Atomic structure of the Au(110)c(2 × 2)
–Sb system: A combined LEED and DFT study
D.D. dos Reis
a,⁎
, F.R. Negreiros
a, V.E. de Carvalho
a, E.A. Soares
a, C.M.C. de Castilho
b,ca
Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970 Belo Horizonte, MG, Brazil
b
Grupo de Física de Superfícies e Materiais, Instituto de Física, Universidade Federal da Bahia, Campus Universitário da Federação, 40210-340, Salvador, BA, Brazil
cInstituto Nacional de Ciência e Tecnologia em Energia e Ambiente-INCT-E&A, Universidade Federal da Bahia, Campus Universitário da Federação, 40170-280, 40210-340, Salvador, BA, Brazil
a b s t r a c t
a r t i c l e i n f o
Article history:
Received 15 September 2012 Accepted 24 November 2012 Available online 30 November 2012 Keywords: Gold(110) LEED DFT Au(110)–Sb Sb adsorption Metal surfaces Surface atomic structure
In this paper we present a combined low-energy electron diffraction (LEED) and a DFT study of the Au(110) c(2 × 2)–Sb surface in order to determine its atomic structure. The DFT calculations, using both LDA and GGA approaches, have indicated that the adsorption of antimony atoms on the Au(110) surface hollow sites is energetically more favored as compared with other possible adsorption sites. The LEED analysis also showed a Sb-overlayer termination with the Sb atoms segregating to the hollow sites instead of forming an Au–Sb surface alloy. This overlayer results to be contracted of about 0.16 Å with thefirst gold layer presenting a small expansion (0.04 Å) with respect to the Au bulk interlayers distance. The agreement between the LEED and DFT results is very good.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
The addition and incorporation of metal atoms on the top few sur-face layers of a different metal substrate, either by alloying or by thin film formation, has revealed as a very important procedure used in the development of materials with new and interesting physical and chemical properties. These materials are aimed for applications in a variety of differentfields such as catalysis, metallurgy, tribology, cor-rosion, design of semiconductors devices and nanotechnology[1,2]. The substrate surface structure, the electronic properties of the de-posited atoms and, thefinal composition, are the main points to be considered when investigating the properties of the metal-metal in-terface systems [3,4]. Historically, the interfaces involving noble metals were the first ones systematically studied. Still today, the most important systems in practical use are such that at least one of the chemical species involved are noble metal, such as platinum, gold, silver and palladium[5,9–11]. Therefore, due to the potentiality of these metal–metal mixing processes, there is a large number of published work on the subject, both experimental as well theoretical (see for example[6–8]). When the deposited atoms have a high mis-cibility with the substrate, an ordered alloy in thefirst layers can be formed. However, if the adsorbed atoms have a tendency to segregate onto the surface, aflat layer (epitaxial film) or else islands may be formed. Therefore, for each system, the atomic geometry of the resul-tant compound is mainly determined by the physical conditions of
the deposition process, so that thefilm growth modes are difficult to predict.
Although noble metals alloyed with other metals, in general may present some important properties, the alloys involving the so-called semi-metals (such as As, Sb and Te) are of substantial interest both for understanding the physics and chemistry involved in such interactions, but also for their promising technological applications. One interesting example is the behavior of antimony deposited on metal surfaces. One of the properties of antimony is that, when de-posited on metal surfaces, it behaves as a surfactant. It has also been observed that for many crystals, depending on the surface orienta-tion, the pre-adsorption of Sb atoms can induce an epitaxial growth of semiconductors on semiconductors[12–15]as well as for metal-on-metal growth[16–19]. When acting as a surfactant, Sb atoms appear to segregate to the surface with a strong tendency to get or-dered on top of the surface. At low Sb coverages, a surface alloy layer is observed and, at higher coverages, nanometer-sized alloy islands can then be formed. Different alloy structural phases have been observed for the low-index single crystal surfaces of many metals: Sb–Ag(111)[20,21], Sb–Ag(110)[23], Sb–Pd(111)[24], Sb– Cu(111)[25,27], Sb–Cu(100)[28,29], Sb–Ni(111)[30], Sb–Mo(110) [26], Sb–Au(100) [31], Sb–Au(111) [32,33], Sb–Cu(110) [34], and Sb–Au(110)[35,36]. Although the determination of the atomic geom-etry of the adsorbed Sb atoms is important to understand both the surfactant properties and the growth mechanism, only few phases have undergone a quantitative surface structure determination. The techniques used were surface X-ray diffraction (SXRD), scanning tunneling microscopy (STM), photo-electron diffraction (PD) and ⁎ Corresponding author. Tel.: +55 31 3409 5617.
E-mail address:ddreis@fisica.ufmg.br(D.D. dos Reis).
0039-6028/$– see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.susc.2012.11.010
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Surface Science
recently and is related to the observation, both experimentally and theoretically, that alloys of Sb-Ag(111) and Sb-Cu(111) exhibit a two-dimensional band structure with a strongly enhanced Rashba-type spin-splitting[37–41]. This spin-orbit splitting effect occurs in systems that present a structural inversion asymmetry and it is a promising characteristic for future applications where spins could be manipulated by an electricfield. These findings certainly have and will give motivation for the study of other Sb–metal surface alloys.
Among the several binary alloy systems already studied, the Sb-Au interface has been attracting some attention mainly because of the in-terest in designing and developing high-temperature solder alloys and, more recently, the growth of thinfilms and nanostructures. With gold Sb forms only one stable compound, namely, AuSb2. However, as a result of its low solubility (about 1%) in bulk Au, under adsorption on Au surfaces antimony is expected to form ordered phases. On the other hand Au surfaces, despite of (or due to) their chemical inertness, present several properties that make them widely used in many appli-cations, from catalysis to nanotechnology, such as self-assembled monolayers, selective functionalization, etc.[42–44]. When clean, all of the three low index Au surfaces show reconstruction, but it has been observed that these reconstructions can be lifted out under molec-ular or metal adsorption. In the latter, many induced reconstructions— other than the ones associated to clean surfaces— can be formed and, specifically with Sb, several surface phases has been observed for Au(001), Au(111) and Au(110) and some of these phases have had their surface structures examined[31–33,35,36]. In the case of Sb de-posited on the Au surfaces, a quantitative surface structural determina-tion has been performed only for the c(2 × 2) phase of Au(110)–Sb. Lyman and co-workers[35], using surface x-ray diffraction (SXRD), de-termined the structure of this phase and concluded that the surface is formed by 1/2 ML Sb and 1/2 ML Au in a centered 2 × 2 geometry, with the Sb atoms occupying substitutional sites of the last layer of the Au(110) substrate. In this paper, it is presented a LEED quantitative surface structural determination of the Au(110)c(2× 2)–Sb phase to-gether with the results of a DFT calculation. Our results show that the Sb atoms occupy the hollow sites on the Au(110) substrate instead of the substitutional ones, as previously observed in the x-ray diffraction analysis.
2. Experiment
The experiments were performed at the Surface Physics Laboratory (Physics Department, UFMG, Brazil) using a standard ultra high vacuum chamber equipped with a range of facilities for sample preparation (cleaning, heating and cooling) and surface characterization by Auger Electron Spectroscopy (AES), as well as a computer controlled LEED dif-fractometer. The chamber base pressure was typically 2 × 10−10Torr. The gold crystal was supplied by the Monocrystals Company (USA) with 99.99+% purity, presenting a mirrorlike (110) surface oriented within ±0.5°. The crystal was then cleaned in situ by several cycles of sputtering and annealing. The best results were obtained by alternating cycles of 0.5 keV Ar+ions sputtering at room temperature and subse-quent annealing at 693 K for half an hour, followed by a 0.5 keV Ar+ ions sputtering at 673 K and annealing again at 693 K for 15 min. After each annealing cycle the sample was cooled down to room tem-perature at a maximum rate of−8 K/min. The temperature was moni-tored using a chromel–alumel thermocouple in contact with the sample surface. Cycles of sputtering and annealing were repeated until a sharp
Quantitative LEED measurements of the diffracted beam intensi-ties were recorded for the 40 to 600 eV energy range, with the sample at 215 K (the reduced temperature being used to lower the vibration-al amplitudes), using a computer-interfaced Omicron video-LEED system at off-normal geometry (θ=2.0oeφ=73.4o). The intensity versus energy curves (I(V) curves) were collected for 21 diffracted beams (15 integer and 6 fractional order beams), normalized with respect to the incident-beam current and smoothed out using a three points Savitzky-Golay algorithm[45]. The total cumulative ener-gy range used was 4590 eV. An off-normal incidence geometry was chosen in order to increase the number of non-equivalent beams. The incidence angle was determined using the method developed by Cunningham and Weinberg, as described by Van Hove et al.[46]. 3. Theoretical calculation of theI(V) curves
A standard LEED structural determination approach for the theoret-ical calculation of the I(V) curves was adopted. The potential and the phase shifts for the gold and antimony atoms were calculated with the Barbieri/Van Hove Phase Shift code [47] using the muffin-tin model. The atomic orbitals were obtained by a self-consistent calcula-tion within the Dirac-Fock approach. Matteiss' prescripcalcula-tion was adopted in the calculation of the muffin-tin potential and a set of 13 rel-ativistic phase shifts (Lmax = 12) was evaluated by numerical integra-tion of the Dirac equaintegra-tion. Different sets of relativistic phase shifts were calculated for antimony and for each gold atom depending on its layer position: second layer, third tofifth layers and gold bulk.
The set of nonstructural parameters that were used in the calcula-tions includes: the gold bulk Debye temperature of 211 K[48], sample temperature of 178 K, off-normal incidence of the primary electron beam (θ=2.0° e φ=73.4°). For the real and imaginary parts of the optical potential, the values of V0= 10.0 eV and V0i= -5.0 eV were adopted as typical values. The full dynamic LEED calculations were car-ried out by using the LEEDFIT[49]computer code. Six different and symmetrically acceptable structural models werefirstly investigated for the Au(110)c(2× 2)–Sb system, with the Sb atoms occupying different adsorption sites: on top (Model A), long-bridge (Model B), short-bridge (Model C), hollow site (Model D) and substitutional sites in thefirst (Model E) and second (Model F) layers. These models are schematically presented inFig. 2.
For each model described above, the theoretical I(V) curves were calculated and compared with the experimental data. The agreement of the experimental I(V) curves with the theoretical ones was quanti-fied by using the Pendry R-factor[50]. After the calculation of the R-factors for all six models, without allowing any kind of relaxation, a set of optimization procedures was performed for each model in order to achieve a better R-factor value.
Next, the Debye temperatures of the bulk and thefirst three atomic layers were optimized for the two best models determined in the previ-ous step (models D and E) using a grid search procedure. As afinal re-finement, a new set of phase shifts was calculated using the optimized structural atomic positions obtained in the last step and afinal search was then performed.
4. The DFT calculations
First-principles DFT calculations were performed with the plane-wave-based Quantum Espresso package[56]. The Kohn-Sham equations
were solved with four different pseudo-potentials (PP) using ultra-soft potentials generated with a scalar relativistic correction[57]and a fully relativistic calculation [58]. The Brillouin-zone integration was performed using a Monkhorst-Pack k point sampling, with a 16× 6 × 2 k-point mesh for the Au(110)c(2 × 2)–Sb surface and with a 24×24× 24 k-point mesh for bulk calculations. For the determination of the en-ergy of an isolated atom a singleΓ -point was used. For all calculations the chosen energy cutoff for the wave functions and for the charge den-sity was equal to 550 eV and 5500 eV, respectively, and the threshold for self-consistency used was 7 × 10−6eV.
The Au(110)c(2× 2)–Sb surface was reproduced using a symmetric slab of 17 layers with a total of 32 atoms in the unit cell. The vacuum region separating neighbor slabs was of 10 Å before relaxation. The middle layer was keptfixed during the geometry relaxation and the po-sitions of all the other atoms were optimized without any constraint until two conditions were simultaneously satisfied: the forces on each atom were less than 0.03 eV/Å and the energy difference of consecutive steps were less than 0.01 eV.
For estimation of the errors in the calculated parameters, we based on our previous work on the structure of the missing-row reconstructed Au(110) surface[48]. In that work it was observed that the predicted equilibrium bulk properties of Au deviate significantly (up to ±2% for the lattice parameter and ±2% for the cohesive energy and the bulk modulus) from the experimental value. Therefore, the LDA (GGA) functionals underestimate (overestimate) the experimental Au lattice
parameter. So, in order to compare the prediction of different PP's, all interlayer distances were evaluated in percentage of the PP's predicted Au bulk lattice parameter. Then, an average of the obtained values was done and an error bar was estimated taking the maximum deviation from the average.
5. Results and discussion
Firstly, in order to have a clue about the most probable model for the structure, a number of six models compatible with the observed LEED pattern symmetry was chosen, and LEED calculations were performed for each one. The obtained results are presented in thefirst (RP) column ofTable 1. In thesefirst calculations no atom relaxation was allowed (a bulk terminated structure was used) and the Debye temperatures of Sb and Au atoms were keptfixed at ΘSb= 200K andΘAu= 211K
[48,51]respectively. As can be seen fromTable 1, the Top, the Long and Short Bridge Site models present r-factors around 0.80 while the model involving Sb atoms in the second layer (Substitutional-2alayer model) is clearly the less suitable, presenting an extremely high r-factor value (RP= 0.91). The latter indicates that Sb atoms prefer to segregate to the surface instead of forming a bulk-like alloy. This is con-sistent with the observed low solubility of Sb in Au (≤1,2%)[52,53]. On the other hand, the lowest r-factor values were obtained for the Substitutional-1st layer and the Hollow Site models. As a result of this, these two models were more deeply investigated. A complete Fig. 1. LEED patterns for: (A) Au(110)(1 × 2) missing row at 130 eV; (B) Au(110)c(2 × 2)–Sb phase, at a Sb coverage of 0.5 ML and energy of 85 eV.
optimization was then performed for both models, allowing the posi-tions, normal to the surface, of the sixfirst layers atoms to be varied. The results of this search are presented in the second (Rp) column of
Table 1, where it is possible to see that model E presents an r-factor about 50 % higher than the model D. This appears to indicate that the hollow sites are preferred by the Sb atoms and thus creating an overlayer on the Au substrate instead of a substitutional surface alloy. The models were further improved by searching for an optimized Debye tempera-ture for the Sb layer and for the four next Au layers— keeping the fifth, sixth and bulk Au values fixed- and also for the optical potential. In this step a standard grid procedure was adopted. The results are presented in the RP(Final) column ofTable 1. Again, it can be seen that the D model (hollow site) presents a much lower r-factor than model E (substitutional).
Esubs ¼
ESbAu110−EAu110−nSbESbisoþ nSbEAubulk
nsb
where nSbis the number of Sb atoms in the unit cell, ESbAu110is the en-ergy of the reconstructed surface, EAn110is the energy of a bulk termi-nated Au110 surface, ESb-isois the energy of an isolated Sb atom and EAu−bulk is the energy of the bulk Au atoms. As it is presented in
Table 2, both LDA and GGA approaches show results that indicate the hollow sites as being the more energetically favorable (0.12 eV and 0.16 eV lower for the LDA and GGA respectively) with respect to the substitutional.
InTable 3are shown the ab initio theoretical (DFT) and the exper-imental (LEED) structural parametersfinal results obtained in this work together with those from SXRD[35]analysis for the Au(110) c(2 × 2)–Sb surface.
The results presented inTable 3lead to some immediate conclusions. Firstly, it is possible to see that there is a very good agreement between the LEED and DFT results for thefirst layer relaxation (contraction) and thefirst interlayer distance. Also, both results indicate the existence of either an expansion of the second layer— although the DFT shows a larger value for this expansion— and rumples in the 3rd and 5th layers. This is in qualitative agreement with what was found for the Au(110)(1 × 2) clean surface[48]but some significant differences on the parameters magnitudes can be observed. Hence, the presence of Sb atoms, besides lifting the missing row reconstruction, promotes some important changes in the values of the structural parameters. For example, thefirst layer relaxation and the third layer rumple are significantly reduced from −0.29 Å and 0.30 Å for the reconstructed surface to−0.16 Å and 0.19 Å for the surface with antimony, respec-tively. On other hand, the expansion of the second layer presents a small increasing (from 0.01 Å to 0.04 Å for the LEED results and from
D Hollow Site 0.62 0.42 0.30 ± 0.03 E Substitutional— 1st layer 0.67 0.59 0.46 ± 0.04 F Substitutional— 2nd layer 0.91 – –
X-ray model[35] Substitutional – – Rp = 0.82
Table 2
Adsorption energy of the Sb atoms for the two most probable models for the structure of Au(110)c(2 × 2)–Sb obtained by first principles calculations using the LDA and also the GGA approaches.
Model Adsorption energy (eV)
LDA GGA
Hollow −3.40 −4.51
Substitutional −3.28 −4.35
Table 3
Experimental and theoretical structural parameters for the Au(110)c(2 × 2)–Sb surface (defined inFig. 3) obtained from this work and those found on the literature.δZ values are the atoms displacements from the bulk positions and dijare the layers distances. Due to the occurrence of rumples, the relaxationΔdijwere calculated considering the
displace-ments of the center of each layer with respect to the bulk interlayer distance (d = 1.4425 Å). The relaxation errors are the same as those of dijused to calculate theΔdij.ΘDis
the Debye temperature.
Experimental results Theoretical results
DisplacementδZ(Å) RelaxationΔdij(Å) Layer distance dij(Å) DisplacementδZ(Å) RelaxationΔdij(Å) Layers distance dij(Å)
Atomtype layer LEED LEED SXRD[35] LEED DFT DFT DFT
1—Sb 1 −0.09 Δd12=−0.16 −0.21±0.04 d12= 1.28 ± 0.03 −0.14 Δd12=−0.18 d12= 1.27 ± 0.04 2—Au 2 +0.07 +0.04 3—Au 2 +0.07 Δd23= +0.04 −0.12±0.03 d23= 1.48 ± 0.03 +0.04 Δd23= +0.08 d23= 1.50 ± 0.01 4—Au 3 −0.07 −0.06 5—Au 3 +0.12 Δd34= +0.01 +0.13 ± 0.03 d34= 1.45 ± 0.03 +0.02 Δd34=−0.02 d34= 1.44 ± 0.01 6—Au 4 +0.02 −0.02 7—Au 4 +0.02 Δd45= +0.04 d45= 1.48 ± 0.04 −0.02 Δd45= 0 d45= 1.43 ± 0.01 8—Au 5 −0.06 −0.03 9—Au 5 +0.02 Δd56= 0 d56= 1.41 ± 0.05 +0.01 Δd56= 0 d56= 1.45 ± 0.01 10—Au 6 +0.01 −0.02 11—Au 6 +0.01 Δd6b= +0.01 d6b= 1.45 ± 0.06 −0.02 Δd6b=−0.02 d6b= 1.42 ± 0.01 Rumple 3 0.19 Å – – – 0.08 Å – – Rumple 5 0.08 Å – – – 0.04 Å – – ΘD(K) 1 180 – – – – – – ΘD(K) 2 120 – – – – – – ΘD(K) 3–5 190 – – – – – – ΘD(K) 6 211 – – – – – – V0(eV) – 4.06 ± 0.05 – – – – – – RP – 0.30 ± 0.03 – – – – – –
0 to 0.08 Å for the DFT calculations). However, the comparison with the SXRD results shows significant discrepancies. By considering only the layer relaxations, Lyman and co-workers[35]found afirst layer con-traction of 0.21 Å what is not so different from the values found from the LEED and DFT analysis, but the same agreement is not observed for the relaxations of the second and third layers. They found a large second layer contraction (0.12 Å) and a large expansion of the 3rd layer (0.13 Å) whereas the LEED and DFT results show a small expan-sion for the 2nd layer and a small contraction for the 3rd layer. But the most significant difference, between the results from the present work and those from XSRD, is related to the surface geometry itself. The SXRD analysis concluded that the Sb atoms adsorb on Au(110) sur-face occupying substitutional sites and therefore forming an Au–Sb alloy. This geometry are not supported neither by LEED and DFT analy-sis. The DFT calculations using both LDA and GGA pseudo-potentials in-dicate that the hollow sites on the Au(110) surface are energetically favored what corroborates the structure obtained by the LEED analysis. As the difference between the calculated energies for the hollow and substitutional sites is small (0.12 eV from LDA and 0.16 eV from GGA), it may be argued that the occurrence of one or other adsorption geometry can depend on the surface preparation process. However, we have analyzed two other LEED data sets collected under indepen-dent surface preparations and both have also indicated a Sb hollow site overlayer termination. An additional support for the results presented in this work can be obtained by considering the published values of the Au lattice constant and the atomic radius of gold and an-timony in the bulk position[59,60]. Thus, taking into account the Au lattice constant as being 4.08 Å and the value of thefirst interlayer distance of 1.28 Å obtained from the LEED analysis, the Au–Sb bond length can be calculated as being (2.81 ± 0.01) Å. This value is consis-tent with the values of gold and antimony atomic radius, in the bulk position, of rAu= 1.35 Å and rSb= 1.45 Å, what leads to a bond length of 2.80 Å and which is in good agreement with the value obtained
from the LEED analysis. Also, the second layer (gold) atoms bonds in-crease about 1% (from 2.88 Å to 2.90 Å).
It is worth to point out that besides the fact that the results from the present work do not agree with the previous SXRD results, they also do not agree with those from experimental (LEED analysis) and theoretical (DFT calculations) of the related systems Ag(110)c(2 × 2)–Sb[23,54] and Cu(110)c(2× 2)–Sb[34,55]. In these last works, it was found that the Sb atoms assume substitutional positions with respect to substrate metal atoms on the surface, resulting in a surface alloy of the type AgSb2and CuSb2respectively. Furthermore, the DFT calculations for both systems showed differences between the calculated energies for the hollow and substitutional sites of 0.23 eV for Ag(110)–Sb[54]and 0.10 eV for Cu(110)–Sb[55]but both favouring the substitutional site. The LEED analysis of the two systems also indicated the sustitutional sites as the most probable for the Sb atoms. We have found differences of energy of 0.12 eV (LDA) and 0.16 eV (GGA) but supporting the hol-low sites. Thus, these values can well discriminate between holhol-low and substitutional sites what gives more confidence to the LEED analy-sis results. Therefore, it may be argued that the hollow site geometry is a particular feature of the Au–Sb system. InFig. 4is presented a compar-ison between the experimental and calculated I(V) curves for the best (hollow) model obtained.
6. Conclusions
The atomic structure of the Au(110)c(2 × 2)–Sb surface phase was investigated using both the low energy electron diffraction (LEED) analysis and the density functional theory (DFT) calculations. The sur-face geometry, the interlayer distances and relaxations were deter-mined for all atomic layers as deeper as the 6th layer into the bulk. Both the experimental and theoretical results indicate that the Sb atoms adsorb to the hollow sites of the unreconstructed Au(110) sur-face. This shows that during the adsorption process the Sb atoms Fig. 3. Schematic representation of thefinal structure for the Au(110)c(2×2)–Sb surface as determined by LEED and DFT analysis. On the right is shown a side-view where the arrows indicate the direction of the atoms displacements; on the left is a top view of the structure. The atom displacements and layers distances are presented inTable 3. The values of b3and b5are the rumples in the 3rd and 5th layers respectively.
Acknowledgments
The authors would like to thank FAPEMIG, CAPES, and CNPq (Brazilian research agencies) forfinancial support.
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