We report on nanoscale strain gradients in ferroelectric HoMnO3 epitaxial thin films, resulting in a giant flexoelectric effect. Using grazing-incidence in-plane x-ray diffraction, we measured strain gradients in the films, which were 6 or 7 orders of magnitude larger than typical values reported for bulk oxides. The combination of transmission electron microscopy, electrical measurements, and electrostatic calculations showed that flexoelectricity provides a means of tuning the physical properties of ferroelectric epitaxial thin films, such as domain configurations and hysteresis curves.

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Giant Flexoelectric Effect in Ferroelectric Epitaxial Thin Films

Flexoelectricity in solids: Progress, challenges, and perspectives

Epitaxial c-axis oriented BiFeO3 (BFO) thin films were deposited on (001) Nb-doped SrTiO3 (Nb-STO) substrates by pulsed laser deposition. Introducing Bi vacancies caused the BFO thin film to evolve to a p-type semiconductor and formed a p-n heterojunction with an n-type semiconductor Nb-STO. The current density versus voltage (J-V) and capacitance versus voltage (C-V) characteristics of the heterojunction were investigated. A typical rectifying J-V effect was observed with a large rectifying ratio of 5×104. Reverse C-V characteristics exhibited a linear 1∕C2 versus V plot, from which a built-in potential of 0.6V was deduced. The results show a potential application of BFO/Nb-STO heterojunction for oxide electronics.

http://absimage.aps.org/image/MAR08/MWS_MAR08-2007-000520.pdf

Rectifying Current-Voltage Characteristics of BiFeO$_{3}$/Nb-doped SrTiO$_{3}$ Heterojunction

Flexoelectricity refers to the mechanical-electro coupling between strain gradient and electric polarization, and conversely, the electro-mechanical coupling between electric field gradient and mechanical stress. This unique effect shows a promising size effect which is usually large as the material dimension is shrunk down. Moreover, it could break the limitation of centrosymmetry, and has been found in numerous kinds of materials which cover insulators, liquid crystals, biological materials, and semiconductors. In this review, we will give a brief report about the recent discoveries in flexoelectricity, focusing on the flexoelectric materials and their applications. The theoretical developments in this field are also addressed. In the end, the perspective of flexoelectricity and some open questions which still remain unsolved are commented upon.

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Flexoelectric materials and their related applications: A focused review

DOI: 10.1002/aelm.201900949 boundaries (MPB), where multiple ferroelectric polar structures coexist,[5,6] as exemplified by their complicated composition-temperature phase diagrams.[7–10] Coexisting fragile polar states can be easily altered by external stress or electric field, thereby resulting in a large piezoelectricity.[5,6,11–15] Among them, lead zirconium titanate (PZT) based ceramics with piezoelectric coefficient d33 = 300–700 pC N−1 (Figure 1) are market-dominating, and widely used in sensors, actuators, and other electronic devices due to their excellence properties.[16,17] In view of the environmental regulations against the use of toxic lead, tremendous efforts have been performed worldwide in search of alternative lead-free piezoelectric materials.[13,18–25] A milestone in the development of lead-free piezoelectric materials was the appearance of a large piezoelectric constant d33 of 416 pC N−1 in (K0.5Na0.5)NbO3 (KNN)-based textured ceramics via a doping-driven MPB approach using templated-graingrowth technique by Saito et al.,[18] which trigged an explosion of world-wide research activities.[5,13,15–17,19,20,23,26–29] In order to further enhance the piezoelectricity of lead-free materials, Liu et al. reported a high value of d33 ≈ 620 pC N−1 in Ba(Zr0.2Ti0.8) O3-x(Ba0.7Ca0.3)TiO3 ceramic system by constructing MPB from a tricritical triple point of a cubic nonpolar, ferroelectric rhombohedral, and tetragonal phases.[13] The development in piezoelectric coefficient enhancement at room temperature is summarized in Figure 1, also including a comparison with several typical PZT ceramics. With regards to actuator applications, the electromechanical properties have also been studied in lead-free piezoelectric materials. In 2007, Zhang et al. reported a giant electric-field induced stain in ternary (Na0.5Bi0.5)TiO3BaTiO3-(K0.5Na0.5)NbO3 (NBT-BT-KNN) ceramics,[22] consequently leading to a rapid surge in the research of macrostrain enhancement and microstructure understanding in bismuth– alkali-based systems.[25,30–34] The origin of the giant strain has been determined to be a phase transition from unclear initial state into a ferroelectric tetragonal phase (P4mm),[32] but the ground state remains controversial concerning whether it is a nonergodic relaxor with an average cubic symmetry according to the dielectric dispersion or antiferroelectric state with extremely small distortion based on its double-hysteresis polarization-field loop.[9,16,30] Either way, long range order was perlocated with rhombohedral R3c and tetragonal P4bm symmetries, as evidenced by high-resolution transmission electron microscopy.[5,9,15] Since industry-standard piezoelectric materials, such as lead zirconium titanate ceramics, contain toxic lead, a rapid surge in research on lead-free piezoelectric materials is occurring due to concerns over environmental safety and human health. A ternary lead-free (Na0.5Bi0.5)TiO3-BaTiO3-(K0.5Na0.5) NbO3 single crystal with a large field induced strain of ≈0.9% and a giant piezoelectric coefficient d33 of 840 pC N−1 at room temperature is reported. It is revealed that the electric-field-induced phase transition and phase boundary between energetically comparable polar states (i.e., R3c and P4mm) play an important role in achieving the ultrahigh piezoelectricity. Transmission electron microscopy and scan probe microscopy are employed to verify the weak-polar ferroelectric R3c and P4bm structure in the ground state. These unprecedentedly high piezoelectric properties make lead-free ternary single crystals a leading candidate for piezoelectric-based device applications, especially toward the era of smart homes and implantable medical devices.

Large Piezoelectricity in Ternary Lead‐Free Single Crystals

Lead-free flexoelectric piezoelectric metamaterials are created by applying an asymmetric chemical reduction to Na1/2 Bi1/2 TiO3 -BaTiO3 ceramics. The reduction induces two gradient-generating mechanisms, curvature structure and chemical inhomogeneity, and enhances the flexoelectric effect. The ceramics behave like piezoelectric materials, exhibiting an enormous and high-temperature stable apparent piezoelectric response, outperforming existing lead-oxide-based piezoelectrics.

Lead‐Free Metamaterials with Enormous Apparent Piezoelectric Response

Nonpoled ferroelectric ceramics are thought to be nonpolar because of randomly oriented grains and the formation of ferroelectric domains in the grains. Here, we discover the surfaces ($\ensuremath{\sim}\mathrm{several}\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ thick) of ferroelectric ceramics are spontaneously polarized. Because the orientations of ferroelectric polarization of the opposite surfaces are antiparallel, ferroelectric ceramics are nonpolar as a whole. However, the ceramics exhibit a strong flexoelectriclike electromechanical response from the piezoelectric response of the polarized surfaces if they are asymmetrically strained (such as bending). Our results reveal a major mechanism to resolve one important but largely unresolved issue: the experimentally measured flexoelectric effect is typically orders of magnitude larger than the theoretically predicted value in ferroelectrics.

Large Flexoelectriclike Response from the Spontaneously Polarized Surfaces in Ferroelectric Ceramics.

The piezoelectric properties of lead-free piezoelectric ceramics are normally lower than those of lead oxide-based ceramics. In order to enhance the electromechanical performance of lead-free piezoelectric ceramics, an asymmetric chemical reduction was applied to sodium bismuth titanate (NBT)-based piezoelectric ceramics. Similar to the lead-containing ceramics, a curvature structure can be induced by the reduction in the NBT-based materials and lead-free RAINBOW (reduced and internally biased oxide wafer) devices can be fabricated. A large displacement (approximately 17 μm) under an electric field of 900 V/mm and high piezoelectric sensitivity (>4000 pC/N) under a stress, which are related to the reduction induced curvature, can be measured in the NBT-based devices. The apparent piezoelectric response of the lead-free RAINBOW devices is comparable to that of Pb(Zr,Ti)O 3 -based devices. We proposed that apart from the piezoelectric properties, flexoelectric effect could also be a contributing mechanism for the observed apparent piezoelectric response in RAINBOW devices.

Sodium bismuth titanate-based lead-free RAINBOW piezoelectric devices

The thermal energy is normally converted into electrical power by the thermoelectric effect or pyroelectricity of materials, and a variation of temperature with time or space is required during the conversion. Here, we demonstrate that the thermal–electrical conversion can be realized in a uniform temperature environment by exploiting the flexoelectric effect of ferroelectrics. After a chemical inhomogeneity is introduced to Na0.5Bi0.5TiO3-based ferroelectric ceramics via an asymmetrical reduction, the ceramics can function as thermal energy harvesters with a large power density of 0.18 mW/cm3. The large thermal–electrical response is attributed to the coupling of a significantly enhanced flexoelectric response, which causes a built-in electric field in the materials and increased conductivity after the reduction. The reduction-induced built-in field has a significant effect on the electrical conduction, and the reduced ceramics exhibit a rectifying conduction behavior even at a high temperature of 350 °C.

Wanfeng Zhou

Papers

Lead‐Free Metamaterials with Enormous Apparent Piezoelectric Response

Large Flexoelectriclike Response from the Spontaneously Polarized Surfaces in Ferroelectric Ceramics.

Sodium bismuth titanate-based lead-free RAINBOW piezoelectric devices

Large Thermal–Electrical Response and Rectifying Conduction Behavior in Asymmetrically Reduced Ferroelectric Ceramics

The surface mechanism for the flexoelectric response in sodium bismuth titanate-based ferroelectric ceramics