Stress-strain measurements on both hard and soft doped PZT, performed by Cao and Evans , have shown that the coercive stress of an acceptor (hard) doped material is larger than that of a donor (soft) doped. Recently, the strong temperature-dependence of the ferroelastic behavior of PZT ceramics in different poling states was investigated by different researchers [137, 138, 149] by characterizing the nonlinear macroscopic constitutive behavior at elevated temperatures. The observed changes in the stress strain behavior with increasing temperature was attributed to a reduction of the spontaneous strain, which leads to a decrease in the energy threshold for ferroelastic switching and obtainable re- manent strain. In this context, it is important to mention that the effective modulus of PZT during stress loading is significantly influenced by the anisotropic elastic properties of the perovskite crystal structure . These phenomena also have a significant influence on the fracture behavior of PZT, making them important for the development of various commercial applications that apply electrical, mechanical, and thermal loads to ferroelectricmaterials. In PZT, most of the material properties depend on the concentration of PbTiO 3 , e.g., the permittivity  and the magnitude of the spontaneous lat- tice distortion, which is caused by internal stresses appearing during cooling from the paraelectric high temperature phase . Moreover, compositions with different PbTiO 3 concentrations show different ferroelectric and ferroelastic responses under electrical and mechanical fields . This behavior is a di- rect consequence of the different crystallographic phases (Figure 4.1) and lattice distortions that change in the critical energy barrier to switch domains [70, 153]. Additionally, Kungl et al. investigated the nonlinear ferroelectric strain behavior of various PZT compositions at different temperatures that could be explained by the influence of domain
Crystal structures can be divided into 32 classes, or point groups, according to the number of rotational axes and reflection planes that leave the crystal structure un- changed. Twenty-one of the 32 crystal classes lack a center of inversion symmetry, and of 20 these are piezoelectric. Of these 20 piezoelectric crystal classes, 10 are pyroelectric (polar). Ferroelectrics are pyroelectrics that possess a spontaneous po- larization, which can be reversed by applying a suitable electric field. The process is known as switching and is accompanied by a hysteresis in the field versus polariza- tion curve. The value of the spontaneous polarization is easily determined from the switching loop. In recent years, ferroelectricmaterials with the perovskite structure ABO 3 (A, B=cations) have attracted attention owing to their prospective technolog-
intensity confirm the suppression of ferroelectric LRO and the enhancement of a nonergodic, relaxor ferroelectric state as deduced from dielectric-permittivity experiments and polarised Raman spectroscopy (Marinova et al., 2006). A strong enhancement of the reflections stemming from (h00) planes, where h = 6, is observed upon cooling. At T = 748 K, neither the corresponding Bragg signal nor diffuse scattering is observed, at T = 300 K, only a weak diffuse scattering along the h110i directions exists, whereas at T = 150 K, a Bragg spot with the typical butterfly-shaped diffuse scattering (see Sec. 1.3.4) appears. A similar suppression is observed for signals stemming from (hh2) planes, where h = 4 (not shown). A similar tendency was found for other hk0 reflections with h + k = 4n, i.e. with nominally additive scattering contributions from both A- and B-site cations. In addition, the Bragg reflections in the (hk1) layer, which are related to chemically B-site ordered regions, become weaker and poorly resolved when the temperature decreases.
Another degradation process in ferroelectricmaterials is ageing, i.e. suppression of certain properties as a function of time without any external electrical or mechan- ical load or temperature treatment. Subject to ageing are: dielectric permittivity, piezoelectric and piezoelastic coefficients. Usually they follow a logarithmic decrease in dependence of time . Qualitative models for ageing explain its origin as grad- ual domain degradation. Domain walls can be stabilised with increasing of time. This can be either caused by the slow reorientation of defects along the spontaneous polarisation direction, or by their diffusion into domain walls. Both mechanisms sta- bilise domain-walls and hinder the switching of polarisation. Aged materials therefore posses internal bias fields which act as additional coercive fields reorienting aligned defects.
To analyze the ferroelectric properties by SPM, much work has been done and different experiment SNAM set-ups based on SPM have been developed [19~37]. Only recently, a model for the study of ferroelectric thin films by piezoelectric response mode of SNAM is presented [33, 77]. Even in that model, the electric field solutions could not satisfy the electric boundary conditions of the presented model. Neither could the introduced theoretical method be used as a systematic theoretical technique even only to analyze the quasi-stationary electric field for different samples such as bulk materials or thin films. For a systematic analysis of the electric and acoustic coupling fields in ferroelectric samples studied by SNAM systems, no other work has been documented because of the complexity. The first difficulty is that the electric and mechanical fields in the near-field in the sample is very difficult to calculate in SNAM systems [77, 78]. The second difficulty results from surfaces of ferroelectricmaterials which are also unknown to us. Although experiment results are presented from both piezoelectric response mode [19,33] and the system developed in this work [34, 37], an explanation of contrast of SNAM can only be qualitative, as the electric and mechanical coupling in near-field is still under study. Although there have been a lot of numerical solutions of the electric field distribution under the tip, it would be difficult to use the numerical solutions to study the contrast mechanism of SNAM systems. Therefore, a simple analytical solution of electric and mechanical coupling will be important for both the analysis of contrast mechanism and the estimation of properties of ferroelectricmaterials studied by SNAM systems.
The etch rates for the two different out-of-plane components were determined as fol- lows. Before etching, part of the sample was covered by photoresist, which is inert to HF and protects the film underneath. After the etching procedure the photoresist was dissolved by acetone and the edge of the etched region measured by AFM. In Fig. 6.2(a), the AFM image taken at the edge of the etched area, which was shown in Fig. 6.1 al- ready, is displayed. From the scan line across the edge shown in Fig. 6.2(d), it can be seen that the remaining islands in the etched area, the domains with polarization downwards (P − ), are inert to the acid or at least almost unetched. The etch depth for the domain pointing upwards (P + ) was determined from the height histogram shown in Fig. 6.2(c). Two peaks are visible, one rather sharp peak, corresponding to the unetched area and as well to the domains P − in the etched area, and one broader peak, corresponding to the etched domains P + . The etch depth was extracted from the separation of the two peaks. The width of the peak corresponding to the etched domains is a measure for the morphology roughness after etching. The relatively high roughness is seen in AFM topography zoomed to the etched area in Fig. 6.2(b) too, and has been reported for other ferroelectricmaterials as well .
Commonly used ferroelectricmaterials are polycrystalline thin films or ceramics that are by nature not defect-free   . There is energetic and spatial disorder due to, for instance, misfit dislocations  , defects in conformation and molecular packing of macromolecular chains , and grain boundaries  . The presence of these defects lowers the barrier for polarization reversal. The macroscopic polarization switching in ferroelectricmaterials with defects involves anisotropic growth of individual domains, termed as extrinsic switching . Here we simulate a P(VDF-TrFE) thin film with defects. We specifically investigate the effects of the pinning sites, i.e. the sporadic small regions with fixed polarity which cannot be switched by an applied electric field. To maintain a metastable polarization within these regions, a typical dimension as several nanometers is calculated, termed as the size of critical nuclei . Pinning sites with a smaller dimension generate and annihilate in dynamic equilibrium, with net contribution to the macroscopic polarization. Here, a critical nucleus is modeled as one site with fixed polarity corresponding to a 1 nm × 1 nm region. We assume that the percentage of pinning sites with opposite polarity is equal. The presence of the pinning sites lowers the value of the remanent polarization; in an extreme case when all sites are pinned, i.e. 50 % are up and 50 % are down, the remanent polarization is zero. We have found that a density of 1.7 % yields a remanent polarization of 8 µC/cm 2 , which is roughly the experimentally measured value.
Another feature of capacitive structures is that they can be employed in cross-bar arrays, allowing an increase of the memory density on a substrate. 145 Inorganic materials when used in these embedded memory arrays, tend to suffer from “half-select” problem. 67 In brief, to target one memory element, the entire row is supplied with (+1/2 V t ) and the column with (-1/2 V t ). The target element receives ± V t and the state is programmed, while the other elements remain unaffected. This, however, practically is not true. Repetitive application of (±1/2 V t ) polarizes the neighboring states and results in corruption of data. This problem was rectified by use of active matrix of transistors with “1T 1C” configuration (one transistor for one capacitor). Despite that, it led to cost increase due to additional fabrication steps and larger surface area per element. 146 However, it has been proven experimentally that it is possible to use organic ferroelectricmaterials (especially P(VDF-TrFE)) in passive geometry without suffering from the “half-select” problem and destructive read out of memory state. 147, 148 This is due to longer switching time of P(VDF-TrFE). This is also optimum enough in order not to disturb the neighboring states and read the desired programmed state at the same time. In addition, the switching time is long enough to read the programmed state and short enough that it does not harm the original polarization of the state, thus, increasing the number of read operations before the need of reprogramming arises.
Dielectric materials are poor conductors of electricity. In other words, when an electric field is applied to a dielectric material, almost no electric current flows through it. This is due to the absence of loosely bonded ions or free electrons as charged carriers. Thus, in the presence of an external field, the negative ions or electrons drift in one direction, and the positive charges move in the opposite direction, also known as polarization. This displacement results in an internal electric field, counteracting the force of the external field and reducing the total field within the dielectric material. There are mainly four mechanisms of polarization in ceramics. Each of these mechanisms involves a short-range drift of the charged elements of the material. These mechanisms are electronic polarization, ionic (atomic) polarization, interfacial polarization, and dipolar (orientational) polarization. Among all, the dipolar polarization is the most dominant type of polarization in ferroelectricmaterials, resulting in dielectric constant values of 10 4 or more .
Ferroelectricmaterials are technically attractive ceramics because of their special properties. They are often used for actua- tors or sensors in the precision range or for the purpose of energy harvesting. Problems arise due to self–heating, caused by sufficiently high frequencies and electric fields, associated with changes in the material properties, thermal stresses and some- times even phase transformations, whereupon the devices finally are inoperative. In low Curie temperature materials, such as barium titanate, even depolarization is possible. It is known that there are different effects leading to temperature change in ferroelectrics, i.e. dissipative effects and linear reversible effects [1–3]. The dissipative effects, observed in our experiments, should be classified as viscoelastic and ferroelectric heating. The latter is due to irreversible domain wall motion and has been investigated on the one hand numerically, based on a micropyhsical model, e.g. in [1,2], and on the other hand experimentally, e.g. in . Since ferroelectric heating in undamaged samples only sets in at electrical loads equal to or larger than the coercive field, the viscoelastic effect can be isolated at electrical loads below the coercive field. Therefore, the temperature change in the material is determined by applying bipolar electrical loads to samples placed in a silicon oil bath and measuring the temperature of the oil surrounding the sample, see Fig. 1a. The experiments lasting for 3–4 hours with each sample have furthermore been recorded by a camera to investigate the possible onset of damage.
To reduce the loss of the varactor, it is necessary to select a conducting electrode ma- terial which would form a high barrier height with the ferroelectric material and not interact chemically with the dielectric material . The conductor layer should have a good crystallographic match with the substrate to allow for growth of high quality epi- taxial BST thin films. Moreover, the electrode material needs to have low resistivity and permeability. Even the best varactors with a highly tunable BST thin film layer and conductive metal electrodes (Au, Pt, and Ni) suffer from high losses due to microstruc- tural defects of the polycrystalline BST films and the dead layer at the interfaces. The metal electrodes have a low resistivity at room temperature but have a very large lat- tice mismatch with BST. The quality factor of 100 at 10 GHz is demonstrated in the BST varactors with the Pt,Au electrode overtaking the performance of the competitive semiconductor varactors . However, due to the defect microstructure of the poly- crystalline BST films, the reported values of the electric tunability and quality factor of the thin film BST/Pt,Au varactors are significantly smaller in comparison to those of the single crystal ferroelectricmaterials.
4.1 Electrical Characterization Methods
The samples are contacted in a probe station (Cascade Summit 9600), which is equipped with a temperature control from -50 °C to 200 °C and BNC cables providing access to the used mea- surement equipment e.g. LCR bridge (HP 4194A). The polarization properties of the films are characterized with the aixACCT TF analyzer 2000 operating in virtual ground mode . For the integration of ferroelectricmaterials one major concern is the reliability. Fatigue, which means a loss of switchable polarization with increasing numbers of switching cycles, is still a drawback for the successful incorporation of ferroelectric thin films (especially in FeRAM technology). Since the polarization is directly related to the piezoelectric properties, also the integration into piezoelectric devices suffers from these failure mechanism and is therefore of special interest. To characterize the sample, it is exposed to a signal sequence of bipolar pulses whereat complete switching is essential . This fatigue treatment is interrupted at regular points for hysteresis measurements.
On the other hand, piezoelectric effect is also obtained in ferroelectricmaterials. That is, the mechanical potential and the electric potential can be mutually transformed to each other. We use the Fig. 1.2 to give an explanation of the piezoelectricity. As we see, electric charge is distributed on the piezoelectric body (the plates) as shown in Fig. 1.2. Therefore, displacement or deformation of the piezoelectric body (for instance increasing the distance between the surface plates, which are interpreted by the bold arrows drawn in Fig. 1.2) will cause the occurrence of electric dipole moments, and hence the applied electric field can be strengthened or weakened. Conversely, if an external electric field is applied, the piezoelectric body can be compressed or stretched by the electric force induced by the electric charge (for instance the forces indicated by the blue arrows given in Fig. 1.2).
The problem (ii) of emerging and varying depolarization eld reveals different features in thin- lm and bulk ferro- electrics. Being solely due to the presence of a very thin nonferroelectric layer below an electrode in the thin- lm case [ 38 , 44 , 71 ] the depolarization eld of this nature can hardly be signi cant in bulk ferroelectrics. In the latter case, a uniform depolarization eld evolving together with the total polarization was conceived in Refs. [ 39 , 40 ]. From our point of view, in an experiment on the dc eld-driven polariza- tion reversal, such a eld should be exactly compensated by charges at electrodes maintaining a constant voltage and thus would not play a role in polarization kinetics. On the other hand, spatial uctuations of depolarization elds due to varying polarization of grains might be important. These elds arising due to mismatching polarizations in neighbor grains are typically much higher than coercive elds of ferroelectricmaterials. Therefore they are effectively reduced inside the grains by various physical mechanisms such as splitting in domains and semiconductor effects including band bending and possible accumulation of charged defects in surface states on grain boundaries. Since these mechanisms prevail during the whole polarization reversal process the statistical eld distributions do not change much as was established in Sec. IV C . This explains why the NLS model [ 7 , 8 , 14 , 22 ] and the IFM model [ 12 , 15 – 17 ] neglecting the feedback due to depolarization elds are nevertheless able to describe the total polarization development in ferroelectric ceramics with high accuracy. We note that the statement on a stable statistical
The effects o f pressure up to 3 • 102 MPa on the 35C1 N Q R line splitting in the ferroelectric phase o f N H 4H (ClCH2C O O ), was studied from 77 K to Tc. The results are interpreted in terms o f the so called pseudo-spin-lattice coupled m ode model. A correlation was found betw een the m agnitude o f the 35C1 N Q R line splitting and the pseudo-spin com ponent (S ’. ) (the order parameter o f the applied m odel).
Before ranking material in the library catalogue, one must first discuss what is really meant by “library material.” While today’s OPACs mainly index “bundles” (i.e. books, journals), it is crucial to make all the material available in or through the library searchable within one system. Most users do not understand the distinction between library-controlled resources (catalogue, local digital repositories, course management systems, and institutional Web sites) and remote resources (abstracting and indexing databases, e-journal collections, subject gateways (Sadeh, 2007), p.310), and, more importantly, most users have no interest in the subject. All these materials should simply be searchable in the library’s information system.
possible and chemical constitution and therefore density and energy of formation are thus easily adjusted by combining cations and anions with different compositions. In addition to ease of synthesis, ionic materials are defined by strong electrostatic interionic interactions in the solid state and often form strong hydrogen bonding networks, the result of which should be considerable stability as well as insensitivity. Furthermore, ionic energetic materials tend to exhibit lower vapor pressure (essentially eliminating the risk of exposure through inhalation) than their neutral non-ionic analogues. In short, ionic energetic materials should be cheaper, more flexible, safer and perform at least as well as their molecular counterparts. 3- 5 With these properties in mind, two families of nitrogen-rich ionic materials were synthesized. One family utilizes methylated 5-amino-1H-tetrazoles as cations with simple nitrogen- and oxygen-rich anions (ClO4 - , NO3 - , N3 - , (NO2)2N - ) and the other 5-nitrotetrazolate in combination with simple, nitrogen-rich cations (ammonium, hydrazinium, guanidinium and amino- and polyaminoguanidinium).