Electrostatic potential mapping at ferroelectric domain walls by low-temperature photoemission electron microscopy
J. Schaab, K. Shapovalov, P. Schoenherr, J. Hackl, M. I. Khan, M. Hentschel, Z. Yan, E. Bourret, C. M. Schneider, S. Nemsák, M. Stengel, A. Cano, D. Meier
Low-temperature X-ray photoemission electron microscopy (X-PEEM) is used to measure the electric potential at domain walls in improper ferroelectric Er0.99Ca0.01MnO3. By combining X-PEEM with scanning probe microscopy and theory, we develop a model that relates the detected X-PEEM contrast to the emergence of uncompensated bound charges, explaining the image formation based on intrinsic electronic domain-wall properties. In contrast to previously applied low-temperature electrostatic force microscopy (EFM), X-PEEM readily distinguishes between positive and negative bound charges at domain walls. Our study introduces an X-PEEM based approach for low-temperature electrostatic potential mapping, facilitating nanoscale spatial resolution and data acquisition times in the order of 0.1-1 sec.
High-resolution X-ray photoemission electron microscopy (X-PEEM) is a well-established method for imaging ferroelectric domain structures. Here, we expand the scope of application of X-PEEM and demonstrate its capability for imaging and investigating domain walls in ferroelectrics with high-spatial resolution. Using ErMnO3 as test system, we show that ferroelectric domain walls can be visualized based on photo-induced charging effects and local variations in their electronic conductance can be mapped by analyzing the energy distribution of photoelectrons. Our results open the door for non-dest…
Trimerization-polarization domains in ferroelectric hexagonal YMnO$_3$ were resolved in all three spatial dimensions by piezoresponse force microscopy. Their topology is dominated by electrostatic effects with a range of 100 unit cells and reflects the unusual electrostatic origin of the spontaneous polarization. The response of the domains to locally applied electric fields explains difficulties in transferring YMnO$_3$ into a single-domain state. Our results demonstrate that the wealth of non-displacive mechanisms driving ferroelectricity that emerged from the research on multiferroics are a…
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…
The correlation between the shift current mechanism for the bulk photovoltaic effect (BPVE) and the structural and electronic properties of ferroelectric perovskite oxides is not well understood. Here, we study and engineer the shift current photovoltaic effect using a visible-light-absorbing ferroelectric Pb(Ni$_{x}$Ti$_{1-x}$)O$_{3-x}$ solid solution from first principles. We show that the covalent orbital character dicates the direction, magnitude, and onset energy of shift current in a predictable fashion. In particular, we find that the shift current response can be enhanced via electrost…
Polar metals characterized by the simultaneous coexistence of ferroelectric distortions and metallicity have attracted tremendous attention. Developing such materials at low dimensions remains challenging since both conducting electrons and reduced dimensions are supposed to quench ferroelectricity. Here, based on first-principles calculations, we report the discovery of ferroelectric behavior in two-dimensional (2D) metallic materials with electrostatic doping, even though ferroelectricity is unconventional at the atomic scale. We reveal that PbTe monolayer is intrinsic ferroelectrics with pr…
Design of novel artificial materials based on ferroelectric perovskites relies on the basic principles of electrostatic coupling and in-plane lattice matching. These rules state that the out-of-plane component of the electric displacement field and the in-plane components of the strain are preserved across a layered superlattice, provided that certain growth conditions are respected. Intense research is currently directed at optimizing materials functionalities based on these guidelines, often with remarkable success. Such principles, however, are of limited practical use unless one disposes o…
Breakdown and polarization contrasts in ferroelectric devices observed by operando laser-based photoemission electron microscopy with the AC/DC electrical characterization system
Electrostatic gating is pervasive in materials science, yet its effects on the electronic band structure of materials has never been revealed directly by angle-resolved photoemission spectroscopy (ARPES), the technique of choice to non-invasively probe the electronic band structure of a material. By means of a state-of-the-art ARPES setup with sub-micron spatial resolution, we have investigated a heterostructure composed of Bernal-stacked bilayer graphene (BLG) on hexagonal boron nitride and deposited on a graphite flake. By voltage biasing the latter, the electric field effect is directly vis…
Piezoresponse force microscopy (PFM) has been extensively utilized as a versatile and an indispensable tool to understand and analyze nanoscale ferro- /piezoelectric properties by detecting the local electromechanical response on a sample surface. However, it has been discovered that the electromechanical response not only originates from piezoelectricity but also from other factors such as the electrostatic effect. In this study, we explore the dependence of off-field PFM hysteresis loops on the surface-potential-induced electrostatic effect in a prototypical ferroelectric thin film by applyi…
Phase field modeling of domain structures in ferroelectrics nanorods of different shape and sizes is presented. The vortex domain configurations in confined ferroelectrics have been explored by varying the ratio of the energies of electrostatic and elastic interactions. It is shown that a strong effect of the electrostatic interactions can cause the formation of 90o domain walls that do not satisfy the condition of strain compatibility. A good agreement between the results of phase field modeling and the results of atomistic calculations for nano ferroelectrics demonstrates that the phase fiel…
Improper ferroelectrics are described by two order parameters: a primary one, driving a transition to long-range distortive, magnetic or otherwise non-electric order, and the electric polarization, which is induced by the primary order parameter as a secondary, complementary effect. Using low-temperature scanning probe microscopy, we show that improper ferroelectric domains in YMnO$_3$ can be locally switched by electric field poling. However, subsequent temperature changes restore the as-grown domain structure as determined by the primary lattice distortion. The backswitching is explained by …
The recent observation of a ferroelectric-like structural transition in metallic LiOsO$_3$ has generated a flurry of interest in the properties of polar metals. Such materials are thought to be rare because free electrons screen out the long-range electrostatic forces that favor a polar structure with a dipole moment in every unit cell. In this work, we question whether long-range electrostatic forces are always the most important ingredient in driving polar distortions. We use crystal chemical models, in combination with first-principles Density Functional Theory calculations, to explore the …
We present experimental evidence for hexagonal domain faceting in the ferroelectric polymer PVDF-TrFE films having the lower orthorhombic crystallographic symmetry. This effect can arise from purely electrostatic depolarizing forces. We show that in contrast to magnetic bubble shape domains where such type of deformation instability has a predominantly elliptical character, the emergence of more symmetrical circular harmonics is favored in ferroelectrics with high dielectric constant.
The electrostatics arising in ferroelectric/dielectric two-dimensional heterostructures and superlatitices is revisited here within a simplest Kittel model, in order to define a clear paradigmatic reference for domain formation. The screening of the depolarizing field in isolated ferroelectric or polar thin films via the formation of 180$^{\circ}$ domains is well understood, whereby the width of the domains $w$ grows as the square-root of the film thickness $d$, following Kittel's law, for thick enough films ($w\ll d$). This behavior is qualitatively unaltered when the film is deposited on a d…
We report first-principles calculations on the coupling between epitaxial strain, polarization, and oxygen octahedra rotations in monodomain (PbTiO$_{3}$)$_{n}$/(SrTiO$_{3}$)$_{n}$ superlattices. We show how the interplay between (i) the epitaxial strain and (ii) the electrostatic conditions, can be used to control the orientation of the main axis of the system. The electrostatic constrains at the interface facilitate the rotation of the polarization and, as a consequence, we predict large piezoelectric responses at epitaxial strains smaller than those that would be required considering only s…
We study theoretically the influence of the underlying domain microstructure on the electromechanical properties of ferroelectrics. Our calculations are based on a continuum approach that incorporates the long-range elastic and electrostatic interactions. The theory is used to simulate the piezoelectric properties of a two dimensional model ferroelectric crystal. Simulation results indicate that the electromechanical response of the ferroelectric is strongly dependent on the domain microsctructure, including domain walls. This is particularly true for the case when an electric field is applied…
The contrast mechanism for the visualization of ferroelectric domain boundaries with lateral force microscopy is generally assumed to be caused by mechanical deformation of the sample due to the converse piezoelectric effect. We show, however, that electrostatic interactions between the charged tip and the electric fields arising from the surface polarization charges dominate the contrast mechanism. This explanation is sustained by quantitative analysis of the measured forces as well as by comparative measurements on different materials.
The control of the electron spin by external means is a key issue for spintronic devices. Using spin- and angle-resolved photoemission spectroscopy (SARPES) with three-dimensional spin detection, we demonstrate operando electrostatic spin manipulation in ferroelectric GeTe and multiferroic Ge1-xMnxTe. We not only demonstrate for the first time electrostatic spin manipulation in Rashba semiconductors due to ferroelectric polarization reversal, but are also able to follow the switching pathway in detail, and show a gain of the Rashba-splitting strength under external fields. In multiferroic Ge1-…
Construction of First Principle Based Adiabatic and Diabatic Hamiltonian for TiO$_6^{8-}$ unit of BaTiO$_3$ Crystal: Photoemission Spectra and Ferroelectricity
We study tunnel junctions consisting of a two-dimensional ferroelectric (FE) material sandwiched between graphene electrodes. We formulate a theory for the interplay of the FE polarization and induced free charges in such devices, taking into account quantum capacitance effects. We predict a gate-sensitive FE voltage difference across the device, which can be measured using electrostatic force microscopy. Incorporating this electrostatic theory in the tunneling current-voltage characteristics, we identify a resonance peak associated with aligned Dirac cones as a highly sensitive probe of the F…
We present in-situ transmission electron microscopy observations of domain wall motion in thin freestanding potassium niobate single-crystals. We observe that not all domains of a given polarization orientation are equally switchable in applied electric fields. Tilted and curved 90 degree domain walls are common and display field-induced mobility, whereas untilted domain boundaries resist such motion. The sensitivity of the domain wall response to field direction suggests that electrostatic energy contributions play a crucial role in the observed switching properties. We can explain our result…
Point defect migration is considered as a mechanism for aging in ferroelectrics. Numerical results are given for the coupled problems of point defect migration and electrostatic energy relaxation in a 2D domain configuration. The peak values of the clamping pressure at domain walls are in the range of $10^6$ Pa, which corresponds to macroscopically observed coercive stresses in perovskite ferroelectrics. The effect is compared to mechanisms involving orientational reordering of defect dipoles in the bulk of domains. Domain clamping is significantly stronger in the drift mechanism than in the o…
The application of PhotoEmission Electron Microscopy (PEEM) and Low Energy Electron Microscopy (LEEM) techniques to the study of the electronic and chemical structure of ferroelectric materials is reviewed. Electron optics in both techniques gives spatial resolution of a few tens of nanometres. PEEM images photoelectrons whereas LEEM images reflected and elastically backscattered electrons. Both PEEM and LEEM can be used in direct and reciprocal space imaging. Together, they provide access to surface charge, work function, topography, chemical mapping, surface crystallinity and band structure.…
By combining angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM), piezoresponse force microscopy (PFM) and first-principles calculations, we have studied the low-energy band structure, atomic structure and charge polarization on the surface of a topological semimetal candidate TaNiTe5. Dirac-like surface states were observed on the (010) surface by ARPES, consistent with the first-principles calculations. On the other hand, PFM reveals a switchable ferroelectric-like polarization on the same surface. We propose that the noncentrosymmetric surface reconstructi…
In a ferroelectric field effect transistor (FeFET), it is generally assumed that the ferroelectric gate plays a purely electrostatic role. Recently it has been shown that in some cases, which could be called 'active FeFETs', electronic states in the ferroelectric contribute to the device conductance as the result of a modulation doping effect in which carriers are transferred from the channel into the ferroelectric layers near the interface. Here we report first-principles calculations and model analysis to elucidate the various aspects of this mechanism and to provide guidance in materials ch…
Micrometric domains of precise ferroelectric polarization have been written into a 20 nm thick epitaxial thin film of BaTiO3(001) (BTO) on a Nb doped SrTiO3 (STO) substrate using PiezoForce Microscopy (PFM). The domain dependent electronic structure has been studied using fully energy-filtered PhotoEmission Microscopy (PEEM) and synchrotron radiation. Shifts, induced by ferroelectric polarization, of up to 300 meV are observed in the work function of the sample. The surface is Ba-O terminated. Polarization-induced distortion of the electronic structure is observed in the valence band and on th…
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…
In epitaxially strained ferroelectric thin films and superlattices, the ferroelectric transition temperature can lie above the growth temperature. Ferroelectric polarization and domains should then evolve during the growth of a sample, and electrostatic boundary conditions may play an important role. In this work, ferroelectric domains, surface termination, average lattice parameter and bilayer thickness are simultaneously monitored using in-situ synchrotron x-ray diffraction during the growth of BaTiO$_3$/SrTiO$_3$ superlattices on SrTiO$_3$ substrates by off-axis RF magnetron sputtering. The…
The coexistence of different ferroelectric phases enables the tunability of the macroscopic properties and extensive applications from piezoelectric transducers to nonvolatile memories. Here we develop a thermodynamic model to predict the stability and low-energy orientations of boundaries between different phases in ferroelectrics. Taking lead zirconate titanate and bismuth ferrite as two examples, we demonstrate that the low-energy orientations of interphase boundaries are largely determined by minimizing the electrostatic and elastic energies. Phase-field simulations are employed to analyze…
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…
The domain size dependence of piezoelectric properties of ferroelectrics is investigated using a continuum Ginzburg-Landau model that incorporates the long-range elastic and electrostatic interactions. Microstructures with desired domain sizes are created by quenching from the paraelectric phase by biasing the initial conditions. Three different two-dimensional microstructures with different sizes of the $90^{o}$ domains are simulated. An electric field is applied along the polar as well as non-polar directions and the piezoelectric response is simulated as a function of domain size for both c…
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 …
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…
Ferroelectric polar displacements have recently been observed in conducting electron-doped BaTiO3. The co-existence of a ferroelectric phase and conductivity opens the door to new functionalities which may provide a unique route for novel device applications. Using first-principles methods and electrostatic modeling we explore the effect that the switchable polarization of electron-doped BaTiO3 (n-BaTiO3) has on the electronic properties of the SrRuO3/n-BaTiO3 (001) interface. Ferroelectric polarization controls the accumulation or depletion of electron charge at the interface, and the associa…
Nonlinear electrostatic interaction between the surface ions of electrochemical nature and ferroelectric dipoles gives rise to the coupled ferroionic states in nanoscale ferroelectrics. Here, we investigated the role of the surface ions formation energy value on the polarization states and polarization reversal mechanisms, domain structure and corresponding phase diagrams of ferroelectric thin films. Using 3D finite elements modeling we analyze the distribution and hysteresis loops of ferroelectric polarization and ionic charge, and dynamics of the domain states. These calculations performed o…
We present a full analysis of the contrast mechanisms for the detection of ferroelectric domains on all faces of bulk single crystals using scanning force microscopy exemplified on hexagonally poled lithium niobate. The domain contrast can be attributed to three different mechanisms: i) the thickness change of the sample due to an out-of-plane piezoelectric response (standard piezoresponse force microscopy), ii) the lateral displacement of the sample surface due to an in-plane piezoresponse, and iii) the electrostatic tip-sample interaction at the domain boundaries caused by surface charges on…
Surprising asymmetry in the local electromechanical response across a single antiparallel ferroelectric domain wall is reported. Piezoelectric force microscopy is used to investigate both the in-plane and out-of- plane electromechanical signals around domain walls in congruent and near-stoichiometric lithium niobate. The observed asymmetry is shown to have a strong correlation to crystal stoichiometry, suggesting defect-domain wall interactions. A defect-dipole model is proposed. Finite element method is used to simulate the electromechanical processes at the wall and reconstruct the images. F…
In this work, we report a massively parallel and time domain implementation of the 3D phase field model that can reach beyond micron scale and consider for arbitrary electrical and mechanical boundary conditions. The first part of the paper describes the theory and the numerical implementation of the model. A mixed-mode approach of finite difference and finite element grid has been used for calculating the nonlocal electrostatic and elastic interactions respectively. All the local and non-local interactions are shown to scale linearly up to thousands of processors. This massive parallelization…
Polar discontinuities and structural changes at oxide interfaces can give rise to a large variety of electronic and ionic phenomena. Related effects have been intensively studied in epitaxial systems, including ferroelectric domain walls and interfaces in superlattices. Here, we investigate the relation between polar discontinuities and the local chemistry at grain boundaries in polycrystalline ferroelectric ErMnO3. Using orientation mapping and different scanning probe microscopy techniques, we demonstrate that the polycrystalline material develops charged grain boundaries with enhanced elect…
Rashba materials have appeared as an ideal playground for spin-to-charge conversion in prototype spintronics devices. Among them, $α$-GeTe(111) is a non-centrosymmetric ferroelectric (FE) semiconductor for which a strong spin-orbit interaction gives rise to giant Rashba coupling. Its room temperature ferroelectricity was recently demonstrated as a route towards a new type of highly energy-efficient non-volatile memory device based on switchable polarization. Currently based on the application of an electric field, the writing and reading processes could be outperformed by the use of femtosecon…
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…
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…
We investigate the ferroelectric phase transition and domain formation in a periodic superlattice consisting of alternate ferroelectric (FE) and paraelectric (PE) layers of nanometric thickness. We find that the polarization domains formed in the different FE layers can interact with each other via the PE layers. By coupling the electrostatic equations with those obtained by minimizing the Ginzburg-Landau functional we calculate the critical temperature of transition Tc as a function of the FE/PE superlattice wavelength and quantitatively explain the recent experimental observation of a thickn…
We have investigated the atomistic structure of the 180-degree and 90-degree domain boundaries in the ferroelectric perovskite compound PbTiO3 using a first-principles ultrasoft-pseudopotential approach. For each case we have computed the position, thickness and creation energy of the domain walls, and an estimate of the barrier height for their motion has been obtained. We find both kinds of domain walls to be very narrow with a similar width of the order of one to two lattice constants. The energy of the 90-dergree domain wall is calculated to be 35 mJ/m^2, about a factor of four lower than …
The control of the in-plane domain evolution in ferroelectric thin films is not only critical to understanding ferroelectric phenomena but also to enabling functional device fabrication. However, in-plane polarized ferroelectric thin films typically exhibit complicated multi-domain states, not desirable for optoelectronic device performance. Here we report a strategy combining interfacial symmetry engineering and anisotropic strain to design single-domain, in-plane polarized ferroelectric BaTiO$_3$ thin films. Theoretical calculations predict the key role of the BaTiO$_3$ / PrScO$_3$ (110)$_O$…
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…
In purely c-axis oriented PbZr$_{0.2}$Ti$_{0.8}$O$_3$ ferroelectric thin films, a lateral piezoresponse force microscopy signal is observed at the position of 180°domain walls, where the out-of-plane oriented polarization is reversed. Using electric force microscopy measurements we exclude electrostatic effects as the origin of this signal. Moreover, our mechanical simulations of the tip/cantilever system show that the small tilt of the surface at the domain wall below the tip does not satisfactorily explain the observed signal either. We thus attribute this lateral piezoresponse at domain wal…
