Screening mechanisms at polar oxide heterointerfaces

Transcription

1 Reports on Progress in Physics REVIEW Screening mechanisms at polar oxide heterointerfaces To cite this article: Seungbum Hong et al 0 Rep. Prog. Phys. 00 Manuscript version: Accepted Manuscript Accepted Manuscript is the version of the article accepted for publication including all changes made as a result of the peer review process, and which may also include the addition to the article by IOP Publishing of a header, an article ID, a cover sheet and/or an Accepted Manuscript watermark, but excluding any other editing, typesetting or other changes made by IOP Publishing and/or its licensors This Accepted Manuscript is 0 IOP Publishing Ltd. During the embargo period (the month period from the publication of the Version of Record of this article), the Accepted Manuscript is fully protected by copyright and cannot be reused or reposted elsewhere. As the Version of Record of this article is going to be / has been published on a subscription basis, this Accepted Manuscript is available for reuse under a CC BY-NC-ND.0 licence after the month embargo period. After the embargo period, everyone is permitted to use copy and redistribute this article for non-commercial purposes only, provided that they adhere to all the terms of the licence Although reasonable endeavours have been taken to obtain all necessary permissions from third parties to include their copyrighted content within this article, their full citation and copyright line may not be present in this Accepted Manuscript version. Before using any content from this article, please refer to the Version of Record on IOPscience once published for full citation and copyright details, as permissions will likely be required. All third party content is fully copyright protected, unless specifically stated otherwise in the figure caption in the Version of Record. View the article online for updates and enhancements. This content was downloaded from IP address 0... on /0/0 at :

2 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Screening Mechanisms at Polar Oxide Heterointerfaces Contents Seungbum Hong,, Serge M. Nakhmanson,, Dillon D. Fong Materials Science Division, Argonne National Laboratory, Argonne, IL 0, USA Department of Materials Science & Engineering, KAIST, Daejeon 0-0, Korea Department of Materials Science & Engineering and Institute of Material Science, University of Connecticut, Storrs, Connecticut 0, USA Department of Physics, University of Connecticut, Storrs, Connecticut 0, USA hong@anl.gov serge.nakhmanson@uconn.edu fong@anl.gov Abstract. The interfaces of polar oxide heterostructures can display electronic properties unique from the oxides they border, as they require screening from either internal or external sources of charge. The screening mechanism depends on a variety of factors, including the band structure at the interface, the presence of point defects or adsorbates, whether or not the oxide is ferroelectric, and whether or not an external field is applied. In this review, we discuss both theoretical and experimental aspects of different screening mechanisms, giving special emphasis to ways in which the mechanism can be altered to provide novel or tunable functionalities. We begin with a theoretical introduction to the problem and highlight recent progress in understanding the impact of point defects on polar interfaces. Different case studies are then discussed, for both the high thickness regime, where interfaces must be screened and each interface can be considered separately, and the low thickness regime, where the degree and nature of screening can be manipulated and the interfaces are close enough to interact. We end with a brief outlook toward new developments in this rapidly progressing field. Introduction Theoretical background. Classification of polarity screening mechanisms.... Surface polarity compensation.... Interface polarity compensation.... Theoretical studies of polar oxide interfaces General procedure for computing Schottky barrier heights with DFT... Centrosymmetric (non-polar) dielectric..... Broken symmetry: polarized dielectric and/or inequivalent electrodes. Point defects and polar surfaces / interfaces... Case studies: High thickness regime. Surfaces..... Water adsorption..... Chemistry at ferroelectric surfaces..... Electrochemistry at ferroelectric surfaces...

3 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS.. Surfaces in the presence of domains and domain walls.... Buried interfaces..... Ferroelectric field effect..... Electronic structure..... Schottky barriers.... Manipulation of screening charges..... Charge injection..... Charge collection... Case studies: Low thickness regime. LaAlO / SrTiO (00).... Ferroelectric control of screening mechanisms... Conclusions and outlook

4 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS. Introduction In recent years, the condensed matter physics community has devoted considerable attention to screening effects in oxide heterostructures. Key examples include screening at polar / nonpolar interfaces [,,,, ] and the surfaces of ferroelectric thin films [,,, ]. While charge compensation mechanisms have been discussed for some time with regard to electroneutrality and space charge effects in polycrystalline systems [0], for single crystal polar surfaces in the theoretical literature [], and semiconductor surfaces [], it has been only recently that researchers have been able to both grow and characterize oxide heterointerfaces with atomic level precision [,, ] and manipulate screening charges at the nanoscale [, ], thereby elucidating how different screening mechanisms can take place. The importance of these compensating charges cannot be overstated, as any perturbation to a perfectly balanced mixture of positive and negative charges can yield interacting forces that can be enormous []. Polar oxide heterostructures represent systems in which we can expect strong interaction between the surfaces / interfaces and screening charges. As already noted by others [, 0,, ], the mechanisms can vary widely from a purely electronic reconstruction to the adsorption or segregation of charged species. Furthermore, as it is clear that bulk oxides with polar surfaces must be charge compensated (at least on the macroscopic level) and growth on such a surface can propagate the polar discontinuity to another location (see, e.g., Refs. [,, ]), the nature of surface and interface screening can change dynamically and adapt based on the current reservoir of available charge either inside the heterostructures or near the surface from the ambient. The effects can be dramatic and lead to secondary phase formation: for example, Lazarov et al. [] observed the polarity-induced nucleation of metallic inclusions within an oxide film grown on MgO(). It is also well known that piezoelectric energy harvesting devices rely on the change of polarization due to the stress applied externally across the sample [,,, 0]. As such, the kinetics of screening will determine the maximum frequency at which one can transduce the mechanical stimuli to electrical charges [], whereas the change of the polarization will determine the driving force behind the flow of the screening charges to the surface or the interface between the electrode and the ferroelectric materials []. Therefore, gaining insight into how and why different screening mechanisms take place is crucial not only for improving growth behavior, or understanding charge transfer at catalytic surfaces or metal-oxide microelectronic junctions, but also for designing new technologies in oxide electronics or energy harvesting / storage devices. Several distinct communities have treated the screening issue in different ways. For instance, in the ferroelectrics community, much of the discussion concerns the depolarizing field and mechanisms by which this field can be reduced in order to obtain stable ferroelectric polarization in ultrathin films. As discussed in several articles [,, ], in the absence of screening charges, ferroelectric films can form domain structures (such as 0 stripe domains, closure domains [] and vortex nanodomain arrays [, ]); however, these films can stabilize in the monodomain state by other mechanisms, such as the adsorption of charged species at the surface [,,,,, 0]. In other oxide communities, where the oxides are either inherently polar (e.g., ZnO) or maintain a polar surface (e.g., LaAlO ), domains are not an option, and they must find screening mechanisms that can be either internal (e.g., the redistribution of electronic defects [,,,, ], ionic defects [,,, ], or both [,,, ]) or external (e.g., the development of rough surfaces during growth [], or the adsorption of compensating layers or foreign species, which can eliminate dynamic surface roughening [,,, 0]) to minimize the total electrostatic energy of the system.

5 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS Regardless, much of the issues are similar, and the ability to manipulate the screening charges dynamically is of particular interest to all these communities. The purpose of this review is to update the reader on the current status of this field, and we cover illustrative examples in the recent literature on different screening mechanisms at oxide heterointerfaces. We begin with a short theoretical description of the problem and describe the results of recent computational studies on the interaction between point defects and polar interfaces. We then discuss screening on oxide surfaces, outlining how defects and adsorbates interact to produce chemistries at the surface that may be unpredictable based on bulk electronic structure [,,, ]. Next, we discuss screening at buried interfaces: here we note that while much has been made of the ferroelectric field effect transistors [,,,,, 0] and the LaAlO / SrTiO (00) interface [,,,, ], similar effects have been observed or predicted for a number of other oxide interfaces [,,,,,,,,, ]. Special attention is paid to systems in which polar surfaces and interfaces can interact. We conclude with an outlook and highlight the need for predictive models of screening behavior such that these effects may be utilized to optimal effect in nextgeneration electronic and energy harvesting devices. As this is an extremely diverse field, involving researchers from condensed matter physics, materials science, physical chemistry, solid state ionics, and surface science, part of our objective is to direct interested readers to the appropriate literature. We hope that this particular subject continues to develop as it touches not only on many core scientific principles [0] but also manifold technologies that would benefit from improved control over charge transfer at interfaces [].. Theoretical background In what follows, we provide a succinct but broad exposition on the issues related to classification and theoretical studies of different polarity-compensation mechanisms in complex-oxide systems. The following discussion is aimed specifically at non-experts in the field, with readers interested in learning more exhaustive details pointed to a number of comprehensive reviews that are referenced below... Classification of polarity screening mechanisms Understanding the behavior of electric polarization at the surfaces of oxide thin films and nanostructures, as well as within interfacial regions between them and other materials, is critically important for the development of the next generation of more advanced and efficient multifunctional electromechanical and electrochemical devices. In the past few decades, some exciting experimental results have been obtained for perovskite-oxide ferroelectrics. These include polar ordering in epitaxial films that are only. nm (three unit cell) thick [, ], a demonstration of reversible [] and continuous [, ] chemical (i.e., controlled by applied chemical potential) switching of polarization in ultrathin PbTiO, and indication of existence of conducting layers on the surface of insulating BaTiO crystals in high vacuum [, ]. At the same time, problems related to polarization emergence and stability in oxide thin films and multilayers have been actively investigated with predictive first-principles-based theory and simulation approaches for a variety of structural arrangements, including both electroded and non-electroded ones. In the former case, substantial efforts have been focused on the studies of ferroelectric perovskite-oxide nanocapacitors [,,,,,, 0,,,,,,,, ] revealing that below a certain critical thickness (usually on the order of a few perovskite unit cells) the depolarizing electrostatic field due to the bound charges

6 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS on the ferroelectric slab surfaces cannot be perfectly compensated by the free charges in the electrodes, which destroys the polar monodomain ground state. Modern classification of surface and by extension of the same principles interface polarity phenomena has been developed by Noguera and coworkers in a series of insightful reviews [, 0,, ]. In the same publications Noguera et al. also discuss possible polarity screening mechanisms for (idealized) electrically uncompensated surfaces. Although a number of older classification schemes are available, e.g., those attributed to Tasker (highly ionic surfaces) [] and Harrison (electron counting for semiconductor surfaces) [], Noguera and coworkers provide examples where such schemes can become inaccurate in quantifying the surface properties, usually for certain more complex materials, such as ternary oxides [0]. However, in most simple cases (e.g., popular binary-oxide compounds) all three schemes deliver similar insights, since all of them involve considerations of the topology of charge distribution ρ(r)=ρ ions + (r)+ρ electrons (r) () in the near-surface region. In what follows we provide a brief review of this surface and interface polarity classification schemes, and outline specific mechanisms that can result in polarity compensation, as well as those that cannot produce it. We should also point out that a number of theoretical approaches for evaluating surface polarity, complementary to the one of Noguera and coworkers, have been recently proposed by Stengel [], based on the modern theory of polarization [0, ], and Hinuma et al [], based on crystallographic symmetry evaluations. Noguera et al. classify possible screening mechanisms as intrinsic or extrinsic, i.e., into categories adopted from semiconductor physics []. Following this approach, we define intrinsic charge carriers as electrons and/or holes provided by the dielectric itself (or its integral components). On the other hand, extrinsic charge carriers include electrons and/or holes donated by neutral or charged point defects (vacancies, interstitials), impurities or foreign atoms present inside the dielectric, and electrons and/or holes provided by the neighboring layer(s) in superlattices. In addition to the two aforementioned screening-mechanism categories, we may also consider external vs internal screening, i.e., charge compensation that occurs either outside of, or within the physical boundaries of the dielectric, respectively. Therefore, external screening processes involve conductive electrons in metallic electrodes, adsorbed foreign charged species (hydroxyl, hydrocarbons, etc), or mobile electronic and ionic species supplied from the environment or external circuitry. In an idealized, defect-free material that is externally screened, polarization distribution is uniform and changes abruptly at the interface. Alternatively, internal screening is provided by electronic carriers or charged point defects (vacancies, interstitials) present within the dielectric. In this case, the carrier and ionic species concentration profiles in the vicinity of surfaces or interfaces may be different from those of the bulk, which in turn can result in rather large changes in local polarization. In real world materials, both of these compensation scenarios may occur simultaneously, with their relative contributions controlled by thermodynamics and kinetics of the respective screening processes... Surface polarity compensation Assuming that all real surfaces that are encountered in experiments are always compensated, this scheme analyzes the behavior of semi-infinite frozen bulk terminations, i.e., twodimensional slabs that are created by piling up macroscopically large numbers of atomic

7 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS layers that have the same geometry and chemical composition as bulk material, and are not in contact with any metallic electrodes. Finite-size effects in slabs consisting of pile-ups of small numbers of atomic layers (i.e., structural arrangements relevant for thin films and nanostructures) are then treated as a special case. The physical variable central to this polarity classification approach is total surface charge density σ S = zs 0 ρ(z)dz, () where ρ(z)= ρ(r)dxdy () S is the plane-averaged total charge density and S is the surface area of the unit cell, while parameter z S demarcates the boundary between the surface and bulk regions. A generic layout for such a semi-infinite slab is shown in Figure (a). When considering arrangements of frozen-bulk atomic layers, or crystal unit cells, it is always possible (see Appendix A in [0]) to choose the unit cell in such a way that its dipole moment is zero along a given direction. However, depending on the specifics of charge distribution within the cell, to satisfy the dipole-free conditions its boundaries may cut either through areas in between the atomic layers or through the layers themselves, leaving them incomplete in the latter case. A simple example describing slab unit-cell choices with nonzero and zero dipole moments is presented in Figure (b-c). If the frozen-bulk slab is made by piling up dipole-free unit cells, its surface is considered non-polar if there is at least one unitcell arrangement that leaves the surface region empty, so that σ S = 0 [this situation is depicted in Figure (c)]. On the other hand, the slab surface is classified as polar if such construction cannot be done i.e., the surface region contains some partial or complete atomic layers, necessitating σ S 0, which in turn leads to the divergence of the slab surface energy. In addition, certain subcategories of polar surfaces, such as the so-called weakly polar ones or surfaces of ferroelectric materials, warrant a further, more subtle classification that takes into account likely polarity-compensation mechanisms acting upon them. For the two general classification categories introduced above it is then implied that (i) non-polar surfaces are charge-compensated by construction and no further surface modification is needed, while (ii) polar surfaces have to be compensated by providing the compensating surface charge density σ C, such that after compensation σ S + σ C = 0. Noguera and coworkers [, 0] have analyzed a variety of different cases involving possible physical origins of the compensating charge σ C and identified two global scenarios that can produce the desired polarity-compensated surface state. Both of these compensating mechanisms (along with their variations) are not mutually exclusive and thus can be at work at the same time. However, in each particular situation i.e., for a specific slab material, its surface cut and termination, as well as the nature of the ambient above the surface the precise knowledge of the dominating mechanism along with the structure of the resulting lowest-energy state of the surface region usually requires more detailed studies and cannot be extracted solely from the electric stability condition σ S + σ C = 0. Scenario : Modification of the number of the surface ions, which results in a formation of non-stoichiometric surfaces. This mechanism depends on the availability (or chemical potential) of the species delivering the compensating charge. These species can be either native (internal screening) [,,,,,, 00, 0]orforeign (external screening) to the surface [0, 0, 0, 0, 0, 0]. In the former case, non-stoichiometric relative to the dipole-free bulk unit cell surfaces are created, that can contain partial or incomplete atomic layers. In the latter case, adsorbates or impurities can be captured by the surfaces from

8 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS (a) (b) (c) σ S 0 p B = 0 σ S 0 p B 0 σ S = 0 p B = 0 ρ(z) ρ(z) ρ(z) 0 z S a z S + ma z S + (m+)a Figure : A structural model for the semi-infinite slab. Periodic boundary conditions are assumed in x and y directions that are parallel to the surface. (a) A generic layout of the system with partitioning into vacuum, surface and bulk regions. A typical behavior of the plane-averaged total charge density ρ(z) is sketched above the slab layout. The shape of ρ(z) for this slab suggests that it should have a total surface charge density σ S 0 and bulk dipole density p B = 0, which would classify its surface as polar. Here, p B can be introduced as z S +(m+)a z S +ma z ρ(z)dz, where unit cell m lies within the bulk region. (b-c) An example of a slab composed of two kinds of inequivalent structural units and possessing a simple form of the associated ρ(z). In (b), a unit cell with p B 0 is chosen, with σ S also being non-zero for this particular slab surface. In (c), a dipole-free unit cell is chosen instead. Since in this arrangement the same surface has σ S = 0, it can be classified as non-polar. Adapted from [0].

9 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS the ambient, with typical well-studied adsorbate varieties including -H, -OH and other small molecules and molecular clusters [0, 0, 0,,, ]. Scenario : Electron charge transfer into or out of the surface region. This compensation mechanism involves substantial modifications in the structure and filling of the surface electron bands. For example, in simple charge-transfer-type oxides with wide E g, surface cations tend to trap excess electrons, while surface anions trap excess holes [,, ]. On the other hand, in Mott-Hubbard-type oxides with narrow E g, surface cations can trap either excess electrons or holes. Such ion traps can be multi- or monovalent. Modification of the electronic population or change in the oxidation state of multivalent ions may be possible without incurring large energy costs, however, the efficiency of this process depends heavily on their local environment (e.g., specific crystal-field splitting of the d band) and on the accessibility of the appropriate oxidation states [, ]. In case of monovalent ions or oxygen, the presence of excess electrons (holes) in the surface region can lead to partial filling of the surface conduction band (depletion of the valence band) and thus can destroy the insulating nature of the oxide resulting in the so-called surface metallization (Fermi-level pinning) [,,,,,, 0]. Special cases (i) Weakly polar (00) perovskite surfaces. The classification of weak polarity has been introduced by Noguera and coworkers specifically for the (00) surface of paraelectric and cubic phases of the ABO perovskite structures, showcasing SrTiO, BaTiO and LaAlO as the most well studied examples. Although in these materials the (00) AO and BO atomic layers are formally supposed to be charge neutral [e.g., in SrTiO and BaTiO ] or have integer charges [e.g., ± in LaAlO ], their actual charges both static and dynamical are quite different from such values. This is due to the fact that mixed ionic and covalent character of the AO and BO bonds results in a substantial amount of charge transfer between the adjacent atomic layers [see Tables and in [0] for details; note how different charge partitioning schemes produce dramatically different results for ionic-layer charges]. Consequently, a dipole-free unit cell constructed for this centrosymmetric perovskite structure would be either of (AO) BO (AO) or (BO ) AO (BO ) type, i.e., with unit-cell boundaries cutting through ionic planes. Since the (00) surface region of a slab created by piling up such unit cells contains incomplete atomic layers, that surface is classified as polar and thus requiring compensation by the amount of charge σ C σ BL, where σ BL is the actual charge of the AO or BO atomic layer in the bulk region. Remarkably, this charge-compensation condition is achieved just by cutting the atomic bonds at the surface, with atomic-layer charges in this region acquiring values that are close to σ BL. As a result, unlike in the case considered in Scenario above, no serious modification of the electronic band structure or band filling occurs near the surface, thus warranting the usage of the special weak polarity classification. We should point out that although on the level of idealized theoretical models above the weak polarity designation is quite clear, experimental situation is much more vague, e.g., with existing reports of both insulating [, 0] and conducting [,, ] SrTiO surfaces. (ii) Surfaces of ferroelectrics. Relaxing the requirement of centrosymmetry for the perovskite unit cell allows for an emergence of polar distortions that result in additional rearrangements of the electron charge density throughout the cell. However, in ferroelectrics, polar distortions can develop along multiple usually two or more symmetrically equivalent crystallographic directions. This leads to yet another compensation mechanism becoming available for reducing the influence of the depolarizing field in ferroelectric slabs: formation of domains. Equilibrium 0 stripe domains reported for thin (00) oriented films subject to biaxial basal-plane compression from the substrate [, ] may be considered as the

10 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS simplest example. The properties of thin slabs of generic ferroelectric compounds, such as BaTiO and PbTiO, have been examined in great detail using first-principles-based methodology [,,,,,, 0,,,,,,,,,, 0,, ], although not all of these studies explicitly focused on exploring the nature of polarization compensation mechanisms. Some of these investigations showed that at certain environmental conditions, monodomain polarized states in ferroelectric films can be stabilized by either breaking their surface stoichiometry or attracting adsorbates [,, 0,, ]. Knowledge accumulated in these and other studies demonstrates that polarization-compensation induced behavior of ferroelectric micro- and nano-objects is subtle, because it involves a delicate balance between phenomena occurring in the surface and bulk regions, as well as flexibility to sustain either polar or nonpolar structural phases [0]. (iii) Finite-size effects in ultrathin slabs. In the low-thickness regime, or for slabs produced by pile-ups of a small number N of atomic layers, σ S = 0 is no longer a necessary condition for ensuring the system stability, i.e., the surface energy is no longer divergent. It may also be impossible to separate the slab into surface and bulk regions, due to the lack of truly bulk-like unit-cell layers. Therefore, uncompensated polar ordering can, in principle, exist in such slabs as long as the electrostatic potential change between their top and bottom surfaces is smaller than the E g, which prevents the flow of electron charge between the surfaces. This uncompensated state was first theoretically predicted in ultrathin (nonferroelectric) binary-oxide films by Goniakowski, Noguera and Giordano [0,,, ]. Although a crossover between low- and high-thickness behavior should exist, in certain cases, such as for ferroelectric materials (that can assume either polar or nonpolar configuration), it may be hard to reach with atomistic simulations. For example, in a recent DFT-based study of polarization compensation in ultrathin monodomain PbTiO films in contact with a bottom electrode [] it was shown that up to the computational limit of unit cells, or approximately nm in thickness, ionic layers within the slab remain unpolarized (paraelectric) and no significant electronic charge transfer between the film surface and the electrode takes place. However, the behavior of an infinitely thick monodomain film can be reproduced by freezing the ionic positions in two bottom unit cells to those of the bulk equilibrium polar structure with polarization pointing towards the electrode. In that case, the rest of the film polarizes at about % of the bulk value and polarization compensation is achieved by metallization of the surface region ( outward-most unit cells) accompanied by the transfer of 0.e per unit cell area from the film surface to the electrode interface. Surface phenomena that do not result in polarization compensation. (i) Change in covalency of the ionic layers, i.e., transfer and rearrangement of electronic charges only within the surface region, which may happen due to broken bonds at the surface. (ii) Surface relaxation or reconstruction that occurs without any changes in its stoichiometry, for example, ionic layer rumpling, or contraction/dilation in the surface region. Note, however, that surface relaxation or reconstruction can lower the surface energy after it is compensated, or for a surface of an uncompensated slab in the low-thickness regime. (iii) Any other event that does not alter the overall charge in the surface region, e.g., adsorption or desorption of charge-neutral species, or changes in interface roughness (although technically not a composition change, the effect of the latter can be similar to formation of stripe domains [])... Interface polarity compensation By extension of the principles discussed above for surfaces, a similar approach has been developed for the analysis of polarization compensation mechanisms at an idealized interface

11 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page 0 of CONTENTS 0 [0], which is represented by a joining of two semi-infinite crystal slabs of well-defined composition and geometry. Instead of the total surface charge density σ S a net interface charge density can be considered for the joining of dipole-free unit cells constructed for both slabs (A,B): zb σ I = ρ(z)dz, () z A where the laterally-averaged total charge density ρ(z) is integrated over the interfacial region ( z A,z B ). Interfaces can then be classified into polar and non-polar types according to the value of σ I : (i) Non-polar, σ I 0, which can be achieved either by joining of two non-polar surfaces, i.e., with σ A = σ B = 0, or by joining of two polar surfaces with equal but opposite charges σ A = σ B 0. (ii) Polar, σ I 0, where one or both of the joined surfaces are polar. For polar interfaces, polarization compensation mechanisms can then be separated into the following types: (i) electronic charge transfer into/out of the interfacial region with partial or full filling/depletion of the interfacial electronic states; (ii) modification of the interfacial region composition/stoichiometry (could be intrinsic or extrinsic); (iii) diffusion/segregation of other charged species (usually extrinsic) within the interfacial region. As in the case of polar surfaces, these compensation mechanisms are not mutually exclusive and can occur at the same time... Theoretical studies of polar oxide interfaces By virtue of an abundance of interesting physical phenomena taking place at perovskite oxide interfaces, or in ultrathin oxide films (e.g., critical thickness for ferroelectricity, emergence of D electron gas, or a promise of strong and tunable magnetoelectric coupling in certain multilayer systems), a substantial amount of effort has been dedicated to theoretical studies of interfaces between perovskite-oxide ferroelectrics and other materials. A wide variety of metallic, semiconducting and insulating structures have been probed as potential mates for the former, with some of these compounds also being perovskite oxides, such as, e.g., SrRuO, lanthanum strontium manganite La x Sr x MnO (LSMO), or Nb-doped SrTiO. For ferroelectric/ferroelectric or ferroelectric/dielectric interfaces or the so-called ferroelectric superlattices, e.g., those including CaTiO, (stoichiometric) SrTiO and BaTiO as components [,,, 0, ] density-functional theory (DFT) formalism in its most popular implementations involving the local density (LDA) or generalized gradient (GGA) approximations to the exchange-correlation energy has proven to be a reliable guide for understanding of their polar and dielectric properties. However, DFT-based investigations of metal/ferroelectric and metal/dielectric interfaces, i.e., typical nanocapacitor structural arrangements, have produced some controversial results that were often hard to explain. These issues were first identified by Junquera and Ghosez [], and then thoroughly addressed by Stengel and coworkers in an extensive review [], which also suggested a number of sanity checks to determine whether DFT computations for a particular metal/dielectric combination make sense. In this section, we follow the spirit and findings of these investigations, discussing the origins of the problems experienced by generic DFT and outlining solutions that would allow its practitioners avoid obtaining spurious results when working with nanocapacitor geometries.

12 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS (a) E F V metal H Δ V φ e φ DFT e φ h E gap V dielectric H E DFT gap E CBM E DFT CBM E VBM (b) E F V metal H V metal H V dielectric H E DFT CBM E VBM Figure : Energy-level alignment schematic in a metal/insulator junction (disregarding the near-interface area effects), including the electrostatic potential lineup across the junction. (a) A generic schematic, including all the terms used in the discussion; explicitly shows the difference between the true and DFT-computed values of E gap, E CBM and φ e. See text for more details. (b) An actual layout of the energy-level alignment in a [non-polar and centrosymmetric] (SrRuO ). /(PbTiO ). nanojunction obtained with DFT-based techniques following the setup described in Ref. []. All the energies are in ev. The nanojunction structural model is shown under the panel. When an interface is established between two dissimilar materials, there is redistribution of electron charge within the interfacial region due to the formation of new bonds at the materials surfaces. Depending on specifics of alignment between the valence band maximum and conduction band minimum (VBM and CBM) levels of the dielectric, and the Fermi level of the metal (E F ), such redistribution of charge may result either in an insulating (Schottky) or a conducting (Ohmic) type of junction. Naturally, for the nanostructure to function as a capacitor, the former type of junction is required, which is equivalent to E F falling in between the VBM and CBM levels, E VBM < E F < E CBM, and Schottky barrier heights for both holes (φ h ) and electrons (φ e ) being positive, as shown in Figure (a). If this energy relationship is not satisfied and E F is either lower than E VBM (φ h < 0) or higher than E CBM (φ e < 0), an Ohmic contact is established instead. In any case, DFT can correctly predict the type of the energy-level alignment (Schottky or Ohmic) across the interface if the band gap of the dielectric E gap = E CBM E VBM can be accurately estimated. Since it is well known that generic DFT formulations with LDA and GGA can severely underestimate the value of E gap, it is precisely this deficiency that is the source of most problems encountered by such DFT techniques when treating metal/insulator interfaces.... General procedure for computing Schottky barrier heights with DFT The procedure for computing Schottky barrier heights utilizing DFT techniques was first developed by Baldereschi, Baroni and Resta in late 0s [,, ]. It was initially applied to study interfaces of semiconductors, such as Si, Ge, GaAs and AlAs, among themselves or with Al, Au, and other simple metals [,, ]. Multiple other groups then adopted this technique to study band offsets for a variety of material interfaces, including those containing oxide compounds [, 0, ]. The procedure could be formally separated into three distinct steps, with only the last step (c) involving any actual calculations for the interface between the metal and the dielectric: E F

13 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS (a) evaluation of the band structure for the bulk metal to determine its E F ; (b) evaluation of the band structure for the bulk dielectric to determine its E VBM and E CBM ; (c) evaluation of the electrostatic potential lineup between the metal and the dielectric in a model that includes both materials forming an interface with each other. Band-structure calculations in steps (a) and (b), necessary for the evaluation of positions of the certain energy levels in bulk systems, are standard tools available in most DFT codes regardless of a particular approximation used for the exchange-correlation energy (granted that the choice of the latter is dependent on the balance between accuracy and efficiency in representing the properties of both materials forming the interface). Most importantly, for each bulk system metal or dielectric these energy levels are obtained with respect to zero of its own electrostatic Hartree potential V H (r)= Ω ρ(r ) r r dr, () where ρ(r) is the total charge density similar to the one of Eq. (), i.e., one including contributions from both positive and negative charges in the periodic unit cell of volume Ω. Naturally, there is no guarantee that zero electrostatic potential levels will be the same within the metal and dielectric, and thus the last step is required to determine the alignment between them to put the Fermi level of the metal on one side of the junction and the VBM and CBM levels of the dielectric on the other side onto the common energy axis. In its raw form which can be obtained in a standard fashion by most popular DFT packages the Hartree potential V H (r) is computed with atomic-level resolution and thus oscillates rapidly within the unit cell. Therefore, a post-processing, or nanosmoothing []) procedure, that includes averaging V H (r) over planes parallel to the interface same as in Eq. () and then convoluting it with a filtering function to suppress the atomic-scale oscillations, is required before the potential alignment across the junction can be determined, i.e., Δ V = VH dielectric VH metal. () Here, the VH dielectric and VH metal are the asymptotic values of plane-averaged and filtered potential Ṽ H (z) far away from the interface [see Figure (a)]. Both the raw and the smoothed incarnations of the plane-averaged V H (z) are shown in Figure (a) for the symmetric, i.e., having SrO TiO interfaces on both sides, (SrRuO ). /(PbTiO ). nanojunction. It is noteworthy that the same nanosmoothing procedure can be applied not only to V H (r), but also to ρ(r), or its ionic and electronic components [see Figure (b-c)]. Plane-averaged and filtered form of the total charge density, ρ(z), can then be used to conveniently estimate both net interfacial charge [cf. Eq. ()] and interfacial dipole densities []: σ I = zb z A ρ(z)dz, () zb p I = z ρ(z)dz. z A () The Schottky barrier heights φ h and φ e can then be computed as φ h = E VBM + E F Δ V, () φ e = E CBM E F + Δ V, (0) where the values of the energy levels are obtained for the bulk compounds on steps (a) and (b) [again, see Figure (a) for the mutual arrangement of all the energy levels]. We should point out that such bulk structures are not necessarily regarded as stress or electric-field

14 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS Plane-averaged V H (z) (ev) (a) raw (polar) smoothed (polar) smoothed (centrosymmetric) z (Å) Plane-averaged (z) (e/å ) Total smoothed (z) (e/å ) 0 - raw (electrons) raw (ions) smoothed (electrons) smoothed (ions) (b) (c) z (Å) Figure : Plane-averaged and nanosmoothed electrostatic potential Ṽ H (z) and charge density ρ(z) in a (SrRuO ). /(PbTiO ). nanojunction. (a) Ṽ H (z) computed for both centrosymmetric (non-polar) and polar configurations of the system. Raw, or unfiltered potential V H (z) is also shown for the latter case. Centrosymmetric potential Ṽ H (z) resembles a step function and therefore the potential alignment term Δ V introduced in Eq. () can be easily determined by taking the difference between its values in the middle of each slab. In the polar configuration, the ramp of Ṽ H (z) provides an estimate of an electric field present inside the ferroelectric PbTiO slab. (b) Plane-averaged raw and nanosmoothed positive ρ ions + and negative ρelectrons components of the charge density in the centrosymmetric arrangement. (c) Total nanosmoothed charge density ρ(z) obtained by combining the nanosmoothed versions of both components. free, but rather have to match any specific elastic or electrostatic conditions (e.g., coherent epitaxial strain) that may be imposed on the system of interest, i.e., the supercell containing the junction. In their review, Stengel et al. [] also suggest comparing local e.g., resolved by atomic layer density of states (DOS) curves computed in the supercell with the junction for areas far away from the interface with those of the bulk compounds to ensure that they match. Such comparisons become problematic when the dielectric slab in the nanocapacitor becomes very thin (i.e., situation similar to the abovementioned case of ultrathin films), since it is then impossible to identify any areas within it that are far enough away from the interface and therefore look bulk-like. Still, some information on the electronic band lineup across the interface may be acquired from the analysis of the layer-by-layer DOS within the supercell, although Stengel et al. [] consider this method to be inferior in accuracy. When step (c) of the same procedure is applied to a slab instead of a periodic structure, such as a nanocapacitor or a superlattice, plotting out nanosmoothed Ṽ H (z) allows one to

15 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS Plane-averaged V H (z) (ev) SrRuO electrode PbTiO slab raw (polarized) smoothed (polarized) smoothed (relaxed) z (Å) Figure : Plane-averaged and nanosmoothed electrostatic potential Ṽ H (z) across the (SrRuO ) /(PbTiO ) slab in vacuum. Potentials for relaxed (non-polar) and pre-polarized PbTiO layers are shown, as well as the raw potential for the latter case where two PbTiO unit cells close to the SrRuO electrode were forced to have bulk crystal polarization. In both cases, Ṽ H (z) becomes flat in the vacuum region, which insures that no spurious electric field exists in the areas between the slab and its periodic images [,, ]. Asymptotic values of Ṽ H (z) in vacuum are different for the SrRuO and PbTiO sides of the slab and can be used to determine the ionization potentials of each [00] surface (including versions of the PbTiO surface with and without pronounced polar ionic rumplings). Adapted from []. easily evaluate ionization potentials (or work functions) of the exposed slab surfaces []. Furthermore, for polar slabs studied under three-dimensional periodic boundary conditions, examining the form of Ṽ H (z) in the vacuum region of the supercell serves as a good check on whether the electrostatic potential is flat far away from the slab. The latter requirement ensures the absence of any spurious electric fields in the space between the slab and its periodic images, which may arise in non-centrosymmetric slab simulations that are conducted without applying a dipole correction or similar procedures [,, ]. The results of a DFTbased calculation of nanosmoothed Ṽ H (z) in a (SrRuO ) /(PbTiO ) slab [] are shown in Figure.... Centrosymmetric (non-polar) dielectric Centrosymmetric nanocapacitor arrangement stipulates an existence of an inversion center (or a mirror plane) in the middle of the dielectric slab. The presence of this symmetry element then guarantees the equivalency of top and bottom interfaces, including the same terminations at the metal/dielectric interface. Also, since the shape of the electrostatic potential has to respect the symmetry of the system, Ṽ H (z) becomes flat in the area around the middle of the dielectric slab [cf. Figure (a)], which in turn implies the flatness of the E VBM and E CBM energy levels and the vanishing of the internal electric field. A nanocapacitor consisting of equivalent electrodes and a ferroelectric slab whose ionic-rumpling pattern respects the inversion symmetry is obviously non-polar and thus complies with these conditions. However, if a cooperative polar distortion (that includes a component perpendicular to the interface plane) is developed within the ferroelectric, the

16 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS (a) E F φ 0 e E CBM E DFT CBM E F (b) (c) E F E F φ e E CBM E DFT CBM V dielectric H E F E F ECBM DFT E VBM V metal H VH metal Figure : A generic schematic of the pathological CBM level alignment in a centrosymmetric metal/insulator junction: (a) before and (b) after spillage of electron charge from the metal into the dielectric. The upward motion of the DFT-computed CBM level is shown by an arrow. The position of the true CBM level is represented by a dashed line. (c) An actual layout of the energy-level alignment in a non-polar (Pt) /(PbTiO ). nanojunction obtained with DFT-based techniques following the setup described in Ref. []. All the energies are in ev and the nanojunction structural model is shown under the panel. Unlike in the case of the non-pathological (SrRuO ). /(PbTiO ). junction described in Figure (b), problematic behavior of the ECBM DFT level, as shown in panels (a-b) is apparent here. inversion symmetry is broken and such a system then has to be considered as a separate case, which is discussed below. Even with DFT techniques underestimating the band gap of the dielectric, the centrosymmetric nanocapacitor structure can operate in a non-pathological (term first introduced by Junquera and Ghosez []), or Schottky regime if the computed gap Egap DFT < E gap is wide enough to ensure that E VBM < E F < ECBM DFT and, consequently, φ e > 0 [see example in Figure (b)]. On the other hand, a pathological, or Ohmic contact is established across the junction if before any electron charge spillage into the dielectric is allowed to happen ECBM DFT < E F < E CBM and φe 0 < 0, as shown in Figure. The subtle point is that although the (pre-spillage) value of φe 0 may in fact be large, it is inaccessible through DFT calculations. As the system is converged towards its ground state, electron charge flows from the metal and into the CBM level of the dielectric, pushing the latter up towards E F. At convergence, this results in a small negative apparent φ e and the self-consistent value of ECBM DFT touching E F

17 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS (a) E F E CBM E VBM E F (b) E F E CBM E VBM Figure : Sloping of the VBM and CBM levels in the (originally non-pathological and centrosymmetric) nanocapacitor under the influence of the developing polarization within the ferroelectric slab. (a) Non-pathological situation before the emergence of the polar state; E VBM < E F < E CBM. (b) Pathological situation after the polarization sets in. If the induced electrostatic potential drop across the slab is large enough, the CBM level can be pushed below E F at one interface and the VBM level above E F at the other, leading to partial metallization of the ferroelectric. Adapted from Ref. []. from below. Therefore, the described energy-level alignment picture should be regarded as a warning sign for the pathological behavior of the metal/dielectric junction induced by the DFT underestimation of the true dielectric E gap. The main and highly pronounced consequence of such behavior is that with any significant amount of spillage charge present, it distributes itself throughout the entire thickness of the dielectric slab, effectively turning it into a metal and thus producing a qualitatively wrong ground state of the system. The metallicity of the dielectric slab can be easily verified by evaluating the layer-by-layer DOS curves and superimposing the system E F level over them.... Broken symmetry: polarized dielectric and/or inequivalent electrodes The state of broken nanocapacitor centrosymmetry can encompass a variety of different situations with either the dielectric slab being polarized (e.g., ferroelectric slab below its Curie temperature), or the top and bottom electrodes being different (which includes different interfacial terminations with the same metal, e.g., Pt TiO and Pt PbO interfaces in the Pt/PbTiO /Pt system), or some combination thereof. It is noteworthy, that only for the case of polarized ferroelectric with equivalent electrode interfaces a reference paraelectric configuration can be straightforwardly constructed by unbuckling all of the ionic distortions. Due to the absence of the inversion center, axial polar distortions are now allowed, and, if actually developed, they can produce a ramp of the electrostatic potential and thus a non-zero electric field within the dielectric. In the latter case, it is possible that even if in the reference paraelectric configuration (described above) nanocapacitor exhibits nonpathological Schottky behavior, it can at least partially switch into the pathological regime after spontaneous polarization of the dielectric. Specifically, if the ramp of the electrostatic potential developed within the dielectric during the DFT relaxation of the polar distortions becomes larger than the Egap DFT (which is, again, smaller than the true E gap ), the electric field can push the VBM level at one interface above E F, or the CBM level at the other interface below E F, or both. A typical situation involving sloped VBM and CBM levels in the polarized P E F

18 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS dielectric is shown in Figure. Such deformation of the bands allows electrons to tunnel across the slab from the VBM level on one side to the CBM level on the other creating regions of metallicity inside the dielectric that can be located near the interfaces or in other areas (elucidating their specific locations deserves a separate in-depth study). At convergence of the DFT calculation, usually just enough electron charge is transferred to partially compensate the electric field, with the remaining electrostatic potential ramp being slightly smaller than the reference state Egap DFT. The resulting arrangement is then quite similar to the one observed in ultrathin binary-oxide films by Goniakowski and coworkers [0,,, ]. The important consequence of the developed polar pathological state is that, essentially, the metal/insulator interface in the system moves away from the electrode interface and to some location inside the dielectric slab. Polar ionic distortions in the vicinity of this interface will be strongly pinned and rendered non-switchable due to the screening effect of the nearby spillout charge. Therefore, such pathological systems can display highly nonuniform patterns of ionic rumplings throughout the dielectric slab (as opposed to mostly uniform rumplings in non-pathological cases), including the ostensible appearance of head-to-head or tail-to-tail polar domains in some extreme situations. We should point out that any quantitative evaluations of ferroelectric polarization within the slab become very difficult in pathological systems. Berry-phase formalism within the modern theory of polarization [0, ] that has been used with great success by DFT practitioners requires the system to be insulating globally and thus calculations employing it cannot be done for junctions that are partially metallic (pathological or not). Instead, a simple linearized approximation for local polarizations P λ (see, e.g., []) based on combinations of ionic rumplings and Born effective charges the latter often computed for bulk dielectric and then used for the dielectric part of the junction is utilized for perovskite oxides in most cases: P λ i P u (0) λi (u λi u (0) λi )= V λ Zλi Δu λi. () Here Zλi and Δu λi are the effective charge and displacement of ion i in unit cell λ, V λ is the volume of the cell, and superscript zero refers to the reference paraelectric structure with ferroelectric displacements removed by unbuckling the AO and BO planes and moving the middle planes back to the center of each primitive cell. In a pathological system, apparent ionic displacements Δu λi can still be present in metallic areas within the dielectric. However, these areas are rendered non-polar by compensating any static or dynamic redistribution of the bound charges by the free spillout charge, which is equivalent to setting Zλi 0. Furthermore, in the adjacent areas that may be somewhat insulating the magnitudes of Zλi would be diminished, compared to their bulk-dielectric values. Therefore, any analysis of the local polarization within the dielectric slab relying on Eq. () has to be accompanied by careful examination of the associated local DOS in order to determine which layers are insulating and indeed can carry polarization, and which ones are metallic and, consequently, non-polar. An example of such an examination is presented in Figure for the nonpolar and pre-polarized configurations of the (SrRuO ) /(PbTiO ) slab, and shows partial metallization of the PbTiO film in the latter case []. A more refined approach for evaluating local polarization within dielectric layers involves utilization of the so-called hermaphrodite [,, ] Wannier functions [], however, this technique is currently not implemented in most popular DFT codes. i

19 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS PbO TiO PbO TiO PbO TiO PbO TiO PbO TiO PbO TiO PbO TiO PbO TiO SrO RuO Energy (ev) Energy (ev) Figure : Atomic-layer resolved electronic density of states (EDOS) for the (SrRuO ) /(PbTiO ) slab in vacuum. Left panel: relaxed (non-polar) configuration. Right panel: pre-polarized configuration where two PbTiO unit cells close to the SrRuO electrode were forced to have bulk crystal polarization. The layer-by-layer changes in the values of VBM and CBM levels are sketched in dashed blue lines (cf. Figure where the curves for Ṽ H (z) have essentially the same shapes. The slab Fermi energy level E F is shown in dotted green lines. In the non-polar configuration, the entire PbTiO film is insulating. When polarized, it becomes partially conductive, including the near surface area that is approximately four unit cells thick, where tops of the layer valence bands are pushed above E F, and a single unit-cell thick area adjacent to the electrode, where bottoms of the layer conduction bands are pushed below E F. Reprinted with permission from J. Appl. Phys. []. Copyright 0, AIP Publishing, LLC. Concluding remarks As discussed in the previous sections, ab initio investigations of nanocapacitor junctions, either ferroelectric or not, involve a variety of subtle issues that DFT practitioners have to be aware of in order to ensure that results of their calculations are error free. Again, we can point the interested reader to the excellent review of Stengel and coworkers [] for further details. While certain tricks of the trade, such as manipulation of a Hubbard U term in the Hamiltonian [0], can be used in combination with the standard LDA and GGA DFT implementations to bring the value of Egap DFT closer to true E gap, a more straightforward approach for alleviating the band-gap underestimation problem is utilization

20 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS of hybrid exchange-correlation energy functionals. For example, the HSE (Heyd-Scuseria- Ernzerhof) [] hybrid functional is now present in popular DFT-simulation packages, like VASP and Quantum Espresso. Nonetheless, the obvious computational costs involved in deploying such functionals cannot be overlooked, especially in the case of nanocapacitor geometries. The latter are usually represented by high aspect-ratio rod-like supercells that both contain a large number of atoms and require fine in-plane k-point grids for an accurate description of the metallic part of the junction. Therefore, even though the usage of hybrid functionals would be strongly preferred for elucidating the properties of metal/dielectric interfaces, it may not always be possible or even warranted for every system, and thus the knowledge of and capability to detect pathological behavior have to remain among essential skills for a materials theorist working in this area... Point defects and polar surfaces / interfaces In much of the above discussion, it is implied that the surfaces and interfaces are free of point and line defects as well as secondary phases. Here we consider briefly point defects and their effects on polar interfaces, as this has been the subject of much recent scrutiny. At non-zero temperatures, point defects are energetically favorable due to the gain in configurational entropy, and their concentrations depend exponentially on their enthalpy of formation [, ]. Interstitial defects generally have a high enthalpy of formation in the close-packed perovskites, but Schottky defects like oxygen and cation vacancies are prevalent. To facilitate the discussion, we focus on defects in SrTiO, which have been recently studied both theoretically [,,,,,, 0, ] and experimentally [,,,,,,, ]. There are several possible defect reactions, e.g., 0 V Sr +V Ti + V O (Schottky disorder) () 0 V Sr +V O (Sr partial Schottky disorder) () 0 V Ti + V O (Ti partial Schottky disorder) () 0 e + h (electronic disorder) () and O O O +V O + e (reduction) () V O + O O O + h, (oxidation) () although many other reactions can also be considered [0]. When combined with the laws of mass action and electroneutrality, one can construct Brouwer diagrams [0], giving equilibrium defect concentrations as a function of the oxygen partial pressure at elevated temperatures. At lower temperatures, less than C for SrTiO [, ], one needs to consider the concentration of frozen-in defects, which depends on the cooling conditions [, ]. Furthermore, not only the defect concentrations, but also the equilibrium structure and composition of the oxide surface depend on the temperature and partial pressures (see, e.g., Ref. [,, ]), such that the modeling of defects and molecules at oxide surfaces [,,,,,, 00, ] and defects in the adjacent space charge region [0, 0] can be highly complex. Following Tanaka et al. [], we show an isothermal cross-section of the Sr-Ti-O phase diagram in Fig. (a). At point A, the SrTiO crystal is only in equilibrium with SrO(s) and O(g) (in an oxidizing condition), while at

21 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page 0 of CONTENTS 0 point F, the crystal is only in equilibrium with Ti(s) and Sr(s) (in a reducing condition). The chemical potentials of the different components can be determined under such constrained conditions, thus allowing calculations of different defects from first-principles as a function of oxygen partial pressure. The one-electron energy levels at Γ point are shown in Fig. (b). The VBM level for a perfect SrTiO crystal with no defects is set at 0 ev, and the defect energies displayed already account for deviations to the VBM due to the defects and are referenced to the defect-free condition []. As seen, cation vacancies create acceptor-like in-gap states, while oxygen vacancies lead to donor-like in-gap states (in addition to modifying electrical transport, it should be noted that oxygen vacancies can also lead to magnetic behavior in SrTiO [0, 0, 0]). With ionization, the cation (oxygen) vacancy-induced levels increase (decrease) in energy. An illustration of the effect of vacancies on the orbital structure is shown in Fig. (c). As observed, the (neutral) states of V Sr and V Ti are mainly comprised of the O p orbitals adjacent to the cation vacancies, and as such mainly affect the valence band. On the other hand, V O mainly consist of the Ti d orbitals, leading to states near the CBM. In all cases, the nearest-neighbors to the vacancy relax outward by more than %, regardless of the particular charge state, although the overall macroscopic dilation can be much smaller. The defect formation energies under oxidizing and reducing conditions are shown in Fig. (d) (upper and lower panels, respectively). As seen, they depend on the Fermi level and thus on whether the SrTiO is more p or n-type. For intrinsic SrTiO, with E F = E gap /, all of the defects are expected to be fully ionized. Tanaka et al. then calculated defect formation energies under different equilibrium conditions, as shown in Fig. (e). As expected, the formation energy of V O decreases under reducing conditions, while the opposite behavior is observed for the cation vacancies. The formation energy (per defect) for Schottky disorder (Eq. ) is relatively low and independent of position in the phase diagram, as this reaction preserves the SrTiO stoichiometry. However, the Sr partial Schottky reaction (Eq. ) is slightly more favorable than the full reaction, while the Ti partial Schottky reaction (Eq. ) is slightly less so, as strontium vacancies are easier to form than titanium ones. This is confirmed by the behavior of V Sr, which is the preferred defect at point B, indicating that oxidizing conditions would favor some Sr deficiency in the crystal. In the case of Sr partial Schottky disorder, Tanaka et al. found that the defect energy of the V Sr-V O pair could be further reduced by forming a defect complex []. Using a similar methodology but considering additional defect reactions, Liu et al. used their calculated defect formation energies to determine defect concentrations as a function of temperature [0], here considering only stoichiometric SrTiO (Fig. (f)). For the defect reactions considered here, defects from Schottky disorder are dominant. We now discuss the interaction between charged point defects and polar interfaces in more detail. A comprehensive theoretical study was recently performed by Lee and Morgan [], who compared the behavior of three oxides with differing amounts of ionicity, LaAlO, SrTiO, and LaMnO, all in the (00) orientation. Again, it should be emphasized that two distinct terminations (AO or BO ) are possible in this orientation, and depending on the oxide in question and the environmental conditions, one may be more stable than the other. Furthermore, the authors considered both symmetric freestanding films or slabs (where both surfaces have the same termination and layers, thus rendering the slab nonstoichiometric) and asymmetric freestanding slabs (where the two surfaces have different termination and layers), examining the effects of oxygen and cation vacancies at each surface. Electronic screening Lee and Morgan [] first studied purely electronic compensation in a point defect-free system. As shown in Fig., all three of the oxides compensate their polar

22 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS Ti (a) (c) (e) Formation Energy (ev per defect) NN displacements V Sr 0 0 V O Oxidation V O Sr F E D TiO TiO TiO V Ti V Sr A B C D E F G G C B Point in Phase Diagram V Ti + V O V Sr +V Ti + V O V Sr +V O A SrO V Ti Reduction O (b) (d) (f) Formation Energy (ev) Formation Energy (ev) VBM Point A (oxidizing) Egap/ Fermi level, E F (ev) V Ti V Sr V O CBM V + + O V Sr V Ti Point F (reducing) + + Figure : Defect energetics in SrTiO. (a) Isothermal cross-section of the Sr-Ti-O ternary phase diagram. (b) One-electron energy level diagram for V Sr, V Ti, and V O in SrTiO in various states of charge. The energy positions are given with respect to the VBM in the cases of V Sr and V Ti, and with respect to the CBM in the case of V O. (c) Formation energies as a function of the Fermi level at equilibrium points A and F. For each type of vacancy, the only charge state depicted is the one that leads to the lowest formation energy with respect to the Fermi level. (a-e) adapted with permission from Ref. []. Copyrighted by the American Physical Society. (f) Concentrations of various charged defect complexes of SrTiO as a function of temperature. Reproduced from Ref. [0] with permission from the PCCP Owner Societies.

23 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS (a) LaAlO LaAlO ΔQ (b) SrTiO SrTiO ΔQ (c) LaMnO ΔQ BO surface layer -Layer Slab_BO -layer slab 0 0 -Layer Slab_BO -Layer Slab Layer Slab-BO -Layer Slab AO surface layer -Layer Slab_AO -layer slab -Layer Slab_AO -Layer Slab -Layer Slab_AO -Layer Slab Figure : The change in charge, ΔQ, relative to the Bader charge of each layer in the bulk. Charge doping for (a) LaAlO (00), (b) SrTiO (00), and (c) LaMnO (00). The cases for the BO termination are shown on the left and AO termination shown on the right. Reprinted with permission from Ref. []. Copyright 0 by the American Physical Society. surfaces by electronic redistribution (charge doping). Consider for example, the symmetric -layer slabs (coloured diamonds or squares): positively charged AO surfaces are screened by electrons (negative ΔQ), while negatively charged BO surfaces are screened by holes (positive ΔQ), typically located in the first (surface) plane. The situation for the asymmetric -layer slabs (open circles) is similar, save for the case of LaAlO, where ionic polarization significantly reduces the polar field, as observed by others [0, 0, 0, 0, 0]. This can be contrasted with LaMnO, which also exhibits relatively strong surface polarity, but can easily undergo charge doping with the Mn as the B-site cation. Although the surface compensating charge leads to a local dipole, the macroscopic polar field is eliminated. As for the weakly polar SrTiO, the redistribution of electrons by bond breaking may be sufficient to charge dope the different surfaces in both the symmetric and asymmetric cases (note the difference in scale of ΔQ). The microscopic electrostatic potentials for the three different (defect free) oxides are shown in Fig. 0, as either thin black lines (for the asymmetric -layer slab), thin blue lines (for the symmetric BO -terminated slabs), or thin red lines (for the symmetric AO-terminated slabs). The thicker solid lines refer to the nanosmoothed or macroscopic average potential profiles. As expected, a macroscopic electric field is evident for the asymmetric LaAlO

24 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS slab (Fig. (a)), despite ionic polarization and electron transfer from the AlO surface to the LaO surface; this was the initial model proposed for the D electron gas (DEG) at the SrTiO interface [], which has been studied in detail both theoretically [, 0] and experimentally [,,, 0, ]. For LaO-terminated or AlO -terminated symmetric slabs, there is no internal field (and no lattice polarization except for the very top layers), but both macroscopic potentials differ substantially from the asymmetric case due to nonstoichiometry. The LaO-terminated (AlO -terminated) slabs experience considerable electron (hole) doping (Fig. (a)) and have surface states that pin the Fermi level higher (lower) with respect to bulk LaAlO. The macroscopic field is largely absent for the weakly polar SrTiO, as shown in Fig. 0(b), but there are considerable differences in the Fermi levels for the three different types of slabs. This stems from surface states near the valence band maximum at the TiO - terminated surface from the less hybridized O p orbitals. The Fermi level is thus effectively increased for both the -layer asymmetric slab and the -layer TiO symmetric slab, relative to bulk SrTiO. Ultimately, this improves the stabilization of cation vacancies in thin slabs of SrTiO. In contrast, the macroscopic and microscopic electrostatic profiles are all closely aligned for different LaMnO slab configurations, as shown in Fig. 0(c), indicating that charge doping can successfully screen each type of interface. As a result of the facile redox behavior of Mn (due to its more delocalized e g electrons), the surface energy of polar LaMnO is considerably lower than that for polar LaAlO. Lee and Morgan found that the surface energy of asymmetric LaMnO slabs did increase with thickness but only up to layers ( unit cells), thereby giving estimated screening length of. nm. In contrast, the surface energy of asymmetric LaAlO slabs continued to increase for thicknesses beyond layers. Electronic and point defect screening Broadly speaking, polar AO surfaces should attract V ( ) A s and V ( ) B s and repel V O s, while polar BO should attract V O s and repel V ( ) A s and V ( ) B s. As already discussed, the charge per defect depends on E F and the chemical environment. For purposes of comparison between the three oxides, however, Lee and Morgan [] treat only defects with their formal charges in the following discussion. Regarding the -layer asymmetric polar slabs of LaAlO and LaMnO, they find that oxygen vacancies indeed segregate to the BO surfaces, as shown in Fig. (a) and (e). On the other hand, the AO surfaces either ignore or repel them. In the -layer symmetric AlO - terminated slab in Fig. (a), V O s remain strongly stabilized in the middle of the slab, at least with respect to bulk LaAlO. The reason for this can be observed in the energy level diagrams depicted in Fig. (a-c), where (a) shows the case for bulk LaAlO, in which oxygen vacancies would create defect states near the conduction band minimum, and (b) and (c) illustrate the cases for LaO and AlO -terminated slabs, respectively. The acceptor states created in the AlO -rich slab (Fig. (c)) lead to hole doping that ultimately help screen these surfaces. With the introduction of oxygen vacancies, the liberated electrons can partially fill these lower energy surface states, leaving the vacancy states empty and improving oxygen vacancy stability compared to stoichiometric LaAlO. Figure (a) shows that for bulk LaAlO, E F is raised such that oxygen vacancy defect states are filled by electrons from the oxygen p (red arrow). When the slab is LaO-rich, as for the electron-doped LaO-terminated slabs in Fig. (b), the Fermi level at the LaO surface is pinned to the donor-like surface states near the conduction band minimum. The location of the V O defect states is lower than these surface states, so oxygen vacancies at the electrondoped LaO surface are similar in energy to that for bulk LaAlO as shown in Fig. (a). As

25 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS (a) LaAlO (a) LaAlO E Pot - E Fermi (ev) layer-(00) AO slab -layer-(00) BO slab -layer-asymmetric (00) slab (b) SrTiO (b) SrTiO SrTiO E Pot - E Fermi (ev) layer-(00) AO slab -layer-(00) BO slab -layer-asymmetric (00) slab (c) LaMnO (c) LaMnO E Pot - E Fermi (ev) layer-(00) AO slab -layer-(00) BO slab -layer-asymmetric (00) slab Fraction coordinate along the c-direction (d) LaAlO -layer asymmetric EPot-EFermi (ev) (e) SrTiO -layer asymmetric EPot-EFermi (ev) (f) LaMnO -layer asymmetric EPot-EFermi (ev) V O 0 Fraction coordinate along the c-direction Figure 0: Electrostatic potential profiles, relative to the Fermi level, are shown for (a) LaAlO (00), (b) SrTiO (00), and (c) LaMnO (00). The microscopic profiles are shown as thin lines while the nanosmoothed, macroscopic profile is shown as thick lines, all plotted along the [00] direction. Results for the -layer AO slab, -layer BO slab, and - layer asymmetric slab are shown in red, blue, and black, respectively. Similar electrostatic profiles are shown in (d), (e), and (f) for -layer asymmetric LaAlO (00), SrTiO (00), and LaMnO (00) slabs, respectively, where a single oxygen vacancy has been placed within the rightmost BO plane (red) as compared to the defect-free case (blue). The corresponding oxygen vacancy concentration in that plane is /. Adapted with permission from Ref. []. Copyrighted by the American Physical Society. a result, although V O s are indeed strongly attracted to the BO surface, they are not repelled by the AO surface for LaAlO due to Fermi level pinning. The trends for V Las and V Al sin LaAlO, as shown in Fig. (b), are opposite to V O and with larger energy magnitudes due to the larger charges per defect. Again, while these negatively charged defects are attracted to positively charged LaO surfaces, they are not repelled by the AlO surface. SrTiO (00) is only weakly polar, and surface metallization does not occur in the defectfree material. Thus, the profiles seen in Fig. (c) and (d) exhibit much smaller segregation energies with respect to LaAlO. The energy level diagrams for bulk SrTiO, the SrO surface, and the TiO surface are shown in Fig. (d-f), respectively. For bulk SrTiO, oxygen vacancies lead to states within the conduction band (red arrow), in this calculation as well as others [, ]. With a SrO-terminated surface, very little changes, as seen in Fig. (e): the Fermi levels for the asymmetric slab (black dashed line) is slightly higher than that for the symmetric slab (black solid line), but electrons liberated from the V O s still go to the conduction band for both the asymmetric (dotted red arrow) and symmetric (solid red arrow)

26 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS (a) (c) (e) (b) BO surface layer AO surface layer BO surface layer AO surface layer BO surface layer AO surface layer BO surface layer AO surfacelayer (d) BO surface layer AO surface layer BO surface layer AO surface layer (f) Figure : Segregation energies of oxygen and cation vacancies in LaAlO (a, b), SrTiO (c, d), and LaMnO (e, f). Larger and smaller symbols are used to highlight defects in the BO and AO planes, respectively. Adapted with permission from Ref. []. Copyrighted by the American Physical Society. cases. Thus, the oxygen vacancies behave similarly near the SrO surface for both cases. Although the TiO surface gives rise to acceptor-like states, the same electron transfer occurs, as indicated by the red arrows. The situation for LaMnO is quite distinct due to the existence of d e g orbitals and the redox behavior of the Mn ion, which leads to a short screening length. As shown by the energy-level diagram in Fig. (g), the creation of oxygen vacancies transfers electrons to the d e g band, near the original Fermi level. The LaO-terminated symmetric slab is intrinsically electron doped, thus partially filling the d e g and increasing the Fermi energy (black solid line); conversely, the MnO -terminated symmetric slab is intrinsically hole doped, partially depleting the d e g band and lowering the Fermi energy. As seen, this intrinsic doping destabilizes V O s in LaO-terminated symmetric slabs but stabilizes them in BO -terminated symmetric slabs. The converse is true for both cation vacancies and Sr dopants on the A-site (Sr La ). As a result, V O s are attracted to the BO surface and are repelled by the AO surface for LaMnO, as shown in Fig. (e). The behavior for the cation vacancies (or for Sr La dopants) is opposite to that for oxygen vacancies, as observed in Fig. (f). We finally note that the effects of oxygen vacancies on the electrostatic potential of -layer asymmetric slabs can be seen in Fig. 0(d), (e), and (f) for LaAlO, SrTiO, and LaMnO, respectively, where a single V O is placed on the BO terminating plane on the right side. As observed, the defect-free profile (in blue) are significantly altered in the case of LaAlO, helping to remove the macroscopic field. This will be discussed further in Section. Smaller changes are seen for SrTiO and even less for LaMnO, illustrating the relative importance of electronic screening in these less ionic systems. In summary, when polar surfaces are considered along with charged point defects, electrostatic interactions can drive the segregation of these defects, leading to potentially large concentrations near polar interfaces. However, the primary consideration must be the energy cost for screening; this is why polar LaMnO and SrTiO (00) surfaces exhibit much lower surface energies (the former due to surface metallization and the latter due to intrinsically

27 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS (a) Bulk LaAlO (b) LaO surface (c) AlO surface (d) Bulk SrTiO (e) SrO surface (f) TiO surface (g) Bulk LaMnO (h) LaO surface (i) MnO surface Figure : Schematic energy level diagrams illustrating electron transfer due to oxygen vacancy formation in LaAlO (00) (a-c), SrTiO (00) (d-f), and LaMnO (00) (g-i). (a), (d), and (g) refer to bulk systems, (b), (e), and (h) refer to the AO surface, and (c), (f), and (i) refer to the BO surface. All energies are referenced to the top of the O p band. The black solid lines in all figures represent the Fermi level, and the red dashed lines indicate the Opband center. The black dashed line in (a) shows the Fermi level for a LaAlO supercell with a V O defect. The black solid (dotted) lines in (e, f) and (h, i) refer to the Fermi levels in symmetric (asymmetric) slabs, for the AO or BO surfaces. Similarly, the solid (dotted) red arrows refer to V O -induced electron transfer in symmetric (asymmetric) slabs. Adapted with permission from Ref. []. Copyrighted by the American Physical Society.

28 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS weak polarity) than LaAlO, even for low thickness slabs. With regard to other transition metal ions, polar oxides with B-site ions in d 0 or d configurations may behave similarly to LaAlO.. Case studies: High thickness regime As noted above, screening effects can be divided into two film thickness regimes, the lowthickness regime, where the energies for uncompensated surfaces may be similar to those for compensated ones, and the high-thickness regime, where the surface energy diverges and screening is required. In this section, we discuss the high-thickness regime where the surfaces and interfaces must be compensated, although the mechanisms by which screening occurs can differ and change depending on the local environment... Surfaces... Water adsorption The issue of adsorbed water at oxide surfaces is longstanding one [0]. For example, Morimoto et al. investigated the portions of physisorbed and chemisorbed water molecules on TiO and Fe O surfaces and found the ratio to be :, which indicates that a water molecule is adsorbed on two hydroxyl groups through hydrogen bonding [0]. As made clear by Baniecki et al., it is likely that SrTiO (00) surfaces are saturated with adsorbates when exposed to atmospheric conditions and room temperature with approximately 0% of the surface sites occupied with CO and 0% with H O[0]. It also appears that the various reconstructions on the SrTiO (00) surface depend not only on the concentration of defects at the surface, but also on the amount of adsorbed H O, which tends to adsorb dissociatively on more defective surfaces [, ]. Thus, which reconstruction appears depends on the kinetics of dehydration and ordering at the surface. Furthermore, water has been predicted to adsorb dissociatively (with adsorption energies of ev) on SrO-terminations and molecularly (with adsorption energies of 0. ev) on TiO terminations []. For clean SrTiO surfaces, oxygen vacancies are commonplace, leading to metallic (and even magnetic) behavior for the (00) surface [,,,,, ] as well as for other, more polar orientations [, 0], although the effect of the X-ray probe on defect formation must also be considered []. To better understand the energetics of water adsorption on polar surfaces, Wang et al. conducted a detailed study of adsorption onto -nm-thick TiO -terminated BaTiO / SrTiO (00) heterostructures []. Prior to BaTiO growth by molecular beam epitaxy, they heated the substrate to 0 C for one hour in po = 0 Torr to remove carbon contamination. After growth, performed in a separate chamber, they exposed the surface to pure H Oat0 Torr for one hour (. 0 L). The sample was then transferred back to the main chamber for temperature programmed desorption (TPD) measurements using a mass spectrometer and X-ray photoelectron spectroscopy (XPS), employing a heating rate of 0 C/min. Low-energy electron diffraction (LEED) patterns measured before and after water adsorption showed slight changes to the ( ) pattern, but no ice structures were observed, suggesting that a single-ordered H O layer is adsorbed epitaxially onto the BaTiO surface. Multiple disordered water layers could be ruled out because of only the slight change to the LEED spot intensities. The TPD measurements were conducted from room temperature to 00 C; after reaching 00 C, the sample was held for 0 min prior to cooling and running the next TPD ramp. This was expected to result in more oxygen vacancies at the surface. Wang et al. found

29 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS (a) Figure : Temperature programmed desorption results for TiO -terminated BaTiO / SrTiO (00). (a) Plot of ln p (H O partial pressure) versus /T corresponding to the onsets of water desorption at the low temperature tail of the TPD spectra. (b) Results of fitting to the LEED I-V curves give the Pendry R-factor as a function of OH coverage of the surface for on-top chemisorption on surface Ti atoms (center of inset). The lowest R-factor indicates an OH coverage of 0. for all surface Ti atoms. Reprinted with permission from Ref. []. Copyright 0 American Chemical Society. that the onset of desorption occurred at 0 C for the initial surface, at 0 C for the 0- minute-annealed surface and C after another 0 minutes of annealing. This could be interpreted as either second-order desorption kinetics with a fixed activation energy or first / second-order kinetics with an activation energy that depends on coverage []. By plotting ln p vs /T from the onset of desorption [], they observed three parallel lines, as shown in Fig. (a). The slope is equal to the desorption energy / ideal gas constant, giving an desorption energy of. ± 0.0 ev for all surfaces, suggesting that the desorption is indeed second-order and coverage independent. Presumably the surface oxygen vacancies serve as sites for the recombination of OH and neighboring protons for the desorption of H O. Detailed analysis of Ba d, Sr d, and O s core-level intensities from XPS [] show that OH groups were already present on the pristine BaTiO surface, presumably from residual hydrogen in the UHV chamber. According to work performed on TiO (0) surfaces [, ], it is expected that H O / BaTiO + V O =OH / BaTiO + 0. ev, such that dissociative adsorption near an oxygen vacancy fills the vacancy with an OH group and transfers the proton to a nearby surface oxygen. However, it is also likely that a surface titanium atom can serve as an active site such that a hydroxyl group bonds directly to Ti. Indeed, the XPS results suggest that the surface titaniums in fact served as the dominant active sites. From fits to the LEED I-V curves, Wang et al. extracted the Pendry R-factor for OH atop the surface Ti. The lowest R-factor (0.) is for a coverage of 0., i.e., / of all surface Ti atoms formed bonds with OH groups, placing an adjacent proton on a nearby surface oxygen. This bonding to OH led to stronger up polarization at the surface of BaTiO, which was observed by LEED [].... Chemistry at ferroelectric surfaces Wang et al. [] found that ferroelectric thin films can even be switched as a function of gas composition (i.e., chemical switching ), in this case the oxygen partial pressure, po. Under oxidizing conditions, ferroelectric heterostructures comprised of PbTiO / SrRuO / SrTiO (00) favor the up polarization monodomain state. This is due to the adsorption of negatively charged species like oxygen or hydroxide ions to the (b)

30 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS PbO-terminated surface []. Under reducing conditions, the PbTiO polarizes downward, albeit relatively slowly as this depends on positively charged species like oxygen vacancies forming and settling at the surface []. This electrochemomechanical coupling adds even greater functionality to the already multifunctional complex oxides [, ], suggesting the possibility of engineering responsive and adaptive electronics []. The coupling between mechanical strain and point defect concentration is another important consideration in these materials [0, ] and becomes yet another knob for controlling electronic behavior. The po T phase diagram is shown in Fig. (a), for PbTiO films of different thickness. Up polarizations are shown in red while down polarizations are in blue. When neither positive nor negative charges can compensate the surface, the film exhibits a suppressed transition temperature and eventually becomes ferroelectric in the form of 0 stripe domains []. The suppression is largest for the thinnest film (here. nm), which exhibits the largest depolarizing field. Similar studies performed on BaTiO nanowires [], show that the stable ferroelectric phase in nanoscale systems relies on the presence of adsorbates such as OH and carboxylates (the latter from the nanowire synthesis process). Such chemisorbed molecules can be maintained in UHV environments, even at temperatures over 00 C. Conversely, pre-poled ferroelectrics can be used to select adsorbates; e.g., CO appears to adsorb on up-polarized domains of BaTiO but not down [], due to the lower potential barrier at the surface of the up-polarized domain for electron transfer to carbon. While others have demonstrated that ferroelectric polarization can affect molecular sticking coefficients [, ] and the adsorption of polar molecules [, ], Zhao et al. investigated the effect of polarization direction on surface reaction kinetics []. They first annealed a -nm-thick BaTiO / Nb-doped SrTiO (00) heterostructure at 00 K for an hour under UHV to clean the surface, which left a small amount of surface carbon. For poling at room temperature, they brought the surface of the BaTiO into contact with a polished Cu electrode biased ±0 V with respect to the sample (Note that unpoled BaTiO is still ferroelectric but is comprised of randomly oriented domains with no macroscopic polarization direction). Zhao et al. then exposed the heterostructure to. L of -fluoroethanol at room temperature and conducted TPD studies while heating the sample at K / sec. Dissociative adsorption led to the formation of an alkoxide that reacts when heated to produce acetaldehyde, ethylene, and fluorine atoms. The TPD results are shown in Fig. (b), where the order of the experiments are shown in the legend. As seen, the peak temperature shifts from 0 K to K with down polarization and returns to 0 K when reannealed briefly at 00 K. On the other hand, up polarization shifts the peak temperature to K. The TPD profiles are broader than would be expected for a first order reaction, but this could be due to multiple factors, such as the inhomogeneity of the BaTiO surface and the relatively slow pumping speed of the chamber. Nevertheless, the standard Redhead analysis could be performed [], using the peak maximum temperature to determine the activation energy for the reaction. For this analysis, the authors poled the BaTiO with ± V to insure better poling uniformity. Then using the standard pre-exponential factor of 0 s, they determined activation energies for acetaldehyde production of.00 ev for unpoled BaTiO,.0 ev for down polarization, and.0 ev for up polarization. While the exact reason for the difference remains unclear, the bonding of various adsorbed species and the local structure of the adsorptions sites are expected to change for the different polarization states. Other work describing reactions at ferroelectric surfaces can be found in Ref. []. It should also be noted that the exposure of these surfaces to UV radiation causes screening from the photo-generated electron-hole pairs [0]. Wang et al. found that the degree of screening was similar to that of dissociative water adsorption [0].

31 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page 0 of CONTENTS 0 (a) (b) (c) Intensity (Arb. Unit) a 0 CH CHO unpoled unpoled c- unpoled c Temperature (K) Figure : Results on studies of the interaction between ferroelectric surfaces and adsorbates. (a) Temperature vs po phase diagrams for three thicknesses of PbTiO on SrRuO coherently strained to SrTiO (00). The colour scale indicates the net polarization. Symbols refer to the points measured and the type of ferroelectric phase observed. The solid lines indicate the ferroelectric transition temperature, T C, and the dashed lines show boundaries of 0 stripe domain regions. Reprinted with permission from Ref. []. Copyright 0 by the American Physical Society. (b) TPD spectra for acetaldehyde obtained from the BaTiO film dosed with. L of -fluoroethanol as a function of the polarization state of the sample. The legend lists the order in which the experiments were performed (going down) and the polarization state of the surface. The unpoled BaTiO is presumed to consist of randomly oriented domains. Reprinted from Ref. [], with permission from Elsevier. (c) The calculated cation-anion splittings, δz = z cation z anion, through a La 0. Sr 0. MnO / BaTiO (00) slab (the bottom half of the LSMO is not shown). The dotted horizontal lines correspond to the average of the AO and BO layer anion-cation splitting for the inward and outward P in bulk BaTiO, strained to NdGaO. Reprinted with permission from Ref. []. Copyright 0 by the American Physical Society.

32 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS Figure : The typical PFM images of domains formed after switching by field pulses with amplitude U =00 V and different durations for various types of surface treatments: (a) cleaning by de-ionized water, (b) cleaning by acetone, and (c) plasma etching. Reprinted with permission from Ref. []. Copyright 0, AIP Publishing, LLC.... Electrochemistry at ferroelectric surfaces In scanning probe or atomic force microscopy (AFM) studies of ferroelectric surfaces, an electrically biased tip can be used to drive changes in polarization. Since the ferroelectric surface is often under atmospheric conditions, these changes can be electrochemical in nature. For example, Garica et al. [] discovered ferroelectric behavior in ultrathin films of BaTiO grown on a conducting La 0. Sr 0. MnO (LSMO) buffer layer on NdGaO (NGO). As shown in Fig. (c), Bristowe et al. found that polarization in the BaTiO must result from charged species at the surface, with oxygen adatoms or OH groups promoting up polarization and oxygen vacancies or H adatoms promoting down polarization; in contrast, ultrathin BaTiO films with pristine surfaces remained paraelectric []. They found that the redox mechanism in the presence of a biased probe tip differs from purely chemical switching in that the biased tip actually removes surface ions that then undergo a redox reaction at the tip. However, as the external circuit is biased, both the buried BaTiO / LSMO interface and BaTiO surface are screened. Furthermore, water molecules at ferroelectric surfaces have been reported to be essential to tip-induced domain nucleation and growth, as shown in Fig. []. The polarization switching process can be represented by the following electrochemical reaction []: ([+P] OH )+H O + e =([ P] H + )+OH. () Here, ([+P] OH ) is the positive polarization charge bound with the screening hydroxyl group, and ([ P] H + ) is the negative polarization charge bound with a screening proton. In order to maintain local electroneutrality during ferroelectric switching or the perturbation of screening charges, the switching process, charge injection, or charge collection is coupled with a surface electrochemical process. The accommodation of screening charges requires the lateral transport of ions across the surface, absorption by the AFM tip, or ionic emission from the surface. Indeed, it was reported that formed hydroxyls diffuse laterally across the sample surface, creating a halo surrounding the switched area []. The spatial extent and lifetime of the halo and the structure of the depolarization fields is controlled by the diffusional mobility of the surface ions and the thickness of the surface water layers. The depolarization fields, in turn, can affect domain nucleation behavior in the adjacent locations (non-local Le Chatelier effect), giving rise to non-trivial proximity effects. This suggests that for ionic compensation,

33 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS Figure : Simplified surface charge distribution (a, b), potential (c, d) and the field (e, f) in the vicinity of ferroelectric surface for unscreened (a, c, e) and completely screened (b, d, f) cases. Charge density is 0. C/m, domain size 0 μm, width of the double layer nm. Reprinted with permission from Phys. Rev. B []. Copyright 00 by the American Physical Society. variation in the state of the water layer can affect the character of switching in the chains (unlike bulk ionic screening or band bending effects) [].... Surfaces in the presence of domains and domain walls Surface with non-zero net charges creates a stray field, which can attract the charge carriers to the surface to compensate the surface []. In case of ferroelectric materials, a completely unscreened surface is extremely unfavorable from an energetic point of view due to the large depolarization fields []. As such, partially or completely screened surfaces are likely to be the equilibrium state of ferroelectric surfaces in air whereas -% overscreened surface is likely to occur during bias-induced domain switching as previously reported [, ]. The partially or completely screened surfaces can be achieved via formation of domains, of which size depends on its boundary conditions []. Formation of domains, which divides the polar ground state into smaller regions with alternating polarity, leads to zero average polarization at the macroscopic scale. Although, it does not completely remove the depolarization at either nanoscale or atomic scale as each individual domain still has a stray field, the mechanism is effective enough to allow ferroelectricity to survive down to films of only a few unit cells thick [, ]. Kalinin et al. calculated the electrostatic potential and electric field above the fully screened, partially screened and unscreened ferroelectric surfaces in the presence of domains with alternating polarities using electrostatic equation. They presented both electrostatic potential and electric field distribution above periodically poled polarization domains in single crystal BaTiO as shown in Fig. []. It is worth noting that even fully screened surface (equal amount of surface screening charges as that of polarization charges) can have variation of electrostatic potential difference between up and down domains in the range of 00 mv. This value, although dependent on polarization vector of the specific materials and the size of the domain, was found to be very close to the experimentally measured values by Kelvin probe force microscopy (KPFM) in PbTiO and Pb(Zr,Ti)O thin films [, ]. Non-uniform

34 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS electric field along the surface normal vector especially near the domain boundaries will be able to attract further screening charges as well as neutral species like dusts from the ambient. As reported by Catalan et al., charge supplied by top and bottom electrodes can also partly screen this depolarization field and, although the screening is never perfect, good electrodes can stabilize ferroelectricity down to films just a few unit cells thick []. It should be mentioned that the top electrode can supply the screening charges to further stabilize the up and down domains in as grown Pt/PZT/Pt heterostructure as evidenced by PFM imaging [0]. In case of the electron beam deposited electrodes, which can have six orders of magnitude higher resistance than pure bulk platinum, a flux closure domains can be developed to mitigate the depolarization field inside a Pt/BaTiO /Pt heterostructure due to the insufficient supply of screening charges through the electrodes []. Domain size is determined by the competition between the energy of the domains (mostly of electrostatic and strain) and the energy of the domain walls. Adding up the energy costs of domains and domain walls, and minimizing the total with respect to the domain size, leads to the famous Kittel s law, i.e. square root dependence []. As such, the thickness of the ferroelectric oxide layer will determine the equilibrium domain size once the ratio of the energy density per unit area of the wall and the volume energy density of the domains are given. Therefore, the knob, in addition to external electric field through electrodes, which experimentalists can use to change the domain width or even its shape and morphology is strain. Strains can be imparted into thin films through differences in lattice parameters and thermal expansion behavior between the film and the underlying substrate, or they can arise from the defects formed during film deposition []. In the case of fully coherent epitaxial films, the biaxial strain can shift the phase transition temperature of ferroelectricity, and change the most stable ferroelectric domain configuration from all out-of-plane polarization domains into alternating in-plane and out-of-plane domains or all in-plane domains or even induce a strong diffuse dielectric anomaly [,,,, ]. As such, strains can change the equilibrium polarization bound charge density either by change in the fractions of c + or c domains or in the overall permittivity of the thick films. Strain gradient can also be used as a control parameter to change the surface screening, which can be developed in the thickness direction by applying localized mechanical force using an AFM tip. This can induce flexoelectric effect and create internal bias field as reported by Hu et al. []. The induced internal electric field not only switches polarization domains but also acts a strong driving force to replace the existing screening charges with equal amount of screening charges with opposite polarity. Another way to develop strain gradient inside the oxide layer has been reported by Lee et al. [], where they induced nanoscale strain gradients in ferroelectric HoMnO epitaxial thin films by controlling the oxygen partial pressure during the film growth. It was shown that the flexoelectric effect due to the strain gradient can strongly affect polarization hysteresis curves as well as domain configurations, which directly affects the driving force of screening phenomena both at the surface and the buried interface of the ferroelectric oxide layer... Buried interfaces... Ferroelectric field effect Polarization screening at a buried interface can influence the charge transport of the underlying bottom layer by changing its carrier density []. As such, there have been considerable efforts to utilize the ferroelectric field effect on buried interface for non-volatile memory applications as well as a tool to non-destructively dope the underlying layer where modulation of transport as well as magnetic and orbital properties,

35 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS Figure : Schematic diagrams of (a) original ferroelectric field effect transistor (FET) [0] and (b) all-perovskite FET. From Ref. []. Reprinted with permission from AAAS. (c) Working principle of a negative-capacitance FET with a ferroelectric material as an insulator, and comparison of its transfer characteristics with a conventional FET based on a metalinsulatorsemiconductor structure. Reprinted by permission from Macmillan Publishers Ltd: Nature Materials [], copyright 0. and superconductivity, were obtained [,, 0]. Since Ross invented the concept of ferroelectric field effect transistor in [0], many research groups have explored the optimum way to fabricate one-transistor ferroelectric random access memories [,,,, ] as shown in Fig.. However, the severe amount of retention loss remains the biggest challenge for applications, which arises from the strong depolarization field across the buried interface between the ferroelectric layer and the underlying semiconducting layer. In order to improve the performance and reliability of ferroelectric field effect transistors, researchers have suggested modification of the buried interface by inserting a quantum metal (a low DOS metal) [], utilizing the negative capacitance of the ferroelectric layer [], or adopting the polarization rotation effect []. Apart from memory device applications, condensed matter physicists have studied ferroelectric field effects for various kinds of buried interfaces. For example, by using an AFM tip, local nonvolatile field effects of the remanent polarization in PZT could modify the electronic density of metallic SrRuO in a Pb(Zr 0. Ti 0. )O (PZT) / SrRuO (SRO) heterostructure and change the sheet resistance by % []. Local changes in the PZT polarization produced by the AFM induced a field effect in the conducting SrRuO layer 00 nm below, modifying its carrier concentration and hence its conductivity, which was measured with standard four-point probes. The same group reported similar effects of polarization on the carrier concentration at the buried interface of a PZT (00 nm) / GdBa Cu O (GBCO, nm) / PrBa Cu O (PBCO,. nm) heterostructure, where the room temperature resistance of the buried interface changed from. kohm to. kohm. The difference in resistance of the GBCO/PBCO bilayer between the two polarization states of PZT was about 0 %, with the sign of the resistance change agreeing with the hole-doped character of GBCO []. The resistance change increased when the heterostructure was cooled down to about 00 K, at which point the contribution of PBCO to the overall conductivity became negligible,

36 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS with the size of the field effect increasing to about 0% at the superconducting transition. More dramatically, at the transition, polarization screening also produced a change in the superconducting transition temperature of K when the low temperature carrier density was 0 holes/cm. Remarkably, it also led to switching between superconducting and insulating behavior when the low temperature carrier density was 0 0 holes/cm [].... Electronic structure While the electronic structure at heterointerfaces can be modeled through the interpretation of electrical transport measurements, XPS is a direct method of probing valence band offsets and, if paired with in situ growth measurements, band bending. Measurement of the valence band and core-level binding energies as a function of distance from the interface, z, allows determination of the surface potential Φ(z) []. Although depth-resolved XPS or hard X-ray photoemission studies [, ] can be performed, extracting Φ(z) is difficult when simply varying the X-ray penetration depth. It is best performed with in situ growth experiments, where the valence band maximum can be measured as a function of film thickness. If there are no sample charging effects (even if charging is reduced with a low energy electron flood gun), the Fermi level of the spectrometer, which is in electrical contact with the sample, sets the Fermi level of the sample []. As the film is grown, the valence band edge is periodically determined by linearly extrapolating the leading edge (at low energy side) to the background level [0]. This, along with knowledge of E gap and (E c E F ) from other techniques, permits a measure of the sign of band bending and the depletion length (these can also be measured when sample charging is present, but the absolute value of the VBM cannot be directly measured). If the penetration depth is similar in magnitude to the depletion length, band bending will also cause broadening in the valence band DOS and core-level peaks. Since the binding-energy difference between the valenceband maximum and any core level is fixed, energy shifts and broadening in core-level peaks from the substrate can also be monitored as a function of thickness to establish the extent of band bending within the substrate. If the separation between the VBM and (shallow) core levels in the pure phases of A and B are known then the valence band offset is determined for the A/B heterostructure by [] ΔE v = ( Ecl A ) EB cl A/B [(E cl E v ) A (E cl E v ) B ]. () Obtaining the offset is difficult when there are no unique core levels between substrate film, but Chambers et al. have shown this to be possible as well using a more elaborate analytical technique []. In addition, it may be possible to deduce band offsets by examining offsets with respect to a common third material, C, such that ΔE v = ΔEv A/C + ΔEv B/C []. Thus, building a library of band alignments for different oxides would be extremely useful for predicting energy-level diagrams or Schottky barrier heights for new heterojunctions. As an example, Chambers et al. [] conducted in situ XPS studies on LaCrO films grown on SrTiO (00) by oxide molecular beam epitaxy (MBE). The Sr d spectra from the substrate and La d and Cr p spectra from the film are shown in Fig. (a) for LaCrO films of various thickness, where all the spectra have been shifted to align the Sr d / peaks for visualization. As seen, the La d and Cr p binding energies shift to lower values for thicker films; similarly, the full widths at half maximum (FWHM) of the peaks decrease with thickness. These FWHM values are shown at the top of Fig. (b, top), not only for La and Cr, but also Sr d and Ti p. The FWHMs increase for the La and Cr peaks initially and then plateau; they then decrease in width for unit cells and higher. The built-in potential for films - unit cells in thickness can be modeled by Gaussian sums, and the resulting potential drop for LaCrO of different thicknesses are shown in Fig. (b, bottom), with a 00 mev/unit cell potential for unit cells and 0 mev/unit cell for unit cells. A

37 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS smaller amount of broadening is also observed in the SrTiO substrate, possibly due to Ti diffusion into the LaCrO. Averages for the valence band offsets were determined using Eq. with the Sr d / and Ti p / for SrTiO and La d and Cr p for LaCrO. The results are shown in Fig. (d), with values ranging from.0 ev for -unit-cell films to. ev for -unit-cell films. Careful analysis of the bulk LaCrO valence band and hybrid functional calculations show that the conduction band offset is given by the valence band offset plus the Cr d t g e g gap minus the SrTiO band gap. A schematic of the energy-level diagram for -unit-cell LaCrO /SrTiO is shown in Fig. (c). As seen, the bands are staggered such that charge transfer from the LaCrO to the SrTiO would be favored if a critical thickness was exceeded. LaCrO / SrTiO, however, remains insulating potentially due to diffusion of Ti into the LaCrO, producing Ti Cr, thus producing a defect state below the SrTiO CBM and trapping electrons [].... Schottky barriers With in situ growth / XPS measurements, one can thus monitor the evolution of the core-level energies during interface formation and directly determine the Fermi-level position at the interface. For semiconductor / metal interfaces, this position is the Schottky barrier height. In polar oxide systems, one can tune the Schottky barrier height by varying the degree of polarization via [] ΔΦ B = λ eff D S /ε 0 (0) where λ eff is the effective screening length, D S is the dielectric displacement, and ε 0 is the permittivity of vacuum. Chen and Klein [] measured the Schottky barrier height at a BaTiO / RuO interface, not by an in situ growth experiment but by an in situ switching experiment. They first grew (metallic) -nm-thick RuO by room temperature sputter deposition onto BaTiO (00) single crystals and coated both the top and bottom with Pt electrodes. The top Pt electrode was grounded, setting the Fermi-level reference for the spectrometer, while the bottom Pt electrode was biased, allowing ferroelectric switching of the BaTiO. The results are shown in Fig. (a), where P r refers to the remanent polarization, and P s refers to the saturation polarization of ±00 V with positive biases indicating up polarization toward the RuO, and negative biases leading to down polarization away from the RuO metal. As seen, there are significant changes to the core-level peaks of the BaTiO, with both the Ba d / and Ti p shifting to lower (higher) binding energies for down (up) polarization. In the initial state, the BaTiO core-level peaks were at intermediate binding energies; as the core levels for bulk BaTiO are at. ev and. ev for the Ba d / and Ti p peaks, in the initial state, the BaTiO / RuO sample shows a Fermi-level difference of E F E v =. ev. With up polarization, the Fermi level increases by 0. ev to. ev for up polarization and decreases by 0. ev to. ev for down polarization. These then are the Schottky barrier heights for hole transport across the interface, with up polarization leading to an upward shift in Fermi level. The barrier heights for electrons can be obtained by subtracting these barriers from the BaTiO band gap (. ev). When the bias was removed, these differences remained intact. Schematics of the results for the initial state, the saturated polarization state, and the remanent polarization state are shown in Fig. (b) for the case of symmetric RuO electrodes. By then carefully tuning the composition of the interface, e.g., adding a single plane or unit cell of another oxide between two different oxides, one can possibly tune the Schottky barrier or band offsets [, ]. Ionic materials may not exhibit the metal-induced gap states commonly found in covalent semiconductors, and for the SrRuO / Nb:SrTiO (00) metal / semiconductor interface, the measured Schottky barrier height is indeed given by the difference between the SrRuO work function, Φ, and Nb:SrTiO electron affinity,

38 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS (a) (c) ΔE c = 0. ev E g CT-STO =. ev STO ΔE v =. ev distance LCO energy E g dd-lco =. ev density of states Cr d t g (b) (d) valence band offset (ev) (top) (bottom) 0 LCO film thickness (u.c.) Figure : XPS results on the polar LaCrO / SrTiO (00) system. (a) Sr d,lad, and Cr p photoemission spectra as a function of film thickness, all measured with an electron take-off angle of 0. The probe depth is nm. (b) The widths of the core-level peaks (top) and the potential drop across the film (bottom) as a function of film thickness. (c) Schematic energylevel diagram illustrating the band offsets and the potential gradients extracted from XPS data for -unit-cell-thick LaCrO. The five dotted (coloured) lines in the LaCrO represent VBMs for each of the unit cell thicknesses and connect to the associated valence band DOS. The dashed lines mark the positions of the intensity-weighted VBM and CBM within the LaCrO film. (d) The average valence band offset as a function of film thickness. Reprinted with permission from Ref. []. Copyright 0 by the American Physical Society. χ [, ]. Thus by adding a layer between SrRuO and Nb:SrTiO, it may be possible modulate the barrier height by Δ, as shown in Fig. 0. Yajima et al. [] showed this was possible by inserting a single layer of (LaO) + or (AlO ) at the interface (Fig. 0(a) and (b), respectively). This, in principle, places an excess layer of positive (negative) charge at the interface that must be screened. From analysis of the measured current-voltage and capacitance-voltage profiles, they found that one unit cell of LaTiO led to removal of the Schottky barrier and an Ohmic contact, whereas two unit cells of SrAlO yielded an increase of. ev. This was confirmed by both internal photoemission spectroscopy and XPS, the latter employing the Ti p /. The insertion of LaTiO (SrAlO ) shifts the p / peak to higher (lower) binding energies or a decrease (increase) in Schottky

39 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS (a) intensity [arb.units] (b) (b) E CB E VB Bad / E F. ev.. -Pr -Ps +Pr +Ps -Pr -Ps +Pr +Ps Initial 0. ev 0. ev Tip Rup /.. -Ps +Ps -Ps +Ps Initial Rud binding energy [ev] P. ev 0. ev Figure : XPS results on Schottky barriers within ferroelectric BaTiO / RuO capacitor structures. (a) Core-level spectra of the Ba d /,Tip, and Ru d under different applied potentials. The initial state and remanent states were measured at 0 V, while positive (+Ps) and negative (-Ps) saturations were measured at +00 and -00 V, respectively. In all cases, the top electrode was electrically connected to the spectrometer, and the voltage was applied to the bottom electrode. (b) Schematic energy diagrams with two RuO electrodes before (left), during (middle), and after poling (right). The arrows indicate the ferroelectric polarization direction within the BaTiO. Reprinted with permission from Ref. []. Copyright 0 by the American Physical Society. barrier height for electrons. These direct XPS results were in in good quantitative agreement with the other methods. Schematics of the charge profiles and energy-level diagrams for the two cases are shown in Fig. 0(c, d) and (e, f), respectively. We note that mesoscale aspects of the charge and defect distributions at non-zero temperatures can be determined by combining first-principles calculations of the specific interface with the Poisson-Boltzmann equation []. While the discussions in this subsection have been largely limited to defect-free examples, point defects will typically dictate the electronic properties of buried interfaces. P -Ps +Ps -Ps +Ps Initial. ev

40 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS (a) (c) Charge (e) Electron energy (SrO) 0 Sr Metallic SrRuO (RuO ) 0 Ru (SrO) 0 Ionic charge Screening charge SrRuO Φ (TiO ) 0 Ti (LaO) + La (TiO ) 0 Depleted Nb:SrTiO (SrO) 0 SBH = Φ χ+δ (TiO ) 0 Space charge Δ Distance Nb:SrTiO χ (SrO) 0 E Vac E C (b) (d) Charge (f) Electron energy (SrO) 0 Sr Metallic SrRuO (RuO ) 0 Ru Screening charge Ionic charge E F + + Φ (SrO) 0 SrRuO (AlO ) Al Δ (SrO) 0 Ti SBH = Φ χ+δ Depleted Nb:SrTiO (TiO ) 0 E F (SrO) 0 Space charge (TiO ) 0 Distance Nb:SrTiO Figure 0: Schematics illustrating the effects of an artificial dipole placed at an oxide heterointerface. (a, b) Depiction of SrRuO /Nb:SrTiO heterointerfaces with (LaO) + and (AlO ) layer insertion. (c, d) The corresponding charge distribution profiles and (e, f) band diagrams for cases (a) and (b). The inserted dipole either decreases (e) or increases (f) the Schottky barrier, maintaining the relationship: SBH = Φ χ + Δ, E vac, E c, and E F denote the vacuum level, the conduction band edge in Nb:SrTiO and the Fermi level of the system. Reprinted from Ref. []. Such defects may form during the interface synthesis stage; e.g., the process of metal deposition onto oxides is known to induce reduction and Fermi-level pinning [, ]. Researchers have even found that the properties of the TiO / SrTiO interface depends sensitively on the particulars of the SrTiO substrate preparation procedure []. The importance of defects has impelled theorists to include specific oxygen vacancy concentrations in ab initio calculations of band offsets [0], but coupled theoretical / experimental studies will be necessary for isolating the effects of the many possible defect structures... Manipulation of screening charges... Charge injection (SrO) 0 E Vac E C

41 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page 0 of CONTENTS 0 Figure : (a) KPFM surface potential distribution and (b) PFM phase image of the area scanned with the applied voltage biases from - to V with V step (from top to bottom) to the bottom electrode. The black scale bar presents μm. (c) Surface potential line profile obtained from Fig. (a). The inset shows piezoresponse hysteresis loop of PTO thin films. Reprinted with permission from Ref. []. Copyright 00, AIP Publishing, LLC. Local charge injection Research groups have studied the local charge injection by electrically biased nanoscale atomic force microscopy (AFM) tip on the naturally screened ferroelectric thin films and created artificial pattern of screening charges that could be imaged by surface charge distribution sensitive probe microscopy such as scanning resistive probe microscopy [, ]. Depending on the amount of injected charges, the surface potential will vary monotonously until it reaches the threshold or the coercive field of the underlying ferroelectric domain, at or beyond which point the injected charges can induce local polarization switching as shown in Fig. []. Charge injection by electrically biased AFM tip has been used to study the screening phenomena by gas phase adsorbates where people have varied the environment from H diluted with Ar to O, and observed a dramatic change of surface potential using both electrostatic force microscopy (EFM) and KPFM as shown in Fig. []. Another example can be found where the charge injection into the oxide layer causes the resistance change of the carbon nanotube deposited on the oxide []. One way to perturb the screened oxide surface and let it reach the equilibrium state is to inject charges using the electrically biased AFM tip and monitor the change of surface potential as a function of time. By doing so, one can identify the sinks that remove the

42 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS Figure : (a) AFM topography, (b) EFM amplitude, and (c) EFM phase images of TiO single crystal surface after the charge injection over μm by μm area using AFM tip at the central region in Ar-% H, Ar, and O environments. Reprinted with permission from Ref. []. Copyright 0, AIP Publishing, LLC. excessive surface charges and help the surface reach its equilibrium, which in the case of polycrystalline ferroelectric thin films is found to be the grain boundaries and their junctions []. In case of polycrystalline ferroelectric thin films, the surface potential change follows the exponential decay with the time constant of about 0 minutes, which corresponds to the surface diffusion rate of screening charges []. Interesting application of charge injection onto the polar surface is the selective deposition of nanoparticles by patterning the ferroelectric domains using biased AFM tip that injects charges on the surface. Kalinin et al. showed that the polarization domain specificity of adsorption illustrates that certain chemical reactions depend on domain orientation, which in turn correlates with the polarity of surface screening charges [].... Charge collection Local charge collection Researchers have found anomalous phenomena when they scanned a grounded AFM tip on the ferroelectric surface, where they intended to locally pattern the ferroelectric domains by applying voltage pulses through the tip. The area where they intended to keep intact underwent a dramatic change in surface potential, as observed by KPFM []. In addition, it was experimentally and theoretically shown that slow dynamics of surface screening can control the kinetics of the ferroelectric switching, and result in backswitching and relaxation phenomena []. Recently, Ievlev et al.

43 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS demonstrated the history dependent polarization reversal by the grounded AFM tip, which they attributed to the induction of the slowly dissipating charges into the surface that induce polarization reversal []. In order to control the interaction between the AFM tip and the surface screening charges, researchers have applied bias voltage to the tip to prevent such interaction []. For those who wanted to write information bits in the form of polarization domains and read the signal by the screening charges on those domains, it was particularly important to make sure that the screen charges did not change their distribution unless the information was written by the tip []. Hong et al. found a way to use the interaction between the moving AFM tip and the surface screening charges to image the underlying ferroelectric domains, which they called charge gradient microscopy (CGM) [,, ]. CGM enabled the community to not only image the ferroelectric domains at high speed, but also led to the study on the kinetics of surface re-screening process by adjacent external ions from the ambient. Tong et al. used CGM to understand the bonding strength between the chemisorbed ions and the polar surface of periodically poled lithium niobate and also characterized the re-screening kinetics of external ions onto the surface []. By combining CGM and KPFM, they were able to create a condition close to unscreened surface by mechanical means at room temperature, where the surface potential difference between up and down domains reached close to V, which diminished down to 0. V in 00 seconds []. It was also found that unscreened polarization charges, which are exposed to the ambient, are rescreened in a matter of minutes following an exponential recovery with a universal half-life time τ of. min. These findings indicate that, with little impact on the ferroelectric polarization, one can control the degree of screening on a ferroelectric surface by a mechanical manner, which opens up an interesting field of mechanochemistry and its dynamics at the nanoscale [].. Case studies: Low thickness regime When films of polar oxides are sufficiently thin, the surface energy is no longer divergent. As a result, screening may occur (and is more likely as the thickness increases) but is no longer a requirement. Furthermore, screening mechanisms that take place at the surface may affect the electrical properties of the buried interface (or vice versa). We describe two examples of such interacting interfaces below, the primary one dealing with LaAlO / SrTiO (00) heterostructures. Ferroelectric systems that may exhibit DEG behavior are also discussed... LaAlO / SrTiO (00) As has been noted in many publications, the appearance of conductivity or DEG behavior at the buried LaAlO / SrTiO (00) interface may result simply from electron transfer, without the need for defects. Once the potential drop across the LaAlO thickness exceeds its band gap (at roughly five unit cells [0]), electrons can tunnel from the O p bands at AlO surface to Ti d bands at the TiO interface. This approximate critical thickness has indeed been observed in multiple experimental investigations and is reproducible when efforts have made to minimize the impact of oxygen vacancies and account for cation intermixing [,,,, 0,, ]. Furthermore, using linearly polarized X-ray absorption spectroscopy, Salluzzo et al. [0] observed a significant difference in the dichroism for films below and above the critical thickness that was consistent with the predicted electronic (and orbital) reconstruction []. Since defect-free systems are not practically achievable, many attempts have been made to fully understand the role of defects on the electronic properties of the LaAlO

44 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS Figure : Trace and retrace CGM images of artificially decorated domains with different sizes. CGM images taken on ribbon-shaped domains poled by V to the bottom electrode of -nm-thick LiTaO films from (A) left-to-right scan (trace) and (B) right-to-left scan (retrace) using Pt tips at scan frequency of 0 Hz. PFM (C) amplitude and (D) phase images are taken at the same region at scan frequency of Hz where bright phase contrast corresponds to positive (upward) domain and dark phase contrast corresponds to negative (downward) domain. Reprinted with permission from Ref. []. Copyright 0, National Academy of Sciences. / SrTiO interface. For example, studies have been conducted on the effect of cation intermixing [,,, ] and other point defects [, ]. We have already noted that the creation of oxygen vacancies transfers electrons to the SrTiO conduction band. The oxygen pressure region with a slope / shown in Fig. (a) refers to conductivity from electronic carriers. When SrTiO crystals are heated to 0 K in low pressure (typical thin film growth conditions), oxygen vacancies can be introduced at the substrate surface. Furthermore, reactions may take place between the SrTiO surface and species from the growing film (e.g., Al in LaAlO, YAlO,orAl O ), again potentially leading to electronic doping at the buried interface [,,,,, 00]. Also noted above is the fact that hydrogen is easily bonded to the SrTiO surface, which can cause hydrogen-induced metallization [0, 0]. Regardless of the particular mechanism, the observation of metallic conductivity at the SrTiO surface is not unusual [,,,, 0, ]. Gunkel et al. [] made it clear, however, that the electronic behavior of LaAlO / SrTiO is distinct from that of simply reduced SrTiO, at least when heated to temperatures allowing thermodynamic equilibration (> C). This can be observed in Fig. (b). At temperatures higher than 0 K, the conductivity is dominated by the bulk SrTiO crystal. At 0 K, the LaAlO / SrTiO heterostructure has a higher conductivity than the SrTiO, at least for moderate pressures. By plotting the conductance at po = 0 bar over a wide (elevated) temperature range, the authors found that the conductance increased at lower temperatures

45 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS log (Conductivity [S/cm]) / SrTiO / log (Oxygen partial pressure [bar]) T (a) log (Conductance [ ms ]) K - LAO/STO STO (b) log (Oxygen partial pressure [bar]) Figure : Conductivity measurements as a function of oxygen partial pressure. (a) Reference measurements on a SrTiO single crystal for increasing temperatures (0 K, 0 K, 000 K, and 00 K). (b) Measurements for a LaAlO / SrTiO (00) heterostructure (red circles) as compared to SrTiO at 0 K. Reprinted from Ref. [] with the permission of AIP Publishing. ( T from 0 to 00 K), thus possessing metallic behavior below 00 K. It should also be noted that LaAlO / SrTiO heterostructures are often annealed in oxygen post-deposition to remove defects like oxygen vacancies; however, this can also increase the number of strontium vacancies [] via V Sr +(SrO) sp Sr Sr + O + e, () which also reduces the concentration of electronic carriers. The transfer of electrons from the top of the LaAlO to the buried interface should produce p-type conductivity at the LaAlO surface, but this has not been experimentally observed []. There has also been no evidence of significant polar fields within the LaAlO for films below the critical thickness [, 0]. This could be due to X-ray induced screening charges, however, and ionic polarization within the LaAlO below the critical thickness has been observed by several groups [0, 0, 0, 0]. Another theoretical model proposed that oxygen vacancies form at the LaAlO surface, which would then result in electrons that could tunnel to the buried interface [, 0]. As shown in Fig., this could occur by a redox reaction, leading to a neutral O molecule leaving the oxide, a positively charged oxygen vacancy at the surface, and free electrons (Eq. ). It is also possible for adsorbed water to lead to protonation at the surface [0]: H O O + H + e, () which will be discussed in more detail below (while adsorbed hydrogen or hydroxyl groups can help to screen polar surfaces, however, they do not necessarily lead to mobile carriers [0, 0, 0]). As for the surface oxygen vacancy mechanism, an electric field should be present across the LaAlO film as already discussed in Section and as displayed in Fig. (a). The creation of an oxygen vacancy at the surface leads to a donor level within the band gap and thus potentially two electrons free to travel to the buried interface, as shown in Fig. (b). As shown in Ref. [], there exists a strong driving force to form these charged defects at the LaAlO surface, tending toward negligible formation energies and charge densities of ±0.e/ surface unit cell as the film thickness increases. Once the

46 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS (a) (b) (c) Figure : Schematic band diagram of the interface between a polar film and a nonpolar substrate along the normal direction z, at three different times. (a) The initial defect-free system at the critical film thickness. (b) The system after a redox reaction leads to the creation of a donor state at the surface and subsequent electron transfer. (c) The system after electron transfer leads to a reduction in the film s electric field and a DEG. Reprinted with permission from Ref. []. Copyright 0 by the American Physical Society. defects compensate the surface, this leads to a general reduction of the electric field, as shown in Fig. (c) (and previously in Fig. 0(d)), and band bending at the SrTiO surface. Thus, for ultrathin oxides with polar surfaces, one can not only produce surface metallicity by some screening mechanism, as for TiO (0) [], BaTiO (00) [, ], or for ZnO (00) [, ], but also manipulate the conductivity of a buried interface via interactions at the surface. This was first discovered for water adsorbed to the AlO surface of LaAlO [0, 0], which dissociates into OH and H +. When a positively biased AFM tip is scanned over the surface of a three-unit-cell LaAlO film (with an initially insulating interface), it can remove the OH and lead to surface protonation [0]. The electric field then drives the electrons to the buried interface, leading to the DEG (i.e., a local insulatorto-metal transition) [0, 0]. With time, however, the hydrogen may eventually desorb or additional H O could block hydrogen adsorption, reducing DEG conductivity. Similarly,

47 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS negative voltages can be used to preferentially remove the adsorbed hydrogen ions and erase conducting regions written by the positively biased tip [0, ]. A similar effect to surface protonation can be induced by the adsorption of polar molecules []. In this case, different mechanisms could be distinguished by using either polar aprotic molecules (like acetone) or polar protic molecules (like water). Since the thickness of the polar liquid can affect the resulting screening charge at the LaAlO surface, the thickness of the polar liquid can be used to modulate the DEG conductivity. It is suspected that the polar molecules align themselves at the LaAlO surface, with increasing misalignment away from the surface. The interplay between charged point defects and polar surfaces was examined more recently by Lu and Zunger []. The cation intermixing observed experimentally at the LaAlO / SrTiO interface [,,, ] can be reframed in terms of antisite defects. These have low enthalpies of formation as shown by the filled symbols in Fig. (a, b). However, Yu and Zunger [] calculated that both the La Sr and Ti Al are stable only when neutral, and the formation enthalpy of V O at the interface (not at the surface) is relatively large. As noted by others [, 0, ], the formation enthalpy of V O s at the surface decreases as the LaAlO becomes thicker, and this dependence is shown in Fig. (c). It reaches 0 ev at approximately four unit cells and would form spontaneously, reaching a maximum concentration of vacancy per eight oxygen ions. As they are necessary for screening the polar surface, they cannot be filled even at high po. The authors postulate that the reason why experimentalists have been unable to observe any significant built-in potential for subcritical thickness LaAlO films has to do with [Ti Al (S)+Al Ti (I)] defect pairs spanning across the film. As shown in Fig. (b), such defect pairs are extremely favorable, with a decreasing negative formation enthalpy with thickness (in the absence of oxygen vacancies). The electron transfer from Ti Al (S) to Al Ti (I) screens the field, but as deep-level dopants, they provide no electronic carriers. Once the critical thickness is exceeded and the energy for V O (S) formation reaches zero, the energy of the defect pair increases (Fig. (d)), and the screening mechanism changes to that of surface oxygen vacancies... Ferroelectric control of screening mechanisms DEG behavior has been observed at the (00) interface of SrTiO with other materials [,,,,,,,, ] and for other orientations [,, ], and work on implementing the DEG for sensors and other heterostructured devices continues to progress [,,, 0]. There has also been speculation regarding the possibility of DEG formation at the interface between a ferroelectric film and an insulating substrate [,,, ]. Experimental evidence of such behavior may already be in the literature: Streiffer et al. [] had previously discovered an F γ phase for PbTiO / SrTiO (00) that consisted of monodomain ferroelectric PbTiO. The existence of such a domain state requires that both interfaces be charge compensated. That is, even if the surface was screened by adsorbates [,, ] (causing the F α to F β transition), compensating charge must still have been present at the PbTiO / SrTiO interface. As shown by both a Landau model [] and an ab initio study [], an electronic reconstruction is expected theoretically. If one constructed a device comprised of ferroelectric film on an insulating substrate with electrodes on top of the ferroelectric surface and below the substrate, interesting polarization and DEG could be obtained depending on the particular film thickness, d. This would enable the possibility of a tunable DEG or D hole gas (DHG) (even switching from one to the other for equivalent ferroelectric interfaces) as well as modifying the effective band gap or critical thickness for ferroelectricity, d c, for inequivalent ferroelectric interfaces.

48 Page of CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R CONTENTS (a) ΔH (ev) (c) c ΔH (ev) V O + n-type: n LAO < L c V Ti V O + V O + V La 0 0 V Sr Al Ti Sr La V Al V O + V O + V Sr n-type: n LAO L c V O + V Ti Al Ti V O + V O + V V Al La Sr La La 0 Sr La 0 0 Ti Sr Al Ti 0 Al SrO TiO LaO AlO SrO TiO LaO AlO V O (S ) n-type (b) ΔH (ev) 0 d(d) Ti Al +Al Ti w/o V O (S) n-type w/ V O (S ) n LAO (uc) d Ti Al (uc) Figure : The formation energies of different point defects near the interface, determined at the equilibrium Fermi energy for n-type interfaces for (a) n LAO < L c and (b) n LAO L c. The dashed lines are guides to the eye(c) The GGA-calculated enthalpy of formation of surface oxygen vacancies (V O (S)s) under an oxygen-rich growth condition. (d) The GGA-calculated enthalpy of formation for a Ti Al +Al Ti defect pair both with and without V O (S)s ina (SrTiO ) /LaAlO ) / vacuum supercell. The orange lines are guides to the eye. Reprinted by permission from Macmillan Publishers Ltd: Ref. [], copyright 0. For the moment ignoring the likelihood of ferroelectric domains and assuming easy electron tunneling between the ferroelectric interfaces, the Landau model showed that the free energy curve for the ferroelectric exhibited a triple-well profile at zero field. An applied electric field, ε, could then be used to switch between the ferroelectric or paraelectric states, thus also turning on or off the DEG or DHG. This tri-stable energy profile furthermore provides interesting hysteretic behavior. A summary is shown in the calculated phase diagram of Fig., mapped as a function of applied electric field and film thickness, where the paraelectric phase is shown in dark gray, the ferroelectric phases are in light gray, and the phases in white indicate variable states depending on the sweep history. Above a thickness of d h, the ferroelectric can switch as usual, from an up to down monodomain state. For thicknesses between d c and d h, the ferroelectric could return to the paraelectric state (with a surface charge density, σ = 0) before switching to the opposite polarity. Below d c, DEG or DHG behavior is still possible provided a large enough electric field. Although ferroelectric domains ignored in this example, the authors did show that with sufficiently large thicknesses monodomain films can be energetically favorable []. Naturally, this thickness depends on the domain wall energy, the band gaps of the ferroelectric 0

49 CONFIDENTIAL - AUTHOR SUBMITTED MANUSCRIPT ROPP-00.R Page of CONTENTS Figure : Phase diagram for a PbTiO thin film as a function of thickness d and external electric field ε. The circles (crosses) indicate an upward (downward) jump in polarization during forward (backward) voltage sweep. The solid (dashed) lines correspond to transitions from σ 0 (σ = 0) to σ = 0 (σ 0), and the paraelectric and ferroelectric regions (with DEG or DHG coexistence) are shown in dark and light gray, respectively. The white regions indicate different states that are accessible depending on the sweeping history. Reprinted with permission from Ref. []. Copyright 0 by the American Physical Society. and substrate, the band offset, and whether redox processes can take place at the interfaces. Regardless, this provides an excellent example of the possibilities available in polar oxide systems in terms of novel physics and new technologies. To exploit such opportunities, however, further experiments detailing how screening mechanisms evolve at surfaces and buried interfaces are necessary.. Conclusions and outlook Complex oxides are well known for their enormous range in electronic properties, and some are prototypical examples of multifunctional materials. While much has been made of the novel phenomena found at polar interfaces, researchers are gradually coming to terms with the vast array of possible screening mechanisms. In this review, we have described a few recent studies focused on understanding the screening process for both non-ferroelectric and ferroelectric systems. We have been selective in our examples and so have naturally omitted many excellent publications. Furthermore, new discoveries continue to be reported in this field at a rapid pace, and so it behooves the interested reader to keep abreast of the recent literature. Aside from providing a general status update, part of the goal of this review is to stimulate further interest in this area, as we believe it to be one rife with exciting scientific and engineering opportunities. For instance, chemical sensors rely on the interactions between reactions at the surface and the induced changes in electrical properties of the semiconductor [,, ]; researchers are now investigating polar heterointerfaces for exploiting similar behaviors [, 0]. Similarly, while the catalytic and electrocatalytic