Ferroelectric Switching Kinetics Research Articles

Numerical simulation of polarization switching kinetics in ferroelectrics based on fractional Kolmogorov – Avrami model

The Kolmogorov – Avrami theory of crystallization is widely used for simulation of polarization switching kinetics in ferroelectrics. In the present study, a fractional modification of the Kolmogorov – Avrami model is examined in view of the application to polarization switching current in ferroelectrics. The approach is based on the numerical calculation of the Caputo fractional derivative with respect to the time-dependent function relating to the switching transients. The results of computational experiments are demonstrated with variation of both the parameters of domain growth and the order of time-fractional derivative. A comparison of the simulation results with experimental data and the corresponding statistical estimates are also carried out.

Kinetics of ferroelectric switching in poled barium titanate ceramics: Effects of electrical cycling rate

Our understanding of the rate-dependent electro-mechanical response of ferroelectric ceramics is incomplete – primarily due to limited experimental data characterizing the material behavior at high rates (or short time scales). Therefore, we experimentally study the effect of cycling rate on polarization switching in poled barium titanate (BaTiO3) ceramics across five orders of magnitude in cycling rate. Mechanical strain data as a function of the applied electric field were collected across three orders of magnitude. We quantify the rate-dependent coercive field, remanent and peak polarization, apparent permittivity and apparent piezoelectric coefficient, and actuation strain. Results reveal a reduction in polarizability of the material with increasing rate and a strong asymmetry in the electromechanical hystereses, which comes with differences in the rate dependence when loading parallel vs. anti-parallel to the direction of poling. Supported by a simple model and ex-situ piezoresponse force microscopy, we conclude that rate effects arise from the mobility of 90∘ domain walls and the competition between nucleation and growth of domains. The asymmetric hysteresis highlights the importance of point charge and dipole defects, which affect the domain wall kinetics and hence the rate effects of polarization switching through the competing time scales of space charge migration, dipole reorientation, and domain wall activity.

Comparative studies on ferroelectric switching kinetics of sputtered Hf0.5Zr0.5O2 thin films with variations in film thickness and crystallinity

Ferroelectric Hf0.5Zr0.5O2 (HZO) thin film capacitors with Pt/HZO/TiN structures were characterized to investigate the effects of oxygen partial pressure (PO2) and film thickness on the ferroelectric properties and switching dynamics of sputter-deposited HZO thin films. The PO2 during deposition and the film thickness varied from 0% to 1.5% and from 20 to 30 nm, respectively. The ferroelectric remnant polarization (2Pr) was 24.8 μC/cm2 for the 20-nm-thick HZO thin film deposited at a PO2 of 0% and decreased with increasing PO2 and film thickness due to variation in the amount of ferroelectric orthorhombic phase. The 2Pr of the 30-nm-thick HZO film deposited at a PO2 of 1% was 9.60 μC/cm2. The switching times and related parameters of the HZO films were estimated and analyzed by Kolmogorov–Avrami–Ishibashi and nucleation-limited switching (NLS) models. The NLS model provided better fitting results over the full range of polarization switching. The switching times could be modulated with variations in PO2 and film thickness from 0.46 to 1.58 μs. The activation field for polarization reversal increased with increasing PO2, and the degree of PO2 dependence was higher for a thinner film.

A phase-field approach to studying the temperature-dependent ferroelectric response of bulk polycrystalline PZT

Ferroelectric ceramics are of interest for engineering applications because of their electro-mechanical coupling and the unique ability to permanently alter their atomic-level dipole structure (i.e., their polarization) and to induce large-strain actuation through applied electric fields. Although the underlying multiscale coupling mechanisms have been investigated by modeling strategies reaching from the atomic level across the polycrystalline mesoscale to the macroscopic device level, most prior work has neglected the important influence of temperature on the ferroelectric behavior. Here, we present a phase-field (diffuse-interface) constitutive model for ferroelectric ceramics, which is extended to account for the effects of finite temperature by considering thermal lattice vibrations based on statistical mechanics and by modifying the underlying Landau-Devonshire potential to depend on temperature. Results indicate that the chosen interpolation of the Landau energy coefficients is a suitable approach for predicting the temperature-dependent spontaneous polarization accurately over a broad temperature range. Lowering the energy barrier at finite temperature by the aforementioned methods also leads to better agreement with measurements of the bipolar hysteresis. Based on a numerical implementation via FFT spectral homogenization, we present simulation results of single- and polycrystals, which highlight the effect of temperature on the ferroelectric switching kinetics. We observe that thermal fluctuations (at the phase-field level realized by a thermalized stochastic noise term in the Allen-Cahn evolution equation) promote the nucleation of needle-like domains in regions of high heterogeneity or stress concentration such as grain boundaries. This, in turn, leads to a faster polarization reversal at low electric fields and a simulated domain pattern evolution comparable to experimental observations, stemming from the competition between nucleation and growth of domains. We discuss the development, implementation, validation, and application of the temperature-dependent phase-field framework for ferroelectric ceramics with a focus on tetragonal lead zirconate titanate (PZT), which we demonstrate to admit reasonable model predictions and comparison with experiments.

Hybrid Stochastic Fractal-Based Approach to Modeling the Switching Kinetics of Ferroelectrics in the Injection Mode

The paper is devoted to the development and implementation of a hybrid stochastic fractal-based approach for modeling electron-induced kinetics of polarization switching in ferroelectrics as the self-similar memory physical systems. The mathematical model of fractal dynamic system includes the initial value problem for the fractional order differential equation. Computational schemes for solving fractional differential problem are constructed using the Adams–Bashforth–Moulton type predictor-corrector methods. The stochastic algorithm based on the Monte Carlo method is proposed to simulate the domain nucleation process during restructuring the domain structure in ferroelectrics. The polarization switching current of ferroelectrics in the electron injection mode is evaluated to demonstrate the computational experiment results with a comparison of the experimental data.

Polarization switching kinetics of the ferroelectric Al-doped HfO2 thin films prepared by atomic layer deposition with different ozone doses

Ferroelectric switching kinetics of the Al-doped HfO2 (Al:HfO2) thin films prepared by the atomic layer deposition process were investigated by varying the dose time of oxygen precursor (O3). When the O3 dose time was reduced to 3 s, the Al:HfO2 films exhibited an enhanced remnant polarization (2Pr) of 10.2 μC/cm2 due to the suppression of the monoclinic phase and the increase in the ratio of oxygen vacancy. Double-pulse switching and the Kolmogorov–Avrami–Ishibashi model were used to obtain detailed quantitative information on the switching kinetics of the Al:HfO2 films. The estimated values of switching time and activation energy showed the strong dependence of O3 dose. This suggests that the O3 dose condition can be a key control parameter to modulate the ferroelectric polarization switching dynamics of the Al:HfO2 thin films.

Dispersion in Ferroelectric Switching Performance of Polycrystalline Hf0.5Zr0.5O2 Thin Films.

Interests in nanoscale integrated ferroelectric devices using doped HfO2-based thin films are actively reviving in academia and industry. The main driving force for the formation of the metastable non-centrosymmetric ferroelectric phase is considered to be the interface/grain boundary energy effect of the small grains in polycrystalline configuration. These small grains, however, can invoke unfavorable material properties, such as nonuniform switching performance. This study provides an in-depth understanding of such aspects of this material through careful measurement and modeling of the ferroelectric switching kinetics. Various previous switching models developed for conventional ferroelectric thin-film capacitors cannot fully account for the observed time- and voltage-dependent switching current evolution. The accurate fitting of the experimental results required careful consideration of the inhomogeneous field distribution across the electrode area, which could be acquired by an appropriate mathematical formulation of polarization as a function of electric field and time. Compared with the conventional polycrystalline Pb(Zr,Ti)O3 film, the statistical distribution of the local field was found to be three times wider. The activation field and characteristic time for domain switching were larger by more than 1 order of magnitude. It indicates that doped HfO2 is inhomogeneous and "hard" ferroelectric material compared with conventional perovskite-based ferroelectrics.

Fractal model of polarization switching kinetics in ferroelectrics under nonequilibrium conditions of electron irradiation

The paper presents the results of the fractal and multifractal analysis of polarization switching current in ferroelectrics under electron irradiation, which allows statistical memory effects to be estimated at dynamics of domain structure. The mathematical model of formation of electron beam-induced polarization current in ferroelectrics was suggested taking into account the fractal nature of domain structure dynamics. In order to realize the model the computational scheme was constructed using the numerical solution approximation of fractional differential equation. Evidences of electron beam-induced polarization switching process in ferroelectrics were specified at a variation of control model parameters.

Enhancement of switching speed of BiFeO3 capacitors by magnetic fields

The effect of a magnetic field on the ferroelectric switching kinetics of BiFeO3 (BFO) capacitors with La0.8Ca0.2MnO3 (LCMO) bottom electrode and Pt top contact has been investigated. We find a strong dependence of the remnant polarization and coercive field on the magnetic field. The switching time can be systematically tuned by magnetic field and reaches a tenfold reduction around the Curie temperature of LCMO at 4 T. We attribute this behavior to the splitting of the voltage drops across the BFO film and the LCMO bottom electrode, which can be strongly influenced by an external magnetic field due to the magnetoresistance. Further experiments on the BFO capacitors with SrRuO3 bottom electrodes show little magnetic field dependence of ferroelectric switching confirming our interpretation. Our results provide an efficient route to control the ferroelectric switching speed through the magnetic field, implying potential application in multifunctional devices.

Tuning the switching time of BiFeO3 capacitors by electrodes' conductivity

The influence of the bottom electrode's resistance on ferroelectric switching kinetics has been investigated in BiFeO3/La0.8Ca0.2MnO3 capacitors with Pt top contacts. Reversible biaxial strain applied using a piezoelectric substrate is employed to control the resistance of manganite bottom electrode. We found strong dependence of both the switching time and the coercive fields on the electrode's resistance. The reason is attributed to the splitting of the applied voltage between the ferroelectric film and the electrode, which becomes more severe with increasing switching speed. This highlights a crucial limitation for fast switching using lower-conductivity electrodes and inspires the external control of switching kinetics via the electrodes' conductivity.

Strain controlled ferroelectric switching time of BiFeO3 capacitors

The ferroelectric switching kinetics of BiFeO3 capacitors grown on a piezoelectric substrate has been investigated in different strain states and at various temperatures. The switching behavior is in good agreement with the Kolmogorov-Avrami-Ishibashi model. The effect of reversible biaxial in-plane compression on the switching time is an enhancement at low electric field and a reduction at high field. The two field regimes are found to correspond to the creep and the depinning of domain walls. The strain effect on the switching time depends strongly on temperature and reaches a tenfold slowing down upon ∼0.1% of biaxial compression at 50 K. This work provides a route to realize strain control of ferroelectric switching kinetics in BiFeO3 and is significant for potential applications.

The Weiss model and the Landau–Khalatnikov model for the switching of ferroelectrics

It is shown that the molecular field theory by P. Weiss formally leads to the switching kinetics of ferroelectrics, which is described by the well-known Landau–Khalatnikov equation. The switching has a critical character, taking place only at Ea>Ec (Ea: external field, Ec: coercive field). The results are checked by computer simulations.

Modeling the switching kinetics in ferroelectrics

The switching process in ferroelectrics with a maximum in time for the switching current as observed by Merz [Phys. Rev. 95, 690 (1954)] is simulated. To this end, the Weiss molecular mean-field model is combined with the fluctuation of dipoles in double-well potentials. A first-order rate equation for the polarization with time-dependent coefficients results. This equation is solved for the time-dependent switching process, as well as for the static polarization hysteresis loop.

Polarity-dependent kinetics of ferroelectric switching in epitaxial BiFeO3(111) capacitors

We report on the intriguing polarity-dependent kinetics of polarization switching in epitaxial BiFeO3(111) capacitors. Two seemingly incompatible switching kinetics were observed depending on the polarity of the applied switching bias. Under a negative switching bias, the polarization switching process occurs mainly through sideways domain wall motion, but under a positive switching bias, domain nucleation governs the polarization reversal. The modified piezoresponse force microscopy reveals these polarity-dependent ferroelectric domain evolutions. This polarity dependence of ferroelectric switching kinetics is attributed to defect-related local fields that have different distributions near film/electrode interfaces, probably due to structural relaxation in the BiFeO3(111) film.

On the theory of domain switching kinetics in ferroelectrics

We investigate theoretically the polarization switching kinetics in ferroelectrics, both bulk and thin films samples. In such substances, the domain walls are pinned by (usually dipole) defects, which are present also in ordered samples as technologically unavoidable impurities. This random interaction with dipole pinning centers results, in particular, in exponentially broad distribution of switching times. Under supposition of low pinning centers concentration, we derive the distribution function of switching times showing that it is not simply Lorentzian (as it was first suggested by Tagantsev et al. [Phys. Rev. B 66 (2002) 214109]), but is a “square of Lorentzian”, which is due to the vector nature of electric field. This improved formalism delivers a better description of available experimental data and elucidates the physical mechanism of domain switching times distribution.

Four switching categories of ferroelectrics

We classify the switching kinetics of ferroelectrics including both epitaxial/polycrystalline thin films and single-crystalline/ceramic bulks at various applied fields into four categories, depending on whether the depolarization field and/or the polarization reversal induced by the switching promotion effect between adjacent parts can be neglected. We show that our statistical model developed very recently [X. J. Lou, J. Phys.: Condens. Matter 21, 012207 (2009)] in its generalized form applies to all these four categories. Finally, we make the comparison between our model and the conventional Kolmogorov–Avrami–Ishibashi model and discuss the behavior of the switching currents for different n.

Fractal Dimensions in Switching Kinetics of Ferroelectrics

Early work by the author with Prof. Ishibashi [Scott et al., J. Appl. Phys. 64 , 787 (1988); 61 , 5467 (1987)] showed that switching kinetics in ferroelectrics, particularly lead zirconate titanate (PZT), satisfy a constraint on current transients compatible with d = 2.5 dimensionality. At that time with no direct observations of the domains, it was not possible to conclude whether this was a true Hausdorff dimension or a numerical artefact caused by an approximation in the theory (which ignored the dependence of domain wall velocity upon domain diameter). Recent data suggest that the switching dimensionality is truly fractal with d = 2.5. The critical exponent β characterizing the order parameter P(T) can be written as a continuous function of dimension d as β(d) = [ν (d)/2] [d+η(d)−2], which is exact within hyperscaling; here ν and η are the exponents characterizing the pair correlation function G(r,T) and the structure factor S(q,T). For d = 2.5 the estimate is that β is approximately 1/4.

Kinetics of ferroelectric switching in unipolar (CH3NH3)5Bi2Br11 crystal

Ferroelectric switching in unipolar (CH3NH3)5Bi2Br11 crystal has been studied by optical observation of the domain structure in low electric fields and switching current registration in high fields. We discuss investigations on the temporal behaviour of the electric polarization in static electric fields as well as polarization decay after removal of the electric field. The backswitching process appears to have a correlation to a defect-induced internal field in the crystal. For the interpretation of experimental data we utilize the classical nucleation and growth model of phase transformation (e.g. Avrami–Kolmogorov theory). An analysis assuming a statistical distribution of the characteristic domain growth times is proposed to explain and to find the functional form of the experimental data.

Kinetics of ferroelectric switching in ultrathin films

The kinetics of polarization switching in ultrathin ferroelectric polymer films exhibit a critical behavior; there is a pronounced slowing just above the coercive field and just below the critical temperature. The critical slowing is observed in the switching kinetics of ferroelectric Langmuir-Blodgett films of 70% vinylidene-fluoride and 30% trifluoroethylene copolymer with thickness up to 30 ML. Thicker films exhibit an exponential dependence on the field and temperature that is normally associated with extrinsic switching by domain nucleation and growth. We show that the critical behavior arises naturally from the dynamics of homogeneous intrinsic switching in the context of mean-field theory. These results have important implications for the modeling and control of the ferroelectric films in nonvolatile computer memories and solid-state data storage media.

Polarization switching kinetics in ferroelectrics in the region of strong metastability

The thermodynamics and kinetics of polarization switching in ferroelectrics are studied in the framework of the field theory in the vicinity of the critical point of first-order phase transitions. The study is exemplified by the switching of intrinsic ferroelectrics with 180° domains. An expression describing the dependence of the domain critical size on the switching field is derived. The switching process is studied at high switching fields. Relationships for calculating the field dependence of the number of switched domains are obtained.