Polarity in Oxide Nano-objects - ACS Publications - American

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Polarity in Oxide Nano-objects Claudine Noguera* and Jacek Goniakowski Institut des Nanosciences de Paris, UMR 7588, CNRS, and Université Pierre et Marie Curie, 4 Place Jussieu, 75005 Paris, France 5.1. Non-oxide Nanoribbons and Islands 5.2. MgO Nanoribbons 5.3. ZnO Nanoribbons 5.4. Other Oxide Nanoribbons 5.5. MgO Nanoislands 5.6. NiO Nanoislands 5.7. Summary 6. Manifestations of Polarity in Two-Dimensional Nanoribbons 6.1. Unsupported Ribbons in the Large Width Limit 6.2. Supported Ribbons 6.3. Summary 7. Summary and Open Questions 7.1. Dimensionality Features 7.2. Mechanisms of Compensation 7.3. Role Played by the Substrate 7.4. Formation of a 2D or a 1D Electron Gas Appendix Author Information Corresponding Author Notes Biographies Acknowledgments Abbreviations References

CONTENTS 1. Introduction 2. Electrostatic Considerations 2.1. Semi-infinite Surfaces 2.2. 3D Polar Objects: Ultrathin Films and Clusters 2.3. 2D Polar Objects: Nanoribbons and Islands 2.4. 1D Objects: Nanowires 2.5. Symmetric Polar Objects 2.6. Compensation Mechanisms 3. Polarity in Ultrathin Films and Finite Size Clusters: Literature Review 3.1. Irreducible Oxides 3.1.1. MgO(111) Ultrathin Films 3.1.2. ZnO(0001) and BeO(0001) Ultrathin Films 3.1.3. Al2O3(0001) Ultrathin Films 3.2. Reducible Oxides 3.2.1. FeO(111) and Other Iron Oxide Ultrathin Films 3.2.2. CoO(111) and Other Cobalt Oxide Ultrathin Films 3.2.3. NiO(111) Ultrathin Films 3.2.4. MnO(111) Ultrathin Films 3.2.5. VO(111) and Other Vanadium Oxide Ultrathin Films 3.2.6. TiOx Ultrathin Films 3.3. 3D Finite Size Clusters 3.4. Summary 4. Polarity in Ultrathin Films: Underlying Concepts 4.1. The Large Thickness Regime for Stoichiometric Films 4.2. The Large Thickness Regime for Nonstoichiometric Films 4.3. Thin Film Phase Diagram and the Low Thickness Regime 4.3.1. Stoichiometric, Unsupported Thin Films 4.3.2. Supported Thin Films: The Concept of Induced Polarization 4.3.3. Electrostatic Contributions to Adsorption 4.4. Summary 5. Polarity in Two-Dimensional Nanoribbons and Islands: Literature Review © 2012 American Chemical Society

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1. INTRODUCTION Polar surfaces of compound materials have been the subject of intense activity in the past. Electrostatic arguments, based on a model of rigid charges, predict that they should have an infinite surface energy, because of the presence of a macroscopic dipole, and thus should never be observed. However, it was proved that the introduction of compensating charges in the outer planes, arising from either a deep modification of the surface electronic structure or strong changes in the surface stoichiometry, could stabilize them. These processes usually lead to original surface configurations, in which the local environment of the surface atoms strongly differs from what is achieved in the bulk or at nonpolar surfaces. Moreover, peculiar electronic surface states may lie in the gap of the oxide and induce enhanced basic or acid character at surface atoms, with important implications on reactivity. Finally, surface reconstructions that are sometimes consequences of the polar instability can be used as nanostructured substrates to grow artificial structures with predetermined conformations. When

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Special Issue: 2013 Surface Chemistry of Oxides Received: July 30, 2012 Published: December 4, 2012

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Figure 1. Examples of rocksalt polar nano-objects: (a) an ultrathin film with polar (111) terminations; (b) a 3D cluster with two opposite polar (111) facets; (c) a planar (100) nanoribbon with infinite polar [110] edges; and (d) a 2D (100) island with two finite polar [110] edges.

microelectronics and heterogeneous catalysis. This is particularly true for ultrathin films, made of only a few atomic layers stacked along a polar direction, which have been shown to display a variety of new characteristics.7−11 There have also been advances in the controlled fabrication of small polar oxide objects, such as nanoribbons, nanoislands, and nanoclusters, with a focus on how to control their growth in view of novel applications in optoelectronics, sensors, transducers, and biomedical sciences. This field is presently very active, and time is ripe to summarize the concepts underlying their properties. However, a key question is: “Does polarity exist at the nanoscale?”12 Indeed, the size of a nano-object is finite and “small” (nanometric) and an actual divergence of the electrostatic potential never occurs. We will nevertheless discover in the following sections that, in nano-objets, polarity is actually relevant and that it induces strong atomic or electronic modifications whenever it yields electrostatic energy contributions comparable to other energy terms, such as the gap energy, the bulk cohesion energy, or the elastic energy. Polar nano-objects raise a number of very new questions related to the relevance of electrostatic interactions and the role of dimensionality (2D or 3D) in driving the polar instability. As compared to semi-infinite surfaces, additional mechanisms of polarity compensation exist at the nanoscale, involving complete changes of structures, strong lattice relaxations, inhomogeneous charge redistributions, among others. Because most nano-objects are grown on (metallic or insulating) substrates, there is an interplay between polarity and substrate effects: interfacial charge transfer, adhesion, and lattice mismatch, particularly important for the stability of monolayer films or 2D polar objects. Finally, the understanding of the 2D or 1D electron gases present at some polar interfaces or at polar

they involve large unit cells, they may orient specific growth modes, favoring for example the formation of size-controlled clusters. This quick overview shows that, contrary to initial expectations, polar surfaces are of prominent interest, both from a fundamental and from an applied point of view. Polar surfaces of compound semiconductors were the first to attract interest, in particular because the (100) surface of zinc-blende compounds serves as a substrate for the growth of nearly all III−V and II−VI device layers.1 The understanding of surface stability and charge compensation in sp3 bonded materials has led to a rich literature, both experimental and theoretical, and to the development of concepts, such as the charge neutrality concept.2−4 However, more diversity is met at polar oxide surfaces, due to the variety of their crystallographic structures, which reflects the subtle mixing of ionicity and covalency in the metal− oxygen bonding and some specificities associated with the d orbitals in transition metal oxides. In addition, playing with multivalent metal atoms and/or controlling experimental parameters, such as temperature, partial oxygen pressure, etc., may yield surface oxides with unusual stoichiometries. In the last two decades, the field has enormously evolved. Detailed experimental studies have focused on the behavior of a larger class of surfaces, under a wider range of preparation and environmental conditions. More systematic theoretical results have been obtained, which allow for comparing the relative strength of the various stabilization mechanisms. For the interested reader, results published on polar oxide surfaces before 2008 have been reviewed in refs 5, 6. Here, the focus is on polar oxide nanostructures, a field much less developed than polar surfaces, but nevertheless the object of important advances in the past decade, largely stimulated by the growing demand of novel materials for applications in 4074


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island edges is related to the very hot physics of confinement effects in new layered materials. It is the aim of this Review to examine fundamental issues regarding polar oxide nano-objects, in light of recent experimental as well as theoretical advances. Using a rigid charge model, we will first examine the electrostatic characteristics of various nano-objects, to get a first insight into the manifestations of polarity. Relying on experimental as well as theoretical results, we then will successively analyze the physics of polarity in ultrathin films, three-dimensional clusters, twodimensional nanoribbons, and islands. This Review concludes with open questions for future investigations. A word of warning, it is important to remark that identification of polarity is not always straightforward in nano-objects. Making a truly exhaustive bibliographic review is thus difficult because a number of authors, although obviously dealing with polar objects, do not even mention the terms “polarity” or “dipole moment” in their publications. Moreover, terminations known for their polar character in the bulk may be nonpolar at the nanoscale. Figure 2. Capacitor models without (a) and with (b) compensating charges on the outer layers and sketch of the electrostatic potential variations across them.

2. ELECTROSTATIC CONSIDERATIONS In the earliest works on semi-infinite polar surfaces,13−15 pure electrostatic considerations have proved to be an essential prerequisite for any understanding of their properties. The goal of this section is thus to shortly reconsider semi-infinite surfaces, and then apply a similar pure electrostatic approach to various polar nano-objects: thin films, 3D clusters, nanoribbons, and 2D islands (Figure 1). This analysis will reveal that polarity characteristics are strongly dependent on the object dimensionality, shape, and symmetry, and will allow one to point out the actual structural parameters responsible for their electrostatic behavior.12

The above presentation, initially due to Nosker and Tasker,13,15 visualizes the stacking repeat units as starting from the surface layer, and associates the polar character with the accumulation of dipole moments μ = σR1 in the repeat units (Figure 3a). An alternative description considers the stacking as

2.1. Semi-infinite Surfaces

The simplest model of a polar surface is a semi-infinite stacking of alternating anionic and cationic infinite layers, with interplane distances R1 and R2, and charge densities ±σ, as shown in Figure 2a. It behaves electrostatically as an assembly of capacitors in series, each bearing a dipole moment density μ = σR1, across which the electrostatic potential V(z) varies monotonically. When the number N of capacitors and the thickness H = N(R1 + R2) − R2 increase to infinity, the total dipole moment and the potential difference between the two sides become infinite, leading to a divergence of the surface energy. Within such a rigid charge model, polar surfaces are thus unstable. The surface instability can be suppressed by an adequate reduction δσ of surface charges, Figure 2b. In the infinite N limit, the dipole moment Hδσ associated with the compensating charges has to exactly cancel the macroscopic part of the total dipole moment NσR1 and suppress the monotonic increase of V(z). In the simple capacitor model, the value of the compensating charge density δσ is related to the layer charge density σ via a geometric factor 9 = R1/(R1 + R2): δσ = 9σ

Figure 3. (a) Tasker’s representation of a polar surface. The repeat units start from vacuum (on the left and right of the atomic layers) and bear a dipole moment. (b) Charge neutrality view of the same system: a neutral and dipole free repeat unit is chosen, which leaves excess charges on the terminations.

made of neutral and dipole free repeat units, for example, those represented in Figure 3b. In that case, the two surfaces bear an excess charge density equal to ±σ9 , which gives rise to a macroscopic dipole moment. For the stability of the system, these excess charges have to be canceled. Whenever they are, the surfaces are said to be “charge-neutral”. The two descriptions are fully equivalent, because they predict the same ground-state charge configuration throughout the system.6 2.2. 3D Polar Objects: Ultrathin Films and Clusters

(1)

Ultrathin films are formed by finite stackings of infinite atomic layers. The simplest model that can represent them is very similar to the capacitor model introduced in the previous section, except for the finite number N of capacitors involved (from now on named “monolayers”, the interlayer distance R1 being called “rumpling”).

A generalized expression exists for more complex structures or charge redistributions, for example, when the latter involve several atomic layers.6 The microscopic origin of δσ is strongly system- and environment-dependent.5,6 However, its very existence is due to electrostatics. 4075


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It is informative to first consider the case N = 1 and get an order of magnitude of the potential difference ΔV across a single monolayer. Taking the value of the charge density in a rocksalt (111) monolayer rigidly cut from the bulk, in a point charge approximation with Q = ±1, a rumpling R1 of the order of 1.6 Å, and an anion−cation distance ≈ 2.8 Å, it turns out that ΔV amounts to several tens of volts. This shows that, already at 1 ML, ΔV is comparable to characteristic energies of the band structure. The effect is obviously amplified when thicker films are considered. As shown in Figure 4a for typical polar films,

potential displays interesting new features. First, the potential profile close to the surface is much steeper than in thin films, in agreement with an early remark made by Nosker13 (Figure 4b). Second, |ΔV| no longer depends on H, but rather grows linearly with L. Additionally, in this regime, V is not constant on the polar facet. It goes through an extremum at its center of gravity, and its maximum variation |ΔV′| also increases linearly with L (Figure 4c and d). The electrostatic characteristics of thin films and 3D clusters can be simply accounted for, using macroscopic electrostatics and the concept of “charge neutral surfaces”. A model representative for both polar films and clusters of thickness H is a stacking of disks of radius L/2 (L → ∞ for thin films), and charge density ± σ. As stated by the charge neutrality principle, the potential difference across the whole system is equivalent to that due to the excess surface charge densities ± δσ on the outer disks. Using the analytic expression of the electrostatic potential due to a single charged disk, the potential difference across the 3D nano-object thus reads (atomic units e = ℏ = m = 1 are used throughout; a is a small radius of atomic size introduced to avoid self-interaction when the potential is evaluated on the charged object): ⎛L ΔV = 2πδσ⎜⎜ − a − ⎝2

⎞ L2 + H2 + H ⎟⎟ 4 ⎠

(2)

It increases linearly with the cluster/film thickness H, ΔV ∝ (H − a) when L ≫ H, or with the size of the polar facet L, ΔV ∝ (L/2 − a) when H ≫ L, thus evidencing the two thickness regimes. To summarize, the linear size variation of the electrostatic potential, relevant at semi infinite surfaces, also occurs across finite 3D polar objects (films and clusters). However, it is driven by the smallest of the two sizes: thickness H of the polar stacking or size L of the polar termination. In addition, strong potential variations are present on finite size polar facets, which also increase linearly with L. 2.3. 2D Polar Objects: Nanoribbons and Islands

Nanoribbons with infinite edges and islands are the 2D equivalents of films and 3D clusters. Indeed, the results, displayed in Figure 5a−d, have strong similarities to those shown previously, except for the logarithmic dependencies, which replace the linear ones found in 3D. This change is characteristic of the reduction of dimensionality. A charged line of uniform charge density λ per unit length generates a Coulomb potential, which varies with distance as λ ln z. Using the charge neutrality principle, across an island of width H and edge size L (Figure 1d), the potential variation is calculated as due to two wires, H apart, bearing charge densities ± δλ (a is an atomic length introduced to avoid self-interaction when the potential is evaluated on the charged object):

Figure 4. Variations of the electrostatic potential at anion sites across the polar thin film and the 3D polar cluster, represented in Figure 1. (a) V(z) in the thin film or the 3D cluster when L ≫ H; (b) V(z) in the 3D cluster when L ≪ H; the insets show |ΔV| as a function of H; (c) V(x) in the 3D cluster when L ≪ H; and (d) in the same regime, dependence of |ΔV| and |ΔV′| on L (see text). V(z) and V(x) are evaluated on a rigid rocksalt lattice (first neighbor distance 2.8 Å), as in sodium chloride, within a point charge model (Q = ±1). Reprinted with permission from ref 12. Copyright 2011 American Physical Society.

⎛ ⎞ LH ⎟ ΔV = 2δλ ln⎜⎜ ⎟ ⎝ a(L + L2 + 4H2 ) ⎠

the electrostatic potential V(z) across the films varies linearly with z, and the potential difference ΔV between the two terminations increases linearly with H. The arguments developed above apply to thin films, that is, to polar 3D objects with infinite polar terminations. In 3D clusters, the size L of the polar termination is finite (Figure 1b), and the picture somewhat changes. Simple electrostatic calculations, within a rigid charge model, evidence two regimes. When L ≫ H, the thin film characteristics are recovered, with a potential difference |ΔV| that increases linearly as a function of H (Figure 4a). However, when L ≪ H, the electrostatic

(3)

When L ≫ H, the behavior of infinite ribbons is found, with ΔV increasing as the logarithm of width H: ⎛H⎞ ΔV = 2δλ ln⎜ ⎟ ⎝ 2a ⎠

(4)

while in the limit L ≪ H, relevant for nanoislands, ΔV grows as the logarithm of the lateral size L of the polar termination: 4076


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Figure 6. (a,b) A 3D and a 2D symmetric object. All facets or edges are polar, and those opposite to each other have the same anionic or cationic character. (c,d) Electrostatic potential V(z) across objects of different sizes (H ≈ L) (c, clusters; and d, islands). Insets show the potential difference |ΔV| between the polar termination and the center of the object, as a function of size. Reprinted with permission from ref 12. Copyright 2011 American Physical Society.

Figure 5. Same as Figure 4 for the 2D polar nanoribbons and islands shown in Figure 1. Reprinted with permission from ref 12. Copyright 2011 American Physical Society.

⎛L⎞ ΔV = 2δλ ln⎜ ⎟ ⎝ 2a ⎠

(5)

The same conclusions as in 3D thus apply for 2D nanoobjects. The electrostatic behavior is driven by the smallest of the two shape parameters: width H of the polar island or length L of the polar edge, and, in the regime L ≪ H, strong potential variations take place on polar edges, which scale as ln L.

four anionic and four cationic (111) facets, and a symmetric 2D (001) square island with two anionic and two cationic [110] edges. These symmetric objects are neutral and may be stoichiometric, subject to a constraint on the values of L and H (in the present case L ≈ H). These objects have clearly a zero total dipole moment, and the discussion of their electrostatic characteristics is thus of great interest. Figure 6c and d shows the behavior of the electrostatic potential V(z) across them. As expected, V(z) is symmetric with respect to the object center and the potential difference across the entire object vanishes. Conversely, between the object center and each polar termination, |ΔV| does not vanish. It increases monotonically with size (H ≈ L), in a linear fashion in 3D objects and a logarithmic one in 2D objects. This is a clear manifestation of polarity. The argument according to which polarity is irrelevant in symmetric objects because their total dipole moment vanishes has no general validity.

2.4. 1D Objects: Nanowires

Ultimately, when the size of an island polar edge is reduced to a single atom, a one-dimensional atomic wire with alternating anions and cations is formed. It possesses a dipole moment, which grows linearly as a function of its length H. However, the potential difference ΔV between the two ends, ΔV = 2λ ln 2, remains finite and independent of H in the large H limit. This absence of polarity signature is in agreement with the previous conclusion that it is the smallest dimension, which drives the value of ΔV. Atomic wires pertain to the limit L ≪ H. Polar instability never occurs in such purely 1D systems. 2.5. Symmetric Polar Objects

2.6. Compensation Mechanisms

Up to this point, discussion has been restricted to asymmetric polar objects in which the two opposite polar terminations bear charges of opposite signs. The actual character of symmetric neutral objects is a much more delicate issue. In the literature, it is generally stated that they are not polar because their total dipole moment vanishes. However, in clusters or islands, one may find examples showing that this statement has no general validity. In Figure 6a and b are represented a symmetric 3D octahedron exposing

Up to this point, electrostatic characteristics of uncompensated polar nano-objects have been deciphered as a starting point for understanding polarity specificities at the nanoscale. From the large values of ΔV obtained already at the smallest sizes, it clearly appears that stabilization effects are required. At semiinfinite surfaces, polarity healing always involves compensating charge densities δσ, resulting from intrinsic or extrinsic (i.e., depending on the chemical environment or thermodynamic 4077


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3.1. Irreducible Oxides

conditions) mechanisms. The most common involve an intrinsic electron redistribution due to partial filling of surface states, a modification of the surface region composition or the adsorption of charged foreign species, in particular, hydroxyl groups. Their efficiency is strongly dependent on the oxide, the surface atomic structure, and the external conditions. While reconstructions and surface hydroxylation are stabilization processes often encountered, there are also examples of polar surface configurations consistent with the metallization mechanism.5,6 More relevant for this Review is the anticipation that, in polar nano-objects, other compensation mechanisms may also be encountered. Because of the absence of “bulk” atoms in nanoobjects, strong lattice distortions, or even total restructuring, may have profound stabilizing effects. The substrate on which most polar nano-objects are grown may also contribute to the charge compensation. The examples found in the literature give an overview of these new mechanisms, their characteristics, and their relative efficiency.

3.1.1. MgO(111) Ultrathin Films. MgO is the prototype of a simple irreducible oxide. It crystallizes in the rocksalt structure, in which the (111) orientation is polar, with equidistant atomic layers (R1 = R2 so that 9 = 1/2) of alternatively anionic and cationic composition. Thin films of magnesium oxide grown along this polar orientation have been synthesized on different substrates such as Ag(111),17−19 Mo(110),20 Au(111),21,22 α-Al2O3,23,24 SiC(0001),25,26 and SrTiO3(111).27 The methods of preparation include MBE, PLD, or alternating Mg deposition and oxidation in an oxygen O2 atmosphere. When the films exceed a few monolayers, surface science investigations and DFT simulations evidence compensation mechanisms similar to those found at the surface of semiinfinite surfaces: metallization20 with magnetic moments on the oxygen atoms,28 hydroxylation,21 and surface roughening or restructuring,21,24 depending upon the formation conditions. At smaller thicknesses (1−10 ML), MgO(111) film grown on Ag(111) displays a (1 × 1) RHEED pattern, with a rather flat surface and a metallic electronic structure, Figure 7. An

3. POLARITY IN ULTRATHIN FILMS AND FINITE SIZE CLUSTERS: LITERATURE REVIEW In the past decade, the controlled fabrication of ultrathin films has been a very active field of research, driven by fundamental as well as applicative purposes.16 Aside from the fact that ultrathin films solve the charging problem, which prevents spectroscopic measurement to be performed on insulating semi-infinite surfaces, they also display very flexible structural and compositional characteristics. Playing with oxygen partial pressure and temperature often allows stabilizing a rich variety of phases, with chemical compositions unknown in the bulk, especially when transition metal atoms are involved. There have obviously been ambiguities, in the literature, in the recognition and discussion of polarity in ultrathin films. This is especially true in the thinnest films, where a simple extrapolation from the known bulk behavior and polarity criteria may break down. As a consequence, many works do not acknowledge polarity effects at all, while others tend to define film polarity simply by the character of the corresponding bulk crystal termination. In section 4, we will show that, because of their structural flexibility, ultrathin films of polar (bulk) orientation may in fact be nonpolar or bear only dipole moments induced by the interaction with the substrate (induced polarity). Similarly, the stoichiometry of ultrathin films being more flexible than that of bulk crystals, many film compositions miss an unambiguous bulk reference, especially when transition metal oxides are concerned. The above effects make the initial guess on film polarity very hazardous, and, in most cases, a precise knowledge of the electronic and structural characteristics is necessary for ascertaining its polar character. Keeping this in mind, in the following, we organize the literature review by first considering irreducible oxide thin films, MgO, ZnO, BeO, and Al2O3, in which the stoichiometry question is less severe or absent, and which allow focusing on structural aspects related to polarity. We then turn to reducible oxides, starting with iron and cobalt oxide thin films in which polarity aspects have been more thoroughly stressed and more explicitly studied. Other transition metal oxides (nickel, manganese, vanadium, titanium) will be considered next, and the section will end with an account of recent results on polar oxide nano-objects.

Figure 7. UPS spectra of the polar MgO(111)(1 × 1) film grown on Ag(111) and, as reference (dotted line), of the nonpolar MgO(100) surface. Reprinted with permission from ref 17. Copyright 2003 American Physical Society.

enlarged 2D lattice parameter, inconsistent with the bulk rocksalt structure, was noted by the authors.17 In the first stages of island growth on Ag(111), STM images reveal atomically smooth one-dimensional lines with elementary dots inside. The dot periodicity was assigned to a coincidence lattice between silver and a 30° rotated hexagonal MgO layer.19 The structural phase diagram and electronic properties of unsupported and supported MgO(111) thin films, derived from DFT simulations, highlight the existence of a critical thickness, below which the ground state is a graphitic-like nonpolar Bk(0001) structure, met for example in the h-BN compound, rather than the bulk rocksalt one. The unsupported monolayer of Bk structure is completely flat, with a structure resembling that of graphene.29 STM images of MgO(111) monolayers on Au(111) confirm the hexagonal symmetry of the 2D unit cell,22 Figure 8. The possibility of having an uncompensated polarity in ultrathin MgO(111) films has also been put forward on theoretical grounds.30 In the monolayer regime, DFT simulations show that a transition from a metallic rumpled structure to an insulating flat one can be induced by an artificial increase of the 2D lattice parameter.18 Excess of an oxygen or magnesium plane as well as interaction with a metallic substrate soundly modify the energetics of the various phases.31 In the extreme low thickness limit (1 ML), the existence of a charge transfer between the thin film and its metallic support induces a finite rumpling on 4078


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has been observed on a 2 ML-thick ZnO(0001) film grown on Ag(111), by SXRD and STM, and was shown to persist up to 3−4 ML thickness where the transition to bulk wurtzite takes place, associated with a considerable roughening,46 Figure 9.

Figure 8. LEED pattern and atomically resolved STM image of a MgO(111) ML grown on Au(111), with indication of the unit cell of the structure. Reprinted with permission from ref 22. Copyright 2012 American Chemical Society.

Figure 9. Structure of ZnO(0001) bilayer in the rocksalt phase (a) and in the as experimentally determined Bk phase (b). Small and large balls represent Zn and O atoms, respectively. Reprinted with permission from ref 46. Copyright 2007 American Physical Society.

the otherwise flat graphene-like MgO Bk(0001) layers, thus being responsible for an induced polarization in the film (induced polarity).31−33,35 Similar electrostatic coupling occurs in the case of adsorption on the film surface.34 These findings will be discussed in more details in later sections. 3.1.2. ZnO(0001) and BeO(0001) Ultrathin Films. Because of the unique properties exhibited by ZnO, such as piezoelectricity, biocompatibility, optical absorption and emission, and catalytic activity, the fabrication of thin films has received a lot of attention. As BeO, it crystallizes in the wurtzite structure. The (0001) orientation is the main polar orientation, with layer alternation such that R2 ≈ 3R1 (and so 9 ≈ 1/4). From the point of view of polarity, the literature review reveals that ZnO(0001) thick films display a wurtzite structure and polar properties close to those of semi-infinite surfaces. When reduced to few monolayers, similarly to MgO(111) films, they rather adopt a graphitic-like Bk structure. Ultrathin films have been successfully produced by a range of techniques and on various substrates such as αAl 2 O 3 (0001), 3 6 − 3 8 α-Al 2 O 3 (112̅ 0 ), 3 6 GaN(0001)/αAl 2 O 3 (0001), 39−42 MgO(111)/α-Al 2 O 3 (0001), 43,44 Si, 45 Ag(111), 46 Pd(111), 47,48 Rh(100), 49 Mo(110), 50 and FeO(111)/Mo(110),51 despite the presence of an important lattice mismatch in several cases. Interfaces between ZnO films and nitridated sapphire αAl2O3(0001) substrate38 were studied by HRTEM, and their polarity was studied by a method developed by Xu et al.37 The composition of the terminal ZnO layer was further confirmed by the observation of a (4 × 4) reconstruction on the Zn termination and a (3 × 3) reconstruction on the O termination. It is also possible to obtain high-quality films with the same reconstructed oxygen termination on an MgO buffer.43,44 On Rh(100), a c(16 × 2) LEED pattern has been observed and interpreted as due to a quasi-hexagonal atomic arrangement corresponding to that of distorted bulk ZnO (0001) surface.49 On Pd(111), well-ordered (4 × 4) and (6 × 6) coincidence phases form, which have been interpreted as due to an Hterminated Zn6O5 and a stoichiometric Zn6O6 structure, respectively. The critical thickness where transition to the wurtzite phase takes place is 4 ML.47,48 As theoretically determined, the ground state of ultrathin (0001) films of wurtzite compounds is a graphitic-like phase Bk(0001).45,52,53 This phase is nonpolar and, in ZnO, turns out to be more stable than the polar (0001) wurtzite phase at low thickness, and also more stable than the nonpolar (101̅0) and (112̅0) orientations. Similar results apply to other wurtzite compounds AlN, BeO, GaN, SiC, and ZnS. The graphitic phase

DFT simulations of the hydrogenation of ZnO graphitic sheets indicate that their electronic structure depends on the adsorption sites of the H atoms, and that the wurtzite structure is preserved in hydrogenated films.54−56 Since the first evidence that it was possible to tailor the ZnO gap by controlled MgO mixing, to increase its efficiency as blue and ultraviolet light emitter and detector,57 several authors have synthesized Zn1−xMgxO thin films on Mo(110),58 ZnO/MgO multilayers, 59 or ZnO/Zn 1−x Mg x O heterostructures. 60 Although the question of polarity in these films was not mentioned, it most likely explains the observation of an interfacial 2D electron gas in the last system. BeO is the only alkaline-earth oxide that crystallizes in the wurtzite structure, a property attributed to the important part of covalent character in the Be−O bonding. It has been shown that, in the bulk, the Bk phase is only slightly above the wurtzite phase in energy.61−63 This explains why, in the monolayer limit, along the (0001) orientation, a graphene-like BeO phase may be stable, in close resemblance to ZnO, which gives the possibility to synthesize a variety of nano-objects such as nanotubes64,65 3.1.3. Al2O3(0001) Ultrathin Films. The interest in alumina substrates, in various technological domains, has stimulated considerable efforts toward a controlled fabrication of well-characterized ultrathin films. The determination of their structure has turned out to be a difficult task, because most of them cannot be interpreted as cuts of bulk alumina polymorphs (amorphous, γ, δ, κ, η, θ). As a consequence, in many cases, the assessment of their polar character remains uncertain. However, in the 1−2 ML regime, polar Al/O/Al/O stackings have been evidenced. Aluminum oxide films have been obtained either by oxidation of aluminum containing substrates such as Al(111),66 CoAl(100),67 NiAl(100),68,69 NiAl(110),70−81 Ni3Al(111),82−91 Cu-9at%Al,92−94 TiAl,95 or FeAl,96 or by deposition of aluminum on foreign substrates like Ni(111)97−99 and subsequent oxidation. A review of most of these works can be found in refs 100 and 101. Here, the focus is on systems in which polar stackings have been identified. From this point of view, by far the two best studied aluminum oxide thin films are those obtained by oxidation of NiAl(110) and Ni3Al(111). In the NiAl(110) case, LEED results evidence a 2D rectangular unit cell and suggest that the thin film is made of two aluminum oxide layers, 5 Å thick, with 4079


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FeO(111), Fe3O4(111), or α-Fe2O3(0001) films on a Pt(111) substrate, including a characterization of their geometric and electronic surface structures and of their reactivity properties, as reviewed in ref 102. While wüstite FeO belongs to the rocksalt family, magnetite Fe3O4 crystallizes in the inverse spinel structure. It is based on a slightly distorted face centered cubic lattice of oxygen atoms, with the iron ions located in tetrahedral A and octahedral B interstitial sites. Along the polar (111) direction, the stacking sequence contains two formula units and is described by: 4O− 3FeB−4O−FeA−FeB−FeA. The corundum structure of hematite Fe2O3, on the other hand, consists of nearly hexagonally closepacked oxygen lattice with cations occupying 2/3 of the available 6-fold coordinated sites. Along the (0001) direction, it displays a sequence of Fe−O3−Fe units with relatively wellseparated consecutive metal layers. Depending upon the termination, the (0001) stacking may be polar or not. When growing iron oxides on Pt(111),104 Ru(0001),105,106 Ag(111),107 Fe(110),108 or α-Al2O3(0001),109 in the first stages of growth, usually FeO(111) films are produced. They are characterized by a reduction of the interlayer spacing and a concomitant expansion of the 2D lattice parameters with respect to the bulk crystal. Iron atoms are at the interface.110,111 Above 2−4 ML coverage, depending upon the experimental conditions, three-dimensional growth of Fe3O4(111) or Fe2O3(0001)109,112,113 begins. In the case of Pt(100), the surface reconstruction of the substrate induces an anisotropy in the structure of the oxide layer, and a coexistence of c(2 × 10) and (2 × 9) superstructures.114 The thermodynamic stability of different iron oxides and their epitaxial films was estimated as a function of temperature and oxygen or water partial pressures.115 The formation of epitaxially grown iron oxide films on platinum and ruthenium substrates agrees well with the calculated phase diagrams. The existence of ordered domains of FeO(111) near the Fe3O4− Fe2O3 phase boundary was however not foreseen by the calculations and attributed therefore to kinetic effects. On Mo(110), changes of the temperature and/or the oxygen partial pressure induce structural transitions between the three iron oxides: FeO(111), Fe2O3(0001), and Fe3O4(111), authorized by their common hexagonal arrangement of oxygen ions.116 On (√3 × √3) R30° and (2 × 2) reconstructed MgO(111) surfaces, a self-organized Fe3O4(111) nanobuffer forms, which persists after subsequent formation of α-Fe2O3(0001). This phase is absent if growth is performed on hydrogen-stabilized MgO(111) (1 × 1) surfaces.117 Fe3O4(111) films have been obtained on various substrates: Pt(111),102,118,119 Pt(911),112 Cu(001),120 Ru(0001),105,106,121 α-Al2O3(0001),122 and Au(111).123,124 Abrupt interfaces between Fe3O4(111) and MgO(111), with a large number of iron nanoclusters both at the interface and in the Fe3O4(111) film, were produced and characterized by XPS, ex situ TEM, and DFT calculations.125,126 The authors proposed a model for the oxide/oxide interface, which is argued to compensate the MgO(111) polarity. Considerable attention has been paid to the epitaxial FeO(111) monolayer grown on an atomically flat Pt(111) substrate. For all magnetic structures, the unsupported FeO film is predicted to assume a perfectly planar graphene-like geometry, with the in-plane lattice parameter about 8% larger than that of a bulk-truncated FeO layer. The rumpling is interpreted as due to a process of induced polarity.131 The lattice mismatch with the Pt substrate is responsible for the

oxygens outward.70 SPA-LEED and STM studies confirm this conclusion,71 while XRD studies show that Al atoms are hosted into a strongly distorted hexagonal oxygen arrangement, both in tetrahedrally and in octahedrally coordinated sites.72 An atomistic model of the film structure was proposed on the basis of STM and DFT results, including two mixed aluminum oxide buckled planes, one with Al16O24 stoichiometry at the interface with the substrate, and a more reduced one with Al24O28 stoichiometry at the surface. Because of the buckling, a polar Al/O/Al/O stacking sequence is produced, with nevertheless small rumplings in both layers. The film is insulating.73 This model was later confirmed by MEIS experiments.76 A LEEM study of the conditions of growth of the film concludes that the oxygen pressure required to stabilize the film is by far much higher than that for bulk alumina, and that applying thermodynamics to the nonequilibrium system of surface oxides on NiAl is clearly not appropriate.77 A similar structural model fits STM and GIXD results on an aluminum oxide film grown on a Ni(111) substrate, which is (5√3 × 5√3) reconstructed and presents a layer sequence Al16/O24/Al24/O28 starting from the substrate. The authors suggest that this atomistic model may be intrinsic to the freestanding film rather than governed by interactions with the substrate.97−99 The same model was also invoked to interpret LEED and STM results for an aluminum oxide film grown on a Cu-9at%Al substrate.92−94 Oxidation of a Ni3Al(111) surface also yields a well-ordered surface oxide.82,83 Two hexagonal superstructures were identified85 with lattice parameters equal to 2.4 and 4.16 nm, respectively. The latter, which represents a coincidence lattice with the Ni3Al substrate, presents a remarkable “dot” feature at the corner of the unit cell, evidenced by STM and SFM,87−89 and refined by DFT. Similarly to the aluminum oxide film grown on NiAl(110), the stacking sequence Al/O/Al/O is polar, with oxygens outside, almost coplanar terminal layers, and distorted Al hexagons, pentagons, and triangles at the interface. The “dot” structure at the corner of the unit cell is composed of six oxygen atoms, surrounding a 0.4 nm-diameter hole reaching down to the metal substrate, and showing as a “flower” in STM images.90 This patterning allows the obtention of well-ordered arrays of metal particles.86 The Al/O/Al/O stacking has been recently confirmed by photoelectron diffraction experiments.91 To summarize, most well-characterized thin aluminum oxide films turn out to be non stoichiometric. However, their common feature is a “polar” stacking of the Al/O/Al/O type, with small rumplings and expanded 2D lattice parameter. 3.2. Reducible Oxides

3.2.1. FeO(111) and Other Iron Oxide Ultrathin Films. Among the many studies devoted to the elaboration, characterization, and properties of iron oxide thin films, it is possible to recognize three main aspects. One is linked to the properties of thicker films whose polar compensation mechanisms are close to those met at semi-infinite surfaces. The second is the competition between wüstite FeO, magnetite Fe3O4, and hematite Fe2O3, leading to structural transitions during the first stages of growth and to different types of polar films. The last one concerns the FeO(111) monolayer, its induced polar character, and the associated properties. Aside from early results on FeO growth on Pt(100) and (111), Mo(100), Cu(100), and α-Al2O3(0001) reviewed in ref 5, many publications report epitaxial growth of single-crystalline 4080


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the adatoms, which get positively charged due to electron transfer from the substrate.34,138 The difference between Pd and Au adsorption behavior on the FeO(111) monolayer was assigned to their different work function, and a systematics of adatom charging was theoretically established along the transition metal series.139 Site selective nucleation of Fe and V clusters has also been reported and analyzed as a function of the local stacking and distortion of the FeO(111) layer.140 The mechanism of adatom charging also applies to molecules on the surface. It is argued that the activation of molecular oxygen together with a stabilization of a polar O−Fe−O film partly due to substrate screening is able to promote CO oxidation. The (√3 × √3) R30° superstructure of the FeO2 islands with respect to pristine FeO(111), revealed by highresolution STM images, was rationalized by DFT simulations in terms of strong relaxations within the Fe sublayer, producing an intermediate state of the FeO(111) transformation into a Fe2O3(0001) film.141−143 The mechanism of reduction of the FeO(111) 1 ML film on Pt(111) by exposure to atomic hydrogen, proposed from TDS, XPS, and LEED measurements,144 starts at oxygen vacancy sites, which may explain its initial autocatalytic acceleration. The reduction stops when an ordered (2 × 2) FeO0.75 layer is formed, which is passive against atomic hydrogen. The FeO monolayer is inactive versus dissociation of water molecules, which are only physisorbed on the surface.145 However, after reduction by atomic hydrogen, the FeOx structures are active toward water splitting, and thus can be reoxidized.146 Coadsorption of oxygen and water may lead to the formation of various hydrated phases as a function of the oxygen and water chemical potentials. The nucleation of Au and the oxidation of CO on an O−Fe−OH film were also studied.147 3.2.2. CoO(111) and Other Cobalt Oxide Ultrathin Films. The studies of cobalt oxide thin films reveal several levels of complexity. One is due to the competition, during growth, between the two oxides of stoichiometries: CoO and Co3O4. Additionally, on some substrates, CoO films with both (100) and (111) orientations can grow under the same formation conditions. Finally, transitions between several structures, rocksalt, wurtzite, and Bk, may take place. The early results on rocksalt cobalt oxide films obtained by oxidation of a Co(0001) surface,148,149 or metal deposition in an oxygen atmosphere on an Au(111)150 or on a Pt(111)151 substrate, suggested the possibility of obtaining rather flat and unreconstructed films of (111) orientation. The existence of a finite density of states at the Fermi level (surface metallization) or hydroxylation of the outer layers during synthesis was invoked to account for their stabilization. On Ag(100), both (100) and (111) monolayers can form, which exhibit quasi-insulating behavior.152,153 On Pd(100), at 1 ML, two well-defined surface structures were identified, c(4 × 2) attributed to CoO(100) and (9 × 2) to CoO(111). Further oxidation leads to a film of O−Co−O stoichiometry, while at higher coverages, spinel Co3O4 and CoO(100) phases develop.154 On the basis of experimental results and DFT simulations, the (9 × 2) phase was interpreted as a distorted CoO(111) layer displaying a zigzag type structure and antiferromagnetic ordering.155 On Pt(111), the 1 ML CoO(111) film exhibits a Moiré pattern after annealing at 740 °C or a zigzag structure if annealed at lower temperature.156 The 2 ML films also exhibits a Moiré pattern but different from the previous one, assigned to a wurtzite-like structure by the authors.

formation of a Moiré pattern, Figure 10, with a periodicity of 25 Å,127−129 which was also observed more recently by STM in the

Figure 10. Top view of a model of the 1 ML FeO/Pt(111) interface, reproducing the experimental Moiré unit cell. Red spheres, O atoms; purple or green spheres, Fe atoms; yellow spheres, substrate Pt atoms. The green lines show the unit cell. Reprinted with permission from ref 103. Copyright 2009 American Chemical Society.

field emission regime.130 Its structural, electronic, and magnetic properties were shown to be inhomogeneous within the inequivalent sites of the Moiré pattern.103,131,132 On this monolayer, in the first stages of deposition, palladium randomly nucleates before the formation of twodimensional islands.133,134 In some cases, it may diffuse through the oxide layer, toward the underlying interface.135,136 At variance, gold atoms preferentially adsorb on specific sites of the Moiré pattern and arrange into a well-ordered hexagonal superlattices,137 Figure 11. This self-organization was attributed to the inhomogeneous surface potential within the FeO(111) Moiré cell and to a substantial electrostatic repulsion between

Figure 11. (a) STM topographic image of Au adatoms on FeO/ Pt(111) taken at 0.55 V and 0.1 nA. (b) Histogram of the occupation probability of different domains in the FeO Moiré cell. The inset shows a power spectrum of (a). (c) Conductance images of the same area as in (a) taken at 0.55 V and (d) at 0.75 V. Images are 430 × 430 Å2 in size. Reprinted with permission from ref 137. Copyright 2005 American Physical Society. 4081


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On Ir(100) substrate, CoO films grow mainly in the rocksalt structure, except in an excess of oxygen for which the spinel structure Co3O4 develops.157 In the surface region of the CoO(111) films, obtained after annealing at elevated temperature, there is a change of structure from rocksalt to wurtzite, associated with a metallicity of the first layers and with a (√3 × √3) R30° reconstruction.158−160 In the monolayer limit, the film is substoichiometric, built from pyramids with triangular or square cobalt basis, and displaying a (3 × 3) unit cell. Upon exposure to oxygen, it transforms into a stoichiometric CoO(111) phase with c(10 × 2) periodicity, which involves building blocks of rocksalt and Bk type.161,162 By introducing a few Co monolayers between the substrate and the oxide, the oxide film orientation switches to (100).163 CoO(111) film formation inside a Co-doped ZnO matrix with a Bk type structure has also been reported.164 A film rumpling is detected by SXRD and confirmed by first-principles calculations of CoO/Ag(111) interfaces, Figure 12. The

Co3O4(111) films, produced by MBE, grow epitaxially on a single-crystal α-Al2O3(0001) surface. They are fully relaxed and display a (1 × 1) LEED pattern, which has been explained in terms of a layer inversion in the spinel structure.165 Similar inversion was also invoked to explain the absence of reconstruction at the surface of polar Co3O4(110) films produced by the same method on a polar MgAl2O4(110) substrate.166 First principles study reveals that the CoO/MnO (111) interface is stable.167 3.2.3. NiO(111) Ultrathin Films. Many metallic surfaces have been used as supports for the growth of NiO(111) thin films: Au(111), 1 6 8 Ni(111), 1 6 9 − 1 7 1 Cu(111), 1 7 2 αAl2O3(0001),173 Mo(110),174 and Rh(111).175 XRD experiments have shown that thin NiO(111) films (5 ML) grown on Au(111) adopt octopolar reconstructed configurations with both Ni- and O- terminations, separated by single steps.168 Some works report formation of a surface monolayer or bilayer of nickel hydroxide on the NiO(111) thin films grown on Ni(111).171,176 NiO(111) 5 ML thick films on Au(111) were found stable against hydroxylation.168 As in the case of single-crystal surfaces, this difference of reactivity has been assigned to surface defects. On Mo(110), 4−6 nm thick films turn out to be faceted, with Ni vacancies in the outer layer.174 On Rh(111), a stoichiometric nickel oxide monolayer forms, which displays a (6 × 1) corrugated superstructure with pronounced troughs. This configuration is more stable than the octopolar NiO bulk termination, according to DFT simulations.175 3.2.4. MnO(111) Ultrathin Films. Epitaxial MnO(111) films, about 13 Å thick, were successfully grown by reactive UHV deposition on Pt(111) in the presence of water,177,178 which, according to XPD data, corresponds to an oxygenterminated bulk-like film with a strongly relaxed outermost double layer. More recently, on the same substrate, a 1 ML thick film was shown to display a (19 × 1) reconstruction, but its building blocks are rather MnO(001)-like.179 On Rh(100), MnO epitaxial islands, one monolayer thick, with hexagonal symmetry were observed.180 On Pd(100), when annealed at high temperature under ultrahigh vacuum, MnO(100) films transform into an MnO(111) surface decorated by triangular pyramids with (100) facets.181 A low coverage, MnOx films display a complex surface phase diagram as a function of the oxygen chemical potential, with nine different phases revealed by STM, associated with different oxidation states of Mn,182 Figure 13. Among them, at least three have hexagonal symmetry, one being produced in oxygen poor conditions, and two at high oxygen chemical potentials. The structure of the two latter was

Figure 12. DFT calculated rumpling uc versus c parameter for bulk ZnO and CoO (solid and dashed lines, respectively). Symbols represent the rumpling values for thin films of ZnO (squares) and CoO (triangles) on Ag(111), where labels 1−3 correspond to layer numbers. Parameters uc and c for ZnO bulk wurtzite (WZ) and Bk (hBN) are indicated for comparison. Reprinted with permission from ref 164. Copyright 2009 American Physical Society.

authors argue that the existence of a rumpling rules out the possibility of the CoO layer being in the Bk structure, contrary to the behavior of ZnO(0001) thin films. They rationalize this result on the basis of a larger ionicity of CoO, as compared to ZnO.

Figure 13. Complex phase diagram of MnOx/Pd(100) films as a function of the oxygen chemical potential μO or partial pressure p(O2). The nominal coverage of Mn is 0.75 ML. Reprinted with permission from ref 182. Copyright 2009 Institute of Physics. 4082


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They predict that on the z-phase, contrary to Pd, Au atoms interact strongly with Ti atoms, which get “extracted” from the surface (flipped geometry) and become negatively charged, Figure 14. Conversely, on the z′-phase, Pd atoms interact

deciphered by DFT simulations and could be described in terms of O−Mn−O planar entities with a MnO(111)-like structure.183 3.2.5. VO(111) and Other Vanadium Oxide Ultrathin Films. Because of the existence of several oxidation states of vanadium atoms and several stable bulk structures (rocksalt VO, corundum V2O3, and rutile VO2), the phase diagrams of ultrathin vanadium oxide films are extremely rich.184 Actually, bulk structures are of little relevance for the first stages of oxide growth on a support. This section focuses on the specificities observed at the lowest coverages, skipping results on thicker films where bulk-like polar surface effects are present. On Pd(111) substrates, thin vanadium films are produced by reactive evaporation of vanadium in an oxygen atmosphere. As a function of coverage, several phases have been identified by STM and confirmed by DFT simulations, ranging from V2O3 p(2 × 2) above half a monolayer, to VO2 at full monolayer coverage (with either hexagonal or rectangular unit cells). Above one monolayer, a V2O3 adlayer forms on top of the hexagonal VO2 monolayer, before bulk V2O3 is stabilized. The structures of the ultrathin films are all different from their bulk analogues and are stabilized by interface effects.185−187 On Rh(111), the phase diagram of vanadium oxide in the submonolayer regime is as rich as on Pd(111). Decreasing the oxygen chemical potential successively leads to (√7 × √7) V6O12, (5 × 5) V11O28, (5 × 3√3) V13O21, (9 × 9) V36O54, and “wagon-wheel” V37O17 phases, associated with a decrease of the vanadium oxidation state and progressive loss of vanadyl groups, as observed by STM and confirmed by DFT simulations.188,189 On the ML film with VO stoichiometry, deposition of cobalt and further annealing in ultrahigh vacuum to 650 K leads to a segregation of the oxide on top of the Co layer.190 3.2.6. TiOx Ultrathin Films. As was true for previous oxides, TiOx ultrathin film structures are not easily related to cuts of the most stable TiO2 polymorphs (rutile, anatase, brookite), so that an initial guess on polarity effects is not easy. Thin films are synthesized on various substrates, Ru(0001), Ni(110), Pt(001), Mo(112), Cu(001), Pt(111), Au(111), but it seems that only in the last two cases have polar structures been obtained. On Pt(111), in an early work,191 depending on the annealing temperature, two well-ordered structures have been identified with large unit cells, a ((43)1/2 × (43)1/2)R7.6° of TiO2 stoichiometry and another one, of 2D unit cell (18.2 Å × 13.9 Å), with Ti4O7 stoichiometry. More recently, depending upon the annealing temperature and the Ti dose, six long-range ordered phases have been obtained, among which five are one monolayer thick, wet the substrate, and are formed by a Ti−O “monolayer” with oxygens outward: a Kagomé incommensurate phase (k-TiO1.5) at 0.4 MLE, two phases with rectangular unit cells and zigzag motifs (z-TiO1.33 and z′-TiO1.25) at 0.8 MLE, and finally two wagon-wheel-like structures (w-TiOx and w′TiOx) with ((43)1/2 × (43)1/2)R7.6° and (7 × 7)R21.8° unit cells at 1.2 MLE.192 As a common feature to these phases, Ti atoms organize in pseudoepitaxial regions at the interface, and the oxygens organize themselves with dislocations lines alternating with regions where Ti vacancies occur.193−196 In situ transformations between these phases were followed by means of a combination of μ-LEED and LEEM.197 Following the observation that the zigzag films provide a good template for the growth of linear arrays of Au clusters,198 DFT simulations of metal adsorption have been performed.

Figure 14. DFT-optimized structures (left) and PDOS (density of states projected on Ti 3s states, right) for the adsorption of a Au atom on two sites of the TiOx/Pt(111) z-phase: an oxygen site (a) and a titanium site (b). Reprinted with permission from ref 199. Copyright 2008 Royal Society of Chemistry.

strongly with the troughs in which they get incorporated. The interaction of Au with the stripes of the z′-phase also strongly resembles that with the striped regions of the z-phase.199 On the other hand, on the z′-phase, Fe competes with Ti to bind oxygen, resulting in a redox process that destabilizes the phase.200−202 On the (22 × √3)-reconstructed Au(111) surface, three different ordered TiOx films can form. At low coverage ( NC, all quantities follow the general trends of compensation by metallicity, below NC, the formation energy and the dipole moment vary linearly with N. Except for N = 1, where it is strictly equal to zero, the rumpling 9 is very small and quasiindependent of N. There is almost no charge modification δσ on the outer layers. The gap between the VB and CB is open and decreases monotonically as the number of layers grows. It closes approximately at NC. At fixed N, the oxygen 2s projected densities of states in the successive layers are shifted with respect to one another, evidencing the variations of the electrostatic potential across the film. The total width of the 2s band keeps increasing as long as N < NC (Figure 21d), then becomes nearly constant in the compensated regime. A similar uncompensated phase was also found in the ZnO and NaCl phase diagrams, with NC ≈ 4−5 for ZnO and NC ≈ 12 for NaCl.30 In this regime, the films are thus uncompensated. They are characterized by an insulating electronic structure and (consequently) negligible δσ. The thickness dependence of the formation energy, dipole moment, and gap is fully consistent with the model developed in previous sections when compensating charges are absent and schematized in Figure 21e. Essential to this uncompensated regime is the structure flexibility, allowing an extremely strong flattening of

Figure 21. MgO B3(111) unsupported film properties: (a) in-plane lattice parameter and formation energy, (b) rumpling 9 = R1/(R1 + R2) and relative surface charge δσ/σ, (c) gap G and dipole moment P, (d) local density of states of oxygen 2s levels (the Fermi level is at E = 0) for increasing film thicknesses, and (e) sketch of the electronic structure across a polar uncompensated film. Reprinted with permission from ref 30. Copyright 2007 American Physical Society.

the layers, and thus a strong reduction of the individual layer dipole moment. To our knowledge, uncompensated phases have not been observed so far in polar 1:1 binary oxide films. However, following the discovery of a 2D electron gas in LaAlO3(100) films grown on a SrTiO3 substrate,242 the existence of a metal− insulator transition at a critical thickness of four repeat units243 was interpreted in terms which present a close resemblance to those used for the B3(111) metastable phase in MgO thin films.244 At low thickness, in the so-called precritical regime, the difference in electrostatic potential across the LaAlO3(100) film is insufficient to close the gap. Above four repeat units, the onset of metallicity (so-called “polarity catastrophe”) arises because the LaAlO3 shifted VB overlaps the SrTiO3 CB. In the X-ray photoemission study of ref 245, in the precritical regime, the progressive shift of the LaAlO3 core levels across the film perfectly resembles that of O 2s states represented in Figure 4089


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21d. “Uncompensated polarity” is never mentioned in these works. Additionally, a recent report of ab initio simulations of kaolinite surfaces actually shows evidence of similar behavior, although the uncompensated mechanism was not referred to.246 Kaolinite is a layered material of chemical formula Al2Si2O5(OH)4. The (0001) layers are composed of two sublayers, one of which involves silicon atoms in a tetrahedral oxygen environment, and the other, aluminum atoms in an octahedral environment consisting of oxygen ions and hydroxyl groups. Because of this dissymmetry, the repeat unit along the (0001) orientation bears a finite dipole moment, and due to the rigidity and the complexity of the structure, there is no phase analogous to Bk that can allow avoiding polarity. The authors of ref 246 have shown that, under a critical thickness NC = 3, the formation energy, the gap, and the density of states present the same features as those shown in Figure 21a and b. The phase diagram is very sensitive to the film stoichiometry, Figure 20c and d. While Bk always remains the most stable structure at low thickness, the addition of an oxygen or a magnesium layer considerably stabilizes the B1 structure in such a way that it may become competitive with the two other phases. A similar effect, although less pronounced, is observed for the B3(111) structure. This stabilization is not driven by the peculiarities of magnesium or oxygen bonding, but rather reflects differences in the way the compensating charges δσ are obtained. Indeed, in B1 and B3 stoichiometric films, δσ results from electron redistribution between the VB and CB and thus requires electronic promotion across the gap, which is not the case in nonstoichiometric films. In summary, at low thickness, there exist two generic scenarios specific to polar films. On the one hand, they may adopt an atomic structure different from the bulk, stabilized by a nonpolar orientation. This is what happens in the Bk(0001) ground state, and it holds for both stoichiometric and nonstoichiometric films in a wide range of thicknesses. On the other hand, as long as their thickness remains below a critical value, polar films may sustain an uncompensated polarity. This often requires a lattice distortion, which reduces considerably the total dipole moment. This scenario, encountered in the metastable “flattened” B3(111) phase becomes marginal in nonstoichiometric films whose stability does not require excitations through the gap. It may however be relevant in polar films of more complex structure. 4.3.2. Supported Thin Films: The Concept of Induced Polarization. In the low thickness regime, when films are supported on a metal substrate, the phase diagram shown above is not qualitatively modified. The relative stability of the three Bk, B1, and B3 phases remains unchanged, although the metal provides stabilization in all cases.31 However, a number of interesting effects take place, which have implications on the film structure and the work function of the whole system. They will be discussed for 1 ML films, although the results are qualitatively similar for larger thicknesses, as long as the nonpolar or uncompensated phases are concerned. It is well recognized that at nonpolar metal−oxide interfaces, there exists a charge transfer, due to interfacial hybridization and/or penetration of the MIGS (metal-induced gap states). Its amount depends on the relative position of the metal Fermi level and the oxide point of zero charge, and the associated dipole moment is a contribution to the Schottky barrier height.247−249

The 1 ML films grown on a metal substrate experience a similar interfacial charge transfer. Contrary to the case of polar compensated films, its sign is not determined by the oxide termination at the interface, but rather by the metal electronegativity, as for constituted interfaces. The effects are exemplified in Figure 22 for MgO(111) films,32 showing that

Figure 22. Ground-state characteristics of MgO(111)/Me(111) (1 × 1) interfaces (MgO monolayer; Me = Al, Mg, Ag, Mo, and Pt; oxygens on-top metal atoms): (a) the charge Qsub borne by the metal substrate (electrons per MgO unit), and (b) the rumpling of the MgO film (Å). Lines are drawn to guide the eye. Reprinted with permission from ref 32. Copyright 2009 American Physical Society.

deposition on a simple metal (Mg, Al) results in an electron transfer from the substrate to the film, while on transition metal substrates (Ag, Mo, Pt) opposite transfer occurs. While perfectly flat when unsupported,29 MgO monolayers get rumpled upon deposition. The sign and strength of this polarization correlate with the interfacial charge transfer, in such a way that the associated dipoles have opposite sign and thus partially compensate each other.32 Anions and cations are displaced in opposite directions by the electrostatic field exerted by the substrate charge Qsub, as sketched in Figure 23a and b. The rumpling ΔR may be seen as a response of the film structure to this electrostatic field:

ΔR ∝ Q sub

(19)

Qsub is related to the difference between the metal Fermi level and the oxide point of zero charge EPZC, corrected by the total dipole potential D: Q sub = −χ (E F − E PZC − D(ΔR ))

(20)

with χ the electronic susceptibility of the interface. Aside from a contribution Dcomp due to the compression of spill-out metal electrons, D depends linearly on both Qsub (charge transfer contribution) and ΔR (rumpling contribution) so that eqs 19 and 20 have to be solved self-consistently. As a result, both charge transfer and rumpling are fixed by EF − EPZC − Dcomp. This argument based on a generic electrostatic coupling between charge transfer and rumpling rationalizes the small and large rumpling values in 1 ML MgO/Ag(111) and FeO/ Pt(111) films, respectively.34 It has nevertheless been argued that for some other oxide monolayers, like NiO, rumpling and charge transfer could yield parallel dipole moments.250 4090


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The ability to promote spontaneous electron flow through an ultrathin oxide film has been first proposed theoretically251−255 and later confirmed experimentally.256,257 While adsorbate charging is mainly determined by the electronic characteristics (e.g., the work function) of the metal−oxide support, atomic relaxation of the oxide film, especially at low thickness, may significantly contribute to stabilize charged adsorbates (polaronic-like effect). Relying on first principles simulation of MgO(111) and FeO(111) monolayers deposited on Pt(111),34 two qualitatively different adsorption modes have been identified, in which the local film distortion either reinforces the existing rumpling or reduces it, or even inverts it (flipped geometry), depending upon the sign and strength of the metal−adatom charge transfer, Figure 23c and d. Similarly to the case of supported bare oxide film, the local dipole moment associated with the local film distortion opposes and partially compensates that due to the charge transfer Qads between the substrate and the adsorbate. As for bare films, the distortion ΔR is a local response to the electrostatic forces generated by Qads:

Figure 23. Top: Schematic representation of the charge transfer and rumpling dipole moments (shown by arrows), for the two cases of negative (a) and positive (b) metal charging. Magnesium, oxygen, and metal atoms are represented as black, white, and gray circles, respectively. Bottom: Same representation in the case of metal adsorption. Reprinted with permission from ref 34. Copyright 2009 American Physical Society.

ΔR ∝ Q ads

(21)

In a linear response approximation, Qads is proportional to the energy separation between the Fermi level of the oxide/metal support EF and the donor or acceptor level of the adsorbate εads (represented by either its ionization potential IP or its electron affinity level EA) modified by the total dipole moment potential D:

The existence of a rumpling in CoO(111) ultrathin films deposited on Ag(111), predicted by first principles simulations, was interpreted by the authors of ref 164 as a proof that the Bk phase is unstable in cobalt monoxide. We note, however, that the calculated rumpling is much weaker than expected in a compensated rocksalt structure, and is thus most likely the result of coupling with the interfacial charge transfer. To summarize, (111) MLs have often an ambiguous character. Considering their orientation, polar in the bulk, and their nonvanishing rumpling, they are often referred to as polar. However, when unsupported, they are perfectly flat and thus nonpolar. Upon deposition, in response to the interfacial charge transfer, they get polarized, with a dipole moment of variable size, depending upon the metal substrate and their own characteristics (point of zero charge, stiffness). Rather than calling them “polar”, it would be more adequate to say that their polarization is induced by the presence of the substrate. Similar polarization effects also occur on nonpolar monolayers, such as rocksalt (100) ones, showing that there is no electrostatic signature distinguishing the two types of orientations in the low thickness regime.32,33 Let us note that, as the compressive strength exerted by the substrate increases, rumpling is expected to also increase to preserve the atomic volumes. Progressively, the character of the oxide layer will then evolve from simply polarized with an insulating electronic structure to actual polar with a metallic electronic structure and with a charge transfer no longer related to the metal electronegativity but to the nature of the interfacial oxide ions, as explained in the section on the large thickness regime.18 4.3.3. Electrostatic Contributions to Adsorption. One step further in complexity is the consideration of adsorption on supported polar oxide films. Indeed, the basic research in model catalysis has adopted thin oxide films as supports. In recent years, it has become clear that supported ultrathin oxide films may exhibit unique properties, in particular concerning the charge state of the adsorbed species, a property of crucial importance, particularly for the growth, chemical, optical, and magnetic properties of adsorbed metal particles.7

Q ads = −χ (E F − εads − D)

(22)

χ is the local electronic susceptibility. D includes a charge transfer contribution DCT ∝ Qads and a contribution due to the distortion ΔR: DΔR ≈ QΔR, where Q > 0 is the absolute value of the ionic charges in the oxide layer. Thus, the solution of the implicit eq 22 for a fixed rumpling is: Q ads(ΔR ) ∝ E F − εads − Q ΔR

(23)

Because ΔR itself is a response to Qads, to lowest order, the equilibrium local distortion is found to be proportional to EF − εads. Such an approach, valid regardless the monolayer orientation, gives grounds to the relationship between the distortion at equilibrium, the adsorbate charge, the metal Fermi level, and the adsorbate electronegativity. For a given support, it explains the negative charging and flipped adsorption mode of adsorbates with high (IP + EA)/2 values, as evidenced in the case of Au adsorption on TiOx.199 Very recently, it has been demonstrated that this scenario applies not only for metal adsorbates but also for gas-phase molecules reacting at the surface.258−260 Indeed, monolayer FeO(111) films supported on Pt(111) have been shown to be much more active in low temperature CO oxidation than Pt(111).141,142 The proposed mechanism involves, prior to the reaction with CO, the transformation of the monolayer Fe−O film into an oxidized O−Fe−O state that further catalyzes CO oxidation via a Mars−van Krevelen-type mechanism. Theoretical modeling142 corroborates this scenario and suggests that the oxidation of the FeO film proceeds through activation of molecular oxygen by electrons that are transferred from the oxide/metal interface. The oxygen charging together with its adsorption site in a flipped geometry eventually result in the 4091


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stabilization of a O−Fe−O film. Similar “trilayer” films were also observed with Co154 or Mn183 cations. 4.4. Summary

In thick films, polarity manifests itself by size-dependent values of the compensating charges, potential difference across the film, and formation energy. The effects are stronger in stoichiometric films than in films possessing a cation or oxygen excess layer. In both cases, when the films are supported on a metal, the compensating charge at the interface is accommodated by the support, yielding strong stabilization. The most spectacular peculiarities of polar films lie in their low thickness phase diagram. Polarity may be healed by a thorough structural change. Exotic phases in which polarity remains uncompensated and electronic and structural properties are strongly thickness dependent may also be found. The ML represents an extreme case in which the distinction between polar and nonpolar orientations becomes tenuous. In both cases, for films deposited on a metal substrate, there exists an electrostatic coupling between the interfacial charge transfer and the film polarization. A lowering of the metal work function results, whose different contributions have been identified. Similar electrostatic couplings influence the properties of molecules, metal atoms, or clusters adsorbed on polar thin films.

Figure 24. Atom-resolved STM image of a triangular single-layer MoS2 nanocluster synthesized under sulfiding conditions (45 × 46 Å2, Vt = −1250 mV, I = 0.86 nA). Reprinted with permission from ref 264. Copyright 2004 Elsevier.

5. POLARITY IN TWO-DIMENSIONAL NANORIBBONS AND ISLANDS: LITERATURE REVIEW Polarity in 2D nano-objects is a quite recent theme of research. This stems from the difficulty in producing them in a wellcharacterized and reproducible way, a difficulty that also explains why most information we have comes from atomistic simulations. Actually there has been a surge of interest for them after the discovery of edge states and 1D conductivity in graphene nanoribbons, as reviewed in refs 261 and 262. While these graphene properties have nothing to do with polarity, most published papers on polar compound ribbons start with an introduction on graphene nanoribbons, and most of them do not even refer to the concept of “polarity” or electrostatic compensating charges. To our knowledge, the first reports that may give hints on edge polarity deal with nonoxide compounds. For the sake of putting the research on oxide 2D nano-objects into perspective, we will first quickly review them.

been abundantly evidenced, their origin is not discussed by the authors in relation to polarity. 5.2. MgO Nanoribbons

One ML nanoribbons and islands may form in the first stages of growth of MgO films with either a (001) or a (111) orientation. Depending upon their edge orientation, they may be nonpolar or polar (Figure 25). While [100] edges on the former and armchair edges on the latter involve as many oxygens as magnesiums and are thus nonpolar, (001) ribbons with [110] edge and (111) ribbons with zigzag edges are made of alternating rows of magnesium and oxygen ions, with inter-row distances R1 and R2 such that R2 = R1 (9 = 1/2) for the former and R2 = 2R1 (9 = 1/3) for the latter. Both of them are polar. In the first stages of growth of MgO on Ag(001), (001) islands limited by [110] edges have been imaged by STM (see section on MgO nanoislands). To interpret their stability, the energetics of (001) nanoribbons, two formula unit wide, with edges oriented along [100] and [110], and supported on the Ag(001) surface or embedded into it, has been studied, using a first principles approach.282,283 The authors find that the interaction with the substrate enormously reduces the instability of the polar borders, especially when the island is embedded in the Ag substrate. However, in the calculation, the nonpolar [100] oriented ribbons remain thermodynamically the most stable, thus suggesting that if [110] borders are experimentally observed, it might be due to kinetic rather than thermodynamic reasons. Water dissociation was predicted to be enhanced at the border sites, regardless of the edge orientation (polar or nonpolar).284 Simulations of stoichiometric 1 ML MgO ribbons of increasing widths show that polarity is healed by edge metallization and stress the size dependence of the polarity characteristics.285 For supported ribbons, compensating charges and strong stabilization are provided by the metallic substrate.286

5.1. Non-oxide Nanoribbons and Islands

MoS2 has a layered quasi-2D structure, with each metal atom plane sandwiched between two sulfur layers in an hexagonal arrangement. MoS2 nanoribbons and islands have received much attention due to their potentialities as hydro-desulfurization catalysts and more recently as possible elements of nextgeneration nanoelectronic devices. Early publications report the growth of (0001) nanoislands of triangular shape on Au(111), with edges displaying a pronounced contrast in the STM images,263,264 Figure 24. With the help of DFT calculations, this contrast was interpreted as due to the presence of metallic states, also found in nanoribbons with similar zigzag edges.265−268 These states strongly influence the properties of MoS2 nanoclusters: reactivity, luminescence, or magnetism.269−271 Similar effects have been predicted in nanoribbons or nanoislands of other non-oxide compounds, displaying hexagonal symmetry and zigzag edges,272 such as BN,273−276 GaN,277,278 AlN,279,280 and ZnS.281 While their existence has 4092


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metallic behavior with unpaired electrons on the oxygen termination. This applies to monolayer ribbons as well as ribbons whose thickness involves an odd number of layers. Ribbons with an even number of layers are semiconducting and nonmagnetic.287−289 This behavior is modified when the edges are passivated with hydrogen or other atoms,289−292 when the ribbon is under an external electric field,293 or submitted to strain.294,295 Chemical doping, for example with carbon atoms, is also an effective way to tune the electronic properties.296 It has been theoretically shown that a 2D phase transition may be induced in zigzag nanoribbons by increasing the lattice constant, leading to a semiconducting square structure.295 Let us note that, at variance with other works, polarity is explicitly referred to in ref 296, and the existence of a dipole across the zigzag ribbons is mentioned in refs 289 and 294. To our knowledge, aside from related results on ZnO nanostructures reviewed in section 3, there exists a single report of ZnO zigzag nanoribbon synthesis.297 It has been performed via thermal evaporation of zinc powder followed by oxidation under a H2O2 atmosphere. Hydrogen peroxide was chosen both as oxidizing agent and because it inhibits growth along [0001]. Nanoribbons were thus formed in the presence of the water vapor produced after reduction of H2O2. 5.4. Other Oxide Nanoribbons

Nanoribbons cut out of other oxides have been considered in the literature, such as TiO2, SnO2, BeO, or V2O5, but only in the last two oxides have polar orientations been studied. The electronic and magnetic properties of BeO(0001) nanoribbons with armchair or zigzag edges, formed as part of a graphitic BeO monolayer, have been studied using a DFT approach. While all armchair terminated ribbons are nonmagnetic insulators, ribbons with zigzag borders display ferromagnetic and metallic character independent of their width and passivation.65 Unlike the hexagonal planar structure of BeO monolayer, the (010) V2O5 monolayer is strongly corrugated and built up of distorted VO5 square pyramids. Despite this difference, the armchair and zigzag V2O5 nanoribbons have been theoretically predicted to behave as their BeO analogues,298 Figure 26. 5.5. MgO Nanoislands

In the first stages of growth of MgO(001) thin films on supports, square domains are usually produced with nonpolar borders. However, domains with borders along [110] may sometimes be observed. On Mo(001), STM images show that MgO islands have random shapes with perimeters exhibiting no preferential orientation.299,300 On Ag(001), at 1 ML coverage, flat square MgO mono- or bilayer islands with [110] edges have been observed, together with multilayer square pyramidal islands exhibiting both [100] and [110] borders,301 Figure 27a. The possibility of having these islands embedded in the substrate grooves was raised, both from experimental observations and from simulations. With support of DFT simulations282,283 (cf. section on MgO nanoribbons), it is concluded that the stabilization of MgO[110] islands may be the result of kinetic hindrance effects associated with the particularly high stability of [110] Ag steps. On Au(111), the orientation of MgO islands depends sensitively on the oxygen and water partial pressures in the preparation chamber. At high oxygen partial pressure, square MgO(100) islands with nonpolar [100] borders are observed, while at lower oxygen partial pressure and in the presence of

Figure 25. Ball representation of polar and nonpolar MgO 1 ML thick nanoribbons. (a) MgO(001) with polar [110] edges; (b) MgO(001) with nonpolar [100] edges; (c) MgO(111) with polar zigzag edges; and (d) MgO(111) with nonpolar armchair edges.

5.3. ZnO Nanoribbons

As MgO(111) in the monolayer limit, ZnO (0001) ribbons display two possible edge terminations: zigzag and armchair. While armchair ribbons are predicted to be nonmagnetic semiconductors, zigzag ZnO ribbons display a ferromagnetic4093


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Figure 26. (a) Top and side views of the spatial spin density distribution in a zigzag V2O5 nanoribbon; and (b) the spin-resolved band structure. Reprinted with permission from ref 298. Copyright 2011 American Chemical Society.

Figure 27. STM images of [110] edges of (a) MgO/Ag(100) islands (the inset shows a multilayer pyramidal island) and (b) NiO/Ag(100) islands, within the oxidic (2 × 1) phase. (a) Reprinted with permission from ref 301. Copyright 2002 American Physical Society. (b) Reprinted with permission from ref 309. Copyright 2006 Institute of Physics.

to a rhombic distribution of Ni vacancies in an epitaxial NiO layer. This c(4 × 2) phase creates an interlayer, which provides a graded interface for subsequent growth of cubic NiO(100). As for the case of growth on the Ag substrate, the island borders appear aligned along the [110] directions.311−313 These polar borders were considered to be responsible for an enhanced activity of the islands toward H2 dissociation.314 Occurrence of polar borders and similar arguments have been put forward in the case of NaCl islands on Ag(001)315 and CeO2 on Pt(111).316,317

small amounts of water, MgO(111) islands with zigzag borders and triangular shapes prevail. This behavior was rationalized by DFT simulations, in terms of the stabilization effect of water kinetically favoring a (111) growth in the monolayer thickness range.21,22 The enhanced STM contrast on the zigzag borders, on the other hand, was assigned to a progressive shift of the lattice register at the MgO−Au interface, associated with the lattice mismatch, yielding less favorable interface configurations on the island borders (Mg on-top Au atoms).302 5.6. NiO Nanoislands

In the first stages of growth of NiO(100) films on Ag(100), obtained by reactive oxidation of Ni by molecular oxygen, a substoichiometric (2 × 1) phase is first seen, which transforms into a (1 × 1) phase after annealing.303−306 The (2 × 1) phase, of hexagonal symmetry and monolayer height, is interpreted as a NiO(111) monolayer, while the (1 × 1) phase displaying square symmetry points toward stoichiometric NiO(100).307 When oxidation is performed with atomic oxygen, the (1 × 1) phase is directly reached.308 STM observations have revealed that the NiO islands are often embedded into the Ag substrate and confined by Ag [110] steps, and thus limited by polar [110] borders,309,310 Figure 27b. As in the case of MgO nanoislands on the same substrate, the prevalence of [110] borders was assigned to kinetic effects.309 Similarly, on Pd(100), a substoichiometric c(4 × 2) phase is observed as a precursor of the growth of NiO(100)(1 × 1). By a combination of experimental and theoretical approaches, a Ni3O4 stoichiometry was assigned to this phase, corresponding

5.7. Summary

As is obvious from the literature review, much less is known on polar oxide nanoribbons and nanoislands than on polar oxide ultrathin films. Growing them is not an easy task. Only zigzag ZnO ribbons, likely hydroxylated, MgO and NiO nanoislands with [110] polar borders, or MgO nanoislands with zigzag borders have been obtained. There is no report of a critical width that would separate large and small width regimes. DFT calculations on unsupported stoichiometric objects predict edge metallization and apparition of magnetic moments mainly located on the outermost oxygen row, together with enhanced reactivity toward hydrogen or adatom adsorption. These findings are quite similar to those found on stoichiometric polar thin films in the large thickness regime. Also parallel to the film behavior is the stabilization of polar borders due to the interaction with a metallic substrate. 4094


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6. MANIFESTATIONS OF POLARITY IN TWO-DIMENSIONAL NANORIBBONS As seen previously, the various approaches, mainly theoretical, used to study polar nanoribbons have provided information on their structural, electronic, and magnetic structures, but, for most of them, without any causal link to polarity. The goal of this section is thus to establish this missing link and develop a conceptual approach similar to that of polar thin films.285,286 It will be restricted to the large width limit, for unsupported as well as supported ribbons, the other regime, if any, being presently completely unexplored.

ε∞ =

(29)

This expression is formally similar to the one derived for thin films, eq 12. The predictions of this model are well supported by quantum mechanical simulations of MgO(111) ribbons with zigzag edges.285 Results for the width variation of the ribbon formation energy, compensating charges δλ, potential difference, and total dipole moment are shown in Figure 28 in a representation that highlights their asymptotic behavior. The latter required to consider widths up to N = 200 due to the slow N → ∞ logarithmic convergence.

6.1. Unsupported Ribbons in the Large Width Limit

As polar thin films, polar nanoribbons are well represented by the model shown in Figure 2, provided that capacitor “plates” are made of 1D atomic rows instead of 2D atomic layers and ±σ is replaced by ±λ, their charge density per unit length. As sketched in section 2, the charged rows exert an electrostatic potential, which varies as the logarithm of distance, yielding expressions for the total potential on each row of a ribbon that are much more involved than for thin films (see the Appendix). As expected, in the absence of compensating charges, in the large N limit, the potential difference across a polar ribbon diverges as ln N (cf., section 2): ΔV → 49λ ln N

G̃ + Ṽ δλ∞ + δw G + (α + β)δλ∞

(24)

while the total dipole moment diverges linearly with N: P = NλR1

(25)

Similarly to what happens in thin films (section 4), when an overlap of the outermost row VB and CB takes place, the ribbon borders become metallic. The equalization of the Fermi level EF = CBM1 + αδλ = VBMN − βδλ fixes the value of the potential difference across the ribbon ΔV = G + (α + β)δλ, with G = CBM0 − VBM0, and allows the determination of the compensating charge density δλ (expression valid to order 1/ N): 49λ ln N − G̃ − δw (26) 4 ln N + Ṽ As in the case of thin films, G̃ is related to the gap width and Ṽ to the U and bandwidth terms (see Appendix). When N goes to infinity, δλ converges toward δλ∞ = 9 λ, and the asymptote is reached with a 1/ln N law: δλ =

δλ ≈ δλ∞ −

G̃ + Ṽ δλ∞ + δw + ... 4 ln N

(27) Figure 28. Properties of unsupported MgO(111) ribbon with zigzag edge:285 (a) formation energy Eform, (b) compensating charges δλ, (c) potential difference, as a function of 1/ln N, and (d) total dipole moment, as a function of N/ln N.

The potential difference across the ribbon, being equal to G + (α + β)δλ, converges toward ΔV∞ = G + (α + β)δλ∞ and has the same N dependence as δλ. The same is true for the electrostatic contribution to the formation energy. As regards the total dipole moment density P = NλR1 − Nδλ(R1 + R2), its terms proportional to N cancel between the λ and δλ contributions. However, the next leading term comes from the product N(δλ − δλ∞), which scales as N/ln N. It thus diverges as N increases. As in the case of thin films, the asymptotic behavior of δλ can be written in terms of the optical dielectric function ε∞: δλ = δλ∞ −

ΔV∞ε∞ + ... 4 ln N

To summarize the characteristics of 2D stoichiometric polar nanoribbons in the large width limit, the potential difference and the formation energy diverge as ln N in the absence of compensation. Polarity can be healed by the presence of compensating charges δλ, produced by the metallization of the ribbon borders. The relationship between δλ and the charge density λ per unit length on the ribbon row is formally similar to that valid for films: δλ∞ = 9 λ. Compensating charges impede the border energy and the potential difference across the ribbon to diverge as the number of rows increase. Asymptotic values are reached in a 1/ln N way. A peculiarity

(28)

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armchair and zigzag edge hydroxylation would bring some element of answer to this question,286 because the atoms are 2fold coordinated in both terminations. However, for metal supported ribbons, as described in the next section, the support provides a large stabilizing effect, more efficient than for thin films. The added value of hydroxylation in polarity healing thus remains an open question.

of 2D ribbons is the size dependence of the total dipole moment, which diverges as N increases both in the uncompensated and in the compensated state. The behavior of the total dipole moment is thus not a good indicator of the polar state of the system. This analytical development accounts well for the results obtained numerically in the literature, for all polar stoichiometric nanoribbons, one monolayer thick, whether made from an oxide or from other compounds. As an example, Figure 29a

6.2. Supported Ribbons

As stressed in several theoretical studies, like MgO polar ribbons on Ag(100),282,283 or MgO polar and nonpolar ribbons on Au(111),22,286 deposition on a metal surface substantially contributes to reducing the instability of the polar border. However, while the role of the metal, whether Ag(100) or Au(111), is not sufficient to stabilize the [110] borders with respect to [100], zigzag ribbons are predicted to become more stable than armchair ribbons on Au(111). This difference was assigned to the initially smaller energy difference between zigzag and armchair borders in unsupported ribbons, as compared to [110] versus [100]. Two effects may be at the origin of this difference. First, edge sites on [100] terminations are 3-fold coordinated, while [110] edge sites are only 2-fold coordinated, thus provoking a large energy difference in addition to polarity effects. Second, zigzag edges, although polar, require compensating charges δλ∞/λ = 1/3 much smaller than on [110] edges (δλ∞/λ = 1/2). An important difference between polar ribbons and polar thin films lies in the way the metal screens polarity. In both cases, a transfer of the compensating charge occurs from the oxide to the metal, thus allowing the oxide ions to recover charges closer to their usual valence. However, such screening occurs only at one thin film termination, that in contact with the support, Figure 18. At variance, both ribbon edges are in contact with the support, Figure 30, which makes the stabilizing

Figure 29. Charge distribution in unsupported (black) and supported (on Au (red) or Mo (green)) polar P(100) and nonpolar NP(100) MgO(100) nanoribbons: Bader charges across the MgO ribbons (a, b), charge distribution in the substrate atoms located under the nanoribbons (c, d).286

and b shows the Bader charge distribution in polar [110] and nonpolar [100] MgO(100) unsupported nanoribbons, highlighting the presence of compensating charges.286 Metallicity has clearly nothing to do with specific border states associated with the low coordination of border atoms, as dangling bonds in graphene zigzag nanoribbons, although it may be reinforced by them in small gap systems. Its very origin is electrostatic, and its signature can be found in the value of the compensating charges, Figure 29, and the progressive shifts of the local band structure on the rows across the ribbon. Interestingly, in ribbons two monolayers-thick, due to the Bk stacking, oxygen atoms are located on-top cations and vice versa. As a consequence, there is a cancelation of polarity effects between the two layers, the potential difference induced by the top layer being opposite to that of the bottom layer. No compensating charges are then needed, and the ribbons keep their insulating or semiconducting character, as found numerically.287−289 This reasoning may be extended to several layers, evidencing an odd−even alternation of the electronic structure. Finally, other compensation mechanisms may be at work, such as border hydroxylation or reconstructions. Hydroxylation seems to have been decisive in the obtention of ZnO zigzag ribbons,297 and polarity was invoked as responsible for an enhanced activity of polar borders of NiO islands toward H2 dissociation.314 However, although these statements are consistent with all known results on polar oxide surfaces and thin films, it should be kept in mind that the extremely low coordination of border sites, by itself, could induce water or hydrogen dissociation. In this respect, a comparison between

Figure 30. Schematic representation of the band structure at the interface between a metal support and a stoichiometric (a) or a nonstoichiometric (b) polar nanoribbon, showing the transfer of compensating charges in the substrate. EF denotes the Fermi level. The negative (respectively positive) slope of the bottom of the metal conduction band indicates the transfer of electrons to (respectively from) the metal substrate.

effect comparatively more efficient. Upon adsorption, an electron excess takes place in the substrate below the cation edge, while an electron depletion occurs under the O edge, as shown in Figure 29a−d in the case of MgO(100) polar and nonpolar nanoribbons on Au(100) and Mo(100). For more electronegative metals (e.g., Au compared to Mo), screening at the Mg edge is more efficient than at the O edge. 4096


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Table 1. Expressions of Compensating Charges, Potential Difference, and Total Dipole in Polar Thin Films, Polar Nanoribbons, and 1D Chainsa

a

physical quantity

thin films

nanoribbons

1D chains

asymptotic values compensating charge potential difference total dipole

δσ∞ = R1σ/(R1 + R2) ΔV∞ = G + (α + β)δσ∞ P∞ = (G + Ṽ δσ∞)/4π

δλ∞ = R1λ/(R1 + R2) ΔV∞ = G + (α + β)δλ∞ P∞ → ∞

δQ = 0 ΔV ∝ Q/a P∞ → ∞

asymptotic behavior compensating charge potential difference dipole moment

δσ − δσ∞ ∝ 1/N ΔV − ΔV∞ ∝ 1/N P − P∞ ∝ 1/N

δλ − δλ∞ ∝ 1/ln N ΔV − ΔV∞ ∝ 1/ln N P ∝ N/ln N

Top: Their N → ∞ values. Bottom: Their asymptotic behavior in the large N limit.

6.3. Summary

1/N to 1/ln N behavior in the compensated regime, Table 1. A remarkable characteristic is the difference of size dependence between the dipole moment density P and the potential difference ΔV (see section 2). For example, in the absence of compensation, while in asymmetric objects, P always increases linearly with H, ΔV may increase linearly with H (thin films or 3D clusters with large polar facets), increase linearly with L (3D clusters with small polar facets), increase logarithmically with H (ribbons or 2D islands with large polar edges), increase logarithmically with L (2D islands with small polar edges), or even remain constant as a function of H (1D chains, and symmetric objects). In particular, in 1D chains, although P diverges, there is no polarity signature in the electronic structure and the energetics. These conclusions apply to uncompensated as well as compensated objects. Polarity healing impedes the potential difference to diverge, but the total dipole may keep increasing with N in the large size limit. As a consequence, although at semi-infinite surfaces and in asymmetric ultrathin films, it is legitimate to indifferently use the dipole moment value or the potential difference to characterize polarity, because these two quantities are proportional, this is no longer valid in other nano-objects. The value of the total dipole moment is insufficient to characterize the electrostatic behavior of polar objects, and one should rather take into account the largest potential differences ΔV. ΔV is the important quantity to consider, because its divergent or nondivergent character has direct implications on the electronic structure and the energetics.

In their large width regime, besides a rather slow size variation of their properties (as 1/ln N), polar nanoribbons present the expected compensation characteristics, that is, compensating charge densities given by the relationship similar to that at semi-infinite surfaces (δλ∞/λ = 9 ) and a finite value of the potential difference and of their formation energy as N → ∞. At variance, their dipole moment diverges as N/ln N. A specificity of polarity compensation when they are supported on a metal comes from the metal screening occurring on both borders, yielding particularly strong stabilization. Little is known on the phase diagram of very narrow polar nanoribbons.

7. SUMMARY AND OPEN QUESTIONS A positive answer to the initial question “Does polarity exist at the nanoscale?” can safely be given at the end of this Review. Indeed, although at the nanoscale relevant sizes are small, structural phase diagrams and electronic properties of polar nano-objects are vastly different from those of nonpolar objects. Moreover, they also differ from their bulk analogues, and most differences can be assigned to electrostatic forces associated to polarity. These forces induce different behaviors in the “small” or “large” size regimes, which are separated by a critical size value, always in the nanometer or subnanometer range. Aside from their applicative interest, a large part of which undoubtedly remains to be discovered, oxide nano-objects thus provide a new approach to polarity, which raises many fundamental questions. 7.1. Dimensionality Features

7.2. Mechanisms of Compensation

Previous sections have demonstrated that dimensionality impacts the properties of polar nano-object. On the one hand, beyond the critical thickness, the stabilization of all polar nano-objects, whether planar or three-dimensional, requires compensating charges on their terminations. This is a strong electrostatic requirement that cannot be bypassed. Nevertheless, the application of Tasker’s or charge neutrality views (Figure 3) slightly differs in 3D and in 2D. In 3D, aside exponential potential tails that are not accounted for by macroscopic electrostatics, the electrostatic potential outside a dipole-free repeat unit exactly vanishes, while, in 2D, long-range potential tails (1/z2 distance dependence) subsist, making it necessary to sum all repeat unit contributions (see section 6). Dimensionality is also reflected in the size dependence of the potential difference across the polar object, and in the behavior of the total dipole moment density. The general trend when passing from 3D to 2D is the transformation from linear to logarithmic behavior in the absence of compensation or from

The well-recognized mechanisms of compensation at semiinfinite surfaces may be at work also in polar nano-objects, especially above the critical size. In the literature, there are numerous examples of reconstructions at polar terminations or adsorption of charged species, which provide the compensating charges. Metallicity or change of oxidation state has been recognized in some experiments and in all of the simulations of stoichiometric objects. However, novel mechanisms of stabilization exist at the nanoscale, which can be rationalized by considering the energetic contributions in competition. For example, at low thickness, some polar films display a ground-state structure different from the bulk. The competition then takes place between the bulk cohesion energy, which favors the bulk ground state, and the surface energy, which favors a nonpolar surface. The latter may win over the former up to a certain critical size. 4097


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ization, MIGS penetration, charge transfer, lattice mismatch, interfacial strain, and/or dislocations, are new elements that interfere with and modify polarity manifestations in comparison with semi-infinite surfaces. Among all of these effects, charge transfer is of key importance with respect to polarity. In most cases, the presence of a metallic substrate induces an important stabilizing effect. For polar films requiring compensation, the metal provides the compensating charge, allowing the oxide atoms in contact with it to recover their usual valency. From this viewpoint, it can be said that metal screening is likely more efficient for polar nanoribbons and nanoislands than for films and supported clusters. This is due to the fact that metal is in contact with a single film termination, while at the surface of the film, metallization remains required. At variance, a metal is in contact with both ribbon terminations. It can thus play a role of electron donor on one side and electron acceptor on the other side, although, usually, one process costs less energy than the other depending on the metal work function (as seen, for example, in Figure 29). Conversely, via an interfacial charge transfer, a metal substrate can induce polarization in an otherwise nonpolar film. This process results from the structural response of the film to the charge transfer, leading to a finite rumpling in the layer. This electrostatic coupling is also present between a metal supported oxide film and adsorbates, allowing a stabilization of adsorbate charged states. In most of this Review, we have restricted ourselves to the case of metallic supports. Oxide nano-objects grown or deposited on oxide substrates represent a completely different family, about which very little is known. It could be naively anticipated that at the polar interface between two oxides of the same structure and close lattice parameters (say, for example, MgO(111) and NiO(111)), nothing happens. There is no charge discontinuity, no need of compensating charges at the interface, only the outer surfaces of the two oxides need compensation. Some heterostructures MgO(111)/ ZnO(0001)59 or ZnO/(Zn,Mg)O60 have been synthesized and studied with the aim of producing artificial materials with flexible gap widths. In the first case, there is no mention of specific interfacial states, simply a change of structure from wurtzite to rocksalt when the thickness of the ZnO layers decreases. The system remains semiconducting, and, as looked for, its gap varies with the Zn/Mg ratio. In the latter, a 2D electron gas has been evidenced, but its origin was not assessed. This leads us to the hot topic of low-dimensional electron gases.

An uncompensated phase may also exist. Its stabilization results from a competition between polarity electrostatic energy and elastic energy, because strong reduction of the layer rumpling enables a decrease of their individual dipole moment. In films or ribbons with a cation or oxygen excess layer, polar phases experience a strong stabilization. Polarity compensation involves a redistribution of electrons or holes between the termination CB or VB, while in stoichiometric objects the redistribution requires excitation of electrons from the VB on one side and the CB on the other side, with an obvious energy cost of the order of the band gap. A new situation occurs in 3D or 2D objects whose polar terminations have a finite size. Rigid charge models evidence an inhomogeneity of the electrostatic potential on the terminations and a maximum amplitude of variation, which scales linearly or logarithmically with their size L. Preliminary results of quantum simulations that we have performed similarly evidence an inhomogeneous distribution of compensating charges, Figure 31. Interestingly, the mean charge density

Figure 31. Charge distribution in a stoichiometric 1 ML MgO(111) island of hexagonal shape, with six polar zigzag terminations. Opposite terminations contain atoms of opposite type. Smaller absolute values are represented by larger spheres and darker shading, highlighting the inhomogeneous charge compensation, particularly strong on the Mg edges. Results obtained with the MgO parametrization of the semiempirical order-N Hartree−Fock method used in ref 318.

value on the terminations is close to the required δλ/λ value, and the degree of inhomogeneity is very different on oxygen and cation terminations. Such inhomogeneities may lead to the spontaneous desorption of some atoms on the terminations, yielding compensation. Finally, in thin nanoribbons or islands, edge polarity may be healed if the object has an even number of layers. The Bk structure is well suited to such a mechanism, because atoms of opposite type are piled on top of each other. As a result, the potential difference across the object due to one layer can cancel that of the next layer, resulting in a nonpolar semiconducting electronic structure, as noticed in simulations of ZnO nanoribbons.287−289

7.4. Formation of a 2D or a 1D Electron Gas

There has long been much interest in the consequences of confinement effects on low-dimensional electron gases, since the first evidence of a 2D electron gas at a GaAs/GaAlAs interface319 until the recent discovery of similar effects at the surface of bare320 or hydrogenated321 SrTiO3(001) surface. Similarly, a great surge of interest has come from the observation of metallic edge states in graphene nanoribbons with zigzag terminations.261,262 Polar terminations of oxide nano-objects could provide new configurations relevant for this theme. For many years, surface “metallization” has been recognized as an intrinsic mechanism of polarity compensation. It corresponds to the creation of holes in a surface VB or electron in a surface CB. As far as oxides are concerned, in many cases, holes are localized on oxygen orbitals, with little

7.3. Role Played by the Substrate

Leaving aside the possibility of producing exfoliated monolayers, all polar nano-objects experimentally studied are supported on a metal or insulating substrate, with a strong predominance of the former. Adhesion forces, orbital hybrid4098


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densities and compensating charge densities per unit length on the ribbon rows and external rows, respectively. The expression of the electrostatic potential created by a charged row at a distance d is the following:

hopping probability, and the corresponding bands have little dispersion. Things may be different for electrons on a cationic termination, which can truly form a 1D (for ribbons) or 2D (for films) electron gas. The fact is that “metallization” is not the most frequent ground state of a polar termination, except in some transition metal oxides. However, there may be ways to stabilize it purposely, in the same spirit as the creation of 2D electron gases, which has been done by hydrogenation of (nonpolar) surfaces. In this respect, a system of interest is the perovskite interface LaAlO3/SrTiO3(001), a polar orientation for LaAlO3. A 2D electron gas has been evidenced at this interface. Is it the manifestation of polarity? There is not yet a definite answer to this question and different hypotheses have been proposed. This is presently a hot topic but much work remains to be done before a full electronic structure and stoichiometry characterization of such complex interfaces is obtained. In stoichiometric polar nanoribbons, all simulations evidence edge bands crossing the Fermi level. The edge states found in simulations of MgO, ZnO, BeO, ZnS, AlN, GaN, BN, etc., are primarily due to polarity compensation, although band narrowing effects at edges can also affect the local density of states. Polarity is nearly never mentioned, but rather reference to edge states in graphene zigzag nanoribbons is put forward. It should be made clear that such comparison has no scientific basis because graphene edge states are built from unsaturated sp2 orbitals (dangling bonds) and, being an elemental system, cannot experience polarity effects. Regarding the question of edge states in polar nanoribbons or islands, there is not yet experimental evidence of their nature. Some display an increased contrast in STM images, but, to our knowledge, no spectroscopic proof of the existence of states at the Fermi level has yet been brought. Other processes, like a change in lattice register between the center and the edge of the object, could also support such observations. Polar nano-oxides provide a novel rich field of research, with important developments to be expected in the near future. Mastering their structure, shape, and composition thanks to the various available synthesis techniques remains a challenge requiring fine-tuning of preparation conditions. This is particularly true in the first steps of nanoribbon or island formation, where little is known on the interplay between thermodynamic and kinetic constraints. Thanks to expert use of scanning local probes, atomic resolution can be achieved, but the question of atom recognition, allowing local stoichiometry determination, remains largely unsolved. Despite the increased power of numerical tools, the simulation of most nano-objects, especially those without periodicity, remains beyond the potentialities of first principles methods. Yet, combined experimental and theoretical efforts would allow not only to solve one complex observed structure, as it has been already done in several instances, but more importantly to understand the foundation principles of this new exciting branch of surface science.

L

V (d) = 2λ ln a+

a2 + d2

(30)

For the sake of simplicity, it will be approximated by V(d) = 2λ ln L/d when d represents any inter-row distance; on the row itself, V(d = 0) = 2λ ln L/2a. The expressions for the total electrostatic potentials on the ribbon rows VCn and VAn are much more involved than for thin films, due to the logarithmic behavior of the Coulomb potential. Using the definition of the gamma function322 Γ(n + 9 ) = (n − 1 + 9 )(n − 2 + 9 )...(1 + 9 )Γ(9 + 1), one finds that on the outermost cation row: (R1 + R 2)Γ(N + 9) 2a Γ(N )Γ(9) 2a + 2δλ ln − aUCδλ + wC (R1 + R 2)(N − 1 + 9)

VC1 = 2λ ln

(31)

while on the other side of the ribbon: (R1 + R 2)Γ(N + 9) 2a Γ(N )Γ(9) 2a − 2δλ ln + aUA δλ + wA (R1 + R 2)(N − 1 + 9)

VAN = −2λ ln

(32)

In the absence of compensating charge, the potential difference ΔV = VC1 − VAN across the ribbon reads (δw = wA − wC): ΔV = 4λ ln

(R1 + R 2)Γ(N + 9) − δw 2a Γ(N )Γ(9)

(33)

Its asymptotic expression, in the large N limit, is obtained by using the Stirling formula Γ(x) ≈ e−xxx−1/2(2π)1/2 for the Γ function when its argument is large: ΔV → 49λ ln N

(34)

which highlights the logarithmic divergence of this quantity in the large N limit. The total dipole moment density of the ribbon, on the other hand, is proportional to the ribbon width, in the absence of compensating charges: P = NλR1

(35)

When compensating charges are considered, within the same approximations as for thin films, the equalization of the Fermi level yields: E F = CBM1 + αδλ = VBMN − βδλ

(36)

which allows one to write (G = CBM − VBM ): 0

ΔV = G + δλ(α + β)

APPENDIX In this Appendix, we indicate the main derivation steps to obtain the expressions of the electrostatic properties of 2D nanoribbons in the large width limit.285 The notations are the same as in section 4. The length L of the ribbon edges is much larger than any other relevant dimension. a is the unit cell length along the ribbon edge, and ±λ and ±δλ are the charge

0

(37)

The value of δλ results, to order 1/N: δλ ≈

49λ ln N − G̃ − δw 4 ln N + Ṽ

(38)

with Ṽ = a(UC + UA) + α + β + 4 ln(R1 + R2)/2a and G̃ = G − 4λ ln(R1/2aΓ(9 + 1)). As in the case of thin films, when N 4099


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goes to infinity, δλ converges toward δλ∞ = 9 λ = λR1/(R1 + R2), and the asymptote is reached with a 1/ln N law: δλ ≈ δλ∞ −

G̃ + Ṽ δλ∞ + δw 4 ln N

Institute of Nanosciences, and numerous evaluation tasks at the national and international level.

(39)

The potential difference across the ribbon thus tends toward a constant value ΔV∞ = G + (α + β)δλ∞, following a 1/ln N law, and the total dipole moment density P = NλR1 − δλN(R1 + R2) no longer diverges linearly with the ribbon width as in the absence of compensating charge (the terms proportional to N cancel between the λ and δλ contributions), but rather scales as N/ln N: P=

N (R1 + R 2) (G̃ + Ṽ δλ∞ + δw) 4 ln N

(40)

AUTHOR INFORMATION

Jacek Goniakowski received his Ph.D. in 1994, for studies on oxide surfaces under the direction of Prof. Claudine Noguera at the Laboratoire de Physique des Solides (University Paris XI, France). He then held a postdoctoral position in the group of Prof. Mike Gillan at Keele University (Great Britain). In 1995, he returned to France to the Centre de Recherche sur les Mécanismes de la Croissance Crystalline (University Aix-Marseille II), where he obtained a faculty position and started his independent research. In 2003, he moved to the newly created Institut des Nanosciences de Paris (University Paris VI), where he is currently Research Director in the group “Oxides in Low Dimensions”. Jacek Goniakowski has worked essentially on structural, electronic, and reactivity properties of oxides, moving progressively from surfaces of bulk materials, to ultrathin films, and, more recently, to nano-objects. His interests focus on the electrostatics-driven phenomena, such as polarity or electrostatic coupling between charge state and atomic structure, which strongly influence properties of ionic oxides and their interaction with environment: surface hydroxylation, metal/oxides interfaces, etc. More specifically, he is involved in ab initio modeling, in development of semiempirical atomistic tools for large-scale simulations, and in theoretical analysis of the underlying microscopic mechanisms.

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. Biographies

ACKNOWLEDGMENTS We thank Cecilia Dolce for the simulations of MgO polar hexagonal islands, Figure 31, and Livia Giordano and Niklas Nilius for stimulating discussions.

Claudine Noguera started her research activity in Orsay (France), with the development of many body techniques applied to the understanding of spectroscopies such as EXAFS and XPS, under the direction of Jacques Friedel. After obtaining her Ph.D. in 1981, she studied the influence of strong correlations on the Peierls’ transition in quasi-one-dimensional (1D) conductors and participated in the establishment of the theory of (at that time) newly developed experimental techniques (surface EXAFS, surface EXELFS, STM). Toward the end of the 1980s, she turned to the physics of oxide surfaces, which was then still in its infancy, and gave important contributions to the understanding of their atomic and electronic structure, of metal−oxide interfaces, hydroxylation processes, and polarity instability, accompanying numerical simulations by theoretical explanatory models. Aside from about 150 original contributions, she is known by the monograph “Physics and Chemistry at Oxide Surfaces” published in 1996, by the creation of the IWOX conference series, which is still alive, and by review papers, especially those on polarity. Her research interests have now turned to oxide ultrathin films and nano-objects. She also drives an interdisciplinary project at the frontier between geochemistry and surface science aiming at introducing the concepts of crystal growth in the description of the precipitation of minerals in the aqueous fluids of the natural environment. Her whole research activity is conducted in parallel to heavy responsibility tasks, including the foundation of the Paris

ABBREVIATIONS 1D one-dimensional 2D two-dimensional 3D three-dimensional CB conduction band CBM conduction band minimum DFT density functional theory GGA generalized gradient approximation GIXD grazing incidence X-ray diffraction HRTEM high-resolution transmission electron microscopy LEED low-energy electron diffraction LEEM low-energy electron microscopy MBE molecular beam epitaxy MEIS medium energy ion scattering MIGS metal-induced gap states ML monolayer MLE monolayer equivalent μ-LEED micro low-energy electron diffraction 4100


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RHEED reflection high-energy electron diffraction SFM scanning force microscopy SPA-LEED spot profile analysis-low-energy electron diffraction STM scanning tunneling microscopy SXRD surface X-ray diffraction TDS thermal desorption spectroscopy TEM transmission electron microscopy UHV ultra-high vacuum VB valence band VBM valence band maximum XPD X-ray photo-diffraction XPS X-ray photoemission spectroscopy XRD X-ray diffraction

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