We present first-principles studies of the adsorption of Sb and Ag on clean
and Sb-covered Ag (111). For Sb, the {\it substitutional} adsorption site is
found to be greatly favored with respect to on-surface fcc sites and to
subsurface sites, so that a segregating surface alloy layer is formed. Adsorbed
silver adatoms are more strongly bound on clean Ag(111) than on Sb-covered Ag.
We propose that the experimentally reported surfactant effect of Sb is due to
Sb adsorbates reducing the Ag adatom mobility. This gives rise to a high
density of Ag islands which coalesce into regular layers.Comment: RevTeX 3.0, 11 pages, 0 figures] 13 July 199

A. Schmalz

C. W. Snyder

D. J. Eaglesham

D. Kuiper

H. M. van Pinxteren

J. Neugebauer

M. Bott

M. Hondros

M. Jenko

M. Methfessel

Matthias Scheffler

N. Grandjean

P. Villars

R. Dreizler

Sabrina Oppo

V. Fiorentini

Vincenzo Fiorentini

W. F. Egelhoff

English

arXiv

We present first-principles studies of the adsorption of Sb and Ag on clean and Sb-covered Ag(111). For Sb, the substitutional adsorption site is found to be greatly favored with respect to on-surface fcc sites and to subsurface sites, so that a segregating surface alloy layer is formed. Adsorbed silver adatoms are more strongly bound on clean Ag(111) than on Sb-covered Ag. We propose that the experimentally reported surfactant effect of Sb is due to Sb adsorbates reducing the Ag adatom mobility. This gives rise to a high density of Ag islands which coalesce into regular layers

OPPO S

SCHEFFLER M.

FIORENTINI, VINCENZO

Archivio istituzionale della ricerca - Università di Cagliari

THEORY OF ADSORPTION AND SURFACTANT EFFECT OF SB ON AG(111)

Oppo, S.

Fiorentini, V.

Scheffler, M.

MPG.PuRe

Theory of adsorption and surfactant effect of Sb on Ag(111)

Crossref

arXiv:cond-mat/9307024v1  13 Jul 1993Theory of adsorption and surfactant effect of Sb on Ag (111)Sabrina Oppo,∗ Vincenzo Fiorentini,∗ and Matthias SchefflerFritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany(Submitted to Physical Review Letters on 13 July 1993)AbstractWe present first-principles studies of the adsorption of Sb and Ag on cleanand Sb-covered Ag (111). For Sb, the substitutional adsorption site is foundto be greatly favored with respect to on-surface fcc sites and to subsurfacesites, so that a segregating surface alloy layer is formed. Adsorbed silveradatoms are more strongly bound on clean Ag(111) than on Sb-covered Ag.We propose that the experimentally reported surfactant effect of Sb is dueto Sb adsorbates reducing the Ag adatom mobility. This gives rise to a highdensity of Ag islands which coalesce into regular layers.PACS numbers : 68.35.-p, 68.35.Bs, 68.35.MdTypeset using REVTEX1The goal of epitaxial crystal growth is to achieve atomically-flat and defect-free surfaces ofspecified crystallographic orientation, under the widest possible range of growth conditions.Significant efforts are devoted since many years to the growth of semiconductors. Theepitaxial growth of metals on metal substrates has also attracted considerable interest (seefor example Ref. [1] and references therein).Layer-by-layer, or two-dimensional (2D), growth is such that the epitaxial layer beingcurrently deposited is completed before further layers begin to grow on top of it; this modeis also named Frank-van der Merwe. In the three-dimensional (3D) or cluster growth, manyoverlayers grow at the same time, none of them being completed, so that the surface ex-hibits 3D islands. For heteroepitaxy, depending on whether the 3D mode manifests itselfimmediately or only after the formation of a few 2D overlayers, the 3D growth is namedeither after Volmer and Weber, or Stransky and Krastanov.With a view at extending the external conditions for the growth of high-quality 2Dsurfaces towards lower temperatures and higher deposition rates, use has been made recentlyof surface contaminants which purportedly act as surfactants. Although by definition [2] asurfactant should reduce the surface formation energy [3], there is at present no consensusas to the actual mechanisms of surfactant action, e.g. as to whether the contaminant affectsthe surface energy or the kinetics of growth [4]; the term surfactant is thus often used in thebroader sense that it promotes 2D growth as opposed to 3D growth.The surfactant technique, although still in its infancy, has been by now rather widelyapplied [3,4] in the field of semiconductors to help regular growth of heteroepitaxial strainedlayers. On the other hand, we are only aware of one report of surfactant-assisted growth ofmetals [5]. This is concerned with the homoepitaxy of the (111) surface of Ag. The growthmode was found to be drastically altered, from 3D to layer-by-layer 2D, by the one-timedeposition of Sb at the beginning of the growth process, at coverages Θ between 0.05 and0.2. Clean Ag (111) was observed to grow in a 3D fashion between 250 and 400 K, assignaled by the exponential decrease of the reflected x-ray beam intensity which monitorsthe degree of coherence of the upper layers of the sample [5]. A crossover to step-flow2growth (corresponding to constant reflected intensity) was observed above 450-500 K. Inthe presence of Sb, an oscillatory behaviour of the reflected intensity was observed instead,which is a fingerprint of 2D growth. The layer-by-layer growth of Sb-precovered Ag (111)continues for a rather long time (typically equivalent to the growth of 25 monolayers ormore), at a nominal Ag deposition rate of 0.02 monolayer per second, even at 280-300 K.The actual growth mode of an ideal clean Ag surface is still unclear. Indeed, Ag would beexpected to grow layer-by-layer even at rather low temperatures; 3D cluster growth mightbe initiated e.g. by nucleation at surface defects. This notwithstanding, Sb unambiguouslypromotes the 2D growth of Ag, and it is therefore important to investigate the pertainingmechanism. With this aim, we have performed ab initio studies of the energetics of Sband Ag adsorption on Ag (111). The calculations presented in this Letter are performedat Sb coverages down to Θ = 1/4. Among the considered adsorption geometries, the moststable one is the substitutional site, Sb being bound into a Ag surface vacancy. This site isconsiderably more favourable than the conventional on-surface fcc sites, and than subsurfacesites. Thus, an Sb-Ag alloy layer forms in the surface layer. Dissolution of adsorbed Sb intobulk Ag is energetically disfavoured. When covered with Ag, the substitutional surface alloyreforms as the topmost surface layer by segregation of Sb. Due to the need of formingsurface vacancies, the formation of the substitutional surface alloy needs thermal activation;we predict that at the relevant temperature, at low enough coverages, disordering of thesurface alloy should take place.Calculations for Ag adsorbed on clean and substitutional Sb-covered Ag (111) give in-formations on the growth mode of Ag. The main result is that Ag is more bound on cleanportions of the surface, while the vicinity of substitutional Sb centers is less favorable. Thisimplies that the average barrier for Ag diffusion is increased, thus Sb reduces the surfacemobility of Ag. This causes a high Ag island density, which reduces the probability of 3Dgrowth. The segregation of Sb to the surface layer allows the process to continue.The calculations were performed within density-functional theory [6] in the local densityapproximation (LDA), using the all-electron full-potential linear muffin-tin orbitals (LMTO)3method [7]. We used a non-relativistic code, which gives a very good description of Ag (bulkequilibrium properties: ath0 = 7.73 bohr, Bth = 1.10 Mbar, zero-point energy not included,to be compared with the low-temperature experimental values aexp0 = 7.74 bohr, Bexp = 1.01Mbar) and Sb, which is only slightly heavier. The (111) surface of fcc Ag, clean or with Sbcoverages of Θ=1, Θ=1/3, and Θ=1/4 (whereby the 1×1, (√3×√3) R30◦, and 2×2 cellswere used respectively), was simulated by slabs of thickness ranging from 5 to 13 atomiclayers, separated by 10 layers of vacuum. The supercells contained a number of atomsranging from 7 to 30. The k-summation was done on a uniform mesh in the irreducible partof the surface Brillouin zone, encompassing 19 points for the 1×1 cell, 7 and 13 points forthe clean and adsorbate-covered√3 ×√3 cell, 5 and 9 points for the clean and adsorbate-covered 2×2 cell. The vertical position of the adsorbates was optimized. Substrate relaxationis neglected, but is expected to change the adsorption energies only marginally. Full detailsof this study will be presented elsewhere [8].The binding energy for Sb on-surface fcc adsorption isEfccad = −(12ESb/Ag(111) −12EAg(111) − ESbatom)with ESb/Ag(111), EAg(111), and ESbatom being the total energies of the adsorbate-covered slab,of the clean Ag slab, and of the spin-polarized Sb free atom; the factor 1/2 accounts forthe facts that we adsorb on both slab sides. In the case of substitutional Sb adsorption, aslightly different definition applies:Esubad = −[(12ESb/Ag(111)sub + EAgbulk) − (12EAg(111) − ESbatom)]where EAgbulk is the bulk total energy per atom of fcc Ag. The substitutional process impliesin fact that a surface vacancy be created, and the kicked-out Ag atom migrates to a kinksite at a surface step, thus gaining the cohesive energy [9]. While the formation of a surfacevacancy costs energy, the subsequent binding of the adsorbate into the vacancy leads to a netenergy gain. While at Θ=1 we only have on-surface adsorption, substitutional adsorptionwith Sb adatoms being not nearest neighbours is possible for all Θ ≤1/3 (we did not considerthe coverage 0.3< Θ <1).4The calculated adsorption energies for the substitutional, fcc on-surface, and sublayeradsorption are given in Table I for all coverages studied. As seen from the Table, thesubstitutional site is greatly favoured with respect to “normal” on-surface fcc adsorption,and also against sublayer adsorption. Sb is thus expected to be adsorbed in substitutionalsites [10].An obstacle to the establishment of a substitutional adsorbate superstructure is theenergy barrier which may exist for vacancy formation. To estimate the barrier, we calculatedthe formation energy of a distant Frenkel pair [9], consisting of an isolated Ag adatom onAg (111) plus a vacancy. The results are summarized in Table II. The resulting maximumbarrier of about 1.5 eV corresponds to an activation temperature of about 500 K. At thattemperature the surface mobility of Ag atoms on Ag (111) is very high, so that migrationof the atom released from the vacancy to a kink site is easily achieved. We note that, ifdissipated locally, the adsorption energy of Sb in the fcc site would be more than enough tocreate a surface vacancy.As a check as to whether Sb might be incorporated into the bulk of Ag, we calculatedthe adsorption energy for Sb in a sublayer site, i.e. below one overlayer of Ag. As seen fromTable I, this site is strongly disfavored with respect to Sb sitting in a substitutional site inthe surface layer. For Sb below two Ag overlayers, the adsorption energy decreases further.We conclude that Sb segregates to the surface and is not incorporated into Ag. Indeed,the segregation of Sb (and the ensuing reduction of surface energy) in transition and noblemetals and alloys has been known for some time in metallurgy [11]. In the present case,segregation is essentially due to the size difference of Ag and Sb, as has been checked byadditional calculations at a 5% increased lattice constant. For Θ=1/3, this gives that thedifference of substitutional and sublayer adsorption energies drops from 1.1 eV/atom toabout 0.65 eV/atom. Sb is just about the right size to fit into a surface vacancy, but it issomewhat too large for a bulk vacancy. Since Sb is confined into the surface layer, an Sb-Agalloy layer will form at the (111) surface of Ag upon submonolayer Sb deposition. It is worthnoticing that the substitutional configuration on the fcc (111) surface has a first-neighbour5geometry very close to that of SbAg3, the only stable ordered Sb-Ag compound known,having a tetragonally-distorted fcc structure [12].The substitutional Sb adsorbate sits in the surface vacancy in a position very close to theideal fcc location of the substituted Ag atom, with an outward relaxation of only 5 to 8 %of the interlayer spacing, ie. about 0.25-0.35 Å. Due to the effective in-plane screening thusprovided by the surrounding substrate atoms, the substitutional Sb adatoms interact onlyweakly with each other; the adsorption energy for the substitutional site does not changemuch at low coverage if the local environment for substitutional Sb is conserved (see TableI). If we assume the Θ=1/4 adsorption energy to be the low coverage limit value, andthe coverage to be low enough, the entropic contribution to the free energy can overcomethe internal energy difference at relatively low temperatures. At a coverage of Θ ≃0.1,the annealing temperature (say, 600 K) is sufficient to cause disordering with respect tothe√3×√3 arrangement. If the substitutional adsorption is activated by annealing, wetherefore expect that the substitutional surface alloy thus obtained will be disordered.To clarify the effects of Sb adsorption on the growth mode of Ag, we studied Ag adsorp-tion on clean and Sb-covered Ag (111). We used the 2×2 cell for these studies, both becauseneighboring adsorbates are reasonably decoupled from each other, and because Ag can beadsorbed on the substitutional Sb-covered surface either as a nearest neighbour to Sb, ornot. We call these two sites “near” and “far”. The adsorption energies are summarized inTable III. The main result is that Ag has a higher adsorption energy on clean Ag than atboth of the sites on Sb-covered Ag. Among the latter sites, the “near” site is marginallydisfavored, and it would be probably more so if Sb had been allowed to relax outwards (seeTable I).It is thus energetically preferrable for Ag to sit on clean portions of the surface, whilethe vicinity of substitutional Sb centers is unfavourable. This could be called long-range“site” blocking, as the interaction giving rise to it is apparently long-ranged. We put “site”in quotes because the adsorbate potential energy is expected to change gradually as theadsorbate approaches the Sb centers, so that the average diffusion barrier for Ag increases6already at some distance from, and not only at, the Sb centers. Diffusion barriers for Agon Ag (111) are smaller than 0.1 eV: near an Sb center, they increase significantly, namelyto about 0.4-0.5 eV. As a consequence, adsorbed Sb in the substitutional configurationreduces the surface mobility of Ag. The presence of substitutional Sb should therefore favorthe growth of small-sized Ag islands. If the island density is high, one expects that theycoalesce into a single layer before overgrowth on the islands can occur, as it is generallybelieved that small islands have lower energy barriers at descending steps. As deposited Agcovers the Ag:Sb surface alloy layer, Sb atoms find themselves in the disfavoured sublayerconfiguration, and will thus tend to segregate to the new surface layer. The alloy surfacelayer is thus reestablished, and the process can start again.Recent STM experiments [13] on this system have indeed shown that on annealed Sb-covered surfaces, Sb induces a high density of small Ag islands on the surface, and that itefficiently segregates upon deposition of Ag. Another observation is that upon annealing atabout 550 K, Sb is adsorbed substitutionally and, at very low coverages, it forms a disordered2D array, in agreement with our prediction. For the unannealed surface, the on-surface fccsite is occupied at room temperature; this agrees with our estimate of the activation ofsubstitutional adsorption. At very low coverage, Sb is observed to form islands. Our largestcalculated adsorption energy for on-surface adsorption is that of the 2×2 superstructure;we cannot exclude however that the adsorption energy may increase further in the extremelow-coverage limit, which is computationally very demanding and has not been addressedhere.In summary, we presented ab initio calculations of Sb and Ag adsorption on clean and Sb-covered Ag (111). For Sb, the substitutional adsorption site is energetically highly favouredwith respect to “normal” on-surface sites; in addition, subsurface positions are also stronglydisfavoured. Sb is thus effectively confined into the surface and forms a segregating surfacealloy. This alloy should disorder, at low coverages, for typical annealing temperatures. As toAg, we find it to be sizably more bound on clean Ag(111) than on substitutional Sb-coveredAg: this indicates that Sb produces a site blocking, or more precisely, a significant increase7of the diffusion barrier for Ag adatoms approaching the Sb centers. Based on these results,we offered an explanation of the recently observed Sb-induced layer-by-layer homoepitaxialgrowth of Ag (111): substitutionally-adsorbed Sb induces, by mobility reduction, a highdensity of small-sized Ag islands which coalesce into a regular 2D layer; as Ag covers thesurface, Sb segregates to the newly formed layer, thus reestablishing the alloy layer at thesurface, and the process starts again. Most of our results seem to be confirmed by recentSTM experiments [13].We thank R. Stumpf for helpful discussions, and J. Vrijmoet for communicating hisresults prior to publication. This work was partly supported by the Deutsche Forschungs-gemeinschaft within Sonderforschungsbereich 1421.8REFERENCES∗ Present address: Dipartimento di Scienze Fisiche, Università di Cagliari, via Ospedale72, I-09124 Cagliari, Italy.[1] F. J. A. den Broeder, D. Kuiper, A. P. van den Mosselaer, and W. Hoving, Phys. Rev.Lett. 60, 2769 (1988); W. F. Egelhoff and I. Jacob,ibid. 62, 921 (1989); M. Bott, T.Michely, and G. Comsa, Surf. Sci, 272, 161 (1992).[2] Oxford Dictionary of Physics (Oxford UP, Oxford 1988).[3] D. J. Eaglesham, F. C. Unterwald, and D. C. Jacobson, Phys. Rev. Lett. 70, 966 (1993),and references therein.[4] C. W. Snyder and B. G. Orr, Phys. Rev. Lett. 70, 1030 (1993); N. Grandjean and J.Massies, ibid., 1031, and references therein.[5] H. A. van der Vegt, H. M. van Pinxteren, M. Lohmeier, E. Vlieg, and J. M. C. Thornton,Phys. Rev. Lett. 68, 3335 (1992).[6] See e.g. R. Dreizler and E. Gross, Density functional theory, (Springer, Berlin, 1990).The exchange-correlation energy is by D. M. Ceperley and B. J. Alder, Phys. Rev. Lett.45, 566 (1980), as parametrized by S. Wosko, L. Wilk, and M. Nusair, Can. J. Phys.58, 1200 (1980).[7] M. Methfessel, Phys. Rev. B 38, 1537 (1988); M. Methfessel, C. O. Rodriguez, and O.K. Andersen, ibid. 40, 2009 (1989). For surface studies, see M. Methfessel, D. Hennig,and M. Scheffler, Phys. Rev. B 46, 4816 (1992).[8] S. Oppo, V. Fiorentini, and M. Scheffler, to be published.[9] J. Neugebauer and M. Scheffler, Phys. Rev 46, 16067 (1992); A. Schmalz, S. Aminpirooz,L. Becker, J. Haase, J. Neugebauer, M. Scheffler, D. R. Batchelor, D. L. Adams, and E.Bøgh, Phys. Rev. Lett. 67, 2163 (1991).9[10] The results may be reformulated in terms of surface energy reduction caused by adsorp-tion. This requires the definition of a chemical potential for the atoms to be adsorbed.Here we adopt the adsorption energy terminology.[11] See e.g. M. Jenko, F. Vodopivec, and B. Praček, Appl. Surf. Sci. 70/71, 118 (1993) andreferences therein; M. Hondros and A. Mc Lean, in Surface Phenomena of Metals, Soc.Chem. Ind. Monograph Nr. 28 (Soc. Chem. Ind., London 1969), p. 39.[12] P. Villars, K. Matthis, and F. Hulliger, in The structure of binary compounds, F. R. DeBoer and D. G. Pettifor eds., p.1 (Elsevier, Amsterdam, 1989).[13] J. Vrijmoeth, private communication.10TABLES√3 ×√3 2×2 1×1Esubad 4.49 4.37 —relaxation +5% +8% —Efccad 3.26 3.34 3.22relaxation –11% –5% +6%Esublayerad 3.41 3.45 2.71TABLE I. Adsorption energies (in eV/atom) of Sb on Ag (111) for the adsorption sites andcoverages studied here. Vertical adsorbate relaxations compared to ideal silver fcc position (inpercentage of interlayer spacing) are also given.√3 ×√3 2×2Evacf 0.69 0.66EFpf 1.46 1.43TABLE II. Vacancy and Frenkel pair formation energies (eV)clean far nearEAgads 2.41 2.02 1.99relaxation –9% –9% –5%TABLE III. Adsorption energy (eV/atom) and relaxation compared to the ideal Ag position(in percentage of ideal interlayer spacing) for Ag on clean and Sb-covered Ag (111). Clean: Ag onAg (111); far: Ag on Sb:Ag(111), “far” site; near: Ag on Sb:Ag(111), “near” site.11

Theory of Adsorption and Surfactant Effect of Sb on Ag (111)

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