Lateral piezoelectric response across ferroelectric domain walls in thin films
J. Guyonnet, H. Bea, P. Paruch
备注：
31 pages, 10 figures. to appear in J. Appl. Phys. Special topic: invited papers from the international symposium on piezoresponse force microscopy and nanoscale phenomena in polar materials. Aveiro - portugal 2009
In purely c-axis oriented PbZr$_{0.2}$Ti$_{0.8}$O$_3$ ferroelectric thin films, a lateral piezoresponse force microscopy signal is observed at the position of 180°domain walls, where the out-of-plane oriented polarization is reversed. Using electric force microscopy measurements we exclude electrostatic effects as the origin of this signal. Moreover, our mechanical simulations of the tip/cantilever system show that the small tilt of the surface at the domain wall below the tip does not satisfactorily explain the observed signal either. We thus attribute this lateral piezoresponse at domain walls to their sideways motion (shear) under the applied electric field. From simple elastic considerations and the conservation of volume of the unit cell, we would expect a similar lateral signal more generally in other ferroelectric materials, and for all types of domain walls in which the out-of-plane component of the polarization is reversed through the domain wall. We show that in BiFeO$_3$ thin films, with 180, 109 and 71°domain walls, this is indeed the case.
The traditional derivation of the elastic anomalies associated with ferroelectric (FE) phase transitions in the framework of the Landau theory is combined with the piezoelectric constitutive relations instead of being explicitly carried out with a definite expression of the FE part of the free energy. In this manner it is shown that the softening within the FE phase is of electrostrictive and hence piezoelectric origin. Such a piezoelectric softening may be canceled by the better known piezoelectric stiffening, when the piezoelectric charges formed during the vibration are accompanied by the d…
We report the first investigation of the piezoelectric response on a nanoscale in the poled ferroelectric crystals with engineered configuration of domains. Piezoresponse force microscopy of tetragonal 0.63PMN-0.37PT relaxor-based ferroelectric crystals reviled that the d33 piezoelectric coefficient is significantly reduced within the distance of about 1 um from the uncharged engineered domain wall. This finding is essential for understanding the mechanisms of the giant piezoresponse in relaxor-based crystals and for designing new piezoelectric materials.
The importance of a high shear coefficient d15 (or d24) to the piezoelectric properties of domain-engineered and polycrystalline ferroelectrics is discussed. The extent of polarization rotation, as a mechanism of piezoelectric response, is directly correlated to the shear coefficient. The terms "rotator" and "extender" are introduced to distinguish the contrasting behaviors of crystals such as 4mm BaTiO3 and PbTiO3. In "rotator" ferroelectrics, where d15 is high relative to the longitudinal coefficient d33, polarization rotation is the dominant mechanism of piezoelectric response; the maximum …
We use first-principles density-functional total energy and polarization calculations to calculate the piezoelectric tensor at zero temperature for both cubic and simple tetragonal ordered supercells of Pb_3GeTe_4. The largest piezoelectric coefficient for the tetragonal configuration is enhanced by a factor of about three with respect to that of the cubic configuration. This can be attributed to both the larger strain-induced motion of cations relative to anions and higher Born effective charges in the tetragonal case. A normal mode decomposition shows that both cation ordering and local rela…
The stability of high-symmetry $P4mm$ polar phase in eleven ferroelectric perovskite superlattices with the polar discontinuity is studied from first principles. In most superlattices, this phase exhibits either the ferroelectric or the antiferrodistortive instability, or both of them. The structure of the ground state and, for a number of systems, also of metastable phases in these superlattices is found. The spontaneous polarization and piezoelectric properties of superlattices are calculated. The appearance of high piezoelectric coefficients (up to 150-270 pC/N) in some superlattices is ass…
The domain size dependence of piezoelectric properties of ferroelectrics is investigated using a continuum Ginzburg-Landau model that incorporates the long-range elastic and electrostatic interactions. Microstructures with desired domain sizes are created by quenching from the paraelectric phase by biasing the initial conditions. Three different two-dimensional microstructures with different sizes of the $90^{o}$ domains are simulated. An electric field is applied along the polar as well as non-polar directions and the piezoelectric response is simulated as a function of domain size for both c…
Piezoelectric and ferroelectric properties in the two dimensional (2D) limit are highly desired for nanoelectronic, electromechanical, and optoelectronic applications. Here we report the first experimental evidence of out-of-plane piezoelectricity and ferroelectricity in van der Waals layered $α$-In2Se3 nano-flakes. The non-centrosymmetric R3m symmetry of the $α$-In2Se3 samples is confirmed by scanning transmission electron microscopy, second-harmonic generation, and Raman spectroscopy measurements. Domains with opposite polarizations are visualized by piezo-response force microscopy. Single-p…
The origin of the functional properties of complex oxide superlattices can be resolved using time-resolved synchrotron x-ray diffraction into contributions from the component layers making up the repeating unit. The CaTiO3 layers of a CaTiO3/BaTiO3 superlattice have a piezoelectric response to an applied electric field, consistent with a large continuous polarization throughout the superlattice. The overall piezoelectric coefficient at large strains, 54 pm/V, agrees with first-principles predictions in which a tetragonal symmetry is imposed on the superlattice by the SrTiO3 substrate.
A method for evaluating the piezoelectric response of unpoled ferroelectric ceramics from elastic and dielectric measurements is proposed and tested on BaTiO$_3$. The method is based on the observation that the softening in a ferroelectric phase with respect to the paraelectric phase is of piezoelectric origin. The angular averages of the piezoelectric softening in unpoled ceramics are calculated for ferroelectric phases of different symmetries. The expression of the orientational average with the piezoelectric and dielectric constants of single crystal tetragonal BaTiO$_3$ from the literature…
A method for the calculation of the temperature dependence of dielectric and piezoelectric responses, based on the use of a first-principles effective Hamiltonian, is described. Results are presented for the ferroelectric perovskite PbTiO3. While the method includes only the soft-mode contributions to the responses, it is argued to give a good description of the divergences or near-divergences of the response functions near the cubic-tetragonal transition. The expression of the response functions in terms of correlation functions is used to provide a real-space interpretation of the responses …
Piezoelectrics with negative longitudinal piezoelectric coefficients will contract in the direction of an applied electric field. Such piezoelectrics are thought to be rare but there is no fundamental physics preventing the realization of negative longitudinal piezoelectric effect in a single-phase material. Using first-principles calculations, we demonstrate that several hexagonal $ABC$ ferroelectrics possess significant negative longitudinal piezoelectric effect. The data mining of a first-principles-based database of piezoelectrics reveals that this effect is a general phenomenon. The origi…
The effective piezoelectric coefficients of twin walls in tetragonal ferroelectric are calculated in the framework of decoupling approximation and Landau-Ginzburg-Devonshire theory allowing for polarization gradient terms, electrostriction and flexoelectric coupling. Using an example of piezoelectric response of a1-a2 twins to a homogeneous electric field, we show that the response is almost independent on the flexoelectric coupling, but is very sensitive to the values of polarization gradient coefficients. This behavior originates from the strong coupling between local dielectric susceptibili…
The effective properties of piezoelectric laminates have been analyzed, based on the calculation of internal fields and making use of a simple matrix manipulation method. The results are expressed in a compact notation which is convenient for numerical implementation and at the same time suitable for further analytical treatments. A detailed analysis of fully compatible ferroelectric domain structures shows, that the results for arbitrary piezoelectric laminates can be further simplified and specific property relationships for rank-1 laminates of tetragonal and rhombohedral crystals are derive…
High-temperature electronic materials are in constant demand as the required operational range for various industries increases. Here we design $(A,A^\prime)B_2$O$_6$ perovskite oxides with [111] ``rock salt" $A$-site cation order and predict them to be potential high-temperature piezoelectric materials. By selecting bulk perovskites which have a tendency towards only out-of-phase $B$O$_6$ rotations, we avoid possible staggered ferroelectric to paraelectric phase transitions while also retaining non-centrosymmetric crystal structures necessary for ferro- and piezoelectricity. Using density fun…
Intrinsic domain wall width is a fundamental parameter that reflects bulk ferroelectric properties and governs the performance of ferroelectric memory devices. We present closed-form analytical expressions for vertical and lateral piezoelectric force microscopy (PFM) profiles for the conical and disc models of the tip, beyond point charge and sphere approximations. The analysis takes into account the finite intrinsic width of the domain wall, and dielectric anisotropy of the material. These analytical expressions provide insight into the mechanisms of PFM image formation and can be used for qu…
The structure of a single antiparallel ferroelectric domain wall in LiNbO3 is quantitatively mapped by piezoelectric force microscopy (PFM) with calibrated probe geometry. The PFM measurements are performed for 49 probes with the radius varying from 10 to 300 nm. The magnitude and variation of the experimental piezoelectric coefficient across a domain wall matches the profiles calculated from a comprehensive analytical theory, as well as 3-dimensional finite element method simulations. Quantitative agreement between experimental and theoretical profile widths is obtained only when a finite dis…
Materials that can produce large controllable strains are widely used in shape memory devices, actuators and sensors. Great efforts have been made to improve the strain outputs of various material systems. Among them, ferroelastic transitions underpin giant reversible strains in electrically-driven ferro/piezoelectrics and thermally- or magneticallydriven shape memory alloys. However, large-strain ferroelastic switching in conventional ferroelectrics is very challenging while magnetic and thermal controls are not desirable for applications. Here, we demonstrate an unprecedentedly large shear s…
In this work, we propose a class of ferroelectrics (which we denote "double-path" ferroelectrics), characterized by two competing polarization switching paths for which the change in polarization is different and in fact of opposite sign. Depending on which path is favorable under given conditions, this leads to different identification of up- and down-polarized states. Since the sign of piezoelectric response depends on the assignment of up- or down-polarized state for a specific structure, this means that the material can exhibit different signs of the piezoelectric response under different …
The contributory mechanisms associated with high piezoelectric response in piezoelectric ceramics have been examined by in-situ electric field dependent high energy synchro x-ray diffraction study. A comparative study of electric field induced lattice strain and the propensity for non-180o domain switching on two closeby compositions of a high performance piezoelectric alloy (1-x)PbTiO3-(x)BiScO3, one within the morphotropic phase boundary (MPB) region exhibiting d33 of 425 pC/N and another just outside the MPB region exhibiting d33 of 260 pC/N, unravelled that, inspite of the MPB specimen exh…
Compound phases often display properties that are symmetry-forbidden relative to their nominal, average crystallographic symmetry, even if extrinsic reasons (defects, strain, imperfections) are not apparent. Here, we investigate macroscopic inversion symmetry breaking in nominally centrosymmetric materials and measure Resonant Piezoelectric Spectroscopy (RPS) and Resonant Ultrasound Spectroscopy (RUS) in 15 compounds, 18 samples, and 21 different phases, including unpoled ferroelectrics, paraelectrics, relaxors, ferroelastics, incipient ferroelectrics, and isotropic materials with low defect c…
There is a general perception that large piezoelectric response in ferroelectric alloys requires tuning the system towards a morphotropic phase boundary (MPB), i.e., a composition driven inter-ferroelectric instability. Here we show that high piezoelectric response can be realized even in non-MPB alloy systems. This is demonstrated on (1-x)PbTiO3-(x)Bi(Zr0.5Ni0.5)O3 (PT-BNZ) by a comprehensive study involving electric-field and temperature dependent XRD, Raman spectroscopy, dielectric, piezoelectric and high field electrostrain measurements. We found that poling-field irreversibly suppresses t…
Polymer-piezoceramic 0-3 composites combine the flexibility of the polymers and the excellent piezoelectric properties of the ferroelectric based ceramic. While grain size of the ceramic powder is one of the important considerations in the fabrication of such composites, a correlation relating poling field induced structural changes and its possible influence on the overall piezoelectric response of the composite is still lacking. In this paper, we examine this issue on a 0-3 piezo-composite comprising of a ceramic powders of a low-lead piezoelectric alloy (x)Bi(Ni1/2Zr1/2O3-(1-x)PbTiO3 in pro…
Surprising asymmetry in the local electromechanical response across a single antiparallel ferroelectric domain wall is reported. Piezoelectric force microscopy is used to investigate both the in-plane and out-of- plane electromechanical signals around domain walls in congruent and near-stoichiometric lithium niobate. The observed asymmetry is shown to have a strong correlation to crystal stoichiometry, suggesting defect-domain wall interactions. A defect-dipole model is proposed. Finite element method is used to simulate the electromechanical processes at the wall and reconstruct the images. F…
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Large Enhancements in Optical and Piezoelectric Properties in Ferroelectric Zn1-xMgxO Thin Films through Engineering Electronic and Ionic Anharmonicities
Tetragonal ferroelectric/ferroelectric BaTiO3/PbTiO3 superlattice under uniaxial tensile stress along the c axis is investigated from first principles. We show that the calculated ideal tensile strength is 6.85 GPa and that the superlattice under the loading of uniaxial tensile stress becomes soft along the nonpolar axes. We also find that the appropriately applied uniaxial tensile stress can significantly enhance the piezoelectricity for the superlattice, with piezoelectric coefficient d33 increasing from the ground state value by a factor of about 8, reaching 678.42 pC/N. The underlying mech…
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Quadratic piezoelectricity from stacking-engineered interference in multilayer sliding ferroelectrics
Inner Mongolia University（内蒙古大学）；Nanjing University（南京大学）；Institute of Metal Research, Chinese Academy of Sciences（中国科学院金属研究所）；University of Science and Technology of China（中国科学技术大学）
An optimization procedure determining the ideal configuration at the microstructural level of ferroelectric (FE) materials is applied to maximize piezoelectricity. Piezoelectricity in ceramic FEs differ significantly from that of single crystals because of the presence of crystallites (grains) possessing crystallographic axes aligned imperfectly. The piezoelectric properties of a polycrystalline (ceramic) FE is inextricably related to the grain orientation distribution (texture). The set of combination of variables, known as solution space, which dictates the texture of a ceramic is unlimited …
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We report a more than 10-fold enhancement of the piezoelectric coefficient $d_{33}$ of polycrystalline CH$_3$NH$_3$PbI$_3$ (MAPbI$_3$) films when interfacing them with ferroelectric PbZr$_{0.2}$Ti$_{0.8}$O$_3$ (PZT). Piezo-response force microscopy (PFM) studies reveal $d_{33}^{MAPbI_3}$ values of ~0.3 pm/V for MAPbI$_3$ deposited on Au and ITO surfaces, with small phase angles fluctuating at length scales smaller than the grain size. In sharp contrast, on samples prepared on epitaxial PZT films, we observe large scale polar domains exhibiting clear, close to 90° PFM phase angles, pointing to …
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The stability of a high-symmetry $P4mm$ polar phase in seventeen short-period ferroelectric perovskite superlattices with polar discontinuity is studied from first principles within the density-functional theory. It is shown that in most superlattices this phase exhibits either the ferroelectric instability or the antiferrodistortive one, or both of them. For each superlattice, the ground-state structure, the structure of possible metastable phases, the spontaneous polarization, and piezoelectric properties are calculated. The properties of superlattices with the polar discontinuity are compar…
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Ferroelectric oxides have attracted much attention due to their wide range of applications, especially in electronic devices such as nonvolatile memories and tunnel junctions. As a result, the monolithic integration of these materials into silicon technology and its nanostructuration to develop alternative cost-effective processes are among the central points in current technology. In this work, we used a chemical route to obtain nanowire thin films of a novel Sr1+δMn8O16 (SMO) hollandite-type manganese oxide on silicon. Scanning transmission electron microscopy combined with crystallographic …
The origins of enhanced piezoelectric coupling along nonpolar crystallographic directions in ferroelectric BaTiO3 are investigated using in situ neutron spectroscopy. It is observed that an electric field applied away from the equilibrium polarization direction causes changes in the phonon spectra that lead to an increase in the interaction between the transverse acoustic and transverse optic branches (TA-TO) near the Brillouin zone center. This provides a direct lattice dynamics mechanism for enhanced electromechanical coupling, and could act as a guide for designing improved piezoelectric ma…
In piezoresponse force microscopy a lateral signal at the domain boundaries is occasionally observed. In recent years, a couple of experiments have been reported and varying explanations for the origin of this lateral signal have been proposed. Additionally, elaborated theoretical modeling for this particular issue has been carried out. Here we present experimental data obtained on different crystallographic cuts of $\rm LiNbO_3$, $\rm BaTiO_3$, and $\rm KTiOPO_4$ single crystals. We could thereby rule out some of the explanations proposed so far, introduce another possible mechanism, and quan…
We present the results of the thermodynamic theory of piezoelectric ferroelectrics and of the phenomenological theory of thermodynamic characteristics of the KH$_{2}$PO$_{4}$ type ferroelectrics. Available experimental data for the dielectric, piezoelectric, and elastic characteristics of the KH$_{2}$PO$_{4}$ type ferroelectrics and NH$_4$H$_{2}$PO$_{4}$ type antiferroelectrics are described using the proposed microscopic theory of these crystals. Using the results of the thermodynamic theory and experimental data we calculate the dielectric, piezoelectric, and elastic characteristics of the K…
Piezoelectric and ferroelectric ceramics with a high Curie temperature (Tc) have attracted a growing attention owning to their applications under severe environments. In this work, phase structure, dielectric, ferroelectric and piezoelectric properties of (0.975-x)BiScO3-xPbTiO3-0.025Pb(Cd1/3Nb2/3)O3 ceramics (x = 0.58-0.64) were studied. A composition-induced structural transformation occurs from rhombohedral phase to tetragonal phase through an intermediate monoclinic phase with the increasing PT concentration. The relationship between structure and electrical properties of the system were d…
Aluminum nitride is piezoelectric and exhibits spontaneous polarization along the $c$-axis, but the polarization cannot be switched by applying an electric field. Adding Sc to AlN enhances the piezoelectric properties, and can make the alloy ferroelectric. We perform a detailed first-principles analysis of spontaneous and piezoelectric polarization. Comparisons between explicit supercell calculations show that the virtual crystal approximation produces accurate results for polarization, but falls short in describing the phase stability of the alloy. We relate the behavior of the piezoelectric …
We report the phase diagram of (Ba1-xCax)(Zr0.1Ti0.9)O3 solid solution. It is found that substitution of smaller Ca ions for Ba ions can slightly increase the cubic-tetragonal(T) para-ferroelectric phase transition temperature and strongly decrease the T-orthorhombic (O) and O-rhombohedral (R) transition. This unique ferroelectric phase evolution is attributed to Ca off-centering effects. More importantly, lowering of the T-O or O-R phase transitions allows us to prepare the piezoelectric ceramics with a strain response as high as S/E~800 pm/V (E=10 kV/cm) over a wide range of compositions wit…
