Ferroelectric ceramics

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).

Important events in the history of ferroelectrics

Piezoelectricity and ferroelectricity in solids

Enantiomorphism

Optical activity (Circular Dichroism)

PiezoelectricitySecond-Harmonic Generation (SHG)

Polar crystals (Pyroelectricity)

3

1

2

1

5

1

5

3

21 noncentrosymmetric crystal classes

T

curr

ent

Piezoelectricity and ferroelectricity in solids

7 Crystal systems - 32 Symmetry Point Groups

21 Noncentrosymmetric 11 Centrosymmetric (Non-piezoelectric)

20 PiezoelectricPolarized under stress

10 Pyroelectric/PolarSpontaneously polarized

Subgroup FerroelectricSpontaneously polarized

Polarization reversible

Tungsten bronzePbNb2O6

Oxygen octahedraABO3

PyrochloresCd2Nb2O7

Layered structuresBi4Ti3O12

Perovskites

BaTiO3 PbTiO3

PT(Pb,La)(Zr,Ti)O3

PLZTPb(Zr,Ti)O3

PZTPbMg1/3Nb2/3O3

PMNBiFeO3 (Na,K)NbO3

Na1/2Bi1/2TiO3

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.

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.

dt

dT

dT

dP

dt

dPi SS

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).

The paraelectric to ferroelectric phase transition

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 - -

Ba

Centrosymmetric T<TC, Polar, noncentrosymmetric

Δz

TC = 2x104 (Δz)2

1/’

r

0

'

TT

Cr For T>TC:

Curie-Weiss law


Discontinuity of Ps at Tc: 1° order transition

Continuous decrease of Ps:2° order transition

Polarization and order of transition

6 orientations

Polarization: order parameter of transition

Ferroelectric hysteresis loop and polarization switching

PS: saturation (spontaneous) polarizationPR: remanent polarizationEC: coercive fieldThe slope of the initial polarization curve gives the dielectric constant

Ideally +PR = -PR and +EC = -EC

-Pr

The Landau-Ginsburg-Devonshire thermodynamic theory

Free energy of a crystal subjected to external stresses and electric field.


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) :

63111

4311

231 PPPG Free energy for zero stress conditions (P = PS)

353444

232

23112

23311

26

25

244413322112

23

22

2112

63111

4311

231

2

1

2

1

PXPXQPXPXQPXQ

XXXSXXXXXXSXXXS

PPPG

The relevant physical properties (Ps, P, x, ε, etc.) can be determined by minimizing G.

PdEdXxSdTdGi

ii

3

1

strain electric field

stress polarization


First order transition (TC > T0)

T0 TC T1 T2

In BaTiO3 : T0 = TC-12

Second order transition (TC = T0)

T0

Phase transitions in barium titanate

Lattice parameters

RO

TC

TC

C

T

O

R

Polarization orientation(001)C

(110)C

(111)C

Spontaneous polarization

TC

R/OO/T

Dielectric constant

TC

R/O

O/T

Phase transitions in ferroelectric perovskites

Polymorphic phase transition (PPT) in ferroelectrics are determined by: - temperature change; - external electric field; - external stress;

CUBICNO POLARIZATION


1st order transitionTC > T0

2nd order transitionTC = T0

Relaxor ferroelectricT(max, ) TC

2

'

m

rTT

C

T > Tm

0

'

TT

Cr T > Tm

Non-linear, hysteretic 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 oppositely oriented polarization (180° walls) minimize the depolarizing field (Ed) associated to the surface charges and are purely ferroelectric domains.

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)

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.

FE domains in tetragonal BaTiO3


180° and 90° domain walls

<90°

c/a = 1.01

1-10nm

1-10nm

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.


W = (1.0 ±0.3) nm

Structure of 90° ferroelastic domain walls in PbTiO3

c

a

P

(001)

(100

)P

P

(101)c

(101)C <90°

c/a = 1.06

d1

d 2


Domain wall configurations

90 and 180° domain walls

60, 90, 120 and 180° domain walls

71, 109 and 180° domain walls

CUBICNO POLARIZATION

The number of possible orientations of Ps as well as the number of domain wall configurations increase with decreasing the crystal symmetry.

180° domain walls

Combinations of 90° and 180° domain walls

The “no bound space charges” principle ( div P = 4Q = 0 in the bulk ) rules the formation of domain structures.


FE domains in single crystal BaTiO3.

FE domains in BaTiO3 ceramics

“harring bone” domain structure

90° domain walls 180° domain walls

180°

90°

FE domains in BaTiO3 ceramicsFine 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

g

d

Model of a cubic grain of size g with 90° domain walls

Single domain

90° dws 2D arrang.

Complex domains3D arrangement

0.3-0.5 μm 5 μm

Eq

uil

ibri

um

en

erg

y d

ens

ity

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)

2

1',

',

',

' gAlatticerdwrlatticerr

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.

2/190gkd

Thickness of domain walls as a function of grain sizeσ90: domain wall energy

g: grain size

FE domains walls as interfaces: conducting domain walls in La:BiFeO3

PFM amplitude PFM phase

BiFeO3 thin film with 109° stripe domains

C-AFM current

Origin: domain wall doping by oxygen vacanciesOxygen vacancies segregate at domain walls (strain gradient, formation of dipoles) and determine a localized increase of the electron concentration.

22

1'2 OeVO OO

3D current plot

FE domain walls as interfaces: free-electron gas at charged domain walls in insulating BaTiO3

tail-to-tail dw head-to-head dw

25 µm

Charge compensation of polarization charge by free carriers forming a q2DEG at the dw

charged dws

Influence of grain size on the dielectric constant of ferroelectric BaTiO3 ceramics

0

1000

2000

3000

4000

5000

6000

10 100 1000 10000

Grain size (nm)

Rel

ativ

e d

iele

ctri

c co

nst

ant

Arlt et al., HPSFrey & Payne, IPRandall et al., CSMRandall et al., HPSTakeuchi et al., SPSZhao et al., SPSBuscaglia et al., SPSDeng at al., SPSZhu et al., SPSWang, 2SS

Domain size and mobility effect

Dilution effect of the non ferroelectric grain boundaries (“dead” layer)

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).

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 BTPR = 0.87 PS in rhombohedral BTPR = 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.

Before poling, PR = 0

After poling, PR 0

Ferroelectric hysteresis loop and polarization switching

PS: saturation (spontaneous) polarizationPR: remanent polarizationEC: coercive fieldThe slope of the initial polarization curve gives the dielectric constant

Ideally +PR = -PR and +EC = -EC

Variation of the hysteresis loop of BaTiO3 with temperature

-Pr

FE hysteresis loop in BaTiO3

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.

Absence of significant polarization fatigue with electric field cycling in SrBi2Ta2O9 films with metal electrodes and PZT films with conducting oxide electrodes (IrO2, SrRuO3).

Fatigue mechanisms:

(i) formation of a surface layer; (ii) pinning of domain walls by defects segregatedin 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

Ferroelectric memories (FERAMs)

Samsung 32 Mb ferroelectric random access memories

-E-PS

+E+PS

Ir/IrO2 electrodes

Ferroelectric material

Pb(Zr0.4Ti0.6)O3

Non-volatile memories, no need for refresh as opposite to DRAMs

Ferroelectric nanocapacitor

1 & 2 MBits 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).

Real ferroelectric (PZT)Intrinsic (lattice) + extrinsic (dws)

contributionsIdeal ferroelectric with only 180° domain walls(pure piezoelectric response - intrinsic)

ABC: elongation (piezoelectric effect S=dE))CD: strain changes from positive to negativeDE: switchingEF: elongationFG: strain changes from negative to positiveGH: switching

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.

P

(A)

PE

PE

P E

P E

Pyroelectricity and ferroelectricity

dP/dT

T (°C)

Pyroelectric coefficient and total released charge in a PZT ceramic

Pyroelectric current

dt

dT

dT

dP

dt

dPi SS

Pyroelectric current

Pyroelectric coefficient

Hysteresis loop

Spontaneous polarization as deduced from pyroelectric data and from hysteresis loops

T

Pp Si

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.

Giant Electrocaloric Effect in Thin-Film PbZr0.95Ti0.05O3 (350 nm)

TC = 220°C

T = -12°C at 480 V/cm (25 V)

2

2P

c

TT

c: specific heatρ: densityT: temperature

P: polarizationβ: coefficient from LGD theory

Electrocaloric effect in a PLZT film (450 nm)

Tc = 115°C

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.

Dielectric constant of ceramic PbZrO3

TC

Curie-Weissbehaviour

Antipolar arrangement in the a-b plane of orthorhombic PbZrO3. The arrows denote the Pb ions displacement.

Cubic cell

Ort

ho

rho

mb

ic

ce

ll

Antiferroelectrics

Double hysteresis loops of PbZrO3 at different temperatures

Double hysteresis loop of PLZT

Stability of different FE and AFE phases in PbZrO3

TC = 230°C

Engineering the phase transitions in ferroelectrics – pressure

Phase diagram of BaTiO3First principles calculation

with quantum fluctuations

Extrapolated from low-P measurements

Experimental

R

O

TC

Engineering the phase transitions in ferroelectrics – strain effects in thin films

Room-temperature ferroelectricity in strained SrTiO3

Incipient ferroelectric

Deviation from CW law:quantum fluctuations

0

'

TT

Cr

Non-strained crystal

Strained epitaxial film

Thermodynamic prediction (LGD)

(100) SrTiO3 film with biaxial in-plane strain

LSAT: (LaAlO3)0.29 (SrAl0.5Ta0.5O3)0.71

>0: tensile<0: compressive

P1=P2=0; P3>0 P1=P2>0; P3=0

Engineering the phase transitions in ferroelectrics – strain effects in thin films

Enhancement of Ferroelectricity in Strained BaTiO3 Thin Films

(001) BaTiO3 film with biaxial in-plane strain

Thermodynamic prediction (LGD)

>0: tensile<0: compressive

P1=P2=0; P3>0

Engineering the phase transitions in ferroelectrics – chemical composition

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.

Ba2+

Ti4+

O2-

T/C

T/O

O/R

SrZr

BaTiO3

Possible phase superposition in solid solutions

Ca


Ca as amphoteric dopant

OTiBa OTiCaTiOCaO 32

OOTiBa OVCaBaBaOCaO 2''

Incorporation at the Ba site

Incorporation at the Ti site with oxygen vacancy compensation


Ferroelectric to relaxor crossover in BaZrxTi1-xO3

FerroelectricLong-range order1st order transition

Macroscopic domains:size >100nm

Diffuse FE transitionDecrease of correlation length

Broadened transition

RelaxorShort-range order

Polar nanoregions: size: 2-10 nm

Frequency dependent properties

Correlation length of Ti off-centre displacementBaTiO3

FEBaZrO3

non FE


Ferroelectric to relaxor crossover in BaZrxTi1-xO3


Variation of transition temperatures with composition in Ba1-xSrxTiO3

Sr1-xBaxTiO3Sr1-xBaxTiO3

TC

TOT

SrTiO3 is a quantum paraelectric or incipient ferroelectric without a ferro/para transition.

Deviation from Curie-Weiss law

BaTiO3SrTiO3

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.

)0(

)()0('

''

r

rrr

En

Tunability

Multilayer ceramic capacitors

Multilayer ceramic capacitorsMLCC: n ceramic layers of thickness dseparated by metal (Ni, Ag-Pd) electrodes.Capacitance per unit volume:

Current market trends:•increase capacitance (increase n and decrease d)•miniaturization (reduce d and size)

2d

nKCV r

Ceramic

d n


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

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

d=0.5 µm

Multilayer ceramic capacitorsSpecifications

X7RZ5U

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: εr = 2000-4000, ±15% from -55 to 125°C

Z5U: εr = 5000-15000, +22/-56% from 10 to 85°C


MLCCs fabrication process (multilayer cofire technology)

Ceramic


Metal electrode

Metal electrode

Dielectric ceramic layer

at least 5-7 grains

d = 10 m


State-of-the-art MLCC:d = 0.5 μm gs ≈100 nm

d=0.5 µm

Miniaturization


Miniaturization

0.4 x 0.2 mm

2.0 x 1.2 mm

L x W

Multilayer ceramic capacitorsPure 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

BaTiO3-Nb2O5-Co3O4

Influence of dopant precursor

Influence of Nb/Co ratioInfluence of sintering temperature

TS=1320°C


BaTiO3-Y2O3-MgO

TS=1250°C


dc voltage characteristics of commercial MLCCs

High εr

BaTiO3-basedceramics

Low εr

non ferroelectricceramics

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)


Applications in power electronicsBus 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


Ferroelectric ceramics

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