We present a thermodynamic analysis of the recently discovered nitride ferroelectric materials using the classic Landau-Devonshire approach. The electrostrictive and dielectric stiffness coefficients of Al1-xScxN with wurtzite structure (6mm) 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 novel wurtzite ferroelectrics, yet both are less sensitive to strain compared to classic perovskite ferroelectrics. These analysis results reported here explain experimentally reported sensitivity of coercive field to elastic strain/stress in Al1-xScxN films, and would enable further thermodynamic analysis via phase field simulation and related methods.
Ferroelectricity enables key integrated technologies from non-volatile memory to precision ultrasound. Wurtzite ferroelectric Al1-xScxN has recently attracted attention because of its robust ferroelectricity and Si process compatibility in addition to being the first known ferroelectric wurtzite. However, the origin and control of ferroelectricity in wurtzite materials is not yet fully understood. Here we show that the local bond ionicity, rather than simply the change in tetrahedral distortion, is key to controlling the macroscopic ferroelectric response, according to our coupled experimental…
The interaction of ferroelectric 180 degree domain wall with a strongly inhomogeneous electric field of biased Scanning Probe Microscope tip is analyzed within continuous Landau-Ginzburg-Devonshire theory. Equilibrium shape of the initially flat domain wall boundary bends, attracts or repulses from the probe apex, depending on the sign and value of the applied bias. For large tip-wall separations, the probe-induced domain nucleation is possible. The approximate analytical expressions for the polarization distribution are derived using direct variational method. The expressions provide insight …
Embedded Ferroelectric Nanoclusters can drive Polarization Reversal in a Non-Ferroelectric Polar Film via the Proximity Effect
Institute of Physics of the National Academy of Sciences of Ukraine（乌克兰国家科学院物理研究所）；Frantsevich Institute for Problems in Materials Science, National Academy of Sciences of Ukraine（乌克兰国家科学院弗伦采维奇材料科学问题研究所）；Department of Materials Science and Engineering, University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校材料科学与工程系）；Department of Materials Science and Engineering, Pennsylvania State University（宾夕法尼亚州立大学材料科学与工程系）；Zone 5 Technologies（Zone 5 科技公司）
Electromechanical hysteresis loop formation in piezoresponse force microscopy of thin ferroelectric films is studied with special emphasis on the effects of tip size and film thickness, as well as dependence on the tip voltage frequency. Here, we use a combination of Landau-Ginzburg-Devonshire (LGD) theory for the description of the local polarization reversal with decoupling approximation for the calculation of the local piezoresponse loops shape, coercive voltages and amplitude. LGD approach enables addressing both thermodynamics and kinetics of hysteresis loop formation. In contrast to the …
High-Sc Al1-xScxN thin films are of tremendous interest because of their attractive piezoelectric and ferroelectric properties, but overall film quality and reproducibility are widely reported to suffer as x increases. In this study, we correlate the structure and electrical properties of Al0.6Sc0.4N with in-situ observations of glow discharge optical emission during growth. This in-situ technique uses changes in the Ar(I) and N2(I) emission lines of the glow discharge during growth to identify films that subsequently exhibit unacceptable structural and electrical performance. We show that a s…
Devonshire theory provides a successful phenomenological description of many cubic perovskite ferroelectrics such as BaTiO3 via a sixth-order expansion of the free energy in the polar order parameter. However, the recent discovery of a novel monoclinic ferroelectric phase in the PZT system by Noheda et al. (Appl. Phys. Lett. 74, 2059 (1999)) poses a challenge to this theory. Here, we confirm that the sixth-order Devonshire theory cannot support a monoclinic phase, and consider extensions of the theory to higher orders. We show that an eighth-order theory allows for three kinds of equilibrium p…
Macroscopic modelling of ferroelectric properties refers usually to Landau-Ginzburg-Devonshire theory. This paper questions the meaningfulness of this term, discussing contributions of the three authors to what is supposed to be a theory. The limitations of every contribution are analyzed. In the main text and, to more extent in the Supplementary Material, the Landau theory is presented from an unusual perspective starting from simple mechanical models of spontaneous symmetry breaking and finishing by the Ising model. The aim of the presentation is to emphasize along with the qualitative break…
Mechanically compatible and electrically neutral domain walls in tetragonal, orthorhombic and rhombohedral ferroelectric phases of BaTiO3 are systematically investigated in the framework of the phenomenological Ginzburg-Landau-Devonshire (GLD) model with parameters of Ref. [Hlinka and Marton, Phys. Rev. 74, 104104 (2006)]. Polarization and strain profiles within domain walls are calculated numerically and within an approximation leading to the quasi-one-dimensional analytic solutions applied previously to the ferroelectric walls of the tetragonal phase [W. Cao and L.E. Cross, Phys. Rev. 44, 5 …
Systematic comparison of approximations and functionals in first-principle calculations of aluminum-based III-V ferroelectric nitrides
University of Arkansas（阿肯色大学）；Guangdong Technion – Israel Institute of Technology（广东以色列理工学院）；Colorado School of Mines（科罗拉多矿业学院）；National Laboratory of the Rockies（落基山国家实验室）；Tel Aviv University（特拉维夫大学）；Université Paris-Saclay（巴黎萨克雷大学）；CentraleSupélec（中央苏佩雷勒高等电信学院）
Thermodynamics of tip-induced nanodomain formation in scanning probe microscopy of ferroelectric films and crystals is studied using the Landau-Ginzburg-Devonshire phenomenological approach. The local redistribution of polarization induced by the biased probe apex is analyzed including the effects of polarization gradients, field dependence of dielectric properties, intrinsic domain wall width, and film thickness. The polarization distribution inside subcritical nucleus of the domain preceding the nucleation event is very smooth and localized below the probe, and the electrostatic field distri…
The experimentally observed temperature dependence of the quartic coefficients in the Landau-Devonshire expansion for BaTiO_3 is naturally accounted for within a proper fluctuation model. It is explained, in particular, why one of the quartic coefficients varies with temperature above T_c while the second is constant. The tetragonal phase in BaTiO_3 is argued to exist essentially due to the thermal fluctuations, while the true Landau-Devonshire expansion with temperature-independent coefficients favours the rhombohedral ferroelectric phase. Certain conclusions concerning the temperature depend…
An effort based on the kinetic model allowed by Landau-Ginzburg-Devonshire theory is presented here. The formation of vortex, antivortex states in ferroelectric films are reported and theoretically explained. Phase transition in toroidal moment is observed. Vortex-antivortex-vortex (V-AV-V) triplet is generated by applying inhomogeneous transverse static localized fields in x-y plane. A specific boundary condition is used to keep the spirit of vortex state i.e. the net polarization across the boundary is always zero. %This is neither a periodic nor an open circuit electric boundary condition.
The nanodomain pattern in ferroelectric/dielectric superlattices transforms to a uniform polarization state under above-bandgap optical excitation. X-ray scattering reveals a disappearance of domain diffuse scattering and an expansion of the lattice. The reappearance of the domain pattern occurs over a period of seconds at room temperature, suggesting a transformation mechanism in which charge carriers in long-lived trap states screen the depolarization field. A Landau-Ginzburg-Devonshire model predicts changes in lattice parameter and a critical carrier concentration for the transformation.
The effects of space charges on hysteresis loops and field distributions in ferroelectrics have been investigated numerically using the phenomenological Landau-Ginzburg-Devonshire theory. Cases with the ferroelectric fully and partially depleted have been considered. In general, increasing the number of charged impurities results in a lowering of the polarization and coercive field values. Squarer loops were observed in the partially depleted cases and a method was proposed to identify fully depleted samples experimentally from dielectric and polarization measurements alone. Unusual field dist…
Using direct variational method with 2-parametric trial function and Landau-Ginzburg-Devonshire thermodynamical approach, we derived analytical expressions for polarization spatial redistribution in the ferroelectrics caused by the biased Scanning Probe Microscope probe. We demonstrate that the shape of nanodomain induced by the probe electric field can be either oblate or prolate depending on the ferroelectric nonlinearity strength. For typical ferroelectric material parameters and probe apex geometry the domain nucleus aspect ratio is close to dielectric anisotropy factor. Corresponding coer…
Epitaxial strain can be used to modify the properties of ferroelectric thin films. From the experimental viewpoint, the challenge is to fine-tune the magnitude of the strain. We illustrate how, by using a suitable combination of composition and substrate, the magnitude of the epitaxial strain can be controlled in a continuous manner. The phase diagram of PbxSr1-xTiO3 films grown epitaxially on (110)-DyScO3 is calculated using a Devonshire-Landau approach. A boundary between in-plane and out-of-plane oriented ferroelectric phases is predicted to take place at $x \approx$ 0.8. A series of PbxSr1…
A phenomenological treatment of domain walls based on the Ginzburg-Landau-Devonshire theory is developed for uniaxial, trigonal ferroelectrics lithium niobate and lithium tantalate. The contributions to the domain wall energy from polarization and strain as a function of orientation are considered. Analytical expressions are developed which are analyzed numerically to determine the minimum polarization, strain, and energy configurations of domain walls. It is found that hexagonal y-walls are preferred over x-walls in both materials. This agrees well with experimental observation of domain geom…
Tunable transmittance response in the $0.1-25$ THz range for a lead Zirconate Titanate Ferroelectric film under imprint effects and surface anisotropy is calculated by adapting the classical Landau Devonshire theory and the Rouard's method. Induced electrical field is introduced by modulating the $P-E$ polarization profile, while the dielectric permittivity frequency dependence enters into the formalism by taking into the account the soft phonon mode E(TO1) contribution in the framework of the Drude-Lorentz model. It is found that two optical states of light transmittance emerge at zero applie…
The effect of polarization rotation on the performance of metal oxide semiconductor field-effect transistors was investigated with a Landau-Ginzburg-Devonshire theory based model. In this analytical model, depolarization field, polarization rotations and the electrostatic properties of the doped silicon substrate are considered to illustrate the size effect of ferroelectric oxides and the stability of polarization in each direction. Based on this model, we demonstrate that MOSFET operation could be achieved by polarization reorientation with a low operating voltage, if the thickness of ferroel…
Using a Ginzburg--Landau--Devonshire model that includes the coupling of polarization to strain, we calculate the fluctuation spectra of ferroelectric domain walls. The influence of the strain coupling differs between 180 degree and 90 degree walls due to the different strain profiles of the two configurations. The finite speed of acoustic phonons, $v_s$, retards the response of the strain to polarization fluctuations, and the results depend on $v_s$. For $v_s \to \infty$, the strain mediates an instantaneous electrostrictive interaction, which is long-range in the 90 degree wall case. For fin…
We studied the phase diagram of thin ferroelectric films with incommensurate phases and semiconductor properties within the framework of Landau-Ginzburg-Devonshire theory. We performed both analytical calculations and phase-field modelling of the temperature and thickness dependencies of the period of incommensurate 180 degree domain structures appeared in thin films covered with perfect electrodes. It is found that the transition temperature from the paraelectric into the incommensurate phase as well as the period of incommensurate domain structure strongly depend on film thickness, and surfa…
Using the modified Landau-Ginsburg-Devonshire thermodynamic theory, it is found that the coupling between stress gradient and polarization, or flexoelectricity, has significant effect on ferroelectric properties of epitaxial thin films, such as polarization, free energy profile and hysteresis loop. However, this effect can be completely eliminated by applying an optimized external, uniform electric field. The role of such uniform electric field is shown to be the same as that of an ideal gradient electric field which can suppress the flexoelectricty effect completely based on the present theor…
We study the effect of depolarization field related with inhomogeneous polarization distribution, strain and surface energy parameters on a domain wall profile near the surface of a ferroelectric film within the framework of Landau-Ginzburg-Devonshire phenomenology. Both inhomogeneous elastic stress and positive surface energy lead to the wall broadening at electrically screened surface. For ferroelectrics with weak piezoelectric coupling, the extrapolation length that defines surface energy parameter, affects the wall broadening more strongly than inhomogeneous elastic stress. Unexpectedly, t…
We analyze theoretically the finite-temperature polarization dynamic in displacive-type ferroelectrics. In particular we consider the thermally-activated switching time of a single-domain ferroelectric polarization studied by means of the Landau-Khalatnikov equation, extended as to capture thermal fluctuations. The results are compared with the switching time formula that follows from the analytical solution of Pauli master equations. In a second step we focus on the phase diagram of a prototypical ferroelectric as described by the temperature-dependent Landau-Devonshire model including therma…
A Landau-Ginsburg-Devonshire-type nonlinear phenomenological theory is presented, which enables the thermodynamic description of dense laminar polydomain states in epitaxial ferroelectric thin films. The theory explicitly takes into account the mechanical substrate effect on the polarizations and lattice strains in dissimilar elastic domains (twins). Numerical calculations are performed for PbTiO3 and BaTiO3 films grown on (001)-oriented cubic substrates. The "misfit strain-temperature" phase diagrams are developed for these films, showing stability ranges of various possible polydomain and si…
Using Landau-Ginzburg-Devonshire approach we calculated the equilibrium distributions of electric field, polarization and space charge in the ferroelectric-semiconductor heterostructures containing proper or incipient ferroelectric thin films. The role of the polarization gradient and intrinsic surface energy, interface dipoles and free charges on polarization dynamics are specifically explored. The intrinsic field effects, which originated at the ferroelectric-semiconductor interface, lead to the surface band bending and result into the formation of depletion space-charge layer near the semic…
Heterostructures consisting of PbZr0.2Ti0.8O3 and PbZr0.4Ti0.6O3 films grown on a SrTiO3 (100) substrate with a SrRuO3 bottom electrode were prepared by pulsed laser deposition. Using the additional interface provided by the ferroelectric bilayer structure and changing the sequence of the layers, the dislocation content and domain patterns were varied. The resulting microstructure was investigated by transmission electron microscopy. Macroscopic ferroelectric measurements have shown a large impact of the formation of dislocations and the a/c domain structure on the ferroelectric polarization a…
In the framework of the Landau-Ginzburg-Devonshire (LGD) approach we studied finite size effects of the phase diagram and domain structure evolution in spherical nanoparticles of uniaxial ferroelectric. The particle surface is covered by a layer of screening charge characterized by finite screening length. The phase diagram, calculated in coordinates "particle radius vs. screening length" has a wide region of versatile poly-domain structures separating single-domain ferroelectric and nonpolar paraelectric phases. Unexpectedly, we revealed a region of stable irregular labyrinthine domains in th…
The possibility of controlling the domain structure in spherical nanoparticles of uniaxial and multiaxial ferroelectrics using a shell with tunable dielectric properties is studied in the framework of Landau-Ginzburg-Devonshire theory. Finite element modeling and analytical calculations are performed for Sn2P2S6 and BaTiO3 nanoparticles covered with high-k polymer, temperature dependent isotropic paraelectric strontium titanate, or anisotropic liquid crystal shells with a strongly temperature dependent dielectric permittivity tensor. It appeared that the tunable paraelectric shell with a tempe…
Thermomechanical cycles with a ferroelectric working substance convert heat to electrical energy. As shown here, magnetoelectrically coupled ferroelectric/ferromangtic composites (also called multiferroics) add new functionalities and allow for an efficient thermal energy harvesting at room temperature by exploiting the pyroelectric effect. By virtue of the magnetoelectric coupling, external electric and magnetic fields can steer the operation of these heat engines. Our theoretical predictions are based on a combination of Landau-Khalatnikov-Tani approach (with a Ginzburg-Landau-Devonshire pot…
Recently, a layered ferroelectric CuInP2Se6 was shown to exhibit domain walls with locally enhanced piezoresponse - a striking departure from the observations of nominally zero piezoresponse in most ferroelectrics. Although it was proposed that such "bright" domain walls are phase-boundaries between ferri- and antiferroelectrically ordered regions of the materials, the physical mechanisms behind the existence and response of these boundaries remain to be understood. Here, using Landau-Ginzburg-Devonshire phenomenology combined with four sub-lattices model, we describe quantitatively the bright…
The conductance of domain wall structures consisting of either stripes or cylindrical domains in multi-axial ferroelectric-semiconductors is analyzed. The effects of the domain size, wall tilt and curvature, on charge accumulation, are analyzed using the Landau-Ginsburg Devonshire (LGD) theory for polarization combined with Poisson equation for charge distributions. Both the classical ferroelectric parameters including expansion coefficients in 2-4-6 Landau potential and gradient terms, as well as flexoelectric coupling, inhomogeneous elastic strains and electrostriction are included in the pr…
Despite multiple efforts, there exist many unsolved fundamental problems related with detection and analysis of internal polarization structure and related phase transitions in ferroelectric domain walls. Their solution can be very important for the progress in domain wall nanoelectronics and related applications in advanced memories and other information technologies. Here, we theoretically study the features of phase transitions in the domain walls, which are potentially detectable by the scanning probe capacitance microwave microscopy. The finite element modelling based on the Landau-Ginzbu…
Analytical description of domain structure morphology and phase diagrams of ferroelectric nanoparticles is developed in the framework of Landau Ginzburg Devonshire approach. To model realistic conditions of incomplete screening of spontaneous polarization at the particle surface, it was considered covered by an ultra-thin layer of screening charge with finite screening length. The phase diagrams, calculated for spherical Sn2P2S6 nanoparticles in coordinates "temperature vs surface screening length" by finite element modeling, demonstrate the emergence of polydomain region at the tricritical po…
In the framework of Landau--Ginzburg--Devonshire (LGD) phenomenological theory, the influence of misfit strains, surface energy, and finite-size effects on phase diagrams, polar properties, and hysteresis loops has been calculated for multilayered thin films of the type ferroelectric/virtual ferroelectric. The influence of elastic deformations that arise at the interface thin film--substrate owing to a mismatch between the lattice constants in the film and the substrate on the phase diagrams of multilayered thin films virtual ferroelectric SrTiO$_{3}$/ferroelectric BaTiO$_{3}$ has been studied…
We present a theoretical description of the influence of misfit strain on mobile defects dynamics in thin strained ferroelectric films. Self-consistent solutions obtained by coupling the Poissons equation for electric potential with continuity equations for mobile donor and electron concentrations and time-dependent Landau-Ginzburg-Devonshire equations reveal that the Vegard mechanism (chemical pressure) leads to the redistribution of both charged and electro-neutral defects in order to decrease the effective stress in the film. Internal electric fields, both built-in and depolarization ones, …
General features of finite size effects in the ferroelectric-semiconductor film under open-circuited electric boundary conditions are analyzed using Landau-Ginzburg-Devonshire theory and continuum media electrostatics. The temperature dependence of the film critical thickness, spontaneous polarization and depolarization field profiles of the open-circuited films are found to be significantly different compared to the short-circuited ones. In particular, we predict the re-entrant type transition boundary between the mono-domain and poly-domain ferroelectric states due to reduced internal screen…
Sizes of Ferroelectricity Appearance and Disappearence in Nanosized Hafnia-Zirconia:Landau-type Theory
Institute of Physics of the National Academy of Sciences of Ukraine（乌克兰国家科学院物理研究所）；Frantsevich Institute for Problems in Materials Science of the National Academy of Sciences of Ukraine（乌克兰国家科学院弗兰采维奇材料科学问题研究所）；Department of Materials Science and Engineering, University of Tennessee（田纳西大学材料科学与工程系）；Faculty of Radiophysics, Electronics and Computer Systems, Taras Shevchenko National University of Kyiv（基辅塔拉斯舍甫琴科国立大学无线电物理、电子和计算机系统学院）；V. Lashkariov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine（乌克兰国家科学院V.拉什卡廖夫半导体物理研究所）
Motion of ferroelectric domain walls greatly contributes to the macroscopic dielectric and piezoelectric response of ferroelectric materials. The domain wall motion through the ferroelectric material is however hindered by pinning on crystal defects which substantially reduces these contributions. Here, using thermodynamic models based on the Landau-Ginzburg-Devonshire theory, we find a relation between microscopic reversible motion of non-ferroelastic 180-degree domain walls interacting with a periodic array of pinning centers and the nonlinear macroscopic permittivity. We show, that the reve…
Current-voltage characteristics and $P-E$ loops are simulated in SrRuO$_{3}$/BaTiO$_{3}$/Pt tunneling junctions with interfacial dead layer. The unswitchable interfacial polarization is coupled with the screen charge and the barrier polarization self-consistently within the Thomas-Fermi model and the Landau-Devonshire theory. The shift of P-E loop from the center position and the unequal values of the positive coercive field and the negative coercive field are found, which are induced by the asymmetricity of interface dipoles. A complete J-V curve of the junction is shown for different barrier…
Thermodynamic theory is developed for the ferroelectric phase transition of an ultrathin film in equilibrium with a chemical environment that supplies ionic species to compensate its surface. Equations of state and free energy expressions are developed based on Landau-Ginzburg-Devonshire theory, using electrochemical equilibria to provide ionic compensation boundary conditions. Calculations are presented for a monodomain PbTiO$_3$ (001) film coherently strained to SrTiO$_3$ with its exposed surface and its electronically conducting bottom electrode in equilibrium with a controlled oxygen parti…
An electro-optic modulator offers the function of modulating the propagation of light in a material with electric field and enables 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 phenomenol…
We develop a phenomenological thermodynamic theory of ferroelectric BaTiO3 (BT) thin films epitaxially grown on cubic substrates using the Landau-Devonshire eight-order potential. The constructed "misfit-temperature" phase diagram is asymmetrical. We found that, overall view of the phase diagram depends on the values of compliances used in calculations and provide two qualitatively different diagrams. A thermodynamic path for BT film grown onto particular substrate can be found using a plot of the room-temperature tetragonal distortion (c-a)/a as a function of misfit strain.
Using Landau-Ginzburg-Devonshire theory, we considered the impact of the flexoelectro-chemical coupling on the size effects inpolar properties and phase transitions of thin ferroelectric films with a layer of elastic defects. We investigated a typical case, when defects fill a thin layer below the top film surface with a constant concentration creating an additional gradient of elastic fields. The defective surface of the film is not covered with an electrode, but instead with an ultra-thin layer of ambient screening charges, characterized by a surface screening length. This geometry is typica…
For advanced applications in modern industry it is very important to reduce the volume of ferroelectric nanoparticles without serious deterioration of their polar properties. In many practically important cases fixed volume (rather than fixed size) corresponds to realistic technological conditions of nanoparticles fabrication. The letter is focused on the theoretical study of the behavior of ferroelectric polarization, paramagnetoelectric coefficient and phase diagrams of semi-ellipsoidal nanoparticles with fixed volume V. Our approach combines the Landau-Ginzburg-Devonshire phenomenology, cla…
Piezoelectrics have long been studied using parameterized models fit to experimental data, starting with the work of Devonshire in 1954. Much has been learned using such approaches, but they can also miss major phenomena if the materials properties are not well under-stood, as is exemplified by the realization that low-symmetry monoclinic phases are common around morphotropic phase boundaries, which was missed completed by low-order Devonshire models, and can only appear in higher order models. In the last 15 years, a new approach has developed using first-principles computations, based on fun…
Bismuth ferrite (BiFeO3) is one of the most promising multiferroics with a sufficiently high ferroelectric (FE) and antiferromagnetic transition temperatures, and magnetoelectric (ME) coupling coefficient at room temperature, and thus it is highly sensitive to the impact of cross-influence of applied electric and magnetic fields. According to the urgent demands of nanotechnology miniaturization for ultra-high density data storage in advanced nonvolatile memory cells, it is very important to reduce the sizes of multiferroic nanoparticles in the self-assembled arrays without serious deterioratio…
