According to a continuous medium theory, in very thin ferroelectric films with real metallic electrodes (or dead layers near the electrodes) the domain structure reduces to sinusoidal distribution of ferroelectric polarization. Such a sinusoidal structure was considered in 1980s for para-ferroelectric phase transition in a capacitor with dead layers near electrode. We give a review of this theory and its further development for the case of real metallic electrodes. The goal of the general theory is to consistently interpret the experimental data in very thin films with real metallic electrodes. This is illustrated on a recent experimental data for 5-30 nm BaTiO3 films with SrRuO3/SrTiO3 electrodes. The screening length by real metallic electrodes is very small small (<1A), but it has a profound effect on ferroelectric properties and its phase behavior. This general theory also allows to formulate the important open problems and show paths towards their solution. In particular, this is a problem of finding parameters of the system, which can sustain the ferroelectric memory over a desired lifetime.
Switching kinetics in ultrathin epitaxial BaTiO3 films confirms the existence of the homogeneous switching (without domains) in ultrathin ferroelectric films. We suppose that the homogeneous switching in ultrathin films is a common phenomenon for all ferroelectric materials.
We study the ferroelectric stability and surface structural properties of an oxygen-terminated hexagonal YMnO$_3$ ultra-thin film using density functional theory. Under an open circuit boundary condition, the ferroelectric state with the spontaneous polarization normal to the (0001) surface, is found to be metastable in a single domain state despite the presence of a depolarizing field. We establish a connection between the result and the role of improper ferroelectric transition. Our results imply that improper ferroelectric ultrathin films can have rather unique properties that are distincti…
Time-dependent polarization relaxation behaviors induced by a depolarization field $E_{d}$ were investigated on high-quality ultrathin SrRuO$_{3}$/BaTiO$_{3}$/SrRuO$_{3}$ capacitors. The $E_d$ values were determined experimentally from an applied external field to stop the net polarization relaxation. These values agree with those from the electrostatic calculations, demonstrating that a large $E_{d}$ inside the ultrathin ferroelectric layer could cause severe polarization relaxation. For numerous ferroelectric devices of capacitor configuration, this effect will set a stricter size limit than…
X-ray photoelectron diffraction is used to directly probe the intra-cell polar atomic distortion and tetragonality associated with ferroelectricity in ultrathin epitaxial PbTiO3 films. Our measurements, combined with ab-initio calculations, unambiguously demonstrate non-centro-symmetry in films a few unit cells thick, imply that films as thin as 3 unit cells still preserve a ferroelectric polar distortion, and also show that there is no thick paraelectric dead layer at the surface.
The ground-state polarization of PbTiO3 thin films is studied using a microscopic effective Hamiltonian with parameters obtained from first-principles calculations. Under short-circuit electrical boundary conditions, (001) films with thickness as low as three unit cells are found to have a perpendicularly polarized ferroelectric ground state with significant enhancement of the polarization at the surface.
Interface effects on the ferroelectric behavior of PbTiO$_3$ ultrathin films deposited on SrTiO$_3$ substrate are investigated using an interatomic potential approach with parameters fitted to first-principles calculations. We find that the correlation of atomic displacements across the film/substrate interface is crucial for the stabilization of the ferroelectric state in films a few unit-cells thick. We show that the minimum film thickness for the appearance of a spontaneous polarized domain state is not an intrinsic property of the ferroelectric film but depends on the polarizability of the…
We have used a first-principles-based scheme to compute the temperature-versus-misfit strain ``Pertsev'' phase diagram of ultrathin films of {\sl incipient} ferroelectric KTaO$_3$. Our results suggest that, at variance with the bulk material, KTaO$_3$ ultrathin films cannot be described as quantum paraelectrics. Rather, the behavior of the films is largely determined by surface/interface effects that favor ferroelectricity and the imperfect screening of the depolarizing fields. This leads to Pertsev phase diagrams that are qualitatively similar to those of {\sl normal} ferroelectrics such as B…
A first-principles-derived approach is developed to study the effects of uncompensated depolarizing electric fields on the properties of Pb(Zr,Ti)O$_3$ ultrathin films for different mechanical boundary conditions. A rich variety of ferroelectric phases and polarization patterns is found, depending on the interplay between strain and amount of screening of surface charges. Examples include triclinic phases, monoclinic states with in-plane and/or out-of-plane components of the polarization, homogeneous and inhomogeneous tetragonal states, as well as, peculiar laminar nanodomains.
A long standing problem of domain switching process - how domains nucleate - is examined in ultrathin ferroelectric films. We demonstrate that the large depolarization fields in ultrathin films could significantly lower the nucleation energy barrier (U*) to a level comparable to thermal energy (kBT), resulting in power-law like polarization decay behaviors. The "Landauer's paradox": U* is thermally insurmountable is not a critical issue in the polarization switching of ultrathin ferroelectric films. We empirically find a universal relation between the polarization decay behavior and U*/kBT.
The instability of ferroelectric ordering in ultra-thin films is one of the most important fundamental issues pertaining realization of a number of electronic devices with enhanced functionality, such as ferroelectric and multiferroic tunnel junctions or ferroelectric field effect transistors. In this paper, we investigate the polarization state of archetypal ultrathin (several nanometres) ferroelectric heterostructures: epitaxial single-crystalline BaTiO$_3$ films sandwiched between the most habitual perovskite electrodes, SrRuO$_3$, on top of the most used perovskite substrate, SrTiO$_3$. We…
Functional devices with ultrathin ferroelectric layers have been attracted as a promising candidate for next-generation memory and logic device applications. Using the ultrathin ferroelectric layers, particularly approaching the two-dimensional limit, however, it is still challenging to control ferroelectric switching and to observe ferroelectricity by spectroscopic tools. In particular, conventional methods such as electrical measurements and piezoelectric response force microscopy are very limited due to leakage currents and the smallness of the ferroelectric signals. Here, we show that the …
Structural studies on ultrathin SrRuO3/BaTiO3/SrRuO3 capacitors, with BaTiO3 thicknesses of between 5 nm and 30 nm, show well-defined interfaces between ferroelectric BaTiO3 and electrode SrRuO3 layers. In these capacitors, we cannot observe any extrinsic electrical effects due to either the formation of an insulating interfacial passive layer or passive-layer-induced charge injection. Such high quality interfaces result in very good fatigue endurance, even for the 5 nm thick BaTiO3 capacitor.
Recent experiments on layered α-In2Se3 have confirmed its room-temperature ferroelectricity under ambient condition. This observation renders α-In2Se3 an excellent platform for developing two-dimensional (2D) layered-material based electronics with nonvolatile functionality. In this letter, we demonstrate non-volatile memory effect in a hybrid 2D ferroelectric field effect transistor (FeFET) made of ultrathin α-In2Se3 and graphene. The resistance of graphene channel in the FeFET is tunable and retentive due to the electrostatic doping, which stems from the electric polarization of the ferroele…
Thickness scaling of ferroelectricity in AlScN is a determining factor for its potential application in neuromorphic computing and memory devices. In this letter, we report on ultrathin (10 nm) Al0.72Sc0.28N films that are ferroelectrically switchable at room temperature. All-epitaxial Al0.72Sc0.28N/Pt heterostructures are grown by magnetron sputtering onto GaN/sapphire substrates followed by an in situ Pt capping approach to avoid oxidation of the Al0.72Sc0.28N film surface. Structural characterization by X-ray diffraction and transmission electron microscopy reveals the established epitaxy. …
Going down to the limit of ultrathin films holds promise for a new generation of devices such as ferroelectric tunnel junctions or resistive memories. However, these length scales also make the devices sensitive to parasitic effects related to miniaturization, and a better understanding of what happens as size is reduced is of practical importance for the future development of these devices. As the experimental advances in materials preparation and characterization have come together with great progress in theoretical modeling of ferroelectrics, both theorists and experimentalists can finally …
We simulate from first-principles the energetic, structural, and electronic properties of ferroelectric domains in ultrathin capacitors made of a few unit cells of BaTiO$_3$ between two metallic SrRuO$_3$ electrodes in short circuit. The domains are stabilized down to two unit cells, adopting the form of a domain of closure, common in ferromagnets but only recently detected experimentally in ferroelectric thin films. The domains are closed by the in-plane relaxation of the atoms in the first SrO layer of the electrode, that behaves more like SrO in highly polarizable SrTiO$_3$ than in metallic…
Previous studies showed that, as ferroelectric films become thinner, their Curie temperature (Tc) and polarization below Tc both typically decrease. In contrast, a recent experiment [Chang et al., Science 353, 274 (2016)] observed that atomic-thick SnTe films have a higher Tc than their bulk counterpart, which was attributed to extrinsic effects. Here, we find, using first-principles calculations, that the 0K energy barrier for the polarization switching (which is a quantity directly related to Tc) is higher in most investigated defect-free SnTe ultrathin films than that in bulk SnTe, and that…
The evolution of tetragonality with thickness has been probed in epitaxial c-axis oriented PbTiO3 films with thicknesses ranging from 500 down to 24 Angstroms. High resolution x-ray pointed out a systematic decrease of the c-axis lattice parameter with decreasing film thickness below 200 Angstroms. Using a first-principles model Hamiltonian approach, the decrease in tetragonality is related to a reduction of the polarization attributed to the presence of a residual unscreened depolarizing field. It is shown that films below 50 Angstroms display a significantly reduced polarization but still re…
The epitaxial growth of multifunctional oxides on semiconductors has opened a pathway to introduce new functionalities to semiconductor device technologies. In particular, ferroelectric materials integrated on semiconductors could lead to low-power field-effect devices that can be used for logic and memory. Essential to realizing such field-effect devices is the development of ferroelectric metal-oxide-semiconductor (MOS) capacitors, in which the polarization of a ferroelectric gate is coupled to the surface potential of a semiconducting channel. Here we demonstrate that ferroelectric MOS capa…
We fabricated ultrathin ferroelectric/correlated electron oxide heterostructures composed of the ferroelectric Pb(Zr0.2Ti0.8)O3 and the correlated electron oxide (CEO) La0.8Sr0.2MnO3 on SrTiO3 substrates by pulsed laser epitaxy. The hole accumulation in the ultrathin CEO layer was substantially modified by heterostructuring with the ferroelectric layer, resulting in an insulator-metal transition. In particular, our thickness dependent study showed that drastic changes in transport and magnetic properties were strongly coupled to the modulation of charge carriers by ferroelectric field effect, …
Perovskite ferroelectric oxides are usually considered to be brittle materials, however, recent work [Dong et al., Science 366, 475 (2019)] demonstrated the super-elasticity in the freestanding BaTiO3 thin films. This property may originate from the ferroelectric domain evolution during the bending, which is difficult to observe in experiments. Therefore, understanding the relation among the bending deformation, thickness of the films, and the domain dynamics is critical for their potential applications in flexible ferroelectric devices. Here, we reported the dynamics of ferroelectric polariza…
Decoupling effects of the resistive-switching behavior on the polarization reversal in ultrathin ferroelectric Hf0.5Zr0.5O2 films
Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Westlake University（西湖大学）；Indian Institute of Science（印度科学学院）；University of Science and Technology Beijing（北京科技大学）
Using density functional theory calculations, ultrathin films of SrVO3(d1) and SrCrO3(d2) on SrTiO3 substrates have been studied as possible multiferroics. Although both are metallic in the bulk limit, they are found to be insulating as a result of orbital ordering driven by lattice distortions at the ultrathin limit. While the distortions in SrVO3 have a first-order Jahn-Teller origin, those in SrCrO3 are ferroelectric in nature. This route to ferroelectricity (FE) results in polarizations comparable with conventional ferroelectrics.
Within the framework of the phenomenological Ginzburg-Landau theory influence of semiconductor electrodes on the properties of thin ferroelectric films is considered. The contribution of the semiconductor electrodes with different Debye screening length of carriers is included in functional of free energy. The influence of highly doped semiconductor electrodes on the depolarization field and the film properties was shown to be great.
Coexistence of ferroelectric and ferrielectric phases in ultrathin antiferroelectric PbZrO3 thin films
Catalan Institute of Nanoscience and Nanotechnology (ICN2)（加泰罗尼亚纳米科学和技术研究所）；School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney（悉尼大学航空航天、机械与机电工程学院）；Institut Català de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚研究与高级研究学院）
The mean-field Landau-type theory is used to analyze the polarization properties of epitaxial ferroelectric thin films grown on dissimilar cubic substrates, which induce biaxial compressive stress in the film plane. The intrinsic effect of the film surfaces on the spontaneous polarization is taken into account via the concept of the extrapolation length. The theory simultaneously allows for the influence of the misfit strain imposed on the film lattice by a thick substrate. Numerical calculations are performed for PbTiO3 and BaTiO3 films under an assumption of the polarization reduction in sur…
Within the framework of the phenomenological Ginzburg-Landau theory influence of metallic electrodes on the properties of thin ferroelectric films is considered. The contribution of the metallic electrodes with different screening length of carriers is included in functional of free energy. The influence of conventional metallic electrodes on the depolarization field and the film properties was shown to be practically the same as for superconductive ones.
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…
We report electrically switchable polarization and ferroelectric domain scaling over a thickness range of 5-100 nm in BiFeO3 films deposited on [110] vicinal substrates. The BiFeO3 films of variable thickness were deposited with SrRuO3 bottom layer using pulsed laser deposition technique. These films have fractal domain patterns and the domain width scales closely with the square root of film thickness, in accordance with the Landau-Lifschitz-Kittel (LLK) law. The Switching Spectroscopy Piezo-response Force Microscopy provides clear evidence for the ferroelectric switching behavior in all the …
Enhancing the performance of nanoscale ferroelectric (FE) field-effect transistors and FE capacitors for memory devices and logic relies on miniaturizing the metal electrode/ferroelectric area and reducing the thickness of the insulator. Although size reductions improve data retention, deliver lower voltage threshold switching, and increase areal density, they also degrade the functional electric polarization. There is a critical, nanometer length $t_\mathrm{FE}^*$ below which the polarization disappears owing to depolarizing field effects. Here we show how to overcome the critical thickness l…
Engraving trenches on the surfaces of ultrathin ferroelectric (FE) films and superlattices promises control over the orientation and direction of FE domain walls (DWs). Through exploiting the phenomenon of DW-surface trench (ST) parallel alignment, systems where DWs are known for becoming electrical conductors could now become useful nanocircuits using only standard lithographical techniques. Despite this clear application, the microscopic mechanism responsible for the alignment phenomenon has remained elusive. Using ultrathin PbTiO$_3$ films as a model system, we explore this mechanism with l…
We describe ferroelectric thin films with circular electrodes and develop a thermodynamic theory that explains previously mysterious experiments. It is found to be especially useful for restricted geometries such as microstructures for which boundary conditions are well known to play an important role in ferroelectric properties. We have explored a new switching mechanism, which consists of an inhomogeneous rotational motion of the polarization and leads to an extended vortex state. The vortex appearance exhibits characteristic properties of a first-order field-induced phase transition: three …
Cornell University（康奈尔大学）；University of Nebraska, Lincoln（内布拉斯加大学林肯分校）；Leibniz-Institut für Kristallzüchtung（莱布尼茨晶体生长研究所）；Pacific Northwest National Laboratory（太平洋西北国家实验室）；The Pennsylvania State University（宾夕法尼亚州立大学）；University of California, Berkeley（加州大学伯克利分校）；Rice University（莱斯大学）；Kavli Institute at Cornell for Nanoscale Science（康奈尔卡弗里纳米科学研究所）；Princeton University（普林斯顿大学）
Epitaxial orthorhombic Hf0.5Zr0.5O2 (HZO) films on La0.67Sr0.33MnO3 (LSMO) electrodes show robust ferroelectricity, with high polarization, endurance and retention. However, no similar results have been achieved using other perovskite electrodes so far. Here, LSMO and other perovskite electrodes are compared. A small amount of orthorhombic phase and low polarization is found in HZO films grown on La-doped BaSnO3 and Nb-doped SrTiO3, while null amounts of orthorhombic phase and polarization are detected in films on LaNiO3 and SrRuO3. The critical effect of the electrode on the stabilized phases…
The structural interface properties of layered Pt/Ti/SiO2/Si electrodes have been investigated using high-resolution specular and diffuse x-ray reflectivity under grazing angles. Currently this multilayer system represents a technological standard as bottom electrodes for ferroelectric thin film applications. For the electronic and ferroelectric properties of integrated devices, the film-electrode interface is of crucial importance. We focused on Pt-100nm/Ti-10nm/SiO2/Si electrodes prepared under annealing conditions as employed in industrial processing, prior to the deposition of ferroelectri…
Ferroelectric (FE) size effects against the scaling law were reported recently in ultrathin group-IV monochalcogenides, and extrinsic effects (e.g. defects and lattice strains) were often resorted to. Via first-principles based finite-temperature ($T$) simulations, we reveal that these abnormalities are intrinsic to their unusual symmetry breaking from bulk to thin film. Changes of the electronic structures result in different order parameters characterizing the FE phase transition in bulk and in thin films, and invalidation of the scaling law. Beyond the scaling law $T_{\text{c}}$ limit, this…
Graphene is attractive for spintronics due to its long spin life time and high mobility. So far only thick and polycrystalline slabs have been used as ferromagnetic electrodes. We report the growth of flat, epitaxial ultrathin Co films on graphene. These display perpendicular magnetic anisotropy in the thickness range 0.5-1nm, which is confirmed by theory. PMA, epitaxy and ultrathin thickness bring new perspectives for graphene-based spintronic devices such as the zero-field control of an arbitrary magnetization direction, band matching between electrodes and graphene, and interface effects su…
We present molecular dynamics simulations of a realistic model of an ultrathin film of BaTiO$_3$ sandwiched between short-circuited electrodes to determine and understand effects of film thickness, epitaxial strain and the nature of electrodes on its ferroelectric phase transitions as a function of temperature. We determine a full epitaxial strain-temperature phase diagram in the presence of perfect electrodes. Even with the vanishing depolarization field, we find that ferroelectric phase transitions to states with in-plane and out-of-plane components of polarization exhibit dependence on thic…
Finite size effects in ferroelectric thin films have been probed in a series of epitaxial perovskite c-axis oriented PbTiO3 films grown on thin La0.67Sr0.33MnO3 epitaxial electrodes. The film thickness ranges from 480 down to 28 A (7 unit cells). The evolution of the film tetragonality c/a, studied using high resolution x-ray diffraction measurements, shows first a decrease of c/a with decreasing film thickness followed by a recovery of c/a at small thicknesses. This recovery is accompanied by a change from a monodomain to a polydomain configuration of the polarization, as directly demonstrate…
Macroscopic properties of ferroelectric samples, including those in form of thin films, are, to large extent, influenced by their domain structure. In this paper the free energy is calculated for a plate-like sample composed of nonferroelectric surface layers and ferroelectric central part with antiparallel domains. The sample is provided with electrodes with a defined potential difference. The effect of applied field and its small changes on the resulting domain structure is discussed. This makes it possible to determine the restoring force acting on domain walls which codetermines dielectric…
We report studies of ferroelectricity in ultra-thin perovskite films with realistic electrodes. The results reveal stable ferroelectric states in thin films less than 10 Åthick with polarization normal to the surface. Under short-circuit boundary conditions, the screening effect of realistic electrodes and the influence of real metal/oxide interfaces on thin film polarization are investigated. Our studies indicate that metallic screening from the electrodes is affected by the difference in work functions at oxide surfaces. We demonstrate this effect in ferroelectric PbTiO$_3$ and BaTiO$_3$ fil…
Understanding and controlling the motion, stability, and equilibrium configuration of ferroelectric domain walls is key for their integration into potential nanoelectronics applications, such as ferroelectric racetrack memories. Using piezoresponse force microscopy we analyse the growth and roughness of ferroelectric domains in epitaxial thin film Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$, driven by the electric fields at straight edges of planar electrodes at two different temperatures. This device relevant geometry allows us to confirm that the domain walls are well described as 1-dimensional monoaffine…
Graphene has exceptional optical, mechanical and electrical properties, making it an emerging material for novel optoelectronics, photonics and for flexible transparent electrode applications. However, the relatively high sheet resistance of graphene is a major constrain for many of these applications. Here we propose a new approach to achieve low sheet resistance in large-scale CVD monolayer graphene using non-volatile ferroelectric polymer gating. In this hybrid structure, large-scale graphene is heavily doped up to 3{\times}1013 cm-2 by non-volatile ferroelectric dipoles, yielding a low she…
A (124)-oriented SrBi4Ti4O15 (SBTi) ferroelectric thin film with high volume fraction of αSBTi(124)=97% was obtained using a metal organic decomposition process on SiO2/Si substrate coated by (110)-oriented LaNiO3 (LNO) thin film. The remanent polarization and coercive field for (124)-oriented SBTi film are 12.1 μC/cm2 and 74 kV/cm, respectively. No evident fatigue of (124)-oriented SBTi thin film can be observed after 1{\times}10e9 switching cycles. Besides, the (124)-oriented SBTi film can be uniformly polarized over large areas using a piezoelectric-mode atomic force microscope. Considering…
A newly developed fast molecular-dynamics method is applied to BaTiO3 ferroelectric thin-film capacitors with short-circuited electrodes or under applied voltage. The molecular-dynamics simulations based on a first-principles effective Hamiltonian clarify that dead layers (or passive layers) between ferroelectrics and electrodes markedly affect the properties of capacitors, and predict that the system is unable to hop between a uniformly polarized ferroelectric structure and a striped ferroelectric domain structure at low temperatures. Simulations of hysteresis loops of thin-film capacitors ar…
