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Process optimization in the latent space of functions via variational autoencoder (VAE) and Bayesian Optimization (BO). We demonstrate this to optimize the curl of a kinetic ferroelectric model.
Abstract The ability of deep learning methods to perform classification and regression tasks relies heavily on their capacity to uncover manifolds in high-dimensional data spaces and project them into low-dimensional representation spaces. In this study, we investigate the structure and character of the manifolds generated by classical variational autoencoder (VAE) approaches and deep kernel learning (DKL). In the former case, the structure of the latent space is determined by the properties of the input data alone, while in the latter, the latent manifold forms as a result of an active learning process that balances the data distribution and target functionalities. We show that DKL with active learning can produce a more compact and smooth latent space which is more conducive to optimization compared to previously reported methods, such as the VAE. We demonstrate this behavior using a simple cards dataset and extend it to the optimization of domain-generated trajectories in physical systems. Our findings suggest that latent manifolds constructed through active learning have a more beneficial structure for optimization problems, especially in feature-rich target-poor scenarios that are common in domain sciences, such as materials synthesis, energy storage, and molecular discovery. The Jupyter Notebooks that encapsulate the complete analysis accompany the article.
Understanding the time-dependent effects of charged vacancies on the electromechanical responses of materials is at the forefront of research for designing materials exhibiting metal-insulator transitions and memristive behavior. A Rayleighian approach is used to develop a model for studying the nonlinear kinetics of the reaction leading to generation of vacancies and electrons via the dissociation of vacancy-electron pairs. Also, diffusion and elastic effects of charged vacancies are considered to model polarization-electric potential and strain-electric potential hysteresis loops. The model captures multiphysics phenomena by introducing couplings among polarization, the electric potential, stress, strain, and concentrations of charged (multivalent) vacancies and electrons (treated as classical negatively charged particles), where the concentrations can vary due to association-dissociation reactions. A derivation of coupled time-dependent equations based on the Rayleighian approach is presented. Three limiting cases of the governing equations are considered, highlighting the effects of (1) nonlinear reaction kinetics on the generation of charged vacancies and electrons, (2) Vegard's law (i.e., the concentration-dependent local strain) on asymmetric strain-electric potential relations, and (3) coupling between a fast component and the slow component of the net polarization on the polarization-electric-field relations. The Rayleighian approach discussed in this work should pave the way for developing a multiscale modeling framework in a thermodynamically consistent manner while capturing multiphysics phenomena in ferroelectric materials. Published by the American Physical Society 2025
Ferroelectric polarization switching is one common example of a process that occurs via nucleation and growth, and understanding switching kinetics is crucial for applications such as ferroelectric memory. Here we describe and interpret anomalous switching dynamics in the wurtzite-structured nitride thin film ferroelectrics Al 0.7 Sc 0.3 N and Al 0.94 B 0.06 N using a general model that can be directly applied to other abrupt transitions that proceed via nucleation and growth. When substantial growth and impingement occur while nucleation rate is increasing, such as in these wurtzite-structured ferroelectrics under high electric fields, abrupt polarization reversal leads to very large Avrami coefficients ( e.g., n = 11), inspiring an extension of the KAI (Kolmogorov–Avrami–Ishibashi) model. We apply this extended model to two related but distinct scenarios that crossover between (typical) behavior described by sequential nucleation and growth and a more abrupt transition arising from significant growth prior to peak nucleation rate. This work therefore provides a more complete description of general nucleation and growth kinetics applicable to any system while specifically addressing the anomalously abrupt polarization reversal behavior in new wurtzite-structured ferroelectrics.
An analytical model is developed to predict the temporal evolution of the lattice polarization in ferroelectric nanomembranes upon the excitation by a terahertz (THz) electromagnetic pulse of an arbitrary waveform and the concurrent transmission of the THz pulse in both linear and nonlinear regimes. It involves the use of the perturbation method to solve the equation of motion for the lattice polarization in both unclamped and strained ferroelectric nanomembranes within the framework of Landau-Ginzburg-Devonshire theory. The model is applicable to perovskite oxides such as BaTiO 3 and SrTiO 3 , wurtzite Al 1−𝑥 Sc 𝑥 N, and trigonal LiNbO 3 . Our analytical model provides a theoretical basis for determining the thermodynamic and kinetic parameters of ferroelectric materials through a THz transmission experiment. The calculation results also suggest an approach to reversing the chirality of a circularly polarized THz pulse by harnessing the resonant polarization-photon coupling in ferroelectrics. This capability of chirality reversal, along with the high tunability from a strain applied along any arbitrarily oriented in-plane axis, provides new opportunities for THz wave modulation without relying on complex metasurface designs.
The growth of nanocrystals obtained from Langmuir-Blodgett films of ferroelectric copolymer consisting of 70% vinylidene fluoride and 30% trifluoroethylene has been investigated by atomic force microscopy (AFM). The radius and concentration of nanocrystals are found to depend on the annealing time of the film. A model for nanocrystal growth is proposed which yields adequate time dependences for nanocrystal size parameters. The switching kinetics of individual ferroelectric nanocrystals with an average diameter of 100-200 nm and a height of 15-20 nm has been investigated in the piezoelectric response mode. It is shown that the switching of nanocrystals has an activation character.
The electric coupling between surface ions and bulk ferroelectricity gives rise to a continuum of mixed states in ferroelectric thin films, exquisitely sensitive to temperature and external factors, such as applied voltage and oxygen pressure. Here we develop the comprehensive analytical description of these coupled ferroelectric and ionic (ferroionic) states by combining the Ginzburg-Landau-Devonshire description of the ferroelectric properties of the film with Langmuir adsorption model for the electrochemical reaction at the film surface. We explore the thermodynamic and kinetic characteristics of the ferroionic states as a function of temperature, film thickness, and external electric potential. These studies provide a new insight into mesoscopic properties of ferroelectric thin films, whose surface is exposed to chemical environment as screening charges supplier.
A high-speed and high-power current measurement instrument is described for measuring rapid switching of ferroelectric samples with large spontaneous polarization and coercive field. Instrument capabilities (±200 V, 200 mA, and 200 ns order response) are validated with a LiTaO 3 single crystal whose switching kinetics are well known. The new instrument described here enables measurements that are not possible using existing commercial measurement systems, including the observation of ferroelectric switching in large coercive field and large spontaneous polarization Al 0.7 Sc 0.3 N thin films.
Ferroelectric materials have been extensively explored for applications in high-density nonvolatile memory devices because of their ferroelectric-ferroelastic domain-switching behavior under electric loading or mechanical stress. However, the existence of ferroelectric and ferroelastic backswitching would cause significant data loss, which affects the reliability of data storage. In this work, we apply in situ transmission electron microscopy and phase-field modeling to explore the unique ferroelastic domain-switching kinetics and the origin of this in relaxor-based Pb(Mg 1/3 Nb 2/3 )O 3 -33%PbTiO 3 single-crystal pillars under electrical and mechanical stimulations. Results showed that the electric-mechanical hysteresis loop shifted for relaxor-based single-crystal pillars because of the low energy levels of domains in the material and the constraint on the pillars, resulting in various mechanically reversible and irreversible domain-switching states. The phenomenon can potentially be used for advanced bit writing and reading in nonvolatile memories, which effectively overcomes the backswitching problem and broadens the types of ferroelectric materials for nonvolatile memory applications.
Abstract The Aurivillius compounds in the Bi 2 O 3 –Fe 2 O 3 –TiO 2 system, combining ferroelectric, semiconducting, and ferromagnetic properties, have attracted particular interest. Formation kinetics and thermodynamic stability are the fundamental knowledge needed for modeling and predicting the temporal microstructure and property evolution during materials processing but have not yet been addressed by quantitative experimental measurement. This article focuses on the Bi n +1 Fe n –3 Ti 3 O 3 n +3 Aurivillius compounds on the Bi 4 Ti 3 O 12 –BiFeO 3 tie‐line to elucidate the mechanisms and thermodynamic controls responsible for phase formation of compounds with various perovskite‐like layers. Five high‐purity Aurivillius compounds Bi 4 Ti 3 O 12 , Bi 5 FeTi 3 O 15 , Bi 6 Fe 2 Ti 3 O 18 , Bi 7 Fe 3 Ti 3 O 21 , and Bi 8 Fe 4 Ti 3 O 24 with integer n = 3–7 values were synthesized and their phase transformation properties and enthalpies of formation were studied by X‐ray diffraction in situ, high temperature differential scanning calorimetry, and high temperature oxide melt solution calorimetry. Thermodynamic stability of the compounds decreases with increasing n , and formation kinetics gradually slow down, demonstrating the inherent difficulty to synthesize pure Aurivillius compounds with n larger than 8. This difficulty was confirmed by an impurity phase coexisting with Bi 9 Fe 5 Ti 3 O 27 .
Abstract not provided
This study reports the thickness scaling of sputtered ferroelectric Zn 0.61 Mg 0.39 O (ZMO) thin films down to 43 nm. Encapsulated IrO 2 /ZMO/Ir capacitors exhibited switchable polarizations exceeding 50 μC cm −2 and coercive fields that increased from 3.9 to 4.4 MV cm −1 as the thickness decreased. Switching kinetics are best described by the simultaneous non-linear nucleation and the growth model. Bimodal switching is prevalent at low thicknesses, with the fastest switching times measured to be approximately 400 ns. Device encapsulation made ZMO switching kinetics more abrupt, potentially due to changes in the concentration of atmosphere-induced defects such as hydroxides. These results demonstrate stable ferroelectricity and sub-microsecond switching in sub-50 nm wurtzite ZMO, highlighting its potential as a low-voltage ferroelectric for integrated nonvolatile memory applications.
The growth rates of the (001) face of triglycine sulfate (TGS) from aqueous solutions were measured at 33.55 C in an apparatus which produced a laminar flow of solution past the crystal. The data of growth rate as a function of relative supersaturation were compared with the results of two well-known models: the Burton-Cabrera-Frank (1951) surface diffusion model and the birth-and-spreading growth model. Both models produced good fits to the growth rate data. However, on the basis of the qualitative aspects of the experimentally-observed growth, it is suggested that the correct growth model for these crystals is the Burton-Cabrera-Frank model.
The switching kinetics of RF-magnetron reactively sputtered ~200 nm thick Zn 1-x Mg x O (ZMO) ferroelectric thin films with x = 0.41 and x = 0.27 prepared on Pt/Ti/SiO 2 /Si substrates were studied at applied fields near the coercive fields, ranging from 3.4 to 5.1 MV cm -1 , and at temperatures ranging from room temperature to 100 °C. Polarization reversal in ZMO followss the Kolmogorov-Avrami-Ishibashi kinetics model for nucleation and growth at applied fields near the coercive field, and obeys an individual column switching (ICS) model at higher applied fields required to switch most of the spontaneous polarization. Switching in the high-applied field regime can be described using either the Gaussian or inverse gamma distribution functions depending on the mole fraction of magnesium in the film. The switching current transients of the high-Mg content ZMO film (x = 0.41) are always bi-modal, whereas the low Mg composition film (x = 0.27) is described by the Gaussian distribution initially following wake-up, and becomes bimodal with continued cycling. Rayleigh-like behavior of the dielectric constant revealed a simultaneous increase of the irreversible and decrease of the reversible contributions to the dielectric constant, which was ascribed to an increase in the density of mobile domain walls with cycling and resulted in faster switching.
Electric field induced polarization switching underpins most functional applications of ferroelectric materials in information technology, materials science, and optoelectronics. In the last 20 years, much attention has been focused on the switching of individual domains using scanning probe microscopy, both as model of ferroelectric data storage and approach to explore fundamental physics of ferroelectric switching. The classical picture of tip induced switching includes formation of cylindrical domain oriented along the tip field, with the domain size is largely determined by the tip-induced field distribution and domain wall motion kinetics. The polarization screening is recognized as a necessary precondition to the stability of ferroelectric phase; however, screening processes are generally considered to be uniformly efficient and not leading to changes in switching behavior. Here, we demonstrate that single-point tip-induced polarization switching can give rise to a surprisingly broad range of domain morphologies, including radial and angular instabilities. These behaviors are traced to the surface screening charge dynamics, which in some cases can even give rise to anomalous switching against the electric field (ionic field effect). The implications of these behaviors for ferroelectric materials and devices are discussed.
A mesospheric approach based on a simple microscopic 2D Ising model in a hexagonal lattice plane is proposed to explain macroscopic “asymmetric in-out domain wall motion” observation in the (0001) plane of MgO-doped stoichiometric lithium niobate. Under application of an electric field that was higher than the conventional coercive field (E{sub c}) to the ferroelectric crystal, a natural hexagonal domain was obtained with walls that were parallel to the Y-axis of the crystal. When a fraction of the coercive field of around 0.1E{sub c} is applied in the reverse direction, this hexagonal domain is shrunk (moved inward) from the corner site into a shape with a corner angle of around 150° and 15° wall slopes to the Y-axis. A flipped electric field of 0.15E{sub c} is then applied to recover the natural hexagonal shape, and the 150° corner shape changes into a flat wall with 30° slope (moved outward). The differences in corner domain shapes between inward and outward domain motion were analyzed theoretically in terms of corner and wall site energies, which are described using the domain corner angle and wall slope with respect to the crystal Y-axis, respectively. In the inward domain wall motion case, the energy levels of the evolving 150° domain corner and 15° slope walls are most competitive, and could co-exist. In the outward case, the energy levels of corners with angles >180° are highly stable when compared with the possible domain walls; only a flat wall with 30° slope to the Y-axis is possible during outward motion.
The ferroelectric polarization loop of an epitaxial BiFeO3 film on a piezoelectric substrate has been measured as a function of the continuously and reversibly varied biaxial strain of e = 0.36 0.51 %. Over this range, the ferroelectric coercive field (Ec) at 80 K increases reversibly by 36 % with the increasing tensile strain. The strain dependence of the remanent polarization agrees with previous experimental results and simulations based on thermodynamic considerations. In contrast, such calculations predict dEc/de <0, contradicting our experiments. Thus, the strain dependence of kinetic barriers influencing the rates of domain wall nucleation and propagation which are neglected in thermodynamic models may dominate the observed positive dEc/de.
In this research program, we have explored the fundamental limits for thin film deposition in both crystalline and amorphous (i.e. non-crystalline) materials systems. For vacuum-based physical deposition processes such as sputter deposition, the background gas pressure of the inert gas (usually argon) used as the process gas has been found to be a key variable. Both a roughness transition and stress transition as a function of pressure have been linked to a common mechanism involving collisions of energetic particles from the deposition source with the process inert gas. As energetic particles collide with gas molecules in the deposition process they lose their energy rapidly if the pressure (and background gas density) is above a critical value. Both roughness and stress limit important properties of thin films for applications. In the area of epitaxial growth we have also discovered a related effect; there is a critical pressure below which highly crystalline layers grow in a layer-by-layer mode. This effect is also though to be due to energetic particle thermalization and scattering. Several other important effects such as the observation of coalescence dominated growth has been observed. This mode can be likened to the behavior of two-dimensional water droplets on the hood of a car during a rain storm; as the droplets grow and touch each other they tend to coalesce rapidly into new larger circular puddles, and this process proceeds exponentially as larger puddles overtake smaller ones and also merge with other large puddles. This discovery will enable more accurate simulations and modeling of epitaxial growth processes. We have also observed that epitaxial films undergo a roughening transition as a function of thickness, which is attributed to strain induced by the crystalline lattice mismatch with the substrate crystal. In addition, we have studied another physical deposition process called pulsed laser deposition. It differs from sputter deposition due to the pulsed nature of the deposition where particles arrive at the growth surface in an interval of a few microseconds. We have observed effects such as transient formation of two dimensional islands on elemental crystalline surfaces. Pulsed deposition may also lead to non-equilibrium phases in some cases, such as the observation anomalously high tetragonality for ferroelectric thin films. All of the results described above feature in-situ synchrotron X-ray scattering as the main experimental method, which has become an indispensable technique for observing the kinetics of structures forming in real-time. We have also investigated in-situ coherent X-ray scattering and have developed methods to characterize temporal correlations that are not possible to observe with low-coherence X-rays. A high profile result of this work is a new technique to monitor defect propagation velocities in thin films. This has practical significance since defects limit the properties of thin films and it is desirable to understand their properties and origin in order to control them for practical applications. More broadly, amorphous thin films and multilayers have applications in optical devices, including mirrors and filters. Epitaxial thin films and multilayers have applications in electronic devices such as ferroelectric multilayers for non-volatile data storage, and thermoelectric nanostructures for energy conversion. Our progress in this project points the way for improved deposition methods and for improved simulation and modeling of thin film deposition processes for nanoscale control of materials with novel applications in these areas.