Ferroelectric liquid crystals (FLCs) couple the direction of their spontaneous electric polarization to the direction of tilt of their optic axis. Consequently, reversal of the electric polarization by an electric field gives rise to an immediate and lasting optical response when an appropriately aligned FLC is observed between crossed polarizers, with one field direction yielding a dark image, and the opposite direction yielding a bright image. Here this peculiar electro-optic response is used to image, with high optical contrast, 180° ferroelectric domains in a crystalline substrate of magnesium-doped lithium niobate. The lithium niobate substrate contains a few domains with upwards electric polarization surrounded by regions with downward electric polarization. In contrast to a reference non-chiral liquid crystal that is unable to show ferroelectric behavior due to its high symmetry, the FLC, which is used as a thin film confined between the lithium niobate substrate and an inert aligning substrate, reveals ferroelectric domains as well as their boundaries, with strong black and white contrast. The results show that FLCs can be used for non-destructive read-out of domains in underlying ferroelectrics, with potential applications in e.g. photonic devices and non-volatile ferroelectric memories.
The interpretation of ferroelectric domain images obtained with piezoresponse force microscopy (PFM) is discussed. The influences of an inherent experimental background on the domain contrast in PFM images (enhancement, nulling, inversion) as well as on the shape and the location of the domain boundaries are described. We present experimental results to evidence our analysis of the influence of the background on the domain contrast in PFM images.
The contrast mechanism for ferroelectric domain imaging via piezoresponse force microscopy (PFM) is investigated. A novel analysis of PFM measurements is presented which takes into account the background caused by the experimental setup. This allows, for the first time, a quantitative, frequency independent analysis of the domain contrast which is in good agreement with the expected values for the piezoelectric deformation of the sample and satisfies the generally required features of PFM imaging.
Piezoresponse force microscopy (PFM) was used to investigate the ferroelectric properties of sol-gel derived LiNbO$_3$ nanoparticles. To determine the degree of ferroelectricity we took large-area images and performed statistical image-analysis. The ferroelectric behavior of single nanoparticles was verified by poling experiments using the PFM tip. Finally we carried out simultaneous measurements of the in-plane and the out-of-plane piezoresponse of the nanoparticles, followed by measurements of the same area after rotation of the sample by 90$^{\circ}$ and 180$^{\circ}$. Such measurements bas…
The contrast mechanism for the visualization of ferroelectric domain boundaries with lateral force microscopy is generally assumed to be caused by mechanical deformation of the sample due to the converse piezoelectric effect. We show, however, that electrostatic interactions between the charged tip and the electric fields arising from the surface polarization charges dominate the contrast mechanism. This explanation is sustained by quantitative analysis of the measured forces as well as by comparative measurements on different materials.
General energy approaches have been applied to study the single-domain polarization reversal induced by the voltage-modulated Atomic Force Microscopy (AFM) in ferroelectric single crystals and thin films. Topographic analysis of energy surfaces in the subspace of domain dimensions is performed, and energy evolutions under an external bias are elucidated. This has let to successfully describe all stages of the AFM switching, including formations of a reversed domain, its growth in a bulk, domain contact instabilities near an electrode, and pure sidewise expansions in a film.
As a consequence of elasticity, mechanical deformations of crystals occur on a length scale comparable to their thickness. This is exemplified by applying a homogeneous electric field to a multi-domain ferroelectric crystal: as one domain is expanding the adjacent ones are contracting, leading to clamping at the domain boundaries. The piezomechanically driven surface corrugation of micron-sized domain patterns in thick crystals using large-area top electrodes is thus drastically suppressed, barely accessible by means of piezoresponse force microscopy.
High-resolution X-ray photoemission electron microscopy (X-PEEM) is a well-established method for imaging ferroelectric domain structures. Here, we expand the scope of application of X-PEEM and demonstrate its capability for imaging and investigating domain walls in ferroelectrics with high-spatial resolution. Using ErMnO3 as test system, we show that ferroelectric domain walls can be visualized based on photo-induced charging effects and local variations in their electronic conductance can be mapped by analyzing the energy distribution of photoelectrons. Our results open the door for non-dest…
Surface Acoustic Wave (SAW) resonances were imaged within a closed domain in the ferroelectric LiTaO$_3$ via scanning Microwave Impedance Microscopy (MIM). The MIM probe is used for both SAW generation and measurement, allowing contact-less measurement within a mesoscopic structure. Measurements taken over a range of microwave frequencies are consistent with a constant acoustic velocity, demonstrating the acoustic nature of the measurement.
In studies using piezoresponse force microscopy, we observe a non-zero lateral piezoresponse at 180$^\circ$ domain walls in out-of-plane polarized, c-axis-oriented tetragonal ferroelectric Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$ epitaxial thin films. We attribute these observations to a shear strain effect linked to the sign change of the $d_{33}$ piezoelectric coefficient through the domain wall, in agreement with theoretical predictions. We show that in monoclinically distorted tetragonal BiFeO$_3$ films, this effect is superimposed on the lateral piezoresponse due to actual in-plane polarization, and…
Reducing the dimensions of ferroelectric materials down to the nanoscale has strong implications on the ferroelectric polarization pattern and on the ability to switch the polarization. As the size of ferroelectric domains shrinks to nanometer scale, the heterogeneity of the polarization pattern becomes increasingly pronounced, enabling a large variety of possible polar textures in nanocrystalline and nanocomposite materials. Critical to the understanding of fundamental physics of such materials and hence their applications in electronic nanodevices, is the ability to investigate their ferroel…
Local domain structures of ferroelectrics have been studied extensively using various modes of scanning probes at the nanoscale, including piezoresponse force microscopy (PFM) and Kelvin probe force microscopy (KPFM), though none of these techniques measure the polarization directly, and the fast formation kinetics of domains and screening charges cannot be captured by these quasi-static measurements. In this study, we used charge gradient microscopy (CGM) to image ferroelectric domains of lithium niobate based on current measured during fast scanning, and applied principal component analysis …
Low-temperature X-ray photoemission electron microscopy (X-PEEM) is used to measure the electric potential at domain walls in improper ferroelectric Er0.99Ca0.01MnO3. By combining X-PEEM with scanning probe microscopy and theory, we develop a model that relates the detected X-PEEM contrast to the emergence of uncompensated bound charges, explaining the image formation based on intrinsic electronic domain-wall properties. In contrast to previously applied low-temperature electrostatic force microscopy (EFM), X-PEEM readily distinguishes between positive and negative bound charges at domain wall…
Understanding the polarization switching mechanisms at play in ferroelectric materials is crucial for their exploitation in electronic devices. The conventional centrosymmetric reference structure-based mechanism which accounts for ferroelectricity in most of the usual displacive ferroelectric materials is too energy-demanding for some newly diagnosed ferroelectric materials such as the Ga2-xFexO3 (0.8 < x < 1.4) compounds. Some alternative theoretical propositions have been made and need experimental confirmation. A dual-scale electron microscopy study is performed on thin films of the Ga0.6F…
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…
We present a full analysis of the contrast mechanisms for the detection of ferroelectric domains on all faces of bulk single crystals using scanning force microscopy exemplified on hexagonally poled lithium niobate. The domain contrast can be attributed to three different mechanisms: i) the thickness change of the sample due to an out-of-plane piezoelectric response (standard piezoresponse force microscopy), ii) the lateral displacement of the sample surface due to an in-plane piezoresponse, and iii) the electrostatic tip-sample interaction at the domain boundaries caused by surface charges on…
Piezoresponse force microscopy (PFM) is a powerful tool for probing nanometer-scale ferroelectric and piezoelectric properties. Hysteretic switching of the phase and amplitude of the PFM response are believed to be the hallmark of ferroelectric and piezoelectric behavior respectively. However, the application of PFM is limited by the fact that similar hysteretic effects may also arise from mechanisms not related to ferroelectricity or piezoelectricity. In this paper we report our studies on regular glass slides that show ferroelectric-like signal without being ferroelectric and frequently used…
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…
The equilibrium sizes of micro- and nano-domains caused by electric field of atomic force microscope tip in ferroelectric semiconductor crystals have been calculated. The domain was considered as a prolate semi-ellipsoid with rather thin domain walls. For the first time we modified the Landauer model allowing for semiconductor properties of the sample and the surface energy of the domain butt. The free carriers inside the crystal lead to the formation of the screening layer around the domain, which partially shields its interior from the depolarization field. We expressed the radius and length…
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…
The interaction of ferroelectric 180 degree domain wall with a strongly inhomogeneous electric field of biased Scanning Probe Microscope tip is analyzed within continuous Landau-Ginzburg-Devonshire theory. Equilibrium shape of the initially flat domain wall boundary bends, attracts or repulses from the probe apex, depending on the sign and value of the applied bias. For large tip-wall separations, the probe-induced domain nucleation is possible. The approximate analytical expressions for the polarization distribution are derived using direct variational method. The expressions provide insight …
Coupling between electrical and mechanical phenomena is a near-universal characteristic of inorganic and biological systems alike, with examples ranging from ferroelectric perovskites to electromotor proteins in cellular membranes. Understanding electromechanical functionality in materials such as ferroelectric nanocrystals, thin films, relaxor ferroelectrics, and biosystems requires probing these properties on the nanometer level of individual grain, domain, or protein fibril. In the last decade, Piezoresponse Force Microscopy (PFM) was established a powerful tool for nanoscale imaging, spect…
In 2014, Charge Gradient Microscopy (CGM) was first reported as a new scanning probe imaging mode, particularly well-suited for the characterisation of ferroelectrics. The implementation of the technique is straightforward; it involves monitoring currents that spontaneously develop between a passive conducting atomic force microscopy tip and Earth, as the tip is scanned across the specimen surface. However, details on the fundamental origin of contrast and what images mean, in terms of associated ferroelectric microstructures, are not yet fully understood. Here, by comparing information from C…
Machine learning has emerged as a powerful tool for the analysis of mesoscopic and atomically resolved images and spectroscopy in electron and scanning probe microscopy, with the applications ranging from feature extraction to information compression and elucidation of relevant order parameters to inversion of imaging data to reconstruct structural models. However, the fundamental limitation of machine learning methods is their correlative nature, leading to extreme susceptibility to confounding factors. Here, we implement the workflow for causal analysis of structural scanning transmission el…
LuFe2O4 is a multiferroic system which exhibits ferroelectricity, charge order, and ferrimagnetic order simultaneously below ~230 K. The ferroelectric domains of LuFe2O4 are imaged with both piezoresponse force microscopy (PFM) and electrostatic force microscopy (EFM), while the magnetic domains are characterized by magnetic force microscopy (MFM). Comparison of PFM and EFM results lead to a conclusion that the ferroelectricity is of electronic origin as opposed to the usual displacive one. Simultaneous characterization of ferroelectric and magnetic domains by EFM and MFM, respectively, on the…
Given that a ferroelectric domain is generally a three dimensional entity, the determination of its area as well as its depth is mandatory for full characterization. Piezoresponse force microscopy (PFM) is known for its ability to map the lateral dimensions of ferroelectric domains with high accuracy. However, no depth profile information has been readily available so far. Here, we have used ferroelectric domains of known depth profile to determine the dependence of the PFM response on the depth of the domain, and thus effectively the depth resolution of PFM detection.
Perceiving nanoscale ferroelectric phenomena from real space is of great importance for elucidating underlying ferroelectric physics. During the past decades, nanoscale ferroelectric characterization has mainly relied on the Piezoresponse Force Microscopy (PFM), however, the fundamental limitations of PFM have made the nanoscale ferroelectric studies encounter significant bottlenecks. In this study, a high-resolution non-contact ferroelectric measurement, named Non-Contact Heterodyne Electrostrain Force Microscopy (NC-HEsFM), has been introduced firstly. It has been unambiguously demonstrated …
The functionality of ferroelastic domain walls in ferroelectric materials is explored in real-time via the in-situ implementation of computer vision algorithms in scanning probe microscopy (SPM) experiment. The robust deep convolutional neural network (DCNN) is implemented based on a deep residual learning framework (Res) and holistically-nested edge detection (Hed), and ensembled to minimize the out-of-distribution drift effects. The DCNN is implemented for real-time operations on SPM, converting the data stream into the semantically segmented image of domain walls and the corresponding uncer…
Electromechanical hysteresis loop formation in piezoresponse force microscopy of thin ferroelectric films is studied with special emphasis on the effects of tip size and film thickness, as well as dependence on the tip voltage frequency. Here, we use a combination of Landau-Ginzburg-Devonshire (LGD) theory for the description of the local polarization reversal with decoupling approximation for the calculation of the local piezoresponse loops shape, coercive voltages and amplitude. LGD approach enables addressing both thermodynamics and kinetics of hysteresis loop formation. In contrast to the …
Cross-coupling of ordering parameters in multiferroic materials by multiple external stimuli other than electric field and magnetic field is highly desirable from both practical application and fundamental study points of view. Recently, mechanical force has attracted great attention in switching of ferroic ordering parameters via electro-elastic coupling in ferroelectric materials. In this work, mechanical force induced polarization and magnetization switching were investigated in a polycrystalline multiferroic Bi0.9La0.1FeO3 thin film using a scanning probe microscopy system. The piezorespon…
Ferroelectrics are technologically important, with wide application in micromechanical systems, nonlinear optics, and information storage. Recent discoveries of exotic polarisation textures in these materials, which can strongly influence their properties, have brought to the forefront questions about the nature of their domain walls -- long believed to be primarily Ising, with locally null polarisation. Here, combining three complementary techniques -- second harmonic generation microscopy, piezoresponse force microscopy, and transmission electron microscopy - to cover all the relevant length…
Hafnium oxide (HfO2)-based ferroelectrics offer remarkable promise for memory and logic devices in view of their compatibility with traditional silicon CMOS technology, high switchable polarization, good endurance and thickness scalability. These factors have led to steep rise in research on this class of materials over the past number of years. At the same time, only a few reports on the direct sensing of nanoscale ferroelectric properties exist, with many questions remaining regarding the emergence of ferroelectricity in these materials. While piezoresponse force microscopy (PFM) is ideally …
Electric Scanning Probe Microscopies are used to characterize the surface behavior of ferroelectric materials. The effects of local charge density on the chemistry and physics of ferroelectric surfaces are investigated. The kinetics and thermodynamics parameters of adsorption are assessed by variable temperature Scanning Surface Potential Microscopy. Contrast formation mechanism of Piezoresponse Force Microscopy (PFM) is analyzed in detail, and the contributions of electroelastic constants of the material to response amplitude are determined. The effect of experimental conditions including ind…
The local hysteresis loop obtained by switching spectroscopy piezoresponse force microscopy (SS-PFM) is usually regarded as a typical signature of ferroelectric switching. However, such hysteresis loops were also observed in a broad variety of non-ferroelectric materials in the past several years, which casts doubts on the viewpoint that the local hysteresis loops in SS-PFM originate from ferroelectricity. Therefore, it is crucial to explore the mechanism of local hysteresis loops obtained in SS-PFM testing. Here we proposed that non-ferroelectric materials can also exhibit amplitude butterfly…
In this Article, we report on the observation of ferroelectric domain pattern in the whole volume of the ferroelectric barium titanate single crystal by means of the digital holographic microscopy (DHM). Our particular implementation of DHM is based on the Mach-Zehnder interferometer and the numerical processing of data employs the angular spectrum method. A modification of the DHM technique, which allows a fast and accurate determination of the domain walls, i.e. narrow regions separating the antiparallel domains, is presented. Accuracy and sensitivity of the method are discussed. Using this …
We report the nanoscale electrical imaging results in hexagonal $Lu_{0.6}Sc_{0.4}FeO_3$ single crystals using conductive atomic force microscopy (C-AFM) and scanning microwave impedance microscopy (MIM). While the dc and ac response of the ferroelectric domains can be explained by the surface band bending, the drastic enhancement of domain wall (DW) ac conductivity is clearly dominated by the dielectric loss due to DW vibration rather than mobile-carrier conduction. Our work provides a unified physical picture to describe the local conductivity of ferroelectric domains and domain walls, which …
Freestanding BaTiO3 nanodots exhibit domain structures characterized by distinct quadrants of ferroelastic 90° domains in transmission electron microscopy (TEM) observations. These differ significantly from flux-closure domain patterns in the same systems imaged by piezoresponse force microscopy. Based upon a series of phase field simulations of BaTiO3 nanodots, we suggest that the TEM patterns result from a radial electric field arising from electron beam charging of the nanodot. For sufficiently large charging, this converts flux-closure domain patterns to quadrant patterns with radial net p…
We investigate the electromechanical interactions in individual P(VDF-TrFE) nanowires in response to localized electrical poling via a conducting atomic force microscope tip. Spatially resolved measurements of piezoelectric coefficients and elastic moduli before and after poling reveal a striking dependence on the polarity of the poling field, notably absent in thin films of the same composition. These observations are attributed to the unclamped nature of the nanowires and the inherent asymmetry in their chemical and electrical interactions with the tip and underlying substrate. Our findings …
The application of PhotoEmission Electron Microscopy (PEEM) and Low Energy Electron Microscopy (LEEM) techniques to the study of the electronic and chemical structure of ferroelectric materials is reviewed. Electron optics in both techniques gives spatial resolution of a few tens of nanometres. PEEM images photoelectrons whereas LEEM images reflected and elastically backscattered electrons. Both PEEM and LEEM can be used in direct and reciprocal space imaging. Together, they provide access to surface charge, work function, topography, chemical mapping, surface crystallinity and band structure.…
We present a near-field optical technique for second harmonic imaging using bare tapered optical fiber tip illuminated with femtosecond laser pulses. Enhancement of electric field at the tip of the fiber results in enhanced second harmonic generation (SHG) from the sample region near the tip. This SH emission is collected by the same tapered fiber. Spatial distribution of SHG from thin ferroelectric Pb(Zr_xTi_1-x)O_3 films and model metal-ferroelectric devices has been studied. Spatial resolution on the order of 80 nm has been achieved. This is the first time diffraction limit is surpassed in …
Emergent functionalities of structural and topological defects in ferroelectric materials underpin an extremely broad spectrum of applications ranging from domain wall electronics to high dielectric and electromechanical responses. Many of these have been discovered and quantified via local scanning probe microscopy methods. However, the search for these functionalities has until now been based by either trial and error or using auxiliary information such as topography or domain wall structure to identify potential objects of interest based on the intuition of operator or preexisting hypothese…
It is thought that the proposed new family of multi-functional materials namely the ferroelectric thermoelectrics may exhibit enhanced functionalities due to the coupling of the thermoelectric parameters with ferroelectric polarization in solids. Therefore, the ferroelectric thermoelectrics are expected to be of immense technological and fundamental significance. As a first step towards this direction, it is most important to identify the existing high performance thermoelectric materials exhibiting ferroelectricity. Herein, through the direct measurement of local polarization switching we sho…
By combining angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM), piezoresponse force microscopy (PFM) and first-principles calculations, we have studied the low-energy band structure, atomic structure and charge polarization on the surface of a topological semimetal candidate TaNiTe5. Dirac-like surface states were observed on the (010) surface by ARPES, consistent with the first-principles calculations. On the other hand, PFM reveals a switchable ferroelectric-like polarization on the same surface. We propose that the noncentrosymmetric surface reconstructi…
Stable and switchable polarization of ferroelectric materials opens a possibility to electrically control their functional behavior. A particularly promising approach is to employ ferroelectric tunnel junctions where the polarization reversal in a ferroelectric barrier changes the tunneling current across the junction. Here, we demonstrate the reproducible tunneling electroresistance effect using a combination of Piezoresponse Force Microscopy (PFM) and Conducting Atomic Force Microscopy (C-AFM) techniques on nanometer-thick epitaxial BaTiO3 single crystal thin films on SrRuO3 bottom electrode…
To date, high-resolution electron microscopy has largely relied on using the phase of the exit wave function at the exit surface to form a high-resolution electron microscopic image. We have for the first time used chromatic aberration correction to implement a new imaging mode to achieve amplitude contrast imaging in high-resolution electron microscopy, allowing us to obtain directly interpretable high-resolution electron microscopic images with discrimination between light and heavy atomic columns. Using this imaging approach, we have successfully visualized the atomic structure in a BaTiO3/…
The extrinsic size effect in Piezoresponse Force Microscopy of ferroelectric and piezoelectric thin films on non-polar dielectric substrate is analyzed. Analytical expressions for effective piezoresponse, object transfer function components, and Rayleigh two-point resolution are obtained. These results can be broadly applied for effective piezoelectric response calculations in thin piezoelectric and ferroelectric films as well as surface polar layers e.g. in organic materials and bio-polymers. In particular, the effective piezoresponse strongly decreases with film thickness whereas the sharpne…
Piezoresponse Force Microscopy contrast in transversally isotropic material corresponding to the case of c+ - c- domains in tetragonal ferroelectrics is analyzed using Green's function theory by Felten et al. [J. Appl. Phys. 96, 563 (2004)]. A simplified expression for PFM signal as a linear combination of relevant piezoelectric constant are obtained. This analysis is extended to piezoelectric material of arbitrary symmetry with weak elastic and dielectric anisotropies. This result provides a framework for interpretation of PFM signals for systems with unknown or poorly known local elastic and…
Breakdown and polarization contrasts in ferroelectric devices observed by operando laser-based photoemission electron microscopy with the AC/DC electrical characterization system
Piezoresponse force microscopy (PFM) has been extensively utilized as a versatile and an indispensable tool to understand and analyze nanoscale ferro- /piezoelectric properties by detecting the local electromechanical response on a sample surface. However, it has been discovered that the electromechanical response not only originates from piezoelectricity but also from other factors such as the electrostatic effect. In this study, we explore the dependence of off-field PFM hysteresis loops on the surface-potential-induced electrostatic effect in a prototypical ferroelectric thin film by applyi…
Correlated domain and crystallographic orientation mapping in uniaxial ferroelectric polycrystals by interferometric vector piezoresponse force microscopy
NTNU Norwegian University of Science and Technology（挪威科技大学）；Asylum Research an Oxford Instruments Company（阿苏姆研究（牛津仪器旗下公司））；University of Duisburg-Essen（杜伊斯堡-埃森大学）；Research Center Future Energy Materials and Systems, Research Alliance Ruhr（鲁尔研究联盟未来能源材料与系统研究中心）
