Self-limited oxide formation in Ni(111) oxidation
aa r X i v : . [ c ond - m a t . m e s - h a ll ] M a r Self-limited oxide formation in Ni(111) oxidation
J. Ingo Flege, ∗ Axel Meyer, and Jens Falta
Institute of Solid State Physics, University of Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
Eugene E. Krasovskii † Departamento de F´ısica de Materiales,Facultad de Ciencias Qu´ımicas,Universidad del Pais Vasco/Euskal Herriko Unibertsitatea,Apdo. 1072, 20080 San Sebasti´an/Donostia,Basque Country, SpainDonostia International Physics Center (DIPC),Paseo Manuel de Lardizabal 4,20018 San Sebasti´an/Donostia, Basque Country, SpainandIKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain (Dated: March 8, 2012)The oxidation of the Ni(111) surface is studied experimentally with low energy electron microscopyand theoretically by calculating the electron reflectivity for realistic models of the NiO/Ni(111)surface with an ab initio scattering theory. Oxygen exposure at 300 K under ultrahigh-vacuumconditions leads to the formation of a continuous NiO(111)-like film consisting of nanosized domains.At 750 K, we observe the formation of a nano-heterogeneous film composed primarily of NiO(111)surface oxide nuclei, which exhibit virtually the same energy-dependent reflectivity as in the case of300 K and which are separated by oxygen-free Ni(111) terraces. The scattering theory explains theobserved normal incidence reflectivity R ( E ) of both the clean and the oxidized Ni(111) surface. Atlow energies R ( E ) of the oxidized surface is determined by a forbidden gap in the k k = 0 projectedenergy spectrum of the bulk NiO crystal. However, for both low and high temperature oxidationa rapid decrease of the reflectivity in approaching zero kinetic energy is experimentally observed.This feature is shown to characterize the thickness of the oxide layer, suggesting an average oxidethickness of two NiO layers. PACS numbers: 68.37.Nq, 81.65.Mq, 71.15.ApKeywords: nickel; oxidation; low energy electron microscopy; surface oxide; augmented plane wave method
I. INTRODUCTION
Surface oxidation is an almost ubiquitous phenomenon,and it is generally associated with profound changes ingeometrical structure and materials properties. The latetransition metals (TMs) have received persistent atten-tion owing to their tremendous importance in a vari-ety of heterogeneously catalyzed chemical reactions. Thegeneral oxidation mechanism may be qualitatively quitesuccessfully described by the Cabrera-Mott model devel-oped more than 60 years ago, from which many commonoxidation phenomena, e. g., the temperature-dependentthickening of oxide films until saturation, can be ratio-nalized. However, the different elemental properties ofthe TMs, arising from the varying d -band occupationthrough the elemental series, give rise to a huge diver-sity in oxidation pathways, and here, using the oxida-tion of Ni as an example, we present a case where eventhis fundamental concept of oxide saturation thicknessincreasing with temperature needs to be rephrased.A prominent example is the interaction of molecularoxygen with Ni(111), which is frequently viewed as amodel system for dissociative adsorption of molecularoxygen on a TM surface. Numerous studies have al- ready targeted the initial adsorption of oxygen onto cleanNi(111), which induces a (2 ×
2) surface reconstruction.
While the structural model of this low-coverage phase,which is established upon low O exposure, is well ac-cepted, there is no general consensus regarding the struc-ture of the nickel oxide layers that form with prolongedoxygen dose. An especially interesting case is the rangeof sample temperatures above 600 K during oxidation,which has so far remained mostly unexplored. Below600 K, different scenarios have been proposed depend-ing on temperature, involving the evolution of few-layer-thick, bulk-like NiO films or the formation of individ-ual oxide grains of thicknesses exceeding 10 nm. Due to this inherent complexity of surface oxidation atits early stages, deeper insight into the underlying physi-cal and chemical processes may be gained from informa-tion gathered in situ, i. e., acquired in real time during reaction in an oxidative environment. Ideally, the ex-perimental tools of choice should enable a simultaneoussurface-sensitive characterization of geometrical and con-comitant electronic structure, establishing a link betweenthe two properties.A promising approach to real-time studies of dynamicsurface processes in TM oxidation is to employ scat-tering of low-energy electrons in full-field microscopy, alsoknown as low-energy electron microscopy (LEEM).
This method is intrinsically sensitive to the near-surfaceregion owing to the strong interaction of slow electronswith condensed matter, and it provides microscopic in-sight on a length scale of a few nanometers. Infor-mation on the surface crystal structure is accessible bythe related technique of low-energy electron diffraction(LEED), which allows to determine the dimension of thesurface unit cell and the point group of the lattice. In ad-dition, for a given reflected beam the dependence of thereflected current I on the acceleration voltage V of the in-cident electrons, the I ( V ) curve, contains information onthe structure of the unit cell. The atomic arrangement onthe surface can be inferred from the multiple-scatteringanalysis of the I ( V ) curves for several reflected beamsover a wide energy range. This technique, commonlyreferred to as intensity-voltage, I ( V )-LEED, has alreadyenabled the determination of many surface structures. The I ( V ) curves also reflect the bulk electronic structure,in particular, the Bragg gaps and critical points, wherethe band structure strongly deviates from free-electron-like behavior. This effect is especially pronounced atlow energies, where the inelastic scattering is rather weak.Experimentally, the much higher intensity of the re-flected electron current at very low energies in the rangeof a few eV, typical of LEEM measurements, makes itvery attractive to record the I ( V ) dependence in a spa-tially and time-resolved manner by sampling the elec-tron energy in imaging mode. This so-called I ( V )-LEEMtechnique facilitates the measurement of the individual I ( V ) dependence of nanosized surface phases and hasalready been applied to processes in epitaxial growth, surface chemical reactions, and oxidation catalysis. However, despite the achievements of the well-established techniques in the interpretation of LEED atthe energies of a few tens of eV, their application at verylow energies is not straightforward: most of the imple-mentations of the multiple scattering theory rely on arapid decay of the electron wave into the solid, while atthe energies of a few eVs the inelastic scattering is weak,and the penetration depth is very large. In addition,low-energy electrons are rather sensitive to details of thecrystal potential, so for a fully conclusive comparisonwith the experiment the LEED calculation should relyon the self-consistent potential – in the sense of densityfunctional theory (DFT) – both in the bulk and at thesurface.In the present work we present a combined experimen-tal and theoretical study of the energy-dependent con-duction properties of oxygen overlayers on Ni(111) withthe aim to relate the observed I ( V ) curves to the elec-tronic properties of the surface and, eventually, to itsatomic structure. We apply an ab initio scattering theorybased on a full-potential augmented-plane-waves (APW)formalism to a model of the oxidized Ni(111) surface.A good agreement between the calculated and the mea-sured LEED spectra allows us to interpret the spectral structures and to conclude on the thickness of the sur-face oxide layer. In particular, we find a forbidden en-ergy gap in the k k = 0 projected spectrum of the (111)surface of the bulk NiO crystal, which causes a rapid in-crease of electron reflectivity from the oxidized Ni(111)surface at low kinetic energies. We show that with de-creasing thickness of the oxide layer the electron trans-mission does not increase uniformly over the gap region,but a narrow transmission channel opens at the bottomof the gap, which is observed in our I ( V ) measurements.The paper is organized as follows: In Secs. II and III,we describe the experimental procedures to oxidize thepristine Ni(111) surface and characterize the oxygen-richphases in situ. The theoretical approach is introduced inSec. IV, and applied to Ni(111) and to thin NiO layerson Ni(111) in Secs. V and VI, respectively. II. EXPERIMENTAL DETAILS
Most experiments were conducted at the National Syn-chrotron Light Source (NSLS) at Brookhaven NationalLaboratory (BNL), Upton, NY (USA) using the spec-troscopic photoemission and low-energy electron micro-scope (LEEM III including hemispherical energy ana-lyzer, Elmitec) installed at beamline U5UA. AdditionalLEEM measurements were performed in the newly-installed LEEM III system (Elmitec, no energy filter) atour home institute at the University of Bremen. Trans-ferability of the results was cross-checked and asserted byperforming experiments under nominally identical condi-tions.A commercially purchased, polished Ni(111) singlecrystal (Mateck) with a nominal orientation better than0 . ◦ was used. After insertion into the UHV chamberthe sample was cleaned by several cycles of 0.5 keV Ar + ion sputtering followed by thermal annealing at 1050 K.In addition, short flashes to 1300 K were found to im-prove the smoothness of the surface on the nano- tosub-micrometer scale. Surface cleanliness following thisrecipe was already asserted in an earlier study. Sam-ple temperatures are given based on the reading of aW/Re thermocouple permanently attached to the samplesupport. In the oxidation experiments, research-grade(99.998%) oxygen (Matheson Tri-Gas Co.) was dosedfrom a high-precision leak valve in back-filling mode. TheBNL-LEEM and the Bremen-LEEM systems exhibitedbase pressures of 2 × − Torr and 7 × − Torr,respectively.The kinetic energy of the incident electrons in all I ( V )curves presented in this article is referenced to the onsetof the mirror electron mode, i. e., with respect to the vac-uum level. Experimentally, this onset has been measuredby determining the inflection point of the abrupt edge insample reflectivity observed when increasing the electronenergy to a few eV. III. EXPERIMENTAL RESULTS ANDDISCUSSIONA. Ni oxidation and NiO structure: status quo
We begin by briefly reviewing the present status quofor oxidation of Ni(111). Depending on oxygen dose,Ni(111) has been found to undergo a (2 ×
2) surface re-construction for coverages up to 0 .
25 monolayer (ML)[for Ni(111), 1 ML corresponds to an atomic density of3 . × cm − ] followed by nucleation of an epitaxialoxide layer for larger oxygen exposures. At room tem-perature, oxidation has been reported to start uponan accumulated dose larger than 10 Langmuir (L) (1 Lamounts to 10 − Torr · s). A three-stage model of theprocess has been proposed, involving (i) dissociativechemisorption, (ii) nucleation of oxide islands exhibitinga thickness of a few atomic layers, and (iii) slow thicken-ing of the oxide film.Depending on sample temperature during oxida-tion, different NiO orientations have been identified.Below 470 K, only NiO(111) formation has beenobserved, while NiO(001) islands have been foundfor more elevated temperatures. These findingshave been rationalized based on the thermodynamicinstability of the unreconstructed NiO(111)-(1 ×
1) sur-face, which, because of its rocksalt structure and withina picture of purely ionic bonding, should carry a di-verging dipole moment. Since the NiO(111) films wereexperimentally determined to be very thin, i. e., onlya few atomic layers thick, a metastable character ofthe NiO(111) orientation has been postulated, in agree-ment with the growth of the thermodynamically sta-ble, unpolar NiO(001) face at 500 K, i. e., at sufficientlyhigh temperature. In other studies, the stability of theNiO(111)-(1 ×
1) surface has been related to the adsorp-tion of hydroxyl species that prevent the surface fromundergoing a so-called “octopolar” (2 ×
2) reconstructionleading to a compensation of the surface dipole.
Since hydroxyl species are easily removed by annealing to600 K, this scenario would provide an alternative expla-nation for the stability of the (1 ×
1) phase at room tem-perature and the preferential growth of NiO(001) above500 K. Yet, it has still remained unclear whether thedriving force for the (2 ×
2) reconstruction at high temper-ature would be the same for thin as well as moderatelythick NiO(111) films—a question raised almost twentyyears ago. Quantitative information on actual oxide thickness,however, has proven difficult to obtain, and substantialvariations in oxide “saturation thickness” have been re-ported depending on both temperature and oxide phase.At 300 K, several studies have concluded on an ox-ide thickness of a few monolayers for the NiO(111)layer.
In the case of NiO(001), this saturationthickness may extend to more than 10 nm according tomedium-energy ion scattering (MEIS) after exposureto O at 500-600 K, which has been noticed to grow at a considerably higher rate. Based on MEIS, it has also been postulated that, inthe elevated oxidation temperature range, the NiO/Niinterface is very rough, consisting of irregularly shapedNiO grains, and indeed multiple oxygen-enriched grainshave been seen in photoelectron microscopy with oxygen-sparse areas in between. However, until the present thehigh-temperature oxidation regime above 500-600 K hasremained largely unexplored with respect to atomic andnanoscale structure. In the following Secs. III B and III C, we present ourresults for Ni(111) oxidation at 300 K and 750 K. In theformer case, we find the formation of a tight patchworkof nanosized NiO(111) domains. The corresponding I ( V )spectrum exhibits a very strong, characteristic peak atabout 6 eV. At a sample temperature of 750 K, which issignificantly higher than the temperature range exploredso far, we observe essentially the same local I ( V ) curvefor the oxidized parts of the Ni(111) surface concomitantwith a local (1 ×
1) LEED pattern, corroborating the nu-cleation of ultrathin (111)-oriented oxide domains evenat these high oxidation temperatures.
B. Oxidation pathway at room temperature
Following the cleaning recipe outlined in Sec. II, aclean, well-ordered Ni(111) surface is established exhibit-ing only steps and step bunches in LEEM (see Fig. 1(a)).Surface crystallinity is asserted by a sharp (1 ×
1) LEEDpattern (Fig. 2(a)). Afterwards, the sample was exposedto molecular oxygen (O ) at a background pressure of7 . × − Torr while the modification of the surface wasmonitored by LEEM (Fig. 1) and LEED (Fig. 2). Afterdosing O for 13 s, which corresponds to an accumulateddose of 1 Langmuir (L), the integral sample reflectiv-ity has considerably decreased, as can be deduced fromFig. 1(b). This change in intensity is accompanied by theadvent of a (2 ×
2) reconstruction in LEED (Fig. 2(b)),which is expected for a nominal oxygen coverage of about0 .
25 ML. However, in addition to the integral change in reflec-tivity, we observe significant local variations of the (00)intensity at structural defects (see Fig. 1(b)) that do notcontribute to the periodic part of the LEED pattern.While the terraces exhibit a rather low reflectivity at thechosen kinetic energy of the incident electrons (8 . we may attribute thesebright areas to the formation of a more oxygen-rich sur-face phase that is associated with a distinct LEED pat-tern (Fig. 2(c)) of apparent six-fold symmetry but in-creased lattice parameter as compared to clean Ni(111).Further dosing of O does not induce any visible changes,neither in the reflectivity nor in the sample morphology.Nevertheless, we note an overall grainy appearance ofthe surface, suggesting the presence of structural features FIG. 1. (color online) (a-c) Low-energy electron micrographsshowing the transformation of the Ni(111) surface at roomtemperature upon exposure to molecular oxygen for 0 L (a),1 L (b), and 265 L (c). (d) I ( V ) spectra of clean Ni(111)(dotted line) and transformed regions (solid line). just below the resolution limit of the microscope.In the following sections, we will mainly focus bothexperimentally and theoretically on the structural iden-tification of this bright phase. A comparison of I ( V ) data(Fig. 1(d)) acquired for the clean Ni(111) surface with thebright, homogeneous area readily corroborates the notionof a distinct phase. Further insight into the crystallo-graphic structure is accessible by the quantitative analy-sis of line profiles extracted from LEED patterns recordedduring thermal annealing from 300 K to 820 K. Whileno LEED spots associated with the Ni(111) substrateare found after preparation at 300 K, which confirmsthe presence of a continuous, oxygen-rich “film”, theseintegral order reflections re-appear at elevated tempera-ture and clearly dominate the LEED pattern at 700 K(Fig. 2(d)), whereas the spots of the oxide film have al-most vanished. Interestingly, additional spots emergeat half-order positions, underlining the formation of a(2 × . ± .
03 ˚A for thefilm, which is in good agreement with the lattice constantof bulk NiO(111) ( a = 4 .
177 ˚A), indicating an almostfully relaxed NiO film. Furthermore, from the width ofthe (1 × ox peaks at 300 K, an average domain size ofapproximately 1 . FIG. 2. (a-d) Low-energy electron diffraction patterns ob-tained after exposing the Ni(111) surface at room temperatureto an oxygen dose of (a) 0 L, (b) 1 L, (c) 265 L, and (d) af-ter subsequent annealing to 700 K. (e) Evolution of the lineprofile extracted from a cut through reciprocal space alongthe direction indicated in (c, d) with annealing temperature.Note that the line profiles were not corrected for variations indetector efficiency and that they were taken from a differentdata set than images (c-d). come slightly sharper while losing intensity (Fig. 2(e)).Comparable integral intensities of the oxide and sub-strate LEED spots are observed at about 620 K. Thisbehavior suggests an Ostwald-like ripening process, inwhich smaller patches either dissolve or coalesce to formlarger oxide islands, which yet remain too small to be im-aged in LEEM mode. These findings confirm the resultsof a scanning tunneling microscopy study that reportedan increase in domain size by about a factor of two afterannealing to 700 K. Finally, at a temperature of 820 K,these islands have completely disappeared, and the orig-inal LEED pattern of the clean substrate is restored.Summarizing, the presented LEED data stronglysuggest the formation of a continuous NiO(111)-likefilm, which is composed of many small domains ofa few nanometers in diameter. The recorded I ( V )curve provides more information on the local crystallo-graphic structure, which will theoretically be addressedin Sec. VI, but at this point it may already serve as afingerprint for a NiO(111)-like phase in the upcomingoxidation studies performed at elevated temperature. C. Oxidation at 750 K
The LEEM time-lapse sequence for oxygen exposure ata sample temperature of 750 K is depicted in in Fig. 3.On the clean surface (Fig. 3(a)) only steps and stepbunches are visible. However, after a 9 L dose we note aqualitatively different behavior as compared to the pre-vious case of oxidation at room temperature. Under thepresent conditions, islands exclusively nucleate at stepbunches whereas the single steps and flat terraces remainunaffected. Apart from any morphological objects on theterraces, we do not find a large-scale change in reflectedintensity as we observed for oxidation at room tempera-ture. This qualitatively different result is confirmed bycomparing the I ( V ) fingerprint of the terraces after anexposure of about 1000 L (Fig. 4(c)), e. g., extracted atpoint “A” in Fig. 4(a), with the I ( V ) reference spectrafor the clean Ni(111) surface (Fig. 1(d)). Since the curvesare virtually identical, this result clearly shows that onlya negligible amount of chemisorbed oxygen is found onthe terraces at this high temperature. Given the compar-atively large oxygen doses needed to achieve substantialsurface coverage, the integral dissociative sticking coeffi-cient for molecular oxygen has to be substantially lowerthan at room temperature, in agreement with previousstudies that targeted Ni(111) oxidation kinetics. The few existing oxide nuclei, however, grow upon pro-longed exposure and gradually spread over the remainingNi(111) terraces, while the crossing of step bunches is notobserved. We also note that essentially no additional, iso-lated nuclei appear on a 10 µ m scale (Fig. 3(b-e)), whichis indicative of a significantly enhanced diffusion length ofthe oxygen species. Interestingly, the reacted areas areby no means single-crystalline domains of nickel oxide,but instead are composed of a variety of small grains ex-hibiting different contrast and irregular shapes. From thetime-lapse sequence (Fig. 3(b-f)), we conclude that theedges of the already oxygen-rich areas serve as effectivenucleation centers for subsequently grown oxide islands, aphenomenon that has already been observed in oxidationstudies of other TM surfaces, e. g., Ru(0001). Because
FIG. 3. Low-energy electron micrographs showing the trans-formation of the Ni(111) surface upon oxygen exposure at asample temperature of 750 K. (a) 0 L, (b) 9 L, (c) 40 L, (d)215 L, (e) 420 L, and (f) 970 L. the lateral growth rate remains steady but slow through-out the remainder of the integral oxygen dose of about1000 L (Fig. 3(f)), a considerable fraction of surface arearemains unreacted to oxygen, in accordance with the in-tensity variations found in oxygen concentration maps attemperatures of 573 K and 673 K. In Fig. 4(a), three main contrast levels are observed,one for the oxygen-free Ni(111) terraces and two in theoxide-covered areas. Hence, it would appear that mainlytwo types of oxide domains have nucleated, labeled “B”and “C” in the figure. The magnified view shown inFig. 4(b), which is a blow-up of the center region indi-cated in Fig. 4(a), illustrates that the transformed ar-eas are composed of a tight network of nanosized oxidepatches exhibiting different contrast, but whose struc-tural properties are nevertheless amenable to I ( V ) anal-ysis. A comparison of the individual I ( V ) spectra ofthese oxygen-rich phases, using phases “B” and “C” inan exemplary fashion, reveals that they are closely re-lated since they all show a very similar characteristic res-onance at about 6 eV (Fig. 4(e)). Moreover, the I ( V )curve for “B” is virtually identical to the one observedfor oxidation at room temperature (Fig. 1(d)). Thus,we may already speculate at this point that all types ofpatches are some form of NiO(111), but apparently differwith respect to certain structural details.Further insight is gained from selected-area LEEDpatterns acquired for all regions individually. Whilethe local diffraction pattern for “A” (Fig. 4(c)) exclu-sively exhibits the expected (1 ×
1) spots of the cleanNi(111) surface, the micro-LEED pattern for region “B”(Fig. 4(d)) shows a well-defined, three-fold (1 ×
1) peri-odicity, whose surface unit cell is rotated by 30 ◦ withrespect to the substrate lattice. A quantitative analy-sis of the peak positions indicates a lattice mismatch of19%, in very good agreement with the presence of a com-pletely relaxed NiO(111) film that shares a different reg-istry with the substrate as compared to our observationsat room temperature. Additionally, for relatively lowelectron energies we also noticed weak, very broad, andthreefold-symmetric facet spots (not shown), which willbe subjected to temperature-dependent investigations us-ing micro-LEED and high-resolution LEED. Interest-ingly, we observed qualitatively similar diffraction pat-terns for both region types “B” and “C” that only dif-fered by the relative intensities of the NiO(111) spots andthe broad facet streaks. These findings suggest the pres-ence of a tight, complicated mosaic structure consisting ofwell-aligned and, probably, considerably tilted NiO(111)domains for both types of regions, albeit exhibiting dif-ferent areal ratios of the untilted versus the tilted regions.In this structural model, the measured shape of the I ( V )curve for region “C” would then represent the sum of theindividual I ( V ) curves of minuscule, untilted NiO(111)regions as well as of tilted NiO(111) regions, with thelatter barely contributing to the integral intensity of thespecular (00) beam.Previous studies argue that for growth tempera-tures of about 500 K, only the (001) orientation of NiOshould be present. Using our in-situ technique, we indeedobserve NiO(001) formation in an intermediate temper-ature range of about 500 K (Ref. 43), but based on themicro-LEED evidence in connection with the strong sim-ilarity of the I ( V ) curves presented here we clearly showthat this is not the case for even higher temperatures ofabout 750 K, where NiO(111) is again prevalent. Theseresults are in agreement with previous findings of a higherthermal stability of the NiO(111) films as compared tothe NiO(001) in annealing experiments, in which the lat-ter was shown to decompose upon annealing to 550 K. It should be stressed, however, that we did not observeany signs of a (2 ×
2) reconstruction of the oxide domains,clearly demonstrating that a NiO(111)-(1 ×
1) structurethat is rotated by 30 ◦ with respect to the Ni(111) sub-strate lattice is still stable at a temperature of 750 K.Evidently, the change in registry adds to the stability ofthese NiO(111) domains at temperatures close to decom-position of the room temperature grown oxide. IV. COMPUTATIONAL METHODOLOGY
There exist two major approaches to an ab initio treat-ment of electron scattering by the surface. The more tra-ditional multiple-scattering Green’s function method employs a representation of the crystal by a finite num-ber of atomic monolayers. It has an advantage of avoid-ing the calculation of the partial Bloch waves inside thecrystal and proceeds immediately to the scattering so-lution. This method is especially efficient within themuffin-tin approximation (MTA) for the crystal potential— although full-potential Green’s function methods haveexisted for many years the MTA is still widely used inthe theory of LEED. In the present work we use thealternative Bloch wave approach: the LEED function in-side the crystal is sought as a linear combination of the
FIG. 4. (color online) (a) Low-energy electron micrographrecorded after Ni(111) oxidation at 750 K. (b) Close-up viewof the center part of the LEEM image shown in (a) with ad-justed color map. (c-d) Selected-area LEED patterns acquiredfrom regions “A” (c) and “B” (d). (e) Local I ( V ) curves ex-tracted at points “A”, “B”, and “C” (shown in (a)) afterNi(111) oxidation at 750 K. partial waves, which facilitates the interpretation of theLEED spectra in terms of the band structure of the sub-strate.To calculate the reflected intensities R ( E ) the LEEDwave function is obtained as a solution of the Schr¨odingerequation for a semi-infinite crystal, see Fig. 5. The scat-tering wave function Φ is defined by its energy E and theincidence direction of the electron beam. In the planeparallel to the crystal surface Φ obeys the Bloch theoremand is characterized by the 2D Bloch vector k || . In thevacuum, far from the crystal surface, it is a superposition R e Φ ( z ) z M z VNi(111) z VO/Ni(111)
Ni NiNi NiNi Ni O-40-200 V ( z ) z (a.u.) substrate scattering region vacuum FIG. 5. (color online) Lower panel: potential profile at theclean Ni(111) surface (thin red line) and with an oxygen over-layer (thick black line). Upper panel: LEED wave function(the surface Fourier component G k = 0) for E − E F = 15 eVfor the clean Ni(111) (thin lines) and for the overlayer (thicklines). The wave functions in the scattering region are shownby dashed lines. of the incident plane wave and reflected (propagating andevanescent) plane waves. Deep in the crystal the poten-tial is periodic, and in the absence of inelastic scattering(electron absorption) the partial waves are propagating(real k ⊥ ) and evanescent (complex k ⊥ ) Bloch waves thatcomprise the complex band structure of the semi-infinitecrystal. Then, the scattering problem consists in find-ing the coefficients of the partial waves.The evanescent waves carry zero current, and the elec-tron beam is completely reflected whenever E falls ina k || -projected band gap. To take into account inelas-tic processes, which reduce the reflectivity, an imaginaryterm, the optical potential − iV i , is added to the potentialin the crystal half-space. The energy E is kept real, sothe absorbing potential leads to a spatial damping of thewave functions, i. e., Bloch vectors of originally propa-gating waves acquire an imaginary part. Hence, electronabsorption is allowed for, and even in the energy gaps ofthe bulk band structure there is no complete reflectionanymore. On average, V i increases with energy, and anapproximate dependence V i ( E ) can be inferred from thecurvature of the measured I ( V ) curve. In the presentcase we used a linear V i ( E ) function chosen so as to ap-proximately reproduce whenever possible the sharpnessof the R ( E ) peaks. An example for Ni(111) is shown inthe inset of Fig. 6(d).The computation starts with constructing self-consistent potentials in the bulk crystal and at the sur-face within the local density approximation (LDA) ofthe DFT. The band structure is calculated with the ex-tended linear augmented plane wave method (ELAPW),using the full-potential augmented Fourier componentstechnique. The potential at the surface is determinedby a repeated-slab calculation. The slabs comprise nineatomic layers and are separated by a vacuum region of16 a.u., see Fig. 5. No structure optimization is per- formed: all atoms occupy the positions of the ideal Ni orNiO lattice, see Fig. 8.The partial Bloch waves ψ k ⊥ are obtained as solutionsof the inverse band structure problem: for a given en-ergy E and k || = 0 they satisfy the Schr¨odinger equa-tion ˆ Hψ k ⊥ = Eψ k ⊥ in the bulk of the crystal. The cal-culations are performed with the ELAPW- k · p method,which reduces the equation to a matrix eigenvalue prob-lem, with k ⊥ being the eigenvalues. To the left fromthe matching plane z M , see Fig. 5, the LEED functionΦ is a linear combination of several ψ k ⊥ (only the waveswith Im k ⊥ not exceeding 1 a.u. − are included).In the surface region, between z M and z V , the poten-tial is different from the bulk potential, and the partialwaves representation is not valid. Here the function Φ isexpanded in terms of the eigenfunctions ξ n of the slab,which contains the scattering region, see Ref. 52. Thefunctions ξ n , thus, have already taken into account thescattering by the overlayers. For each energy E the threerepresentations are matched at the two planes z M and z V to construct a smoothly continuous function that satis-fies (with certain accuracy) the equation ˆ H Φ = E Φ inthe embedded region. (The Schr¨odinger equation is sat-isfied by construction both in the bulk and in the vacuumhalf-spaces.)
V. CLEAN Ni(111)
The ability of the substrate to conduct current can becharacterized by the current carried by individual Blochwaves ψ . For the clean Ni(111) surface the complex bandstructure in the Γ L direction and the energy-momentumdistribution of the current are shown in Fig. 6(a). Thecurrent carried (absorbed) by an individual Bloch waveis shown by the thickness of the dispersion curves. Below23 eV and above 34 eV relative to the Fermi energy thebehavior of the main conducting branch is close to free-electron-like, i. e., the electron transmission is effectedby a single bulk band with almost parabolic dispersion.Between 23 eV and 34 eV, there is a wide Bragg gapcentered at 28 eV and a number of special points, wherethe conducting branch switches from one bulk band toanother. They give rise to the sharp peaks A, B, and Cin the elastic (i.e., V i = 0) R ( E ) spectrum of Ni(111).In the present experiment only the peaks A and B arevisible (in agreement with earlier work, Ref. 24). Thisis explained by a strong effect of the inelastic scatteringon the peak C. Figure 6(d) compares the measured R ( E )spectrum (specular reflectivity) for clean Ni(111) to thecalculations with realistic values of the optical potential.The theoretical curve is the ratio of the specularly re-flected current to the incident current, and the experi-ment is the arbitrarily scaled I ( V ) curve. At moderatevalues of V i ∼ VI. NiO(111) CRYSTAL AND FILMS
To illustrate the effect of a thin overlayer on the elec-tron reflection from Ni(111), we have presented in Figs. 5and 6(c) calculations for an oxygen monolayer fully com-
10 20 30 40 50 60
E - E F (eV) R ( E ) ( % ) O/Ni(111)(c)
10 20 30 40 50 60 LL Γ R e ( k ⊥ ) (a) A B C R ( E ) ( % ) Ni(111)(b)
E - E F (eV) R ( E ) ( % ) experimenttheory
10 20 30 40
E - E F (eV)0.51.01.5 V i ( e V ) (d) FIG. 6. (color online) (a) Conducting branches of the com-plex band structure (thick lines) superimposed onto the bulkband structure in the L Γ L interval (thin lines). (b) Normalincidence R ( E ) spectrum of Ni(111) for V i = 0 .
05 eV. (c)Normal incidence R ( E ) spectrum of an oxygen overlayer onNi(111), see Fig. 5. (d) Measured R ( E ) normal incidencespectrum of Ni(111) (full line) and calculations (dashed anddot-dashed) for two choices of the energy dependence of theoptical potential V i ( E ). Inset shows the two functions V i ( E )with respective line styles. The bars in the inset show thelocations of the peaks A and B. mensurate with the substrate (thereby strongly com-pressively strained in the lateral direction if single-layerNiO(111) is used as reference). Figure 5 compares theLEED functions for a clean Ni(111) surface and for anoxygen overlayer on Ni(111) at a kinetic energy of 10 eV.Already at the second Ni layer the wave function is seento acquire the character of the substrate Bloch wave, butthe oxygen overlayer reduces its amplitude. The compar-ison of the spectra in Figs. 6(b) and 6(c) shows that inthe interval 7–22 eV, where the band structure of the sub-strate is free-electron-like, the oxygen overlayer increasesthe specular reflectivity to as much as 50%. However,its presence does not result in any sharp structures inthis energy interval: the reflectivity steadily increases atlow kinetic energies similar to the case of clean Ni(111).On the contrary, the measured spectrum of the oxidizedsurface, Fig. 1(d), shows a sharp decrease at low kineticenergies.Naturally, at low energies the electron reflection isvery sensitive to the shape of the potential barrier be-tween the crystal half-space and the vacuum. Thiscan be illustrated by a simple one-dimensional system,Fig. 7(a), in which the potential barrier is modeled bya two-step function. For a step-like potential barrier ofheight V [with V = 0, in the notation of Fig. 7(a)], theelectron reflection R ( E ) steadily decreases with energy: R ( E ) = ( √ E + V − √ E ) / ( √ E + V + √ E ) . However,when the width of the surface layer (with a different po-tential V ) is increased up to several atomic units, the R ( E ) curve becomes non-monotonic, and at low ener-gies transmission resonances appear – R ( E ) minima thatcharacterize the surface layer. In the following, we willpresent an interpretation of the experimentally observedlow-energy structure in the I ( V ) curve for an oxidizedNi(111) surface as caused by a thin oxide layer. R ( E ) L = 5 a.u. (c) V = 0.10 Ry V = 0.20 Ry L V V (a) kinetic energy (eV) R ( E ) L = 9 a.u. (d) V = 0.10 Ry V = 0.20 Ry50% R ( E ) L = 2 a.u. (b) V = 0.02 Ry V = 0.20 Ry FIG. 7. (color online) (a) Modeling of the overlayer by atwo-step potential barrier. The constant bulk potential is V = 1 Ry. Effect of the surface layer potential V on theelectron reflection for the width of the surface layer L = 2 a.u.(b), 5 a.u (c), and 9 a.u. (d). nickeloxygen FIG. 8. (color online) NiO trial structures on a model Ni(111)substrate with the same Ni lattice as in NiO. From left to rightone, two, and three layers of NiO(111) on Ni(111) as well asa truncated-bulk NiO(111) crystal are shown. experimental kinetic energy (eV) R ( E ) ( % ) experiment3 NiO layers2 NiO layers
10 20 30 40theoretical kinetic energy (eV)
FIG. 9. (color online) Measured R ( E ) normal incidencespectrum of O/Ni(111) (circles) and calculations for three(dashed) and two (solid line) surface layers of oxygen on amodel Ni(111) substrate with the same Ni lattice as in NiO.Theoretical curves are the ratio of the specularly reflectedcurrent to the incident current. They are shifted by 1.7 eV tohigher energies to bring the main structures in agreement withtheir measured locations. The experiment is the arbitrarilyscaled I ( V ) curve. The inset compares theoretical results forone, two, three layers of NiO, and for a NiO(111) crystal. Because the formation of more than one NiO layer inthe Ni(111) lattice is improbable, we now consider themore realistic situation where the oxidized surface lay-ers have the structure of bulk NiO (see Fig. 8). In viewof the large lattice mismatch between the Ni substrateand the surface NiO layers, to construct a fully realis-tic model of the oxidized surface is beyond our compu-tational capabilities. However, we can make use of theobservation that in the 15 eV wide energy region abovethe surface barrier, Ni(111) has a free-electron-like bandstructure. Hence, we can model the underlying crystal byan expanded lattice of Ni, with the same lattice constantas NiO. Because the expanded Ni(111) crystal too has afree-electron-like conduction band below E − E F = 18 eV,this model appears quite plausible at low energies andcapable of providing a qualitative understanding of theeffect of the Ni substrate. We have performed calculations of R ( E ) for one, twoand three NiO layers on the model Ni substrate, as wellas for bulk NiO(111) (cf. Fig. 8), which are shown in theinset of Fig. 9: apart from the region of very low kineticenergies, the gross features of the R ( E ) curve are de-termined by the outermost NiO layers: the raise of thereflectivity below 12 eV is caused by the NiO overlayer,and the reflection from the Ni-NiO interface brings aboutonly relatively weak wiggles. However, for the few-layerthin surface oxides, in contrast to bulk NiO, in approach-ing the vacuum level the reflectivity rapidly falls down toproduce a very sharp minimum, in agreement with ourmeasurements, where it is found at about 2.7 eV abovethe vacuum level. This dip is a signature of the con-ducting substrate: the bulk energy spectrum of NiO hasa wide gap in this region, so the reflection by the bulk NiO crystal is complete, see the upper curve in the in-set of Fig. 9 (inelastic scattering is negligible at such lowenergies). The most interesting observation is that thepresence of the conducting substrate does not lead to auniform reduction of the reflectivity over the entire NiOband gap, but it leads to a sharp structure at a low kineticenergy. This minimum becomes deeper with decreasedthickness of the NiO film, which resembles the transmis-sion resonances of the simple two-step model (Fig. 7).The calculated specular reflectivity spectrum for twoNiO layers agrees rather well with the measurements re-garding the overall shape, as well as the relative energylocations of main spectral structures: the discrepanciesare within the expected error range due to possible errorsin the quasiparticle self-energy. The structures in the cal-culated spectrum are much sharper than in the measuredcurve, which may be attributed to the imperfect qualityof the surface as well as to a finite angular and energy res-olution of the experiment. Additional discrepancies mayalso arise from the nanoscale heterogeneity of the system(cf. Sec. III B), which experimentally may lead to partialaveraging over surface areas containing regions with onlya single NiO layer.
VII. CONCLUSION
We have studied the oxidation of the Ni(111) surfacein a concerted experimental and theoretical approach us-ing in-situ low-energy electron microscopy and ab ini-tio scattering theory. Upon exposure to molecular oxy-gen under ultrahigh-vacuum conditions, we observed thegradual formation of ultrathin NiO(111) nuclei, which,at room temperature, form a quasi-continuous film. Theresulting surface oxide exhibits a characteristic energy-dependent reflectivity R ( E ), which has been shown toprovide detailed information on its electronic and geo-metric structure.For oxidation at room temperature, our results are ba-sically in line with previous publications by other groupsreporting the formation of ultrathin surface oxides ex-hibiting thicknesses of two to three NiO layers. At0elevated temperatures of 750 K, we have identified thegrowth of NiO(111)-like patches, contrary to previousstudies that have not suggested the growth of a locallywell-defined surface oxide under these conditions. How-ever, in the present article we have also demonstratedthat the evolving oxide “film” is highly heterogeneouswith unreacted, essentially oxygen-free Ni(111) areas in-between. An intriguing result of the paper is that a (1x1)periodicity is found for oxidation at high temperaturewhere hydroxyl species should not be stable. Since weknow from LEED investigations that the grain size isconsiderably larger for oxidation at 700-750 K instead of300 K, we conclude that neither a very small grain sizenor termination by hydroxyls are necessary conditions forthe stabilization of the unreconstructed (1 ×
1) structure.While the (1 ×
1) structure found at 300 K might still beinduced by hydroxyls, this is not possible for oxidationat 750 K, leading us to the conclusion that its stabilityshould rather be related to the finding of (i) an oxide sur-face unit cell that is rotated by 30 ◦ as compared to theNi(111) substrate, providing a changed interface to theunderlying Ni and (ii) the ultrathin nature of the oxidefilm.Strong support for our findings is provided from thepresent ab initio scattering theory, which explains theobserved normal incidence LEED spectra at very low en-ergies of both the clean and the oxidized Ni(111) surface.In the latter case, the increase of the reflectivity in go-ing to lower energies is caused by a forbidden energy gapin the spectrum of the bulk NiO crystal along Γ L . Therapid decrease of R ( E ) at still lower energies appearsonly for a sufficiently thin NiO layer. Here, the charac-teristic feature is that the electron transmission throughthe oxide film does not increase uniformly over the gapwith decreasing thickness of the oxide layer. Instead, anarrow transmission channel opens at the bottom of the gap, and it disappears again at the thickness of a singleatomic NiO layer. These results indicate that in the ex-periment the oxide layer thickness is mostly two atomiclayers, and that it can hardly be larger than three atomiclayers.In essence, our experimental and theoretical findingssupport the formation of an ordered, ultrathin nickeloxide layer whose thickness is limited to less than onenanometer even at very high temperatures, while, in ac-cordance with ellipsometry data, additional oxygen israndomly incorporated into the near-surface region uponprolonged oxygen exposure. This result implies that inthe case of epitaxial oxide growth the general predictionby Cabrera and Mott may only hold for certain crys-tallographic orientations of the oxide film or the oxygenconcentration profile in general, but does not necessarilyallow conclusions on the actual thickness of the orderedoxide film. ACKNOWLEDGMENTS
The authors would like to thank Jurek Sadowski, PercyZahl, Peter Sutter (Center for Functional Nanomateri-als, BNL) and Gary Nintzel (NSLS, BNL) for techni-cal support. Stimulating discussions with Sanjaya D.Senanayake (BNL) are acknowledged. The authors alsothank Faisal M. Alamgir (Georgia Institute of Technol-ogy) for providing the Ni(111) crystal. Research carriedout in part at the National Synchrotron Light Source andthe Center for Functional Nanomaterials, BrookhavenNational Laboratory, which are supported by the U. S.Department of Energy, Office of Basic Energy Sciences,under Contract No. DE-AC02-98CH10886. The authorsacknowledge partial support from the Spanish Ministeriode Ciencia e Innovaci´on (Grant No. FIS2010-19609-C02-02). ∗ fl[email protected] † eugene [email protected] K. Reuter, “Nanocatalysis,” (Springer, Berlin, Heidelberg,New York, 2007) Chap. Nanometer and SubnanometerThin Oxide Films at Surfaces of Late Transition Metals,pp. 343–376, 1st ed. H. H. Kung,
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