1.

Introduction:

Ferroelectric materials possess pyroelectric properties and spontaneous

polarisation. All ferroelectric materials are pyroelectric, however, not all

pyroelectric materials are ferroelectric. Below a transition temperature called

the Curie temperature ferroelectric and pyroelectric materials are polar and

possess a spontaneous polarization or electric dipole moment. Inhomogeneous

polarization is the typical property of ferroelectric materials, particularly

at the surface region. Different mechanisms can cause decrease of polarization

near the surface.1

Example: High electric

fields

Structural

variation of the sample near the surface

Applications for Ferroelectric Materials:

Capacitors, Non-volatile memory, Piezo electrics for ultrasound imaging

and actuators, Electro-optic materials for data storage applications,

Thermistors, Switches, Oscillators and filters, Light deflectors, modulators

and display.

Here we are working on PVDF and P (VDF-TrFE) materials. The used P

(VDF-TrFE) compositions are P (VDF-TrFE) 56/44 mol% and P (VDF-TrFE) 70/30

mol%. Bi and multilayer films of P (VDF-TrFE) and PVDF are produced and

measured the polarization distributions using LIMM method.

To measure the charge and polarization distributions, various

experimental techniques are available, which are based on the piezoelectric or

on the pyroelectric effect. Pyroelectric effect methods are implemented in the

time or in the frequency domain. The time domain is the thermal pulse method,

while the LIMM uses thermal waves in the frequency domain. Thermal methods are

good enough to achieve high resolution near the sample surface. With LIMM we

can achieve 0.5µm resolution. The results of polarization investigations in bi

and multilayer samples of PVDF and P (VDF-TrFE) are presented.2

1.1 Principle of operation:

Charge and polarization distribution in the sample is measured based on

the pyroelectric response to a non uniform variation of temperature. Sample is

prepared in the form of round shape and the film is covered with electrodes on

both sides of surface. Laser light is focused on one side of the surface of the

film and that surface gets heated due to absorption of laser light. Heat goes

inside the sample through the surface it causes change in the temperature

inside the sample.1

1.2 LIMM (Laser Intensity Modulation

Method):

Figure 1: Laser Intensity Modulation

Method (LIMM)

For the Measurement of pyroelectric current a current to voltage

converter, lock in amplifier has been used in computer controlled equipment.

The pyroelectric specimen and the reference photo diode both are connected to

the input of the current to voltage converter. For the measurement of

pyroelectric spectrum laser light is incident on the specimen, for the

measurement of reference spectrum laser light is incident on the photo diode.

Through a fast operational amplifier with a gain band width product of 1.7GHZ

is used in the I-U converter, a significant amount of phase shift can be

avoided in MHZ.1

1. Theory

2.1

Ferroelectric effects

Solid materials are

classified as ferroelectric if they show two or more orientation states of

spontaneous polarization Ps without

a permanent electric field forcing the crystal in a polarization. Polarization

in this sense is the fixed separation of charges. These charges are arranged

through chemical bonding or through motions of sub lattices 14.

To be ferroelectric

the spontaneous polarization must be switchable in two or more different states

and the states must be stable in zero field. The value of the polarization

measurable at zero field is called remnant polarization Pr. Normally the polarization will be compensated through free

charges in the crystal and the surrounding media. The arrangements of charges

which are polarized in the opposite direction are also compensating the

spontaneous Polarization. This is possible because the whole crystal does not polarize

in the same direction if it’s not been forced through an electric field. Only

certain areas polarize in the same direction this area is called domains 14.

Furthermore, the spontaneous polarization is

temperature dependent and disappears continually with higher temperature or

disappears suddenly above a certain temperature. This is called pyroelectric

effect. The temperature where the spontaneous polarization disappears

discontinuously is called the Curie temperature TC. Under the TC point the material is ferroelectric. Some

materials also show that the ferroelectric effect disappear under a certain

temperature, so the material is ferroelectric in certain temperature range 14.

Another property is

piezoelectric effect. This means that the material shows a spontaneous

polarization under mechanical stress and if an electric field is applied to

polarize the material, it shows a strain. The effect is linear 14.

In addition a

ferroelectric material shows nonlinear optic effects. It should be noted that

nonlinear optic effects can appear in more than ferroelectric materials. The

effects appearing in ferroelectrics are the spontaneous Kerr effect (or

electro-optic effect) which leads to birefringence and piezo-optic effect which

also occurs in any crystal material. With the change of the polarization in

ferroelectrics the birefringence changes as well 14.

2.2 Phenomenology of ferroelectrics

A for this work

required perspective is the thermodynamic model of free energy to model the

above mentioned effects of ferroelectrics without knowing the process on an

atomic level. To model a dielectric material six variables are needed for the

internal energy. 14

(1)

With U the internal

energy per unit volume, T the absolute temperature, S entropy, Xi

stress, xi strain, Ei electric field and Di

displacement. The small letter “i” show that this variables show be vectors. If

now conditions from the outside of the system can be changed like in the

following experiments we can define the free energy as follows:

(2)

with F the free energy

per unit volume. This term is called Gibbs free energy. Because the aim of this

work is not to measure strain or apply stresses, we assume this term as 0. This

leads to:

(3)

The experiments in

this work as will be described down will change the temperature and the polarization

of the system so the free energy should be modeled as follows:

(4)

The model will be

continued with the modeling of the system at the phase change from paraelectric

to ferroelectric phase. The Landau theory is the model normally used in these

cases. This theory asks to model the free energy as a power series. The effect

of polarization is the important effect and the origin is dielectric, so that

the free energy will be a function of the displacement:

(5)

with ?, ? and ? the Landau coefficients. The reason why the power

series is only with even powers is because the free energy cannot depend on the

sign of D. Furthermore, the power series is listed until the 6th power. The

reason is the influence of higher orders is lower and it simplifies the

treatment. The phase change takes place with falling temperature. So we assume

that the first coefficient ? is linearly

temperature dependent

, ? and ? are constant. Here ? is constant

and T0 the transition temperature. This is the Devonshire

approximation:

(6)

Furthermore, is the

displacement equal to the polarization of the material if no electric field is

applied and the problem will be modeled only in one dimension. So if E=0 we can

write:

(7)

With this model it is

possible to say something about the behavior of the crystal. The reader should

be reminded that the material tries to be in state with the lowest energy and

this state is the stable state of the material. If now the Landau coefficients ? and ? are bigger than 0 and

the parameter ? can be a positive or

negative value depends on the temperature, we can see if the temperature falls

under a value where ? gets negative the

function will have to minima at symmetric points from the energy axis where the

P is unequal to zero Ps =±Ps1,2 (see figure 1).

At these points the

material is polarizable because it can have one or the other state. The material

is ferroelectric because the polarization can be switched by an electric field.

If now the temperature rises ? at some point gets

positive and the function of the free energy will just have one minimum at the

point Ps =0 (see figure 1). The material is paraelectric. The phase

transition from ferroelectric to paraelectric is continuously and named as

second order transition.

Figure 2 The free energy as function of P

for different coefficients of ? 16

Now we focus on the behavior

of the function if ? is negative and ? remains positive and ? again depends on temperature. Here we have to

distinguish three cases. First is ? is smaller or equal

to zero what causes that the minimum is at Ps =±Ps1,2.

Second case is that ? is 0 < ? <
. This case causes that the minima of the function will be at Ps
=±Ps1,2 and Ps =0. This means that the shift from ±Ps1,2
to 0 is suddenly at one temperature. The third case ? ?
means Ps = 0. This is the
paraelectric phase again (see fig. 2). Because of the second case the phase
transition is discontinuously and named as first order transition.
Figure 3 The free energy as function of P
for different coefficients of ? with negative ? 16
We continue the model
to get an idea of the relation of electric field and displacement. We know that
the derivative of free energy as function of displacement is equal to the
electric field:
(8)
The derivative of the
sixed power was neglected. In the ferroelectric state with ? < 0 and ? > 0 the function

leads a third-degree polynomial with local extreme points in the second and

fourth quadrants in a Cartesian coordinate system. The inverse function would

describe the relation D=f(E). The inverse graph looks like figure 4 but it is

not unambiguously. This mean it cannot be described with a unique function. In

a physical sense the graph can be interpreted as follows: With the points

ABCDEF we see that the state of the material would be uncertain between the

points B and C. So the state of the material would chance suddenly from B to E

and from C to F forming the typical D-E hysteresis loop of a ferroelectric

material.

Figure 4 The inverse function of E vs. D

16

Furthermore, we can

see that the function D=f(E) can be modeled as a power series of E near to the

point of E = 0:

(9)

with

(n=1,2,3,…) the first, second and

third dielectric nonlinearities and ?0 electric field

constant. With the derivative we can determine the nonlinear permittivities on

the point E =0 as follows:

(10)

and with the

derivative of the function E = f(D) we can see:

(11)

This is giving a

direct connection between the nonlinear permittivities and the Landau

coefficients. From this relationship Ploss 13 launched the following

relationship between Ps and the nonlinear permittivities:

(12)

Furthermore, this

relationship was simplified by Ploss 13 to:

(13)

with m an constant

proportionality factor.

2.3 The copolymer (VDF-TrFE)

Before the

copolymer was in use the polymer from VDF was studied as a ferroelectric

polymer. The polymer crystallized as a semi-crystalline plastic with a

crystallinity up to 50%. The crystal parts which are the parts which can be

switched are chains having an axis along the carbon chain call chain axis and

in the crystal parts the chain axes are parallel to each other. Furthermore,

the on each carbon atom added substituent can rotate between certain stable positions

around the chain axis. The states where the chain is stable are called

conformations and the material crystallizes in the same conformation called a

phase 15. It should be noted that the material can crystallize in different

conformation at the same time. PVDF has 4 distinct phases called ?, ?, ? and ? phase.

The ?, ? and ? phase are

ferroelectric and of these phases the ? phase is the phase with the highest remanent

polarization because the substituent of hydrogen on one carbon atom and

fluorine on the next carbon atom in the chain build up dipoles with the same direction

over the whole chain. This leads to that only the full chain of PVDF can rotate

if an electric field is applied, which is causing the ability to switch the

dipoles. PVDF doesn’t crystallize in a ferroelectric phase from the melt under

normal conditions. Through different treatments of the material the phases can

be changed e.g. the ? phase can

be reached through stretching the material. The supplementation of the VDF

monomers with TrFE monomers now forces the crystal parts of the material to

crystallize in a conformation similar to the ? phase

from the melt and the copolymer is ferroelectric below the Curie point. As a

copolymer the two monomers are mixable in any ratio and crystallized as a

semi-crystalline plastic with crystallinity up to 90%. The copolymer

polymerized in carbon chains with random distribution of the monomers. The two

important factors for the value of the remnant polarization for the copolymer

are the crystallinity and the VDF content 15.

The best

ratio for the VDF content is between 50% and 80% 15 and the crystalline can

be increased through annealing the material at a temperature above the Curie

point and lower the melting point 15. Another for this work important

ferroelectric properties are the dielectric nonlinearities ? which will be

modeled after 13 as complex because of the conductivity of the amorphous

parts and nonlinearity at the crystal parts. The amorphous parts are chains in

between the parallel chains, but having no order 13. This leads to that the

dipoles of the chain are distributed in a way that the force caused by the

dipoles cancel each other out. In addition, the amorphous part makes no

contribution to the remnant polarization still the amorphous parts are needed

in small amounts. Furthermore, the samples must be thin films with a thickness

not stronger 1?m. The

reason is simply the needed electric fields are too high to work with bulk

material.

2.4 Theory of Polymer-Based Ferroelectric Multilayer Systems

The growth of

superlattices is a promising approach to create artificial materials with

unique properties. Like described by Koehler 6 this is done by the

combination of two or more materials with diffeerent electronic properties and

lattice parameters in an alternating layer system while each layer has a

thickness of several nanometers.

As stated by Lichtensteiger et al. 7 it has

been focused on perovskites during the past years due to their well known

ferroelectric properties. Material combinations that has been researched on are

for example BaTiO3/SrTiO3, KNbO3/KTaO3, PbTiO3/SrTiO3, PbTiO3/PbZrO3 and a so

called tricolor superlattice of SrTiO3/BaTiO3/CaTiO3. The layers of the

materials are grown by epitaxial deposition techniques such as pulsed laser

deposition, sputtering or oxide molecular beam epitaxy.

The created unique properties are varying dramatically

between the different material combinations. In the case of BaCuO2/SrCuO2

superconductivity can be seen although none of the two materials is

superconducting 8. The same can be observed in SrZrO3/SrTiO3 superlattices

with respect to ferroelectricity 9. The above mentioned tricolor structure of

SrTiO3/BaTiO3/CaTiO3 breaks the inversion symmetry which allows

ferroelectricity 10. By varying the composition of the tricolor superlattice

the ferroelectric properties are tunable. Superlattices consisting of more than

one ferroelectric, for example PbTiO3/BaTiO3, are considered to be useful to

study polarisation switching processes and domain dynamics 11, especially

when the polarisation of the used ferroelectrics exhibits similar magnitudes,

while the polarisation switching behaves differently. LaAlO3/SrTiO3

superlattices possess charge discontinuities at the LaO/TiO2. Theoretical Model

of Electrostatic Coupling and Interface Intermixing interface, which form a

conduction channel between the single layers consisting of nonferroelectric

insulators. Combining a ferroelectric insulator and another insulator resulting

in a similar conduction channel could lead to the tunability of ferroelectric

coupling between superlattice layers 12.

It becomes obvious

that there are multiple ways to combine a wide range of materials in

superlattices with a variety of different effects that can be studied.

Moreover, they have an immense potential of being used for innovative

applications. In the next passages the focus lies on superlattices where

ferroelectric and paraelectric materials are combined since these multilayer

systems seem to be realizable most easily with the well studied polymer PVDF

and its copolymer P(VDF-TrFE).

As a matter of fact,

the behaviour of materials in superlattices differs from that in bulk material.

The neighboring layers in influence each other in an electrical and a

mechanical way. Additionally, intermixed layers can form at the interfaces

between the layers. The formation of these intermixed layers can hardly be

controlled and their properties are different from the adjacent layers, which

may affect the behavior of superlattices.