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 that the annealing temperature was 650°C and the thickness of each deposited layer was merely 30 nm, a long-range epitaxial relationship between SBTi(124) and LNO(110) facets was proposed. The epitaxial relationship was demonstrated based on the crystal structures of SBTi and LNO.
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.
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.
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…
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 …
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…
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…
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…
Noncentrosymmetric bulk crystals generate photocurrent without any bias voltage. One of the dominant mechanisms, shift current, comes from a quantum interference of electron wave functions being distinct from classical current caused by electrons' drift or diffusion. The dissipation-less nature of shift current, however, has not been fully verified presumably due to the premature understanding on the role of electrodes. Here we show that the photocurrent dramatically enhances by choosing electrodes with large work function for a $p$-type ferroelectric semiconductor SbSI. An optimized device sh…
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…
The influence of depolarizing field on the magnitude and stability of a uniform polarization in ferroelectric capacitors and tunnel junctions is studied using a nonlinear thermodynamic theory. It is predicted that, in heterostructures involving strained epitaxial films and metal electrodes, the homogeneous polarization state may remain stable against transformations into the paraelectric phase and into polydomain states down to the nanoscale. This result supports the possibility of depolarizing-field-related resistive switching in ferroelectric tunnel junctions with dissimilar electrodes. The …
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…
The effective barrier height between an electrode and a ferroelectric (FE) depends on both macroscopic electrical properties and microscopic chemical and electronic structure. The behavior of a prototypical electrode/FE/electrode structure, Pt/BaTiO3/Nb-doped SrTiO3, under in-situ bias voltage is investigated using X-Ray Photoelectron Spectroscopy. The full band alignment is measured and is supported by transport measurements. Barrier heights depend on interface chemistry and on the FE polarization. A differential response of the core levels to applied bias as a function of the polarization st…
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…
We examine the application of short-circuit electrical boundary conditions in density functional theory calculations of ferroelectric thin films. Modeling PbTiO$_3$ films with Pt electrodes, we demonstrate that under periodic boundary conditions of supercells, short-circuit conditions for the electrodes are equivalently satisfied in two repeated slab geometries: a PbTiO$_3$/metal superlattice geometry and a periodic metal/PbTiO$_3$/metal/vacuum geometry, where the metal is Pt or SrRuO$_3$. We discuss the benefits of each geometry in the study of ferroelectricity in thin films.
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…
Organic spintronic devices have been appealing because of the long spin life time of the charge carriers in the organic materials and their low cost, flexibility and chemical diversity. In previous studies, the control of resistance of organic spin valves is generally achieved by the alignment of the magnetization directions of the two ferromagnetic electrodes, generating magnetoresistance.1 Here we employ a new knob to tune the resistance of organic spin valves by adding a thin ferroelectric interfacial layer between the ferromagnetic electrode and the organic spacer. We show that the resista…
The critical impact of epitaxial stress on the stabilization of the ferroelectric orthorhombic phase of hafnia is proved. Epitaxial bilayers of Hf0.5Zr0.5O2 and La0.67Sr0.33MnO3 electrodes were grown on a set of single crystalline oxide 001-oriented, cubic or pseudocubic setting, substrates with lattice parameter in the 3.71 - 4.21 A range. The lattice strain of the La0.67Sr0.33MnO3 electrode, determined by the lattice mismatch with the substrate, is critical in the stabilization of the orthorhombic phase of Hf0.5Zr0.5O2. On La0.67Sr0.33MnO3 electrodes tensile strained most of the Hf0.5Zr0.5O2…
Electron transport through fully depleted ferroelectric tunnel barriers sandwiched between two metal electrodes and its dependence on ferroelectric polarization direction are investigated. The model assumes a polarization direction dependent ferroelectric barrier. The transport mechanisms, including direct tunneling, Fowler-Nordheim tunneling and thermionic injection, are considered in the calculation of the electroresistance as a function of ferroelectric barrier properties, given by the properties of the ferroelectric, the barrier thickness, and the metal properties, and in turn of the polar…
In thin film ferroelectric capacitor the chemical and electronic structure of the electrode/FE interface can play a crucial role in determining the kinetics of polarization switching. We investigate the electronic structure of a Pt/BaTiO3/SrTiO3:Nb capacitor using time-resolved photoemission spectroscopy. The chemical, electronic and depth sensitivity of core level photoemission is used to probe the transient response of different parts of the upper electrode/ferroelectric interface to voltage pulse induced polarization reversal. The linear response of the electronic structure agrees quantitat…
Recent experimental results demonstrate that in thin films ferroelectricity persists down to film thickness of a few unit cells. This finding opens an avenue for novel electronic devices based on ultathin ferroelectrics, but also raises questions about factors controlling ferroelectricity and the nature of the ferroelectric state at the nanoscale. Here we report a first-principles study of KNbO3 ferroelectric thin films placed between two metal electrodes, either SrRuO3 or Pt. We show that the bonding at the ferroelectric-metal interface imposes severe constraints on the displacement of atoms,…
First-principles modeling of ferroelectric capacitors presents several technical challenges, due to the coexistence of metallic electrodes, long-range electrostatic forces and short-range interface chemistry. Here we show how these aspects can be efficiently and accurately rationalized by using a finite-field density-functional theory formalism in which the fundamental electrical variable is the displacement field D. By performing calculations on model Pt/BaTiO3/Pt and Au/BaZrO3/Au capacitors we demonstrate how the interface-specific and bulk-specific properties can be identified and rigorousl…
Using an experimental setup designed to scan a submicron sized light spot and collect the photogenerated current through larger electrodes, we map the photovoltaic response in ferroelectric BiFeO3 single crystals. We study the effect produced by a unique 180{\textdegree} ferroelectric domain wall (DW) and show that the photocurrent maps are significantly affected by its presence and shape. The effect is large in its vicinity and in the Schottky barriers at the interface with the Au electrodes, but no extra photocurrent is observed when the illuminating spot touches the DW, indicating that this…
A modified model of metal-semiconductor contacts is applied to analyze the capacitance-voltage and current-voltage characteristics of metal-ferroelectric-metal structures. The ferroelectric polarization is considered as a sheet of surface charge situated at a fixed distance from the interface. The presumable high concentration of structural defects acting as active electric traps is taken into account by introducing a deep acceptor-like level. The model is applied on a set of metal-PZT--metal samples with different Zr/Ti ratios, deposited by different methods, and having different thickness, e…
Unconventional ferroelectricity, robust at reduced nanoscale sizes, exhibited by hafnia-based thin-films presents tremendous opportunities in nanoelectronics. However, the exact nature of polarization switching remains controversial. Here, we investigate epitaxial Hf0.5Zr0.5O2 (HZO) capacitors, interfaced with oxygen conducting metals (La0.67Sr0.33MnO3, LSMO) as electrodes, using atomic resolution electron microscopy while in situ electrical biasing. By direct oxygen imaging, we observe reversible oxygen vacancy migration from the bottom to the top electrode through HZO and reveal associated r…
We present the concept of ferroelectric tunnel junctions (FTJs). These junctions consist of two metal electrodes separated by a nanometer-thick ferroelectric barrier. The current-voltage characteristics of FTJs are analyzed under the assumption that the direct electron tunneling represents the dominant conduction mechanism. First, the influence of converse piezoelectric effect inherent in ferroelectric materials on the tunnel current is described. The calculations show that the lattice strains of piezoelectric origin modify the current-voltage relationship owing to strain-induced changes of th…
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…
A ferroelectric tunnel barrier in between two ferromagnetic electrodes (multiferroic tunnel junction, MFTJ), is one of the most promising concepts for future microelectronic devices. In parallel, Hafnia based ferroelectrics are showing great potential for device miniaturization down to the nanoscale. Here we utilize ferroelectric Hf0.5Zr0.5O2 (HZO) with thickness of only 2 nm, epitaxially grown on La0.7Sr0.3MnO3 (LSMO) ferromagnetic electrodes, as a large band-gap insulating barrier integrated in MFTJs with cobalt top electrodes. As previously reported for other MFTJs with similar electrodes, …
Ferroelectrics have shown potential as a promising alternative material for future photovoltaic applications. Observance of high open circuit voltages in ferroelectric thin films, have generated considerable interest in the field of ferroelectric photovoltaic in recent years. The field of ferroelectric photovoltaic is evolving and not yet completely understood compared to the semiconductor based photovoltaic technology. This dissertation investigates photovoltaic characteristics of ferroelectric films in an attempt to further the understanding of ferroelectric photovoltaic. This dissertation p…
We study ferroelectricity in thin films of pseudo-proper ferroelectrics such as the so-called spiral multiferroics. We find that this type of ferroelectricity stands better against depolarizing fields than conventional one. Its single-domain state can be easily preserved by metallic electrodes even in ultrathin films. In fact, single-domain ferroelectricty can be generated as a metastable state in the absence of electrodes. We also find a new regime of small thickness where unscreened films develop unusual multi-domain states with properties determined by non-electrostatic boundary conditions.
My research is dedicated to the electronic properties of functional oxides. My activity specifically focuses on ferroelectric tunnel junctions in which an ultrathin layer of ferroelectric material is intercalated between two metallic electrodes. In these devices, polarization reversal induces large modifications of the tunnel resistance, leading to a non-destructive readout of the information. After a demonstration of the concept with scanning probe microscopy techniques, I have been exploring the properties of ferroelectric tunnel junctions with various ferroelectric materials (BaTiO3, BiFeO3…
We discuss ferroelectric phase transitions into single- and multidomain states in very thin films using continuous theory. It is shown that in nearly cubic ferroelectrics the domain state may survive down to atomic film thicknesses, unlike the single domain state, which is almost always unstable or metastable. This conclusion is valid almost irrespective of the nature of electrodes (metallic or semiconducting) and whether or not the screening carriers may be present in the ferroelectric itself.
General energy approaches have been applied to study the single-domain polarization reversal induced by the voltage-modulated Atomic Force Microscopy (AFM) in ferroelectric single crystals and thin films. Topographic analysis of energy surfaces in the subspace of domain dimensions is performed, and energy evolutions under an external bias are elucidated. This has let to successfully describe all stages of the AFM switching, including formations of a reversed domain, its growth in a bulk, domain contact instabilities near an electrode, and pure sidewise expansions in a film.
We investigated the ferroelectric properties of strontium titanate (STO) thin films deposited on SrTiO3 (001) substrate with SrRuO3 electrodes. The STO layer was grown coherently on the SrTiO3 substrate without in-plane lattice relaxation, but its out-of-plane lattice constant increased with a decrease in the oxygen pressure during deposition. Using piezoresponse force microscopy and P-V measurements, we showed that our tetragonal STO films possess room-temperature ferroelectricity. We discuss the possible origins of the observed ferroelectricity.
Magnetic tunnel junctions (MTJs), composed of two ferromagnetic electrodes separated by a thin insulating barrier layer, are currently used in spintronic devices, such as magnetic sensors and magnetic random access memories. Recently, driven by demonstrations of ferroelectricity at the nanoscale, thin-film ferroelectric barriers were proposed to extend the functionality of MTJs. Due to the sensitivity of conductance to the magnetization alignment of the electrodes (tunnelling magnetoresistance) and the polarization orientation in the ferroelectric barrier (tunnelling electroresistance), these …
A model for Metal-Ferroelectric-Metal structures with Schottky contacts is proposed. The model adapts the general theories of metal-semiconductor rectifying contacts for the particular case of metal-ferroelectric contact by introducing: the ferroelectric polarization as a sheet of surface charge located at a finite distance from the electrode interface; a deep trapping level of high concentration; the static and dynamic values of the dielectric constant. Consequences of the proposed model on relevant quantities of the Schottky contact such as built-in voltage, charge density and depletion widt…
We investigate the fatigue and refreshment by dc-electrical field of the electrical properties of Pt/Pb(Ti,Zr)O$_3$/Pt ferroelectric capacitors. We find an asymmetry in the refreshment, that is, the fatigued state can be refreshed by application of negative high dc-voltage to the top electrode, but no refreshment is measured by positive dc-voltage application. We also find that the fatigue can be prevented by driving the capacitor asymmetrically.
Thin film growth of ferroelectric or multiferroic materials on SrTiO3(111) with a buffer electrode has been hampered by the difficulty of growing flat electrodes on this polar orientation. We report on the growth and characterization of SrRuO3 thin films deposited by pulsed laser deposition on SrTiO3(111). We show that our SrRuO3(111) films are epitaxial and display magnetic bulk-like properties. Films presenting a thickness between 20 and 30nm are found to be very flat (with an RMS of about 0.5 nm) and therefore suitable as bottom electrodes in heterostructures.
It is known that the permittivity of the ferroelectric films is affected by several phenomena, which deteriorate the material quality (e.g. the redistribution of the crystal lattice defects, appearance of the electrode-adjacent non-ferroelectric layers or the spontaneous polarization screening due to a free charge injection across the electrode-adjacent layer, etc.). It is also known that the permittivity of ferroelectric polydomain films is controlled by the sum of two contributions: the crystal lattice (intrinsic) contribution and the domain wall movement (extrinsic) contribution. It is the …
Pt/Ti metallisation bilayers are used as bottom electrodes for ferroelectric thin films. During deposition of the ferroelectric films, these electrodes are exposed to elevated temperatures causing modifications of the Pt/Ti bottom electrode. Diffusion and oxidation of the Ti adhesion layer have been studied by the application of factor analysis to AES depth profile data and by RBS. Factor analysis was employed to extract the chemical information from the measured AES spectra and to derive semiquantitative depth profiles of the identified material compounds. RBS was used to obtain the quantitat…
Tunable Defect Engineering of Mo/TiON Electrode in Angstrom-Laminated HfO$_2$/ZrO$_2$ Ferroelectric Capacitors towards Long Endurance and High Temperature Retention
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.
A Ginzburg-Landau model is used to demonstrate how depletion layers give rise to thickness-dependent ferroelectric properties in thin films. It is shown that free charge layers at the film-electrode interface can result in an internal electric field in the bulk of the film even when no external voltage is applied. At high values of the donor dopant density and small thicknesses, this internal electric field can be strong enough to lead to the formation of a domain pattern. This causes a drop in the remnant polarization; a direct demonstration of the important role free charge plays in thin fer…
Pressure-induced polarization switching in ferroelectric thin films has emerged as a powerful method for domain patterning, allowing to create predefined domain patterns on free surfaces and under thin conductive top electrodes. However, the mechanisms for pressure induced polarization switching in ferroelectrics remain highly controversial, with flexoelectricity, polarization rotation and suppression, and bulk and surface electrochemical processes all being potentially relevant. Here we classify possible pressure induced switching mechanisms, perform elementary estimates, and study in depth u…
As a new type of self-healing material, room-temperature liquid metal (LM) composed of Ga, In and Sn is a promising anode in lithium-ion batteries (LIBs). It is difficult to directly prepare an electrode slurry with pure LM. Here, the LM electrode slurry was successfully prepared by simple high-speed stirring method. The LM in the slurry was evenly distributed in the form of liquid particles (average size 100 μm) and no aggregation occurred. The initial discharge specific capacity of LM is 1148 mAh g-1, and the stable discharge specific capacity is 350 mAh g-1. Cyclic voltammetry measurements …
Epitaxial ferroelectric HfO2 films are the most suitable to investigate intrinsic properties of the material and for prototyping emerging devices. Ferroelectric Hf0.5Zr0.5O2(111) films have been epitaxially stabilized on La2/3Sr1/3MnO3(001) electrodes. This epitaxy, considering the symmetry dissimilarity and the huge lattice mismatch, is not compatible with conventional mechanisms of epitaxy. To gain insight into the epitaxy mechanism, scanning transmission electron microscopy characterization of the interface was performed, revealing arrays of dislocations with short periodicities. These obse…
By performing first-principles calculations on four capacitor structures based on BaTiO3 and PbTiO3, we determine the intrinsic interfacial effects that are responsible for the destabilization of the polar state in thin-film ferroelectric devices. We show that, contrary to the established interpretation, the interfacial capacitance depends crucially on the local chemical environment of the interface through the force constants of the metal-oxide bonds, and is not necessarily related to the bulk screening properties of the electrode material. In particular, in the case of interfaces between AO-…
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…
