Domains In Ferroelectric Thin Films Research Articles

Superdomain dynamics in ferroelectric-ferroelastic films: Switching, jamming, and relaxation

Recent experimental work shows that ferroelectric switching can occur in large jumps in which ferroelastic superdomains switch together, rather than having the numerous smaller ferroelectric domains switch within them. In this sense, the superdomains play a role analogous to that of Abrikosov vortices in thin superconducting films under the Kosterlitz-Thouless framework, which control the dynamics more than individual Cooper pairs within them do. Here, we examine the dynamics of ferroelastic superdomains in ferroelastic ferroelectrics and their role in switching devices such as memories. Jamming of ferroelectric domains in thin films has revealed an unexpected time dependence of t−1/4 at long times (hours), but it is difficult to discriminate between power-law and exponential relaxation. Other aspects of this work, including spatial period doubling of domains, led to a description of ferroelastic domains as nonlinear processes in a viscoelastic medium, which produce folding and metastable kinetically limi...

Periodic arrays of flux-closure domains in ferroelectric thin films with oxide electrodes

Flux-closure domain structures in ferroelectric thin films are considered to have potential applications in electronic devices. It is usually believed that these structures are stabilized by the depolarization field and the contact with electrodes tends to screen the depolarization field and may limit their formation. In this work, the influence of oxide electrodes (SrRuO3 and La0.7Sr0.3MnO3) on the formation of flux-closure domains in PbTiO3 thin films deposited on (110)-oriented GdScO3 substrates by pulsed laser deposition was investigated by Cs-corrected transmission electron microscopy. It is found that periodic flux-closure domain arrays can be stabilized in PbTiO3 films when the top and bottom electrodes are symmetric, while a/c domains appear when asymmetric electrodes are applied. The influence of asymmetric electrodes on the domain configuration is proposed to have a connection with their different work functions and conductivity types. These results are expected to shed light on understanding the nature of flux-closure domains in ferroelectrics and open some research possibilities, such as the evolution of these structures under external electric fields.

Anomalous domain periodicity observed in ferroelectric PbTiO3 nanodots having 180° stripe domains.

Nanometer-scale ferroelectric dots and tubes have received a great deal of attention owing to their potential applications to nonvolatile memories and multi-functional devices. As for the size effect of 180° stripe domains in ferroelectric thin films, there have been numerous reports on the thickness-dependent domain periodicity. All these studies have revealed that the domain periodicity (w) of 180° stripe domains scales with the film thickness (d) according to the classical Landau-Lifshitz-Kittel (LLK) scaling law (w ∝ d1/2) down to the thickness of ~2 nm. In the case of PbTiO3 nanodots, however, we obtained a striking correlation that for the thickness less than a certain critical value, dc (~35 nm), the domain width even increases with decreasing thickness of the nanodot, which surprisingly indicates a negative value in the LLK scaling-law exponent. On the basis of theoretical considerations of dc, we attributed this anomalous domain periodicity to the finite lateral-size effect of a ferroelectric nanodot with an additional effect possibly coming from the existence of a thin non-ferroelectric surface layer.

The 90° domain splitting and electromechanical behaviors in ferroelectric thin films with triangle anti-dot array

The 90°-domain structure in ferroelectrics of tetragonal symmetry is one of the core ingredients determining the ferroelectric and electromechanical performances. We perform Monte Carlo simulations on the splitting of the 90° twin-like domains in ferroelectric thin films with differently oriented triangle anti-dot arrays. It is revealed that the domain splitting is substantially dependent of the array orientation, and thus the piezoelectric and dielectric responses are the orientation-dependent too. The mechanism for the domain structure evolution is the competition between the dipole–dipole interaction and electromechanical energy, similar to the cases of square anti-dot arrays. The present work suggests the role of geometry and symmetry of the anti-dot array in modulating the electromechanical behaviors of 90°-domained ferroelectric thin films.

Interface-induced nonswitchable domains in ferroelectric thin films.

Engineering domains in ferroelectric thin films is crucial for realizing technological applications including non-volatile data storage and solar energy harvesting. Size and shape of domains strongly depend on the electrical and mechanical boundary conditions. Here we report the origin of nonswitchable polarization under external bias that leads to energetically unfavourable head-to-head domain walls in as-grown epitaxial PbZr(0.2)Ti(0.8)O3 thin films. By mapping electrostatic potentials and electric fields using off-axis electron holography and electron-beam-induced current with in situ electrical biasing in a transmission electron microscope, we show that electronic band bending across film/substrate interfaces locks local polarization direction and further produces unidirectional biasing fields, inducing nonswitchable domains near the interface. Presence of oxygen vacancies near the film surface, as revealed by electron-energy loss spectroscopy, stabilizes the charged domain walls. The formation of charged domain walls and nonswitchable domains reported in this study can be an origin for imprint and retention loss in ferroelectric thin films.

Investigation of ferroelectric domains in thin films of vinylidene fluoride oligomers

High-resolution vector piezoresponse force microscopy (PFM) has been used to investigate ferroelectric domains in thin vinylidene fluoride oligomer films fabricated by the Langmuir-Blodgett deposition technique. Molecular chains are found to be preferentially oriented normal to the substrate, and PFM imaging shows that the films are in ferroelectric β-phase with a predominantly in-plane polarization, in agreement with infrared spectroscopic ellipsometry and X-ray diffraction measurements. The fractal analysis of domain structure has yielded the Hausdorff dimension (D) in the range of ∼1.3–1.5 indicating a random-bond nature of the disorder potential, with domain size exhibiting Landau-Lifshitz-Kittel scaling.

X-ray diffraction studies of stripelike ferroelectric domains in thin films of BiFeO3

We have used x-ray diffraction to study the structure of strained, epitaxial ${\text{BiFeO}}_{3}$ (BFO) films, which exhibit ordered arrays of stripelike ferroelectric domains, in which the polarization vector P alternates by either 109${}^{\ensuremath{\circ}}$ or 71${}^{\ensuremath{\circ}}$. Diffraction maps exhibit an intricate satellite structure that arises from coherent, gratinglike diffraction from the domain structure. In the case of the 109${}^{\ensuremath{\circ}}$ arrays, the domain structure was found to exert a strain modulation on the ${\text{DyScO}}_{3}$ substrate, with the same periodicity, indicating that domains in BFO can have an influence on the substrate structure. In the case of the 71${}^{\ensuremath{\circ}}$ arrays, in which there is no contrast between neighboring domains and coherent scattering is not expected, weak scattering is nonetheless observed, which we interpret as evidence for previously unobserved, internal strains in these domain walls. To understand the x-ray data, we introduce a simple, single-scattering model that incorporates Gaussian disorder and fits the diffraction maps, providing domain periods and surface ``puckering'' angles that are in good agreement with atomic force microscopy and piezoresponse force microscopy measurements. Our study demonstrates a simple, computationally inexpensive technique for semiquantitatively interpreting coherent domain scattering in ferroelectric films, and suggests that tuning domain structures is a potential route to engineering the near-surface properties of perovskite oxides.

First-order morphological transition of ferroelastic domains in ferroelectric thin films

Ferroelastic domains are common defects in epitaxial ferroelectric thin films, being typically observed around interfacial dislocations due to attractive elastic interactions. Because of their large stress fields, domain size and shape can influence local ferroelectric switching behavior. Here the morphology of ferroelastic domains in Pb(Zr0.2, Ti0.8)O3 thin films is investigated as a function of film thickness and substrate strain using phase field modeling in combination with transmission electron microscopy. Increasing film thickness or strain is found to induce switching from typical ferroelastic domains extending to the free surface of the film to nanosized domains localized near the substrate interface. An analysis of thermodynamic properties reveals hysteretic and discontinuous changes in the first derivatives of the free energy resulting from competing electrostatic and elastic energies. Such first-order morphological transitions are expected to be very common in epitaxial thin films during switching under an external electric or stress field.

Fully inverted single-digit nanometer domains in ferroelectric films

Achieving stable single-digit nanometer inverted domains in ferroelectric thin films is a fundamental issue that has remained a bottleneck for the development of ultrahigh density (>1 Tbit/in.2) probe-based memory devices using ferroelectric media. Here, we demonstrate that such domains remain stable only if they are fully inverted through the entire ferroelectric film thickness, which is dependent on a critical ratio of electrode size to the film thickness. This understanding enables the formation of stable domains as small as 4 nm in diameter, corresponding to 10 unit cells in size. Such domain size corresponds to 40 Tbit/in.2 data storage densities.

Evolution of 180°, 90°, and vortex domains in ferroelectric films

A Landau-like theory of phase transition and its time-dependent generalization are shown to be sufficient for describing the formation and kinetics of 180°, 90°, and vortex (toroidal) domains in ferroelectric thin films. The theory relies only on the choice of boundary conditions and does not require at the outset the presence of either anisotropy or strain fields. An ingredient in the calculational scheme is the incorporation of finite element methods in the kinetic equations for the ferroelectric order parameter.

Imaging and alignment of nanoscale 180° stripe domains in ferroelectric thin films

Nanometer-period ferroelectric 180° stripe domains are observed in epitaxial PbTiO3 films using atomic force microscopy. Stripe domains can be aligned with surface step edges or in preferred crystallographic directions. A stripe alignment map as a function of temperature and film thickness is determined using synchrotron x-ray scattering. Pinning by step edges permits control of stripe domain morphology, as demonstrated by a film grown on a vicinal surface.

Ferroelectric Domains in Thin Films and Superlattices: Results of Numerical Modeling

In micro- and nanoscale ferroelectric samples, a formation of periodic polarization domains is the efficient mechanism of reducing depolarization field that is produced by the surface bound charges. This makes the physics of these samples different from the bulk samples. We present the results of modelling of ferroelectric domains and domain textures in ferroelectric thin films and periodic paraelectric/ferroelectric superlattices, basing on the self-consistent solution of the coupled electrostatic and Ginzburg-Landau equations. We go beyond the traditionally used low-temperature Kittel approximation (in which the polarization is assumed to be temperature independent and constant across domains) and explore the temperature evolution of the domain-induced properties. For numerical solution of the problem, we use the finite-element PDE tool-box that allows to work over the entire temperature interval and in a wide region of sample parameters.

Strained Rhombohedral Stripe Domains in BiFeO3 (001) Thin Films

This is a copy of the slides presented at the meeting but not formally written up for the volume. Stripe domains in ferroelectric thin films form in order to minimize the total energy of the film. It has been known for some time that a stable configuration is reached when the decrease in elastic energy from domain formation is balanced by the energetic costs of domain wall formation, local elastic strains in the substrate, and internal electric field formation from domain polarizations. The size and strain of each domain is determined by the lattice mismatch and the energetic costs of interface formation. Recent piezoelectric force microscopy measurements have shown that BiFeO3 (BFO) films on SrRuO3/SrTiO3 (001) substrates form striped polarization domains. Since the details of the local structure and polarization cannot be measured at the same time with conventional techniques, we have used synchrotron x-ray microdiffraction to study these effects. Probing only a few domains at a time with the submicron x-ray spot resulted in a diffraction pattern near the substrate (103) reflection consisting of several BFO peaks. We have unambiguously assigned these peaks to individual structural variants. Based on these results, we propose a physical model that includes the striped domains. The structural variants within the stripes are similar to those predicted by striped patterns in rhombohedral films which minimize elastic energy. The local piezoelectric properties were measured using time-resolved microdiffraction in order to examine the role of the striped domains in the linear responses of the film. The out of plane piezoelectric coefficient d33 was approximately 50 pm/V and the piezoelectric strain was proportional to electric field was up to 0.55%, the maximum strain we have measured. The projection of the in-plane piezoelectric coefficients onto the reciprocal space maps for different structural variants had vastly different values due to the differences in orientation of the domains.

Higher-order electromechanical response of thin films by contact resonance piezoresponse force microscopy

Piezoresponse scanning force microscopy (PFM) has turned into an established technique for imaging ferroelectric domains in ferroelectric thin films. At least for soft cantilevers, the piezoresponse signal is not only dependent on the elastic properties of the material under investigation but also on the elastic properties of the cantilever. Due to this dependency, the cantilever response and, therefore, the measured properties depend on the frequency of the small alternating current (AC) testing voltage. At the contact resonance, the cantilever response is maximum, and this increased sensitivity can be used to detect very small signals or to decrease the voltage applied to the sample. We have shown that by using the hysteretic ferroelectric switching, it is possible to separate the signal into its components (viz. electromechanical and electrostatic contributions). Additionally, the measurement frequency can be tuned such that the second and third harmonics of the electromechanical response can be detected at the cantilever resonance, providing information about the higher-order electromechanical coefficients. We assume that this nonlinear behavior seen in local and macroscopic measurements is rooted in the nonlinearity of the dielectric permittivity. Our results are of crucial importance for the study of ferroelectric and electromechanical properties of nanostructures.

Theory for equilibrium 180° stripe domains in PbTiO3 films

A thermodynamic theory is developed for equilibrium 180° stripe domains in ferroelectric thin films on insulating substrates. Such stripe domains form to minimize the energy of the depolarizing field, and lead to a suppression of TC in thin films. Expressions including depolarizing field and domain wall energy are developed and applied to coherently strained PbTiO3 films on SrTiO3 substrates, with an upper boundary condition of either a dielectric (SrTiO3), a conductor, or vacuum. An elastic solution appropriate for epitaxially strained stripe domains and 180° domain walls is presented. We minimize the full nonlinear free energy using a numerical technique to obtain equilibrium polarization and field distributions, and determine the equilibrium stripe period as a function of temperature and film thickness for each upper boundary condition. While the stripe periods found agree reasonably well with the existing analytical solution using a linearized free energy, the suppression of TC as film thickness decreases is as much as a factor of 10 smaller than that given by the linear solution.

Minimum size of 180 degree domains in ferroelectric thin films covered by electrodes

Ferroelectric domain switching under low voltage or short pulses is of interest for the development of high-density random access memory (FRAM) devices. Being necessarily very small in size, instability and back switching often occur when the external voltage is removed, which creates serious problems. In this investigation, a general approach to determine the minimum size of ferroelectric domain to avoid back switching was developed, and as an example, a 180° domain in a ferroelectric thin film covered by the upper and lower electrodes was considered in detail. We note that our approach is generally applicable to many other fields, including phase transformation, nucleation and expansion of dislocation loops in thin films, etc.

Modeling of ferroelectric domains in thin films and superlattices

We have developed the set of numerical (finite-element) and analytical tools that are based on the self-consistent solution of the electrostatic equations coupled with material Ginzburg–Landau equations with an objective to model the profile of domain textures in the entire temperature region. We calculated the evolution of principal parameters of domain texture: modulation vector, distribution of polarization, renormalization of critical temperature etc. In contrast to the Kittel approximation we conclude that the profile of polarization across domains in nanometric ferroelectric thin films is highly nonuniform.

Possibilities and Limitations of Voltage-Modulated Scanning Force Microscopy: Resonances in Contact Mode*

Voltage-modulated scanning force microscopy in contact mode (or piezoresponse scanning force microscopy) is now an established technique for imaging ferroelectric domains in ferroelectric thin films. The quantities measured are not the ferroelectric polarization but the amplitude and phase of a locally induced piezoelectric strain. Although piezoresponse images are providing interesting information about the ferroelectric domain configuration, a quantitative analysis is a very challenging task given the tensorial nature of piezoelectricity. Additionally, the overall piezoresponse signal comprises both the electromechanical and electrostatic contributions depending on the frequency of the small ac testing voltage. We establish that for soft cantilevers the piezoresponse signal is not only dependent on the elastic and piezoelectric properties of the material under investigation but mainly governed by the elastic properties of the cantilever. Indications for optimal measurement regimes are given. *Originally presented at 10th European meeting on Ferroelectricity, Cambridge, UK, August 3–8, 2003.

Dynamics of ferroelastic domains in ferroelectric thin films.

Dynamics of domain interfaces in a broad range of functional thin-film materials is an area of great current interest. In ferroelectric thin films, a significantly enhanced piezoelectric response should be observed if non-180 degrees domain walls were to switch under electric field excitation. However, in continuous thin films they are clamped by the substrate, and therefore their contribution to the piezoelectric response is limited. In this paper we show that when the ferroelectric layer is patterned into discrete islands using a focused ion beam, the clamping effect is significantly reduced, thereby facilitating the movement of ferroelastic walls. Piezo-response scanning force microscopy images of such islands in PbZr0.2Ti0.8O3 thin films clearly point out that the 90 degrees domain walls can move. Capacitors 1 microm2 show a doubling of the remanent polarization at voltages higher than approximately 15 V, associated with 90 degrees domain switching, coupled with a d33 piezoelectric coefficient of approximately 250 pm V-1 at remanence, which is approximately three times the predicted value of 87 pm V-1 for a single domain single crystal.

Piezoresponse Scanning Force Microscopy: What Quantitative Information Can We Really Get Out of Piezoresponse Measurements on Ferroelectric Thin Films

Voltage modulated scanning force microscopy in contact mode or piezoresponse scanning force microscopy is now turning into an established technique for imaging ferroelectric domains in ferroelectric thin films. The quantities measured, however, are the amplitude and phase of a locally induced piezoelectric strain, and not the ferroelectric polarization itself. As all ferroelectrics possess piezoelectric properties, the domain structure visualized does correspond to that of the ferroelectric domains whose polarization is partly normal to the film surface, but the amplitude of the signal is actually not proportional to the magnitude of the normal component of the polarization. Likewise, the shear mode of scanning force microscopy allows the imaging of domains with a polarization component in the plane of the film. Methods to relate the amplitude of the piezoresponse signal to the magnitude of the ferroelectric polarization taking into account the anisotropic nature of the piezoelectric coefficients are described and discussed for the most common ferroelectric materials.