Dielectric and Ferroelectric Properties of Materials -...

P.Ravindran, PHY085 – Properties of Materials, April 2014: Dielectric and Ferroelectric Properties of Materials

http://folk.uio.no/ravi/PMAT2013

Prof.P. Ravindran, Department of Physics, Central University of Tamil

Nadu, India

Dielectric and Ferroelectric Properties of Materials

1


Dielectric Materials

Dielectric means a non-conductor or poor conductor of electricity.

Dielectric means a material that presents electric polarization.

The dielectric is an insulating material or a very poor conductor of electric

current. When dielectrics are placed in an electric field, practically no

current flows in them because, unlike metals, they have no loosely bound, or

free, electrons that may drift through the material. Instead, electric

polarization occurs.

The positive charges within the dielectric are displaced minutely in the

direction of the electric field, and the negative charges are displaced minutely

in the direction opposite to the electric field. This slight separation of charge,

or polarization, reduces the electric field within the dielectric.

The resistivity of insulators is: m1010 187


If a material contains polar molecules, they will generally be in random

orientations when no electric field is applied. An applied electric field will

polarize the material by orienting the dipole moments of polar molecules.

This decreases the effective electric field between the plates and will increase

the capacitance of the parallel plate structure. The dielectric must be a good

electric insulator so as to minimize any DC leakage current through a

capacitor.

Dielectric Materials


Polarization in dielectrics

Capacitor – An electronic device, constructed from alternating layers of a dielectric and a conductor, that is capable of storing a charge. These can be single layer or multi-layer devices.

Permittivity - The ability of a material to polarize and store a charge within it.

Linear dielectrics - Materials in which the dielectric polarization is linearly related to the electric field; the dielectric constant is not dependent on the electric field.

Dielectric strength - The maximum electric field that can be maintained between two conductor plates without causing a breakdown.


Dielectric strength

Maximum electric field that an insulator can withstand

before it loses its insulating behavior

Lower for ceramics than polymers

Dielectric breakdown - avalanche breakdown or carrier

multiplication


Dielectric Loss

When the relaxation time is much faster than the frequency of the applied electric field, polarization occurs instantaneously.

When the relaxation time is much slower than the frequency of the applied electric field, no polarization (of that type) occurs.

When the relaxation time and the frequency of the applied field are similar, a phase lag occurs and energy is absorbed. This is called dielectric loss, it is normally quantified by the relationship

tan d = er”/er’

where er’ is the real part of the dielectric constant and er” is the imaginary part of the dielectric constant.


Polarization mechanisms in materials:

(a) electronic,

(b) atomic or ionic,

(c) high-frequency dipolar or orientation (present in ferroelectrics),

(d) low-frequency dipolar (present in linear dielectrics and glasses),

(e) interfacial-space charge at electrodes, and

(f ) interfacial-space charge at heterogeneities such as grain

boundaries.


Dielectric ConstantIf you apply an electric field, E, across a material the charges in the material will

respond in such a way as to reduce (shield) the field experienced within the material,

D (electric displacement)

D = eE = e0E + P = e0E + e0ceE = e0(1+ce)E

where e0 is the dielctric permitivity of free space (8.85 x 1012 C2/N-m2), P is the

polarization of the material, and ce is the electric susceptibility. The relative

permitivity or dielectric constant of a material is defined as:

er = e/e0 = 1+ce

When evaluating the dielectric properties of materials it is this quantity we will use

to quantify the response of a material to an applied electric field.


Contributions to Polarizability

a = ae + ai + ad + as

1. Electronic Polarizability (ae)

Polarization of localized electrons

2. Ionic Polarizability (ai)

Displacement of ions

3. Dipolar Polarizability (ad)

Reorientation of polar molecules

4. Space Charge Polarizability (as)

Long range charge migration

Polarizability (a) increases

Response Time

Increases (slower

response)


Electronic Polarizability

Let’s limit our discussion to insulating extended solids. In the

absence of charge carriers (ions or electrons) or molecules, we only

need to consider the electronic and ionic polarizabilities.

The presence of an electric field polarizes the electron distribution about an atom creating a dipole moment,

m=qxThe dipole moment per unit volume, P, is then given by

P = nmmwhere nm is the number of atoms per unit volume.

- q

+ q

E

without

fieldwith field x


Frequency DependenceReorientation of the dipoles in response to an electric field is characterized by a relaxation time, t. The relaxation time varies for each of the various contributions to the polarizability:

1. Electronic Polarizability (ae)

Response is fast, t is small

2. Ionic Polarizability (ai)

Response is slower

3. Dipolar Polarizability (ad)

Response is still slower

4. Space Charge Polarizability (as)

Response is quite slow, t is large

Audiofrequencies (~ 103 Hz) a = ae+ai+ad+as

Radiofrequencies (~ 106 Hz) (as 0) a = ae+ai+ad

Microwave frequencies (~ 109 Hz) (as, ad 0) a = ae+ai

Visible/UV frequencies (~ 1012 Hz) (as, ad, ai 0) a = ae


Symmetry Constraints and Dielectric Properties

Dielectric properties can only be found with certain crystal symmetries

Piezoelectric

Do not posses an inversion center (noncentrosymmetric)

Ferroelectric/Pyroelectric

Do not posses an inversion center (noncentrosymmetric)

Posses a Unique Polar Axis

The 32 point groups can be divided up in the following manner (color coded according to crystal system: triclinic, monoclinic, etc.).

Piezoelectric

1, 2, m, 222, mm2, 4, -4, 422, 4mm, 42m, 3, 32, 3m,

6, -6, 622, 6mm, 6m2, 23, 43m

Ferroelectric/Pyroelectric

1, 2, m, mm2, 4, 4mm, 3, 3m, 6, 6mm

Centrosymmetric (Neither)

-1, 2/m, mmm, 4/m, 4/mmm, -3, 3/m, 6/m, 6/mmm, m3, m3m


Frequency Dependence

e(w)

e

e0

log(w)

Mic

row

av

es

IR

UV

ad+ai+ae

ai+ae

ae only

tan d(Loss)

er (Dielectric Const.)


Ionic Polarization and Ferroelectricity

Most dielectric materials are insulating (no conductivity of either electrons or ions) dense solids (no molecules that can reorient). Therefore, the polarizability must come from either ionic and electronic polarizability. Of these two ionic polarizability can make the largest contribution, particularly in a class of solids called ferroelectrics. The ionic polarizability will be large, and a ferroelectric material will result, when the following two conditions are met:

1. Certain ions in the structure displace in response to the application

of an external electric field. Typically this requires the presence

of certain types of ions such as d0 or s2p0 cations.

2. The displacements line up in the same direction (or at least they

do not cancel out). This cannot happen if the crystal structure has

an inversion center.

3. The displacements do not disappear when the electric field is

removed.


What is a Ferroelectric

A ferroelectric material develops a spontaneous polarization

(builds up a charge) in response to an external electric field.

•The polarization does not go away when the external field is removed.

•The direction of the polarization is reversible.

Applications of Ferroelectric Materials

•Multilayer capacitors

•Non-volatile FRAM (Ferroelectric Random Access Memory)


Ferroelectricity

Ferroelectricity is an electrical phenomenon whereby certain materials may exhibit a spontaneous dipole moment, the direction of which can be switched between equivalent states by the application of an external electric field.

The internal electric dipoles of a ferroelectric material are physically tied to the material lattice so anything that changes the physical lattice will change the strength of the dipoles and cause a current to flow into or out of the capacitor even without the presence of an external voltage across the capacitor.


Ferroelectrics:

•There is a class of materials which shows spontaneous polarization

and for which the relation between P and E is non-linear. Such

materials also exhibit Hysteresis.

•These substances whose properties are similar to ferromagnetics in

many respects are called Ferroelectrics.

Spontaneous polarization is a function of temperature. Ps

decreases with increase in temperature and vanishes at the curie

temperature Tc.


T < Tc

T > Tc

At E = 0

At E = 0

Ferroelectric behavior

Paraelectric behavior

Above Tc , the substance is in

the paraelectric state in which

the elementary dipoles of the

various unit cells in the

crystal are randomly

oriented.

In paraelectric state the substance

is found to obey the Curie-Weiss

Law

.

andasknownconstantsareTcandCwhere

,

etemperaturWeissCurie

TT

ClitysusceptibiElectric

C

T

χ

Tc


Ferroelectricity

Two stimuli that will change the lattice dimensions of a material are force and temperature.

The generation of a current in response to the application of a force to a capacitor is called piezoelectricity.

The generation of current in response to a change in temperature is called pyroelectricity.


Ferroelectricity

Placing a ferroelectric material between two conductive plates creates a ferroelectric capacitor.

Ferroelectric capacitors exhibit nonlinear properties and usually have very high dielectric constants.

The fact that the internal electric dipoles can be forced to change their direction by the application of an external voltage gives rise to hysteresis in the "polarization vsvoltage" property of the capacitor.

Polarization is defined as the total charge stored on the plates of the capacitor divided by the area of the plates.

Hysteresis means memory and ferroelectric capacitors are used to make ferroelectric RAM for computers and RFID cards.


Ferroelectricity

The combined properties of memory, piezoelectricity, and pyroelectricity make ferroelectric capacitors some of the most useful technological devices in modern society.

Ferroelectric capacitors are at the heart of medical ultrasound machines, high quality infrared cameras, fire sensors, sonar, vibration sensors, and even fuel injectors on diesel engines.

The high dielectric constants of ferroelectric materials used to concentrate large values of capacitance into small volumes, resulting in the very tiny surface mount capacitor.

The electrooptic modulators that form the backbone of the Internet are made with ferroelectric materials.


Ferroelectric properties

Most ferroelectric materials undergo a structural phase transition from a high-temperature nonferroelectric (or paraelectric) phase into a low-temperature ferroelectric phase.

The paraelectric phase may be piezoelectric or nonpiezoelectric and is rarely polar.

The symmetry of the ferroelectric phase is always lower than the symmetry of the paraelectric phase.


Ferroelectric properties

The temperature of the phase transition is called the Curie

point, TC.

Above the Curie point the dielectric permittivity falls off

with temperature according to the Curie–Weiss law

– where C is the Curie constant, T0 (T0 ≤TC) is the Curie–Weiss

temperature.

Some ferroelectrics, such as BaTiO3, undergo several

phase transitions into successive ferroelectric phases.


Ferroelectric Materials

A group of dielectric

materials that display

spontaneous polarization.

In other words, they

possess polarization in the

absence of an electric field.


Types of Ferroelectric Materials

Ferroelectric Materials can be structurally categorized into 4 groups:

1. Corner Sharing Octahedra:

1.1 Perovskite-Type Compounds

(such as BaTiO3, PT, PZT, PMN, and PLZT)

1.2 Tungsten-Bronze-Type Compounds

(such as PbNb2O6)

1.3 Bismuth Oxide Layer Structured Compounds

(such as Bi4Ti3O12 and PbBi2Nb2O9)

1.4 Lithium Niobate and Tantalate

(such as LiNbO3 and LiTaO3)

2. Compounds Containing Hydrogen Bonded Radicals

(such as KDP, TGS, and Rochelle Salt)

3. Organic Polymers (such as PVDF and co-polymers)

4. Ceramic Polymer Composites (such as PZT-PE)


•There are mainly three types of crystal

structures which exhibit ferroelectricity:

1. Rochelle salt structure or Rochelle salt,

NaK(C4H4O6).4H2O:Sodium Potassium

Tartrate

2. Perovskite group consisting mainly of

titnates and niobates

BaTiO3 : Barium titanate

3. Dihydrogen phosphates and arsenates

KH2PO4 : Potasium di phosphate (KDP)

• The ferroelectricity can be explained by the

domain theory.

)213(42 KPOKD

)147(42 KPORbH

)111(42 KAsORbH

)96(42 AsOKH

)393(3 KBaTiO

)0(~3 KSrTiO

)713(3 KKNbO

)763(3 KPbTiO

)890(3 KLiTaO

)1470(3 KLiNbO

)123(42 KPOKH

Examples of ferroelectric materials:


Corner Sharing Octahedra

Mixed Oxide Ferroelectrics with

Corner Sharing Octahedra of O2- Ions

Inside each Octahedron Cation Bb+ (3 < b < 6)

Space between the Octahedra Aa+ Ions (1 <a < 3)


Corner Sharing Octahedra

In prototypic forms, Aa+, Bb+, and O2- ions geometrically coincide

Non-Polar Lattice

Phase Transitions Changes in Lattice Structure

Aa+ and Bb+ ions displaced w.r.t. O2- ions

Polarized Lattice


Ferroelectrics

When a ferroelectric material is heated above its Curie

Temp. then the unit cell becomes cubic, all the ions assume

symmetric positions within the cubic unit cell and

ferroelectric behavior ceases.

Spontaneous polarization is a result of interactions between

adjacent permanent dipoles which mutually align, all in the

same direction.

Ferroelectricity is defined by the appearance of a macroscopic electric

polarization and its reversibility by applying an external field

For some ferroelectric materials, electron degrees of freedom and/or

electronic interactions directly give rise to a macroscopic electric

polarization and a ferroelectric transition electronic

ferroelectricity


Outstanding Properties of ferroelectrics

The reversibility of the permanent polarization by an

electric field. Reversibility is a result of the fact that the

polar structure of a ferroelectric is a slightly distorted

nonpolar structure. The distortion gives rise to nonlinear

dielectric behavior.

Ferroelectrics have very high dielectric constants at

relatively low applied field frequencies. Capacitors made

from these materials can be significantly smaller than

capacitors made out of other dielectric materials.

Eg: Barium Titanate, Rochelle salt, potassium

dihydrogen phosphate, potassium niobate, and lead

zirconate-titanate (PZT)


Curie Point & Phase Transitions

All ferroelectric materials have a transition temperature called the Curie point (TC).

At T > TC the crystal does not exhibit ferroelectricity, while for T < TC it is ferroelectric.

On decreasing the temperature through the Curie point, a ferroelectric crystal undergoes a phase transition from a non-ferroelectric phase to a ferroelectric phase.

If there are more than one ferroelectric phases, the T at which the crystal transforms from one phase to another is called the transition temperature.



For example, the variation of the relative permittivity er with temperature as a BaTiO3

crystal is cooled from its paraelectric cubic phase to the ferroelectric tetragonal, orthorhombic, and rhombohedral phases.

Near the Curie point or transition temperatures, thermodynamic properties including dielectric, elastic, optical, and thermal constants show an anomalous behavior.

This is due to a distortion in the crystal as the phase structure changes.



Variation of dielectric constants (a and c axis) with temperature for BaTiO3


BaTiO3

BaTiO3 has a paraelectric cubic phase above its Curie point of about 130°C.

In the T of 130°C to 0°C, the ferroelectric tetragonal phasewith a c/a ratio of ~ 1.01 is stable.

The spontaneous polarization is along one of the [001] directions in the original cubic structure.

Between 0°C and -90°C, the ferroelectric orthorhombic phaseis stable with the polarization along one of the [110] directions in the original cubic structure.

On decreasing T below -90°C the phase transition from the orthorhombic to ferroelectric rhombohedral phase leads to polarization along one of the [111] cubic directions.


The phase transition sequence in perovskites

[001]

directions

[110]

directions

[111]

directions


Phase diagram of BaTiO3: (a) bulk single crystal and (b) epitaxial (001)

single domain thin films grown on cubic substrates of high

temperatures as a function of the misfit strain. The second- and first-

order phase transitions are shown by thin and thick lines, respectively.


The perovskite structure ABO3 shown here for PbTiO3 which has a cubic

structure in the paraelectric phase and tetragonal structure in the

ferroelectric phase.


Antiferrolectric Materials

“Crystals that are isomorphous to ferroelectrics,

undergo with decreasing temperature phase transitions

from a state of higher symmetry to a state of lower

symmetry which are connected with slight distortions

of the crystal lattice. This leads to twinning. However,

the twins have no net electric dipole moment. In most

cases the crystal structure of the low symmetry phase

can be described in terms of equivalent sublattices with

equal but opposite polarization.”


PZT Phase Diagram

Pb(Zr1-xTix)O3 (PZT) is probably the most important piezoelectric material. The piezoelectric properties are optimal near x = 0.5, This composition is near the morphotropic phase boundary, which

separates the tetragonal and rhombohedral phases.


Hysteresis Loops in PbZr1-xTixO3

PbTiO3

Ferroelectric

Tetragonal

PbZr1-xTixO3

x ~ 0.3

Ferroelectric

Rhombohedral

PbZrO3

Antiferroelectric

Monoclinic

PbZr1-xTixO3

Paraelectric

Cubic

An antiferroelectic material does not polarize much for low applied fields, but higher applied fields can lead to a polarization loop reminiscent of a ferroelectric. The combination gives split hysteresis loops as shown above.

Dielectric and Ferroelectric Properties of Materials -...

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