Landau Devonshire Research Articles

A phenomenological thermodynamic energy density function for ferroelectric wurtzite Al1−xScxN single crystals

A Landau–Devonshire thermodynamic energy density function for ferroelectric wurtzite aluminum scandium nitride (Al1−xScxN) solid solution is developed. It is parametrized using available experimental and theoretical data, enabling the accurate reproduction of composition-dependent ferroelectric properties, such as spontaneous polarization, dielectric permittivity, and piezoelectric constants, for both bulk and thin films. The maximum concentration of Sc for the wurtzite structure to remain ferroelectric is found to be 61 at. %. A detailed analysis of Al1−xScxN thin films reveals that the ferroelectric phase transition and properties are insensitive to substrate strain. This study lays the foundation for quantitative modeling of novel ferroelectric wurtzite solid solutions.

Field dependence of the electrocaloric effect in BaTiO3 and Ba(Zr0.12Ti0.88)O3: High-resolution measurements around the phase transition

The electric field dependence of the electrocaloric effect is investigated in BaTiO3 and Ba(Zr0.12Ti0.88)O3 by a direct method with sub-mK temperature resolution. The field dependence of the caloric temperature change ΔT(E) shows a pronounced change within a few Kelvin around the Curie temperature for the first-order phase transition in BaTiO3. The transition from a linear field dependence in the ferroelectric phase over a butterfly-shaped to a quadratic field dependence in the paraelectric phase is compared to predictions of Landau–Devonshire theory. The simultaneous measurement of caloric and dielectric properties further allows for the investigation of the polarization dependence ΔT(P) of the electrocaloric effect. We find clear deviations from the predicted quadratic polarization dependence for temperatures close to the Curie temperature. Ba(Zr0.12Ti0.88)O3 shows in contrast only a slow and gradual change of the field dependence over a broad temperature range as a consequence of its diffuse phase transition.

Designing high piezoelectric properties at the BaTiO3–PbZrO3–PbTiO3 phase boundary by Landau–Devonshire theory

Ferroelectric materials possessing exceptional piezoelectric attributes have garnered widespread utilization in various applications. Solid solution systems improve piezoelectric properties through multiphase mixing, but the methodologies for effective design remain wanting. Based on the Landau–Devonshire theory, we propose a theoretical design method. Binary materials with morphotropic phase boundary (MPB) compositions are added with new elements to increase the free energy of the original stabilized phase and lower the energy barrier (EB). Flatter EBsand higher piezoelectric coefficients are found at the phase boundaries of the ternary system. By calculating the phase diagram, piezoelectric coefficient, dielectric constant, polarization, and EBs, we reveal the origin of the highest piezoelectric coefficient at the phase boundaries. This study underscores the importance of the EBs for polarization rotation in characterizing piezoelectric properties and proposes a theoretical design method for exploring materials with high piezoelectric coefficients.

Stress and electric field induced phase transitions for ultra high energy conversion in ferroelectrics

This work focuses on energy harvesting of ferroelectric relaxors PMN-25PT and PZN-8PT single crystals with high uniaxial stress and electric field. Ericsson cycle, which consists of applying and releasing electric field and stress at different steps of the cycle, has been used. A large energy density for PZN-8PT high as 410 mJ/cm3 was obtained. Different working temperatures were tested by experiment and modeled via Landau–Devonshire theory. Optimal working temperatures were identified for high level energy conversion and were successfully predicted by simulation. It appeared that the optimum working temperature was different from that optimizing the d33. Polarization mechanisms induced by these extreme conditions for energy harvesting are explained in the frame of experimental and modeling results. The results obtained at high stress levels tend to indicate that operating along the polarization direction yields the best results, which contradicts conclusions drawn in the case of domain engineered crystals.

Numerical modeling of anisotropic ferroelectric materials with hybridizable discontinuous Galerkin methods

We investigate a gradient flow structure of the Ginzburg–Landau–Devonshire (GLD) model for anisotropic ferroelectric materials by reconstructing its energy form. We show that the modified energy form admits at least one minimizer. Under some regularity assumptions for the electric charge distribution and the initial polarization field, we prove that the gradient flow structure has a unique solution. To simulate the GLD model numerically, we propose an energy‐stable semi‐implicit time‐stepping scheme and a hybridizable discontinuous Galerkin method for space discretization. Numerical tests are provided to verify the stability and convergence of the proposed numerical scheme as well as some properties of ferroelectric materials.

A Theoretical Study of Negative Capacitance Field‐Effect Transistors Using Ferroelectrics Having First‐ and Second‐Order Phase Transitions

Herein, a theoretical study of negative capacitance field‐effect transistors (NCFETs) using ferroelectrics (FEs), having first‐ and second‐order phase transitions (FPT and SPT, respectively), applying the Landau–Devonshire (LD) theory, is presented. The expressions for the Landau parameters for FPT FEs are derived from the basic relations, and subsequently, these are used in the numerical models for the surface potential, gate charge, and drain current for NCFETs with FPT FEs, developed in this work. The results show an excellent match with those obtained from technology computer‐aided design (TCAD) simulations. Next, the Landau parameters and the numerical models for the charge and drain current for NCFETs with SPT FEs are developed, following a similar procedure, and then the results of these two structures are compared, along with those obtained from TCAD simulations, which shows an excellent match. The results bring out some interesting observations—notable among them is a higher Ion/Ioff ratio for FPT structures, as compared to that for SPT ones, caused by a reduction in the subthreshold current, with a marginal increase in the strong inversion current in the former. This feature, by itself, may make NCFETs with FPT FEs more suitable than those with SPT FEs for low‐power applications.

Modeling of Olsen cycle for pyroelectric energy harvesting and assessment of abnormal electrocaloric effect in ferroelectric single crystals

The energy conversion potential of ferroelectric materials originating from their phase transitions, in particular temperature ranges and electric field values, is very promising. Pyroelectric energy harvesting consists of directly converting thermal energy into electrical energy. Due to its high energy conversion potential, the Olsen cycle is the most favorable for pyroelectric energy harvesting. This cycle includes two isothermal and two constant electric field branches. In this study, the Olsen cycle was modeled, then varying temperatures and applied electric field directions for different crystal orientations were simulated. Polarization responses were obtained via the Landau–Devonshire theory. Then, an innovative way to model the electrocaloric effect was proposed; experimental results and first-principle calculations confirmed the simulation results. The resulting negative electrocaloric effect due to crystal orientation, previously reported in the literature, has been successfully simulated through a phenomenological approach. Finally, we identified which phase transitions are interesting for pyroelectric energy harvesting applications depending on crystal orientations while obtaining an energy density in the order of ≈102mJ/cm3. This value corresponds to previous results in the literature.

A Landau–Devonshire analysis of strain effects on ferroelectric Al1−xScxN

We present a thermodynamic analysis of the recently discovered nitride ferroelectric materials using the classic Landau–Devonshire approach. Electrostrictive and dielectric stiffness coefficients of Al1−xScxN with a wurtzite structure (6 mm) are determined using a free energy density function assuming a hexagonal parent phase (6/mmm), with the first-order phase transition based on the dielectric stiffness relationships. The results of this analysis show that the strain sensitivity of the energy barrier is one order of magnitude larger than that of the spontaneous polarization in these wurtzite ferroelectrics, yet both are less sensitive to strain compared to classic perovskite ferroelectrics. These analysis results reported here explain experimentally reported sensitivity of the coercive field to elastic strain/stress in Al1−xScxN films and would enable further thermodynamic analysis via phase field simulation and related methods.

Multi-objective optimization of pyroelectric thermal–electrical cycles

Pyroelectric thermal–electrical cycles enable a class of solid-state heat engines that convert waste heat to electrical energy. This article numerically investigates thermal-to-electrical energy conversion in a PbZr0.52Ti0.48O3 (PZT) pyroelectric layer near room temperature and optimizes operating parameters to maximize the electrical energy output. A general thermodynamic cycle is modeled after the prototypical pyroelectric Ericsson cycle—implemented based on the Ginzburg–Landau–Devonshire theory—with variable operating temperature range, and heating/cooling and charging/discharging time intervals. We used a Pareto optimization approach to simultaneously maximize electrical energy density and power density for different PZT sample and cycle parameters. The evaluated Pareto optimal fronts showcase the possibility of achieving multiple optimal solutions and highlight the trade-off between output energy density and power density in pyroelectric energy conversion. Specifically, we demonstrate that a 4× enhancement in power density is achievable with a less than 10% reduction in energy density for the same sample and operating conditions primarily by optimizing heat transfer. The multi-objective optimization approach and results presented in this study could provide a framework to facilitate the design and operation of pyroelectric cycles for waste heat energy harvesting systems.

Investigation of Compositional Effect on Dielectric and Variable Range Hopping Mechanism of Dysprosium Doped BNT-BT Ceramics

The manuscript describes the dielectric properties and conduction mechanism of Dysprosium doped 0.92Na0.5Bi0.5TiO3–0.08BaTiO3 (BNT-BT8) composition prepared by solid-state reaction method. Rietveld refinement study of X-ray diffraction data shows that all the samples exhibit a combination of rhombohedral (R3c) and tetragonal (P4mm) crystallographic phases. It is found that with an increase in Dy content, the pseudo-cubic lattice parameter of R3c phase gradually decreases. The modification in the microstructure of the doped samples was investigated by scanning electron microscope. The temperature and frequency-dependent dielectric data show enhancement of the dielectric dispersion in the region of the dielectric peak with doping. To achieve more insight into the evolution of disorder in the system, the Landau-Devonshire (LD) cluster theory was employed to evaluate the local order parameter. The change of ac-conductivity with the temperature of the studied samples was analyzed using Arrhenius’s law and Mott’s variable range hopping mechanism. The fitting of the model parameters such as density of states (N(EF)), hopping length (RH), and hopping energies (WH) were calculated for all the compositions. The activation energy associated with the samples was calculated from the Arrhenius diagram, which reflects the conduction process is different at different temperature ranges.

Modeling temperature, frequency, and strain effects on the linear electro-optic coefficients of ferroelectric oxides

An electro-optic modulator offers the function of modulating the propagation of light in a material with an electric field and enables a seamless connection between electronics-based computing and photonics-based communication. The search for materials with large electro-optic coefficients and low optical loss is critical to increase the efficiency and minimize the size of electro-optic devices. We present a semi-empirical method to compute the electro-optic coefficients of ferroelectric materials by combining first-principles density-functional theory calculations with Landau–Devonshire phenomenological modeling. We apply the method to study the electro-optic constants, also called Pockels coefficients, of three paradigmatic ferroelectric oxides: BaTiO3, LiNbO3, and LiTaO3. We present their temperature-, frequency-, and strain-dependent electro-optic tensors calculated using our method. The predicted electro-optic constants agree with the experimental results, where available, and provide benchmarks for experimental verification.

Strain Engineering of Domain Coexistence in Epitaxial Lead-Titanite Thin Films

Phase and domain structures in ferroelectric materials play a vital role in determining their dielectric and piezoelectric properties. Ferroelectric thin films with coexisting multiple domains or phases often have fascinating high sensitivity and ultrahigh physical properties. However, the control of the coexisting multiple domains is still challenging, thus necessitating the theoretical prediction. Here, we studied the phase coexistence and the domain morphology of PbTiO3 epitaxial films by using a Landau–Devonshire phenomenological model and canonic statistical method. Results show that PbTiO3 films can exist in multiple domain structures that can be diversified by the substrates with different misfit strains. Experimental results for PbTiO3 epitaxial films on different substrates are in good accordance with the theoretical prediction, which shows an alternative way for further manipulation of the ferroelectric domain structures.

Landau theory of ferroelastic phase transitions: Application to martensitic phase transformations

The peculiarities of two Landau-type theories of ferroelastic phase transitions have been analyzed. The predictions of both theories have been compared with well-known experimental data obtained for the shape memory alloys (SMAs) undergoing the first-order martensitic transformations (MTs). It has been shown that the predictions of the Landau–Devonshire theory, which disregards the third-order term in power expansion of Gibbs free energy, contradict the experimental data, while the results of the symmetry conforming Landau theory, which takes into account this term, are in agreement with experimental data. The impossibility of occurrence of the second-order MT is demonstrated starting from the thermodynamic definition of the second-order phase transition. It is argued that the stress–strain loops, obtained for SMAs, can imitate the stress-induced phase transition in the absence of such transition.

Explicating the irreversible electric-field-assisted ferroelectric phase transition in the otherwise antiferroelectric sodium niobate for energy storage systems

By means of a first-principles-based Landau–Devonshire model, we predict and explain why newly discovered intermediates can rationalize the persistent lack of a double polarization–electric field hysteresis for NaNbO3 under an applied field.

Phenomenological Circuit Modeling of Ferroelectric-Driven Bulk Acoustic Wave Resonators

A nonlinear circuit model has been developed to model electrostriction in thin-film ferroelectric bulk acoustic wave (BAW) resonators. This new model is based on nonlinear coupling relations among strain, stress, electric field, and polarization, derived from the Landau–Devonshire theory. The coupling relations and the mechanical vibrations are then represented as lumped circuit elements using an improved approximation procedure along with an enhanced model for dielectric loss. The response from the simulation is compared with the measurement results obtained for a barium strontium titanate (BST) thin-film bulk acoustic resonator (FBAR) at different dc bias levels. The improved approximation procedure enables one to achieve accurate simulation results with reduced circuit model complexity.

Analytical properties of switching current transients in ferroelectrics

The increasing application of ferroelectrics in technological applications such as nonvolatile ferroelectric random access memories, capacitors, and energy harvesters highlights the importance of investigating how the characteristics of switching current transients change in response to variation of factors that affect it. This work presents a completely analytical approach based on the Landau-Devonshire (LD) model of phase transitions to quickly study the changes to the properties of switching current transients and back-switching currents in ferroelectric material. The non-linear nature of polarization decay is analyzed based on an exact solution of the Landau-Khalatnikov equation. Exact expressions of the temporal changes in polarization and back-switching current that incorporate the cubic polarization are derived. Comparison of differences between the exact non-linear model of polarization decay phenomena from the linearized model of polarization decay are discussed. This work shows that the characteristics of the critical switching time phenomenon in partial switching current experiments can be explained by the analytical LD model. Many features of complete and partial switching current transients produced by bipolar electric pulses are successfully modeled analytically by varying factors such as temperature, electric field amplitude, pulse-width and off-time. This work shows that pulse powered switching current behaviour in ferroelectric material can be modeled analytically instead of relying only on numerical approaches to the Landau-Khalatnikov equation.

Analysis of the Nonlinear Response of Piezo-Micromirrors with the Harmonic Balance Method

In this work, we address the simulation and testing of MEMS micromirrors with hardening and softening behaviour excited with patches of piezoelectric materials. The forces exerted by the piezoelectric patches are modelled by means of the theory of ferroelectrics developed by Landau–Devonshire and are based on the experimentally measured polarisation hysteresis loops. The large rotations experienced by the mirrors also induce geometrical nonlinearities in the formulation up to cubic order. The solution of the proposed model is performed by discretising the device geometry using the Finite Element Method, and the resulting large system of coupled differential equations is solved by means of the Harmonic Balance Method. Numerical results were validated with experimental data collected on the devices.

Full Control of Polarization in Ferroelectric Thin Films Using Growth Temperature to Modulate Defects

AbstractDeterministic control of the intrinsic polarization state of ferroelectric thin films is essential for device applications. Independently of the well‐established role of electrostatic boundary conditions and epitaxial strain, the importance of growth temperature as a tool to stabilize a target polarization state during thin film growth is shown here. Full control of the intrinsic polarization orientation of PbTiO3 thin films is demonstrated—from monodomain up, through polydomain, to monodomain down as imaged by piezoresponse force microscopy—using changes in the film growth temperature. X‐ray diffraction and scanning transmission electron microscopy reveal a variation of c‐axis related to out‐of‐plane strain gradients. These measurements, supported by Ginzburg–Landau–Devonshire free energy calculations and Rutherford backscattering spectroscopy, point to a defect mediated polarization gradient initiated by a temperature dependent effective built‐in field during growth, allowing polarization control not only under specific growth conditions, but ex‐situ, for subsequent processing and device applications.

Calibration of material parameters based on 180^circ and 90^circ ferroelectric domain wall properties in Ginzburg\u2013Landau\u2013Devonshire phase field models

Ferroelectric phase field models based on the Ginzburg–Landau–Devonshire theory are characterized by a large number of material parameters with problematic physical interpretation. In this study, we systematically address the relationship between these parameters and the main properties of ferroelectric domain walls. A variational approach is used to derive closed form solutions for the polarization fields at the phase transition regions as well as for the propagation velocities of the domain walls. Introducing a modified set of material parameters, which appropriately scales different contributions to the free energy, we are able to accurately calibrate these parameters based on domain wall thickness and energy of both 180^circ and 90^circ domain walls. Moreover, the mobility parameter appearing in the Ginzburg–Landau evolution equation can be accurately calibrated based on the propagation velocity of the domain walls.

Cascaded pyroelectric conversion: Optimizing the ferroelectric phase transition and electrical losses

The dramatic increase in the pyroelectric coefficient around the ferroelectric–paraelectric phase transition suggests high potential energy conversion efficiencies, but the reality is more complicated when thermal and electrical losses are considered. The performance of prototype mono-domain lead titanate thin films is simulated around phase transition using a phenomenological modeling approach. Thermodynamic properties are calculated using a modified Landau–Devonshire potential that is a function of temperature, applied electric field, and uniaxial tensile stress for bulk films. Significant performance enhancement near the ferroelectric–paraelectric phase transition is observed. However, increases in both the specific heat and the dielectric constant reduced the anticipated improvement. Critically, electrical losses during charging and discharging processes within the energy conversion cycle are included and calculated using the dielectric dissipation factor. Cascaded pyroelectric conversion cycles are considered where heat for each subsequent stage is provided by the previous stage, allowing for the segmentation of large temperature changes into multiple cycles. The implementation of a multi-stage or cascade approach could greatly increase the cycle efficiency over a large temperature range while utilizing lower, more realistic, electric field strengths. We show how each stage could be optimized through a secondary multi-caloric effect where the ferroelectric–paraelectric transition temperature is shifted using an applied biaxial stress. Loss tangents as low as 5% are shown to negate the benefits of cascading for high number of stages (n > 10). Using a stress-tuned optimum phase transition temperature for cascade stages provides roughly a 100% increase in thermal efficiency vs the unoptimized material for low electric field cycles.