1. Introduction:Ferroelectric materials possess pyroelectric properties and spontaneouspolarisation.
All ferroelectric materials are pyroelectric, however, not allpyroelectric materials are ferroelectric. Below a transition temperature calledthe Curie temperature ferroelectric and pyroelectric materials are polar andpossess a spontaneous polarization or electric dipole moment. Inhomogeneouspolarization is the typical property of ferroelectric materials, particularlyat the surface region. Different mechanisms can cause decrease of polarizationnear the surface.1 Example: High electricfields Structuralvariation of the sample near the surface Applications for Ferroelectric Materials: Capacitors, Non-volatile memory, Piezo electrics for ultrasound imagingand actuators, Electro-optic materials for data storage applications,Thermistors, Switches, Oscillators and filters, Light deflectors, modulatorsand 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) 70/30mol%. Bi and multilayer films of P (VDF-TrFE) and PVDF are produced andmeasured the polarization distributions using LIMM method. To measure the charge and polarization distributions, variousexperimental techniques are available, which are based on the piezoelectric oron the pyroelectric effect.
Pyroelectric effect methods are implemented in thetime 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 aregood enough to achieve high resolution near the sample surface. With LIMM wecan achieve 0.
5µm resolution. The results of polarization investigations in biand multilayer samples of PVDF and P (VDF-TrFE) are presented.21.1 Principle of operation: Charge and polarization distribution in the sample is measured based onthe pyroelectric response to a non uniform variation of temperature. Sample isprepared in the form of round shape and the film is covered with electrodes onboth sides of surface. Laser light is focused on one side of the surface of thefilm and that surface gets heated due to absorption of laser light. Heat goesinside the sample through the surface it causes change in the temperatureinside the sample.
1 1.2 LIMM (Laser Intensity ModulationMethod): Figure 1: Laser Intensity Modulation Method (LIMM) For the Measurement of pyroelectric current a current to voltageconverter, lock in amplifier has been used in computer controlled equipment.The pyroelectric specimen and the reference photo diode both are connected tothe input of the current to voltage converter. For the measurement ofpyroelectric spectrum laser light is incident on the specimen, for themeasurement of reference spectrum laser light is incident on the photo diode.
Through a fast operational amplifier with a gain band width product of 1.7GHZis used in the I-U converter, a significant amount of phase shift can beavoided in MHZ.1 1. Theory2.1Ferroelectric effectsSolid materials areclassified as ferroelectric if they show two or more orientation states ofspontaneous polarization Ps withouta permanent electric field forcing the crystal in a polarization.
Polarizationin this sense is the fixed separation of charges. These charges are arrangedthrough chemical bonding or through motions of sub lattices 14.To be ferroelectricthe spontaneous polarization must be switchable in two or more different statesand the states must be stable in zero field. The value of the polarizationmeasurable at zero field is called remnant polarization Pr. Normally the polarization will be compensated through freecharges in the crystal and the surrounding media. The arrangements of chargeswhich are polarized in the opposite direction are also compensating thespontaneous Polarization. This is possible because the whole crystal does not polarizein the same direction if it’s not been forced through an electric field. Onlycertain areas polarize in the same direction this area is called domains 14.
Furthermore, the spontaneous polarization istemperature dependent and disappears continually with higher temperature ordisappears suddenly above a certain temperature. This is called pyroelectriceffect. The temperature where the spontaneous polarization disappearsdiscontinuously is called the Curie temperature TC. Under the TC point the material is ferroelectric. Somematerials also show that the ferroelectric effect disappear under a certaintemperature, so the material is ferroelectric in certain temperature range 14.Another property ispiezoelectric effect.
This means that the material shows a spontaneouspolarization under mechanical stress and if an electric field is applied topolarize the material, it shows a strain. The effect is linear 14. In addition aferroelectric material shows nonlinear optic effects. It should be noted thatnonlinear optic effects can appear in more than ferroelectric materials. Theeffects appearing in ferroelectrics are the spontaneous Kerr effect (orelectro-optic effect) which leads to birefringence and piezo-optic effect whichalso occurs in any crystal material. With the change of the polarization inferroelectrics the birefringence changes as well 14.2.
2 Phenomenology of ferroelectricsA for this workrequired perspective is the thermodynamic model of free energy to model theabove mentioned effects of ferroelectrics without knowing the process on anatomic level. To model a dielectric material six variables are needed for theinternal energy. 14 (1)With U the internalenergy per unit volume, T the absolute temperature, S entropy, Xistress, xi strain, Ei electric field and Didisplacement. The small letter “i” show that this variables show be vectors.
Ifnow conditions from the outside of the system can be changed like in thefollowing experiments we can define the free energy as follows: (2)with F the free energyper unit volume. This term is called Gibbs free energy. Because the aim of thiswork is not to measure strain or apply stresses, we assume this term as 0.
Thisleads to: (3)The experiments inthis work as will be described down will change the temperature and the polarizationof the system so the free energy should be modeled as follows: (4) The model will becontinued with the modeling of the system at the phase change from paraelectricto ferroelectric phase. The Landau theory is the model normally used in thesecases. This theory asks to model the free energy as a power series.
The effectof polarization is the important effect and the origin is dielectric, so thatthe free energy will be a function of the displacement: (5)with ?, ? and ? the Landau coefficients. The reason why the powerseries is only with even powers is because the free energy cannot depend on thesign of D. Furthermore, the power series is listed until the 6th power. Thereason is the influence of higher orders is lower and it simplifies thetreatment.
The phase change takes place with falling temperature. So we assumethat the first coefficient ? is linearlytemperature dependent , ? and ? are constant. Here ? is constantand T0 the transition temperature. This is the Devonshireapproximation: (6)Furthermore, is thedisplacement equal to the polarization of the material if no electric field isapplied and the problem will be modeled only in one dimension. So if E=0 we canwrite: (7)With this model it ispossible to say something about the behavior of the crystal. The reader shouldbe reminded that the material tries to be in state with the lowest energy andthis state is the stable state of the material.
If now the Landau coefficients ? and ? are bigger than 0 andthe parameter ? can be a positive ornegative value depends on the temperature, we can see if the temperature fallsunder a value where ? gets negative thefunction will have to minima at symmetric points from the energy axis where theP is unequal to zero Ps =±Ps1,2 (see figure 1). At these points thematerial is polarizable because it can have one or the other state. The materialis ferroelectric because the polarization can be switched by an electric field.If now the temperature rises ? at some point getspositive and the function of the free energy will just have one minimum at thepoint Ps =0 (see figure 1). The material is paraelectric. The phasetransition from ferroelectric to paraelectric is continuously and named assecond order transition. Figure 2 The free energy as function of Pfor different coefficients of ? 16Now we focus on the behaviorof the function if ? is negative and ? remains positive and ? again depends on temperature.
Here we have todistinguish three cases. First is ? is smaller or equalto 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 ±Ps1,2to 0 is suddenly at one temperature. The third case ? ? means Ps = 0. This is theparaelectric phase again (see fig.
2). Because of the second case the phasetransition is discontinuously and named as first order transition. Figure 3 The free energy as function of Pfor different coefficients of ? with negative ? 16We continue the modelto get an idea of the relation of electric field and displacement.
We know thatthe derivative of free energy as function of displacement is equal to theelectric field: (8)The derivative of thesixed power was neglected. In the ferroelectric state with ? < 0 and ? > 0 the functionleads a third-degree polynomial with local extreme points in the second andfourth quadrants in a Cartesian coordinate system. The inverse function woulddescribe the relation D=f(E). The inverse graph looks like figure 4 but it isnot unambiguously.
This mean it cannot be described with a unique function. Ina physical sense the graph can be interpreted as follows: With the pointsABCDEF we see that the state of the material would be uncertain between thepoints B and C. So the state of the material would chance suddenly from B to Eand from C to F forming the typical D-E hysteresis loop of a ferroelectricmaterial.
Figure 4 The inverse function of E vs. D16Furthermore, we cansee that the function D=f(E) can be modeled as a power series of E near to thepoint of E = 0: (9)with (n=1,2,3,…) the first, second andthird dielectric nonlinearities and ?0 electric fieldconstant. With the derivative we can determine the nonlinear permittivities onthe point E =0 as follows: (10)and with thederivative of the function E = f(D) we can see: (11)This is giving adirect connection between the nonlinear permittivities and the Landaucoefficients. From this relationship Ploss 13 launched the followingrelationship between Ps and the nonlinear permittivities: (12)Furthermore, thisrelationship was simplified by Ploss 13 to: (13)with m an constantproportionality factor. 2.
3 The copolymer (VDF-TrFE) Before thecopolymer was in use the polymer from VDF was studied as a ferroelectricpolymer. The polymer crystallized as a semi-crystalline plastic with acrystallinity up to 50%. The crystal parts which are the parts which can beswitched are chains having an axis along the carbon chain call chain axis andin the crystal parts the chain axes are parallel to each other.
Furthermore,the on each carbon atom added substituent can rotate between certain stable positionsaround the chain axis. The states where the chain is stable are calledconformations and the material crystallizes in the same conformation called aphase 15. It should be noted that the material can crystallize in differentconformation at the same time. PVDF has 4 distinct phases called ?, ?, ? and ? phase.The ?, ? and ? phase areferroelectric and of these phases the ? phase is the phase with the highest remanentpolarization because the substituent of hydrogen on one carbon atom andfluorine on the next carbon atom in the chain build up dipoles with the same directionover the whole chain. This leads to that only the full chain of PVDF can rotateif an electric field is applied, which is causing the ability to switch thedipoles. PVDF doesn’t crystallize in a ferroelectric phase from the melt undernormal conditions. Through different treatments of the material the phases canbe changed e.
g. the ? phase canbe reached through stretching the material. The supplementation of the VDFmonomers with TrFE monomers now forces the crystal parts of the material tocrystallize in a conformation similar to the ? phasefrom the melt and the copolymer is ferroelectric below the Curie point.
As acopolymer the two monomers are mixable in any ratio and crystallized as asemi-crystalline plastic with crystallinity up to 90%. The copolymerpolymerized in carbon chains with random distribution of the monomers. The twoimportant factors for the value of the remnant polarization for the copolymerare the crystallinity and the VDF content 15.
The bestratio for the VDF content is between 50% and 80% 15 and the crystalline canbe increased through annealing the material at a temperature above the Curiepoint and lower the melting point 15. Another for this work importantferroelectric properties are the dielectric nonlinearities ? which will bemodeled after 13 as complex because of the conductivity of the amorphousparts and nonlinearity at the crystal parts. The amorphous parts are chains inbetween the parallel chains, but having no order 13.
This leads to that thedipoles of the chain are distributed in a way that the force caused by thedipoles cancel each other out. In addition, the amorphous part makes nocontribution to the remnant polarization still the amorphous parts are neededin small amounts. Furthermore, the samples must be thin films with a thicknessnot stronger 1?m. Thereason is simply the needed electric fields are too high to work with bulkmaterial. 2.4 Theory of Polymer-Based Ferroelectric Multilayer Systems The growth ofsuperlattices is a promising approach to create artificial materials withunique properties.
Like described by Koehler 6 this is done by thecombination of two or more materials with diffeerent electronic properties andlattice parameters in an alternating layer system while each layer has athickness of several nanometers. As stated by Lichtensteiger et al. 7 it hasbeen focused on perovskites during the past years due to their well knownferroelectric properties. Material combinations that has been researched on arefor example BaTiO3/SrTiO3, KNbO3/KTaO3, PbTiO3/SrTiO3, PbTiO3/PbZrO3 and a socalled tricolor superlattice of SrTiO3/BaTiO3/CaTiO3. The layers of thematerials are grown by epitaxial deposition techniques such as pulsed laserdeposition, sputtering or oxide molecular beam epitaxy. The created unique properties are varying dramaticallybetween the different material combinations. In the case of BaCuO2/SrCuO2superconductivity can be seen although none of the two materials issuperconducting 8.
The same can be observed in SrZrO3/SrTiO3 superlatticeswith respect to ferroelectricity 9. The above mentioned tricolor structure ofSrTiO3/BaTiO3/CaTiO3 breaks the inversion symmetry which allowsferroelectricity 10. By varying the composition of the tricolor superlatticethe ferroelectric properties are tunable. Superlattices consisting of more thanone ferroelectric, for example PbTiO3/BaTiO3, are considered to be useful tostudy polarisation switching processes and domain dynamics 11, especiallywhen the polarisation of the used ferroelectrics exhibits similar magnitudes,while the polarisation switching behaves differently.
LaAlO3/SrTiO3superlattices possess charge discontinuities at the LaO/TiO2. Theoretical Modelof Electrostatic Coupling and Interface Intermixing interface, which form aconduction channel between the single layers consisting of nonferroelectricinsulators. Combining a ferroelectric insulator and another insulator resultingin a similar conduction channel could lead to the tunability of ferroelectriccoupling between superlattice layers 12.It becomes obviousthat there are multiple ways to combine a wide range of materials insuperlattices with a variety of different effects that can be studied.Moreover, they have an immense potential of being used for innovativeapplications. In the next passages the focus lies on superlattices whereferroelectric and paraelectric materials are combined since these multilayersystems seem to be realizable most easily with the well studied polymer PVDFand 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 amechanical way. Additionally, intermixed layers can form at the interfacesbetween the layers. The formation of these intermixed layers can hardly becontrolled and their properties are different from the adjacent layers, whichmay affect the behavior of superlattices.