Abstract
Thickness effect and mechanical tuning behavior such as strain engineering in thin-film ferroelectrics have been extensively studied and widely used to tailor the ferroelectric properties. However, this is never the case in freestanding single crystals, and conclusions from thin films cannot be duplicated because of the differences in the nature and boundary conditions of the thin-film and freestanding single-crystal ferroelectrics. Here, using in situ biasing transmission electron microscopy, we studied the thickness-dependent domain switching behavior and predicted the trend of ferroelectricity in nanoscale materials induced by surface strain. We discovered that sample thickness plays a critical role in tailoring the domain switching behavior and ferroelectric properties of single-crystal ferroelectrics, arising from the huge surface strain and the resulting surface reconstruction. Our results provide important insights in tuning polarization/domain of single-crystal ferroelectric via sample thickness engineering.
INTRODUCTION
The successful fabrication of relaxor–PbTiO3 (PT)–based ferroelectric single crystals in the 1980s (1, 2), such as Pb(Zn1/3Nb2/3)O3-PbTiO3 (PZN-PT) and Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT), is considered an important milestone in the piezoelectric research field. These crystals have ultrahigh piezoelectric coefficients d33 of >1500pC/N, which are far superior to those of conventional ferroelectric ceramics [e.g., Pb(Zr, Ti)O3] (3). This has been the driving force for emerging applications of high-performance piezoelectric sensors and transducers (4–11), where the high piezoelectric and electromechanical properties are demanded. The high piezoelectric properties of relaxor-PT single crystals can be successfully explained by the engineered domain configurations (12) and the existence of collinear polar nanoregions that facilitate macroscopic polarization rotation (13). On the basis of these concepts, extremely high d33 of ~3400 to 4100 pC/N has been achieved in Sm3+-doped PMN-PT crystals (14). In addition to the piezoelectric properties, ferroelectric domain switching behavior under electric field is also important in ferroelectric materials, which has been at the center stage and extensively studied (15, 16).
Many approaches have been proposed to tailor the ferroelectric domain switching behavior, where the application of external stress/strain confinement was confirmed to be an effective way to facilitate the domain switching and thus modify the ferroelectricity in thin films (17, 18). Regardless of the improvement in ferroelectricity, the way to provide external strain field will lead to an extra energy consumption that is not practically desirable. On the contrary, intrinsic strain manipulation is found to be an ideal solution for tailoring the ferroelectricity of thin-film materials by changing their thickness (structural tuning) (19, 20), where the interfacial constraint, induced by the lattice mismatch or thermal expansion difference between a film and its substrate, is expected to modify the structural parameters including lattice parameters and the strain, thus substantially altering the ferroelectricity (21). It was observed that ferroelectricity still exists in 1.5 unit cell of thin films due to the help of the substrate/film interface to persist the polarization order in the thin-film ferroelectric (19). The film/substrate interface clamping energy is so large that even a small change in film thickness can markedly alter the properties. However, this is never the case in freestanding single crystals because of the lack of a strained interface. For a long time, a freestanding single crystal is expected to relax in all directions, which is insensitive to thickness.
With the fast growth of internet of things, millions of micro/nanoelectromechanical systems (MEMS/NEMS) are in demand. In this scenario, the thin-film ferroelectric has its own advantages because of its excellent ferroelectric behavior, controllable film thickness, and the possibility that the ferroelectricity can be tuned by film thickness and substrate. Single-crystal ferroelectrics, however, have shown much better fatigue behavior because of the stand-free condition and much improved crystallinity (a thin film crystallizes at about 600° to 700°C, while a single crystal is grown directly from melt at above 1280°C) compared with thin films (14, 22). Furthermore, single-crystal ferroelectrics can be easily integrated on silicon substrate on modern devices by lithography methods (23) without the clamping effect from the substrate, which is advantageous for memory device applications. However, it is extremely difficult to measure or tune the ferroelectricity on the nanometer scale for single crystals. Nevertheless, the size-dependent phenomena and relevant ferroelectric domain switching dynamics have not been investigated, which is critical for designing ferroelectric NEMS/MEMS and nonvolatile ferroelectric memory devices. Therefore, it is desired to explore the impact of sample thickness on ferroelectricity and the underlying mechanism controlling the properties in nanoscale single-crystal ferroelectrics.
Ferroelectric surfaces that have a broken symmetry layer with thickness down to the nanometer size affect the nearby structure substantially (24). Recent studies suggested that the polarization of the surface of ferroelectric materials was different than that underneath, forming a reconstructed surface layer that could alter the physical and chemical properties (25) of the materials. The bound charges and lattice distortion from the reconstructive surface could dramatically affect internal polarization rotation (5, 17). Thus, the combination of the surface energy (26), domain wall energy (27, 28), structural defects (29, 30), and/or surface chemical variation (31) has great potential to tailor the ferroelectricity, especially when a material has a large specific surface (17). The ferroelectric properties of a nanometer-scale single-crystal ferroelectric can therefore be affected by such internal factor where the reconstructed surface layer becomes more important, thus greatly affecting the rotation and/or switching of polarization. Thanks to the development of modern in situ electron microscopy, the unmeasurable piezoelectric responses in nanoscale samples that have large surface volume ratios can now be captured through imaging the dynamic polarization rotation processes (32–34). With the help of the state-of-art aberration-corrected (scanning) transmission electron microscopy [(S)TEM] that provides information on atomic displacements in the sample surface region, it is now possible to explore the in situ polarization rotation behavior.
Here, we used in situ biasing TEM and aberration-corrected STEM to study the thickness dependence of polarization rotation behavior in Pb(Mg1/3Nb2/3)O3-38%PbTiO3 (PMN-38%PT) single crystals with submicrometer to nanoscale thicknesses. We discovered that the domain switching behavior is substantially affected by the sample thickness. There is a reconstructed randomly polarized surface layer with a thickness of ~30 atomic columns (~4.5 nm), which produces a local strain field that prohibits domain switching/polarization rotation across domain walls. This effect is greatly weakened with decreasing the surface volume ratio, revealing that the ferroelectricity can be substantially tailored by varying the sample thickness. These results open a new door for structurally tuning the ferroelectricity in single-crystalline ferroelectrics.
RESULTS
Figure 1A presents the schematic setup of the in situ biasing experiments of electron transparent PMN-38%PT samples to reveal the sample thickness effect on the ferroelectric domain switching at the nanoscale. The crystallographic orientation of the samples is also shown in Fig. 1A: [100] was parallel to the sample width. [010] was opposite to the electron beam direction and along the thickness direction. [001] was along the sample length and parallel to the biasing direction. The three samples used in this study were made from a large single crystal and marked with 1, 2, and 3 in Fig. 1A, with the same dimension of 20 μm by 2 μm by 1 μm (length by width by thickness). They are fixed on a copper platform using platinum deposition. A thin “window” was prepared in the middle of each of the dumbbell-shaped sample with a dimension of length of 3 μm and width of 2 μm and varying thickness of 170 nm (sample 1), 50 nm (sample 2), and 50 nm (sample 3), ensuring that the sample thickness was the only variable in the experiments. More samples with different thicknesses have also been examined. The results of the samples with thicknesses of 120 nm (sample S1) are given in section S8. A sample with thickness of 70 nm in the center and 100 nm in the outer area (sample S3) is also given in section S9. In situ electrical loading was applied by a conductive probe in TEM. The copper platform and the conductive probe served as the two electrodes. A thin layer of platinum was deposited at the front end of each sample to ensure uniform electrical loading through each sample. It is confirmed from the experiment presented in section S10 that platinum electric contact does not affect domain switching dynamic. Lamellar-like 90° ferroelastic domains (polarization directions are indicated by colored arrows) were observed in all three samples, in which the polarization was determined using electron diffraction and atomic-resolution high-angle annular dark-field (HAADF) imaging (details of the polarization determination are available in sections S1 to S4). Throughout the paper, tetragonal domains with polarization along the positive and negative [100], [010], and [001] axes are referred to as
(A) Schematic diagram of the experimental setup. Samples marked “1,” “2,” and “3” were of thicknesses of 170, 50, and 50 nm, respectively. A dark-field TEM image of the three samples represents their initial domain configurations. Head-to-tail tetragonal domains with their polarization directions are marked using colored vectors. (B) A STEM-HAADF image showing a typical 90° ferroelastic domain. Scale bar, 2 nm. (C) STEM-HAADF image overlaid with strain color map (strain tensor εxx, the magnitude ranges from −1 to 1%) determined by geometric phase analysis. The εxx component represents the field strains for in-plane direction. Scale bar, 2 nm. (D) A series of images showing the evolution of ferroelectric/ferroelastic domains in the thick sample (sample 1) with increasing bias and after the bias was withdrawn. Colored arrows represent local polarization directions. The switched domain areas are marked by brown/yellow colors, while the newly formed domain boundaries are marked by dashed lines. Diffraction patterns were taken for sample 1 at 0 and +10 V to confirm the domain orientation (see section S2 for detailed information). Scale bar, 500 nm. (E) Schematic diagrams of the domain evolution behavior in (D). The domain evolution exhibited the crossing mode. (F) A series of images showing the evolution of ferroelectric/ferroelastic domain switching behavior in a thin sample (sample 2) with increasing bias and after the bias was withdrawn. The switched domain areas are marked by yellow/purple colors, while the newly formed domain boundaries are marked by dashed lines. The domain switching directions are marked by dashed arrows in different colors. Scale bar, 500 nm. (G) Schematic drawing of the domain evolution behavior in (F). The domain evolution exhibits the directional mode.
Both samples 1 and 2 have
Compared with sample 1 with a large thickness, sample 2 with a much thinner thickness shows a completely different domain evolution process. Four types of domains were observed and found joining into a quad point. With increasing electric bias,
The crossing mode and the directional mode in samples 1 and 2, respectively, illuminate how polarization rotation or domain switching responds to the electric field on different thickness scales. Note that domain width in the sample does not affect the domain switching dynamic, as shown in section S8. The sample with gradient thickness of 70 nm in the center and 100 nm in the outer area (section S9) shows coexisting directional and crossing modes in the same sample. No other mode was found in thickness between 50 and 170 nm. The result of sample S3 in section S9 reveals there is a critical thickness that the polarization rotation mode switches from the crossing mode to directional mode. The crossing mode is dominated with the thickness above the critical value, while the directional mode prevails with the thickness below the critical value. The ferroelectricity, including coercive field, remanent polarization, and piezoelectric coefficients, is closely related to the polarization rotation. For example, the energy required for aligning all domains is notably higher in sample 2, considering that +7-V bias induced a single domain in sample 1 with large thickness, while only part of the domain is switched in sample 2 with thin thickness. The coercive field in sample 2 is higher than that in sample 1, considering that the polarization switching is slower and delayed in sample 2 under the same conditions.
It is concluded from the above observation that the 90° ferroelastic domain walls behave as strong barriers for polarization rotation in thin samples. Nevertheless, the tip of domain walls with a unique structural feature (35) leads to different domain switching behaviors under electrical bias. Therefore, it is desired to understand the role of the tip of a domain wall in thin samples. The tip of a domain is unstable (36), where charges accumulate at the tip of a domain, making it easy to initiate domain switching (37). Figure 2 shows snapshot TEM images of an electric biasing process of sample 3, which had the same thickness as sample 2, while having a
(A) A series of images (extracted from movie S3) showing the switching behavior of ferroelectric/ferroelastic domains in a thin sample. The switched domain areas are marked by green/brown colors, while the newly formed domain boundaries are marked by dashed lines. High-resolution HAADF-STEM images were taken for sample 3 before and after biasing to confirm the domain orientation (see section S4 and Materials and Methods for details). Scale bar, 500 nm. (B) Schematic drawing of the domain evolution behavior in (A). Domain evolution exhibits a mixture of the crossing and directional modes due to the existence of domain walls and domain wall tips. (C) A STEM-ABF image showing a domain tip area (scale bar, 20 nm). (D and E) Two STEM-HAADF images overlaid with strain color map (strain tensor εxx) showing the strain areas around the domain tip. Scale bars, 2 nm.
Figure 2C shows a STEM annular bright-field (ABF) image capturing the geometry of the domain tip. Similar to Fig. 1C, large local strain fields existed on both sides of the domain, as shown in Fig. 2D. Of particular importance is that no strain field was found from the area nearby the domain tip, as shown in Fig. 2E, in which less energy is required to trigger domain switching, suggesting the easier domain switching from the domain tip.
DISCUSSION
To understand the thickness effect on domain switching, atomic-resolution HAADF was used to study the microstructure of the sample surface and beneath the surface. A rich variety of structures and properties were found at the surface of ferroelectric materials (38, 39), which are different from those beneath the surface, especially in thin-film ferroelectrics (25). This is because of the strong lattice mismatch in the film/substrate interface that constrains the depolarization field and therefore controls the polarization configuration on the surface. Although such a lattice constraint caused by a lattice-mismatched interface is not available in single-crystalline ferroelectric materials, the defect and charge accumulation in the amorphous/sample interface can largely affect the surface structure, thus inducing local lattice distortion and surface reconstruction. Figure 3A shows an atomic-resolution HAADF image at the edge of a sample, where it can be observed that a surface region with ~30 atomic layers had random polarization. An enlarged interfacial region between the aligned polarization region and the randomly polarized region is shown on the right of Fig. 3A. A large amount of oxygen vacancies are expected to form on the amorphous/sample interface because the asymmetric bonding will lower the formation energy of oxygen vacancies (25). These positively charged defects would migrate to the lattice beneath the surface, thus affecting the depolarization field up to ~30 atomic layers.
(A) A high-resolution STEM-HAADF image showing that a randomly polarized region with a thickness of ~30 atomic layers existed in the sample surface layer. The interfacial region of random/aligned polarization is enlarged on the right. (B) A high-resolution STEM-ABF image showing lattice distortion in the sample surface region. The original tetragonal lattice was distorted into an irregular quadrilateral. (C) A STEM-HAADF image overlaid with a strain color map (strain tensor εxx) showing a huge strain field in the ferroelectric surface layer. (D) Schematic drawing showing the effect of strain field on a thick and thin sample. Strain fields (marked with red color) exist in the random/aligned polarization interface and the corner region where ferroelastic domain walls interact with the sample surface. It is obvious that the thick sample is affected less by the surface strain field.
The reconstructed surface of a single-crystal sample is also reflected by its huge lattice distortion. In perfect crystalline PMN-38%PT structures, the four neighboring Mg/Nb/Ti atoms form a perfect square (nonpolarized) or a rectangle (polarized) lattice (17). However, the atomic-resolution ABF image of a sample surface area in Fig. 3B shows a distorted irregular quadrilateral lattice. Because of the near-surface lattice distortion, a giant local strain region exists in the random polarized region on the proximity of the aligned polarization region. Geometric phase analysis exhibits a huge local strain (~10%) in the random polarized region (Fig. 3C), which is one order of magnitude higher than that measured at 90° ferroelastic domain boundaries (Fig. 1C), revealing the existence of high local strain field area near the ferroelectric surface.
It is well known that 90° ferroelastic domain walls are stressed because of the slight lattice mismatch at the walls between the two neighboring 90° ferroelastic domains. Oxygen vacancies and other defects prefer to accumulate at these domain walls (40, 41). Positive charges exist at domain wall regions near the sample surfaces and internal high-strain domain walls, effectively expanding the local lattice because of the increased Coulomb repulsion between cations. Therefore, an irregular strain region formed at the corner of 90° ferroelastic domain walls and random/aligned polarization interface, as shown in Fig. 3D. Thus, the strained regions in a thin sample will strengthen the pinning of domain walls, substantially restrict the domain wall motion, and slow the domain switching process. The strong strain pinning field between the surface/domain wall was also confirmed by the residual contrast of the domain wall even after the formation of a single domain under the electric field, as shown in Fig. 1D. The strained interface strongly prohibited the complete switching of domains near the interface, leading to a small amount of residual polarization even under strong electrical loading. With increasing the sample thickness, the domain switching process is less affected by the surface/corner strained areas, as it requires less energy for polarization rotation inside the sample. Statistical measurement (details in section S6) showed that the thickness of the reconstructed layer remained almost the same for samples with different thicknesses, suggesting that the ratio of the thicknesses of the reconstructed layer and the whole sample was the major reason that determines the domain switching dynamics.
Figure 4A illustrates the schematics of the domain reorganization dynamic for both the crossing mode and the directional mode. Two schematic diagrams with a
(A) Schematic illustration of the difference between the crossing mode and directional mode. The 90° and 180° domain walls are marked with orange solid ellipse and dashed ellipse, respectively. (B and C) Phase-field simulations of a thick sample (strain free) and a thin sample (strained). Domain merging into a single domain is found in the strain-free (thick) sample, while domain reversal (switching) along the domain wall direction occurs in the strained (thin) sample.
It is understandable that a stand-alone cuboid sample with six surfaces is constrained by the strain field. In an extreme scenario, a thick sample and a thin sample can be considered as a stress-free and a constrained sample, respectively, because of the change of the volume fraction of the strained area to the entire sample. To better understand the observed domain reorganization dynamic processes, phase-field simulations (42, 43) were used to simulate the domain switching dynamics in stress-free and constrained conditions for tetragonal relaxor-PT crystals, as given in Fig. 4 (B and C, respectively). The 90° domain configurations are found in both conditions, confirming the similarity between the initial status of the experimental and simulation results. In the stress-free mode, the domain switching process shows the typical crossing mode. The switched domains propagate easily and rapidly across domain walls, forming a single domain when sufficiently large bias (along the −x direction) is applied to the sample. As shown in the case when electric field reaches 1.4 kV/mm in the simulation, both 180° and 90° polarization reversals occur in the crossing mode. In contrast, only 180° ferroelectric domain switching occurs (when electric field reaches 1 kV/mm) along the direction of the 90° ferroelastic domain walls under electrical bias (along the −y direction) in the strained mode. No 90° polarization reversal occurs, and no further switching across the domain walls is observed even at higher bias. In the constrained condition, the single domain state is quite difficult to achieve since the switching of ferroelectric domains involves a huge variation of elastic energies under constrained condition when compared with the stress-free condition. The phase-field simulations provide solid evidence, confirming that domain evolutions in samples with different thicknesses follow the constraint or stress-free conditions. The variation of domain switching dynamics due to local strain confinement will directly affect the properties of a ferroelectric, such as the dielectric, piezoelectric, and ferroelectric properties.
In summary, we revealed an unambiguous thickness effect on domain switching dynamic and giant ferroelectricity tailoring in single-crystalline ferroelectrics. For thick samples, switched domains propagate continuously through domain walls. Rapid propagation takes place to align all polarization along the direction of the applied electric field. For thin samples, however, switched domain propagation is much slower and is constrained at domain walls. Substantial strained layers that formed in the random polarized region and the intersection corner of the surface region and 90° ferroelastic domain walls are responsible for the different domain switching dynamics in samples with different thicknesses. The tip of a domain benefits from the lack of strain field nearby, assists the domain switching process, and speeds up the domain evolution even in a thin sample with surface constrained. Phase-field simulations confirm the important role of the reconstructed layer in affecting domain switching behavior. The substantial difference in domain switching dynamics reflects the change of ferroelectricity of single-crystalline ferroelectrics, which provides a potential method to tune ferroelectric properties in nanoscale ferroelectric devices via thickness control.
MATERIALS AND METHODS
Materials synthesis and characterization
The PMN-38%PT single crystal was grown by a modified Bridgman method. In situ TEM samples were prepared using focused ion beam (FIB) milling in a Zeiss Auriga scanning electron microscope. A bulk PMN-38%PT sample was first mechanically polished to a thickness of ~1 μm at the edge. Three bars with dimensions of 20 μm by 2 μm by 1 μm was cut from the thin edge of the sample using FIB, was lifted using a tungsten manipulator, and put on a precut copper base. Platinum deposition was used to fix the bar on the Cu base. A thin region was milled from the bar using FIB operated at 30 kV and 50 nA for coarse milling and 10 kV and 10 nA for fine milling. The thickness of the sample is determined by the SEM. TEM observations were carried out using a JEOL JEM-2100 microscope operated at 200 kV. In situ electrical biasing was conducted using a Hysitron PI 95 TEM PicoIndenter with a flat conductive tip. The bias was supplied by a Keithley 2602A SourceMeter integrated in the Electrical Characterization Module. Gentle contact between the conductive tip and the pillar was held for the close-loop electrical loading experiments. The bias was raised from 0 to +10 V (or −10 V) in 40 s (see movies S1 to S3) with a ramping rate of 0.25 V/s (or −0.25 V/s). High-resolution STEM-HAADF images were obtained using a JEOL ARM 200 STEM equipped with a spherical-aberration corrector operated at 200 kV. All STEM images were Fourier filtered using a lattice mask to remove noise. Atomic positions were determined by fitting them as two-dimensional Gaussian peaks using Ranger 2.4 script in MATLAB. Atomic displacement was calculated using MATLAB and presented as the difference vector between the center of a B-site cation and the centers of its four nearest neighboring A-site cations.
Phase-field simulation
The temporal evolution of a polarization field is described by the time-dependent Ginzburg-Landau (TDGL) equation
The total free energy of the system includes the bulk free energy, elastic energy, electrostatic energy, and the gradient energy
The bulk free energy density is expressed by Landau theory, i.e.
The gradient energy density, associated with the formation and evolution of domain walls, can be expressed as
The corresponding elastic energy density can be expressed as
The electrostatic energy density is given by
A semi-implicit Fourier spectral method is adopted for numerically solving the TDGL equation (43). The elastic constants and electrostrictive coefficients are set to be
In the simulations, we used a periodic boundary condition for phase-field modeling. For the stress-free condition, the surface stress is zero. For the constrained condition, the total strain is not changed so that the presence of surface stresses is to prevent the strain variation. The constrained strain condition means that the average (homogeneous) strains of the system (e1, e2, e3, e4, e5, and e6) are zero during the application of electric field. This means that the surface tension is positive if the surface is inclined to shrink, while it is negative if the surface is inclined to extend.
SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/42/eabc7156/DC1
This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.
REFERENCES AND NOTES
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