1 Introduction to Ferroelectric Materials and Devices 426415.

1

Introduction to Ferroelectric Materials and Devices

426415

2

Objectives

• To have basic knowledge of ferroelectric material

• To understand piezoelectric effects

• To describe its application

• To understand lead zirconate titanate (PZT) solid solution system

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What is this material ?

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(1)

(2)

(3)

Piezoelectric effects

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Piezoelectric effects

Direct effect

Converse effect

D = dT + TE

S = sET + dE

D is dielectric displacement = polarization, T is the stress, E is the electric field, S = the strain, s = the material compliance (inverse of modulus of elasticity), = dielectric constant, d = piezoelectric (charge) constant

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Piezoelectric constants

Piezoelectric Charge Constant (d)

The polarization generated per unit of mechanical stress applied to a piezoelectric material

alternatively The mechanical strain experienced by a piezoelectric

material per unit of electric field applied

Electro-Mechanical Coupling Factor

(i) For an electrically stressed component

k2 = stored mechanical energy total stored energy

(ii) For a mechanically stressed component

k2 = stored electrical energy total stored energy

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8

Polarization

Dipole moment 5 Basic polarizations

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Polarization

Five basic types of polarisation: (a) electronic polarisation of an atom, (b) atomic or ionic polarisation of an ionic crystal, (c) dipolar or orientational polarisation of molecules with asymmetry structure (H2O), (d) spontaneous polarisation of a perovskite crystal,and (e) interface or space charge polarisation of a dielectric material. (Left-hand-side pictures illustrate the materials without an external electrical field and the right-hand-side pictures with an external electrical field, E.)

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Crystallographic point group

32 crystallographic point groups. The remark “ i ” represents centrosymmetric crystal which piezoelectric effect is not exhibited, both remark “ * ” and “ + ” represent noncentrosymmetric crystal where the remark “ * ” indicates that piezoelectric effect may be exhibited and the remark “ + ” indicates that pyroelectric and ferroelectric effects may be exhibited.

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Symmetry elements

There are 3 types of symmetry operations: 1.Rotation2.Reflection3.Inversion

An example of 4-fold rotation symmetry

http://www.tulane.edu/~sanelson/eens211/introsymmetry.htm

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Symmetry elements

1-Fold Rotation Axis2-fold Rotation Axis3-Fold Rotation Axis6-Fold Rotation Axis


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Symmetry elements

Mirror Symmetry

Mirror symmetry No mirror symmetry


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Symmetry elements

Center of Symmetry


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Symmetry elements

Center of Symmetry


In this operation lines are drawn from all points on the object through a point in the center of the object, called a symmetry center (symbolized with the letter "i").If an object has only a center of symmetry, we say that it has a 1 fold rotoinversion axis. Such an axis has the symbol , as shown in the right hand diagram above

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Symmetry elements

Rotoinversion Combinations of rotation with a center of symmetry perform the symmetry operation of rotoinversion.


2-fold Rotoinversion - The operation of 2-fold rotoinversion involves first rotating the object by 180o then inverting it through an inversion center. This operation is equivalent to having a mirror plane perpendicular to the 2-fold rotoinversion axis. A 2-fold rotoinversion axis is symbolized as a 2 with a bar over the top, and would be pronounced as "bar 2". But, since this the equivalent of a mirror plane, m, the bar 2 is rarely used.

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Symmetry elements

Rotoinversion


3-fold Rotoinversion - This involves rotating the object by 120o (360/3 = 120), and inverting through a center. A cube is good example of an object that possesses 3-fold rotoinversion axes. A 3-fold rotoinversion axis is denoted as (pronounced "bar 3"). Note that there are actually four axes in a cube, one running through each of the corners of the cube. If one holds one of the axes vertical, then note that there are 3 faces on top, and 3 identical faces upside down on the bottom that are offset from the top faces by 120o.

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Combinations of Symmetry Operations As should be evident by now, in three dimensional objects, such as crystals, symmetry elements may be present in several different combinations. In fact, in crystals there are 32 possible combinations of symmetry elements. These 32 combinations define the 32 Crystal Classes. Every crystal must belong to one of these 32 crystal classes.

Symmetry elements

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(a) A simple square lattice. The unit cell is a square with a side a.(b) Basis has two atoms.(c) Crystal = Lattice + Basis. The unit cell is a simple square with two atoms.(d) Placement of basis atoms in the crystal unit cell.

Crystal system

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(a) A simple square lattice. The unit cell is a square with a side a.(b) Basis has two atoms.(c) Crystal = Lattice + Basis. The unit cell is a simple square with two atoms.(d) Placement of basis atoms in the crystal unit cell.

Crystal system

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The seven crystal systems (unit cell geometries) and fourteen Bravais lattices.

7 crystal systems and 14 bravais lattices

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crystal system axis lengths angles between axes

common symmetryelements

triclinic a ≠ b ≠ c ≠ ≠ ≠ 90° 1-fold rotation w/ orw/out i

monoclinic a ≠ b ≠ c = = 90°, β >90° 2-fold rotation and/or 1m

orthorhombic a ≠ b ≠ c = = = 90° 3 2-fold rotation axesand/or 3 m

hexagonal a1 = a2 = a3, a ≠ c 60° btw a’s, = 90o 1 3-fold or 6-fold axis

tetragonal a = b ≠ c = = = 90° 1 4-fold rotation orrotoinversion axis

cubic a = b ≠ c = = = 90° 4 3-fold axes

Crystal system and symmetry elements

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Crystal system and symmetry elements

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)


Crystal directions

Fig 1.41


Labeling of crystal planes and typical examples in the cubic lattice

Crystal planes


Crystal planes

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Zr+4 or Ti+4

Pb+2

O-2

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Polarization

Classification of piezoelectric, pyroelectric and ferroelectric effects based on the symmetry system.

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A NaCl-type cubic unit cell has a center of symmetry.(a) In the absence of an applied force, the centers of mass for positive and negative ions coincide.(b) This situation does not change when the crystal is strained by an applied force.

Crystal with a centre of symmetry

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A hexagonal unit cell has no center of symmetry. (a) In the absence of an applied force the centers of mass for positive and negative ions coincide. (b) Under an applied force along y the centers of mass for positive and negative ions are shifted which results in a net dipole moment P along y. (c) When the force is along a different direction, along x, there may not be a resulting net dipole moment in that direction though there may be a net P along a different direction (y).

Noncentrosymmetric crystal

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Lead Zirconate Titanate (Pb(Zrx,Ti1-x)O3 or PZT) System

PZT Solid Solution Phase DiagramZr/Ti ratio 52/48 MPB (Morphotropic Phase Boundary)

MPB

RhombohedralHigh Temperature

RhombohedralLow Temperature

Cubic

TetragonalPb+2

O-2

Zr+4 or Ti+4Perovskite

P

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PZT (xPbZrO3 – (1-x)PbTiO3)

Binary Solid Solution PbZrO3 (antiferroelectric matrial with orthorhombic structure)

andPbTiO3 (ferroelectric material with tetragonal perovskite structure)

Perovskite Structure (ABO3) with Ti4+ and Zr4+ ions “randomly” occupying

the B-sites

Important Transducer Material (Replacing BaTiO3)

• Higher electromechanical coupling coefficient (K) than BaTiO3

• Higher Tc results in higher operating and fabricating temperatures• Easily poled

• Wider range of dielectric constants• relatively easy to sinter at lower temperature than BaTiO3

• form solid-solution compositions with several additives which results in a wide range of tailored properties


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Composition dependence of dielectric constant (K) and electromechanical planar coupling coefficient (kp) in PZT system

This shows enhanced dielectric and electromechanical properties at the MPB

Increased interest in PZT materials with MPB-compositions for applications


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Advantages of PZT Solid-Solution System

• High Tc across the diagram leads to more stable ferroelectric states over wide temperature ranges

• There is a two-phase region near the Morphotropic Phase Boundary (MPB) (52/48 Zr/Ti composition) separating rhombohedral (with 8

domain states) and tetragonal (with 6 domain states) phases • In the two-phase region, the poling may draw upon 14 orientation

states leading to exceptional polability• Near vertical MPB results in property enhancement over wider

temperature range for chosen compositions near the MPB


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Compositions and Modifications of PZT System

1. Effects of composition and grain size on properties

MPB compositions (Zr/Ti = 52/48)

Maximum dielectric and piezoelectric properties

Selection of Zr/Ti can be used to

tailor specific properties

High kp and r are desired Near MPB compositions

ORHigh Qm and low r are desired

Compositions away from MPB

Grain Size (composition and processing)

Fine-Grain ~ 1 m or less

Coase-Grain ~ 6-7 m

Some oxides are grain growth inhibitor (i.e. Fe2O3)

Some oxides are grain growth

promoter (i.e. CeO2)

Dielectric and piezoelectric properties are grain-size

dependent

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2. Influences of low level “off-valent” additives (0-5 mol%) on dielectric and piezoelectric properties

Two main groups of additives:1. electron acceptors (charge on the replacing cation is smaller)

(A-Site:K+, Rb+ ; B-Site: Co3+, Fe3+, Sc3+, Ga3+, Cr3+, Mn3+, Mn2+, Mg2+, Cu2+)(Oxygen Vacancies)

Reduce both dielectric and piezoelectric responses Increase highly asymmetric hysteresis and larger coercivity

Much larger mechanical Q

““Hard PZT”Hard PZT”

2. electron donors (charge on the replacing cation is larger)(A-Site: La3+, Bi3+, Nd3+; B-Site: Nb5+, Ta5+, Sb5+)

(A-Site Vacancies) Enhance both dielectric and piezoelectric responses at room temp

Under high field, symmetric unbiased square hysteresis loops low electrical coercivity

““Soft PZT”Soft PZT”


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Piezoelectric effects 1. mechanical energy electrical energy :sensors 2. 2. electrical energy mechanical energy :actuators3. noncentrosymmetric crystal, perovskite structure

Lead Zirconate Titanate Pb(Zrx,Ti1-x)O3 PZTnear MPB high piezoelectric response (high K and d)

Hard PZT additive = electron acceptors (A-Site:K+, Rb+ ; B-Site: Co3+, Fe3+, Sc3+, Ga3+, Cr3+, Mn3+, Mn2+, Mg2+, Cu2+)low piezoelectric response

Soft PZT additive = electron donors (A-Site: La3+, Bi3+, Nd3+; B-Site: Nb5+, Ta5+, Sb5+)high piezoelectric response

Conclusion

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““Hard PZT” MaterialsHard PZT” Materials

Curie temperature above 300 C NOT easily poled or depoled except at high temperature

Small piezoelectric d constants Good linearity and low hysteresis

High mechanical Q values Withstand high loads and voltages

““Soft PZT” MaterialsSoft PZT” Materials

Lower Curie temperature Readily poled or depoled at room temperature with high

field Large piezoelectric d constants

Poor linearity and highly hysteretic Large dielectric constants and dissipation factors

Limited uses at high field and high frequency

Modified PZT System

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Domain structure

Zr+4 or Ti+4

Pb+2

O-2

Tc ~ 350 oC

(a) Domain structure of a tetragonal ferroelectric ceramic (lead zirconate titanate) with 180o and 90o domain walls is revealed by etching in HF and HCl solution. The formation of parallel lines in the grains of the ceramic (a) is due to 90o orientation of the polar direction. (b) A schematic drawing of 90o and 180o domains in a ferroelectric ceramic.

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ferroelectric domain switching

The application of an electric field causes (a) the reorientation of a spontaneous polarisation, Ps, in a unit cell to the field direction; (b) the sum of the microscopic piezoelectricity of the unit cells result in the macroscopic piezoelectricity of piezoceramics.

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2. Modification by element substitutionElement substitution cations in perovskite lattice (Pb2+, Ti4+, and Zr4+) are replaced partially by other cations with the same chemical valence

and similar ionic radii and solid solution is formed

Pb2+ substituted by alkali-earth metals, Mg2+, Ca2+, Sr2+, and Ba2+

PZT replaced partially by Ca2+or Sr2+

Tc BUT kp, 33 , and d31 Shift of MPB towards the Zr-rich side

Density due to fluxing effect of Ca or Sr ions

Ti4+ and Zr4+ substituted by Sn4+ and Hf4+ , respectively

Ti4+ replaced partially by Sn4+ c/a ratio decreases with increasing Sn4+ content

Tc and stability of kp and 33


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Polarizatio

n

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Electrode

Electrode

Electrode

Electrode

Electrode

Electrode

Electrode

Electrode

Electric FieldElectrode

Electrode

(3)

Reference: 3. Ferroelectric Materials, n.d. DoITPoMs teaching and learning package, viewed 8 December 2008, <http://www.doitpoms.ac.uk/tlplib/ferroelectrics/printall.php>

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Polarizatio

n

43

Electrode

Electrode

Electrode

Electrode

Electrode

Electrode

Electrode

Electrode

Electric FieldElectrode

Electrode

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Dielectric Hysteresis loop

A 2 dimensional schematic sketch of an ideal polarisation hysteresis loop. The dashed line presents the initial polarisation process of the thermally unpoled ceramic. The domain orientation state is represented by arrows in the boxes.

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Butterfly Hysteresis loop

A 2 dimensional schematic sketch of an ideal butterfly hysteresis loop. The dashed line presents the initial polarisation process of the thermally unpoled ceramic. The domain orientation state is represented by arrows in the boxes

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ferroelastic domain switching

(a) 90o switching of a polarisation in a unit cell induced by a mechanical loading; the polarisation direction of each unit cell is represented by a black arrow beside it. (b) 90o domain switching under a compressive loading in a polycrystal; the polarisation direction is represented by the black arrow in each grain.

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represents unsysmetric ferroelastic hysteresis and domain switching states after applying tensile and compressive loading. The sketch simply simulates the possible position of c-axis orientation with in a unit cell.

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Compressive stress-strain curve of poled soft and hard PZT

?

?

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Piezoelectric Effect

Pi = induced polarization along the i direction, dij = piezoelectric coefficients, Tj = mechanical stress along the j direction

Di =Pi= dij Tj

Converse Piezoelectric Effect

Sj = induced stain along the j direction, dij = piezoelectric coefficients, Ei = electric field along the i direction

Sj = dij Ei

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k = electromechanical coupling factor

energy electrical ofInput

energy mechanical toconvertedenergy Electrical2 k


k = electromechanical coupling factor

energy mechanical ofInput

energy electrical toconvertedenergy Mechanical2 k

51

Piezoelectric Equations and Constants

Piezoelectric Charge Constant (d)

The polarization generated per unit of mechanical stress applied to a piezoelectric material

alternatively The mechanical strain experienced by a piezoelectric

material per unit of electric field applied

Piezoelectric Voltage Constant (g)

The electric field generated by a piezoelectric material per unit of mechanical stress applied

alternativelyThe mechanical strain experienced by a piezoelectric material per unit of electric displacement applied.

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Piezoelectric Materials

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Piezoelectric Figures of merit*

*A figure of merit is a quantity used to characterize the performance of a device

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Piezoelectric Figures of merit

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Coupling factor K

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The mechanical quality factor , QM

= (Strain in phase with stress)/(Strain out of phase with stress)

High QM low energy lost to mechanical damping. So piezoelectric material with high QM is desirable in a piezoelectric driver or resonator

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Permittivity

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Basic Piezoelectric mode

The piezoelectric constants of a ferroelectric material poled in 3-direction. (a) shows d33

and d31-effect and (b) shows d15-effect.

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Basic Piezoelectric mode

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Piezoelectric transducers are widely used to generate ultrasonic waves in solids and also to detect such mechanical waves. The transducer on the left is excited from an ac source and vibrates mechanically. These vibrations are coupled to the solid and generate elastic waves. When the waves reach the other end they mechanically vibrate the transducer on the right which converts the vibrations to an electrical signal.

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Piezoelectric Voltage Coefficient

E = electric field, g = piezoelectric voltage coefficientT = applied stress

E = gT

g = d/(or)

64The piezoelectric spark generator.

The piezoelectric spark generator, as used in various applications such as lighters and car ignitions, operates by stressing a piezoelectric crystal to generate a high voltage which is discharged through a spark gap in air as schematically shown in picture (a). Consider a piezoelectric sample in the form of a cylinder as in this picture. Suppose that the piezoelectric coefficient d = 250 x 10-12 mV-1 and r = 1000. The piezoelectric cylinder has a length of 10 mm and a diameter of 3 mm. The spark gap is in air and has a breakdown voltage of about 3.5 kV. What is the force required to spark the gap? Is this a realistic force?

Piezoelectric Spark Generator

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When a suitably cut quartz crystal with electrodes is excited by an ac voltage as (a), it behaves as if it has the equivalentCircuit in (b). (c) and (d) The magnitude of the impedances Z and reactance (both between A and B) versus frequency,neglecting losses.

Piezoelectric Quartz Oscillators

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Mechanical Resonant Frequency

fs = mechanical resonant frequency, L = mass of the transducer, C = stiffness

fs 1

2 LC

Antiresonant Frequency

fa = antiresonant frequency, L = mass of the transducer, C is Co and C in parallel, where Co is the normal parallel plate capacitance between

electrodes

For oscillators, the circuit is designed so that oscillations can take place only when the crystal in the circuit is operated at fs

CCCLf

O

a

11

C

1 where;

2

1

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Design of Buzzer

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Design of Buzzer

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A typical 1 MHz quartz crystal has the following properties:

fs = 1 MHz, fa = 1.0025 MHz, Co = 5 pF, R = 20 .

What is C in the equivalent circuit of the crystal? What is the quality factor Q of the crystal, given that

RCfQ

s2

1

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Piezoelectric measurement

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