching
PS: saturation (spontaneous) polarization
PR: remanent polarization
EC: coercive field
The slope of the initial polarization curve
gives the dielectric constant
Ideally +PR = -PR and +EC = -EC
FE hysteresis loop in BaTiO3
-Pr
Variation of the hysteresis loop of BaTiO3
with temperature
PR = 25 μC/cm2
PR = 8 μC/cm2
Ferroelectric (polarization) fatigue
The ferroelectric fatigue is defined as the loss of the switchable remanent polarization in a
ferroelectric material as a function of the number of bipolar switching cycles. It is an irreversible
phenomenon of primary importance in the development of FERAMs.
Fatigue mechanisms:
(i) formation of a surface layer;
(ii) pinning of domain walls by defects segregated
in the wall region;
(iii) clamping of polarization reversal by volume defects;
(iv) suppression of nucleation of oppositely oriented
domains at the surface;
(v) damage of electrode/film interface.
Oxygen vacancies have an important role in the
fatigue process of ferroelectric thin films as they can
segregate at electrode/ceramic interface and/or act
as pinning centers for the domain walls
Absence of significant polarization fatigue with electric field cycling in SrBi2Ta2O9 films with
metal electrodes and PZT films with conducting oxide electrodes (IrO2, SrRuO3).
Ferroelectric memories (FERAMs)
Non-volatile memories, no need for refresh as opposite to DRAMs
Samsung 32 Mb ferroelectric
random access memories
Ferroelectric material
Ir/IrO2 electrodes
1 & 2 MBits
Ferroelectric
nanocapacitor
Pb(Zr0.4Ti0.6)O3
-PS
-E
+PS
+E
4 MBits
Strain-field loops in ferroelectrics
In addition to the polarization–electric field hysteresis loop, polarization switching
by an electric field in ferroelectric materials leads to strain–electric field hysteresis
(butterfly loops).
E
P
E
P
P
(A)
E
P
P
E
Ideal ferroelectric with only 180° domain walls
(pure piezoelectric response - intrinsic)
ABC: elongation (piezoelectric effect S=dE))
CD: strain changes from positive to negative
DE: switching
EF: elongation
FG: strain changes from negative to positive
GH: switching
Real ferroelectric (PZT)
Intrinsic (lattice) + extrinsic (dws)
contributions
Multidomain (90 + 180° dws) structure.
Contribution (non-linear and hysteretic) to strain
from movement and switching of non-180°
domain walls in addition to pure piezoelectric
response. Can be comparable or even greater
than the pure piezoelectric response.
Pyroelectricity and ferroelectricity
Pyroelectric coefficient
 P 
pi   S 
 T 
dP/dT
Pyroelectric current
i
T (°C)
Pyroelectric coefficient and total released
charge in a PZT ceramic
Hysteresis loop
Spontaneous polarization as deduced
from pyroelectric data and from hysteresis
loops
dPS  dPS  dT 



dt  dT  dt 
Electrocaloric effect
If polarization changes rapidly (under adiabatic conditions) the entropy remains unchanged and
temperature changes by ΔT. The effect is maximum slightly above TC, when an electric field can
induce a large polarization which goes to zero when the field is removed.
T 2
T  
P
2c
Giant Electrocaloric Effect in ThinFilm PbZr0.95Ti0.05O3 (350 nm)
c: specific heat
ρ: density
T: temperature
P: polarization
β: coefficient from
LGD theory
Electrocaloric effect in a PLZT film (450 nm)
Tc = 115°C
TC = 220°C
T = -12°C at 480 V/cm (25 V)
Nearly constant ECE at 20-120°C
Antiferroelectrics
In FEs, the off-center displacement occurs in the same direction in all unit cells and results in a
macroscopic polarization. In contrast, in same compounds such as PbZrO3 and NaNbO3, the
unit cell has a spontaneous electrical dipole but with opposite orientation in adjacent cells,
giving a net zero polarization. Like FEs, the AFE compound show a sharp permittivity peak
corresponding to transition from a cubic paraelectric phase. The transition temperature is again
denoted as Curie temperature.
Cubic cell
Orthorhombic
cell
Curie-Weiss
behaviour
Antipolar arrangement in the a-b plane of
orthorhombic PbZrO3. The arrows denote the
Pb ions displacement.
TC
Dielectric constant of ceramic PbZrO3
Antiferroelectrics
Double hysteresis loop of PLZT
Double hysteresis loops of PbZrO3 at different temperatures
TC = 230°C
Stability of different FE and
AFE phases in PbZrO3
Engineering the phase transitions in ferroelectrics – pressure
Phase diagram of BaTiO3
First principles calculation
with quantum fluctuations
Experimental
C
T
O
R
Extrapolated from low-P
measurements
Engineering the phase transitions in ferroelectrics – strain effects in thin films
Room-temperature ferroelectricity in strained SrTiO3
Non-strained crystal
Incipient ferroelectric
Thermodynamic prediction (LGD)
Deviation from CW law:
quantum fluctuations
(100) SrTiO3 film with
biaxial in-plane strain
 r' 
C
T  T0
Strained epitaxial film
<0: compressive
P1=P2=0; P3>0
>0: tensile
P1=P2>0;
P3=0
LSAT: (LaAlO3)0.29 (SrAl0.5Ta0.5O3)0.71
Engineering the phase transitions in ferroelectrics – strain effects in thin films
Enhancement of Ferroelectricity in Strained BaTiO3 Thin Films
Thermodynamic prediction (LGD)
(001) BaTiO3 film with
biaxial in-plane strain
<0: compressive
P1=P2=0; P3>0
>0: tensile
Engineering the phase transitions in ferroelectrics – chemical composition
BaTiO3
Sr
Zr
Ca
Ba2+
Ti4+
O2-
T/C
Dopant
Site
Charge
compensation
Ca2+, Sr2+, Pb2+
Ba
-
Zr4+, Sn4+
Ti
-
Na+, K+
Ba
Oxygen vac.
La3+, Nd3+, Sb3+
Ba
Cation vac. / e’
Mg2+, Ca2+, Al3+, Fe3+, Yb3+,
Co3+, Mn3+, Cr3+
Ti
Oxygen vac.
Y3+, Dy3+, Ho3+, Er3+
Ba & Ti
Depends on
incorp. site
Nb5+, Sb5+, W5+
Ti
Cation vac.
T/O
O/R
Possible phase superposition
in solid solutions
Engineering the phase transitions in ferroelectrics – chemical composition
Ca as amphoteric dopant
Incorporation at the Ba site
Incorporation at the Ti site with
oxygen vacancy compensation
CaO  TiO2  CaBa  TiTi  3OO
CaO  BaO  BaBa  CaTi''  VO  2OO
Engineering the phase transitions in ferroelectrics – chemical composition
Ferroelectric to relaxor crossover in BaZrxTi1-xO3
BaTiO3
FE
Ferroelectric
Long-range order
1st order transition
Macroscopic domains:
size >100nm
Diffuse FE transition
Decrease of correlation length
Broadened transition
Correlation length of
Ti off-centre displacement
BaZrO3
non FE
Relaxor
Short-range order
Polar nanoregions:
size: 2-10 nm
Frequency dependent
properties
Engineering the phase transitions in ferroelectrics – chemical composition
Ferroelectric to relaxor crossover in BaZrxTi1-xO3
Engineering the phase transitions in ferroelectrics – chemical composition
Variation of transition temperatures with composition in Ba1-xSrxTiO3
Sr1-xBaxTiO3
Sr1-xBaxTiO3
TC
TOT
SrTiO3
BaTiO3
SrTiO3 is a quantum paraelectric
or incipient ferroelectric without a
ferro/para transition.
Deviation from
Curie-Weiss law
Tunability of ferroelectric ceramics
Ferroelectric and related materials (SrxBa1-xTiO3) have
strongly non linear dielectric properties and their
permittivity decreases with increasing dc electric field. To
avoid hysteretic behaviour they are usually used in the
paraelectric region. However their application in tunable
MW devices (varactors) is limited by the high losses.
Tunability
 r' (0)   r' ( E )
nr 
 r' (0)
Multilayer ceramic capacitors
Multilayer ceramic capacitors
Ceramic
MLCC: n ceramic layers of thickness d
separated by metal (Ni, Ag-Pd) electrodes.
Capacitance per unit volume:
n
r 2
CV  K
d
Current market trends:
•increase capacitance
(increase n and decrease d)
•miniaturization (reduce d and size)
d
n
Multilayer ceramic capacitors
Some data
 Main dielectric material: BaTiO3. Yearly production: 11000 tons
 2x1012 MLCCs (2011);
 Dielectric properties are modified by adding dopants (Zr, Ca,
Mg, Nb, Y, Ho, Dy, etc.);
 State of the art capacitors: dielectric layer thickness of 0.5
micron (Murata, Japan);
 Production technology: tape casting;
 Metal electrodes:
- Noble metals: Ag-Pd, sintering in air with addition of glass to
reduce temperature to 1100°C (Ag-30Pd);
- Ni (base metal technology, Philips, 1990s): sintering in N2-H2
atmosphere. Addition of “magic” dopants (Y, Dy, Ho) to reduce
d=0.5 µm
formation of oxygen vacancies and improve lifetime.
 Applications: consumer electronics (mobile phones, smart
phones, PCs, laptops, TVs, etc.), automotive (cars, hybrid cars,
electric vehicles).
State-of-the-art MLCC:
d = 0.5 μm  gs ≈100 nm
Multilayer ceramic capacitors
Specifications
Class 1: εr = 5-300, tanδ <<0.01,
TCε: 0 to 8000 ppm
Class 1: εr = 1000-20000, tanδ: 0.01-0.03,
moderate to high TCε
X7R
X7R: εr = 2000-4000, ±15% from -55 to 125°C
Z5U: εr = 5000-15000, +22/-56% from 10 to 85°C
Z5U
Multilayer ceramic capacitors
MLCCs fabrication process (multilayer cofire technology)
Multilayer ceramic capacitors
Ceramic
d = 10 m
Metal electrode
Dielectric ceramic layer
at least 5-7 grains
Metal electrode
Multilayer ceramic capacitors
Miniaturization
d=0.5 µm
State-of-the-art MLCC:
d = 0.5 μm  gs ≈100 nm
Multilayer ceramic capacitors
Miniaturization
L x W
0.4 x 0.2 mm
2.0 x 1.2 mm
Multilayer ceramic capacitors
Pure FE phases can not be used as dielectrics due
to the unacceptable variation of permittivity with
temperature.
Dielectric properties of FE ceramics can be tailored
by forming solid solutions and by optimizing
microstructure
(i) TC and other phase transitions can be shifted and
even merged together
(ii) The order of the phase transition can be changed:
1°  2°  diffuse  relaxor
(iii) The dielectric constant can be increased by
decreasing grain size (limit: 1 μm)
A flat temperature dependence of the permittivity can be
achieved using ceramics with core-shell grains.
The grain consist of a nearly pure ferroelectric BaTiO3
core (
) with TC = 125°C and of a shell with diffuse
ferroelectric of relaxor behaviour and maximum dielectric
constant around RT.
Most common dopants:
Nb2O5, Co3O4, Y2O3, Ho2O3, Dy2O3, MgO
Multilayer ceramic capacitors
BaTiO3-Nb2O5-Co3O4
Influence of dopant precursor
Influence of sintering temperature
TS=1320°C
Influence of Nb/Co ratio
Multilayer ceramic capacitors
BaTiO3-Y2O3-MgO
TS=1250°C
Multilayer ceramic capacitors
dc voltage characteristics of commercial MLCCs
Low εr
non ferroelectric
ceramics
High εr
BaTiO3-based
ceramics
 Emerging applications (e.g. ac/dc inverters) require new dielectric materials
with high permittivity and low tunability able to operate in wide temperature range
(-50 – 200°C)
Multilayer ceramic capacitors
Applications in power electronics
Bus capacitors act as an energy source to stabilize the dc bus voltage in power
electronic circuits such as dc/ac inverters in hybrid electric systems. They possess
large capacitance (100–2000 μF), and operate under a stable dc bias with a
superimposed ac transient voltage.
Functions of inverter:
 Power the traction motors using energy stored in batteries
 Regenerative breaking (inverter takes power from motor and store it in batteries)
Requirements for dielectric materials:
o High and constant permittivity under high dc fields
o Low hysteretic losses (especially at high fields)
o High energy density