Influence of surfactants on atomic diffusion

Surface Science 459 (2000) 135–148www.elsevier.nl/locate/susc

Influence of surfactants on atomic diffusion

J. Ferron a, L. Gomez b, J.M. Gallego c, J. Camarero d,1, J.E. Prieto d, V. Cros d,2,A.L. Vazquez de Parga d, J.J. de Miguel d,*, R. Miranda d

a Grupo de Fısica INTEC-FIQ, CONICET, Universidad Nacional del Litoral, 3000-Santa Fe, Argentinab Instituto de Fısica Rosario, Facultad de Ciencias Exactas, Ingenienıa y Agrimensura, 2000-Rosario, Argentina

c Instituto de Ciencia de Materiales (CSIC), Cantoblanco, 28049-Madrid, Spaind Departamento de Fısica de la Materia Condensada and Instituto de Ciencia de Materiales ’Nicolas Cabrera’,

Universidad Autonoma de Madrid, Cantoblanco, 28049-Madrid, Spain

Received 4 August 1999; accepted for publication 30 March 2000

Abstract

We have used Monte Carlo simulations with realistic interatomic potentials, combined with experimental resultsobtained by He diffraction (thermal energy atom scattering) and STM to investigate the effect of a surfactant agentsuch as Pb on the mechanisms of atomic diffusion involved in epitaxial metal growth. We find that the main role ofthe surfactant is to hinder fast diffusion by hopping over the surface, which is the dominant mechanism on a compactface such as Cu(111), and to promote exchange. As a side effect, this facilitates interlayer diffusion and hence layer-by-layer growth, because islands are smaller and have rougher borders; adatoms reaching an edge have moreopportunities to cross them by exchange with a step atom. © 2000 Elsevier Science B.V. All rights reserved.

Keywords: Atomistic dynamics; Copper; Growth; Lead; Metal–metal interfaces; Monte Carlo simulations; Surface diffusion

1. Introduction strate: this allows us to obtain phases that are notfound in the bulk. The main problem that the

In recent years, research in materials science experimentalist has to face is how to control thehas focused on growing and analysing artificial morphology of the growing film. The latter’s struc-materials. This move has been driven by the new, tural perfection depends on the ability of thesesometimes surprising physical properties found in atoms to reach the appropriate sites within thethese systems. In general, these novel materials are crystal lattice, which in turn is influenced by veryobtained by depositing the different components fine details of the different diffusion processeson the substrate surface, which must have been involved. Therefore, a good knowledge of surfacethoroughly cleaned and prepared prior to that. diffusion is a prerequisite for the production ofThe newly arrived atoms accommodate at sites artificial materials and heterostructures.determined by the crystalline structure of the sub- Investigations of diffusion at the atomic level

are complicated because individual processes are* Corresponding author. Fax: +34-91-397-3961. difficult to observe directly. For this reason, earlierE-mail address: [email protected] (J.J. de Miguel ) research was carried out by indirect methods [1].1 Present address: Laboratoire Louis Neel-CNRS,

Later, field ion microscopy (FIM) made it possibleGrenoble, France.2 Present address: DPM Thomson-CNRS, Orsay, France. to monitor the displacement of individual atoms

0039-6028/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.PII: S0039-6028 ( 00 ) 00459-3

136 J. Ferron et al. / Surface Science 459 (2000) 135–148

under controlled conditions [2–4]. Unfortunately, the mechanisms of atomic diffusion on Cu surfaces.We have combined Monte Carlo (MC ) simulationsFIM experiments can only be performed on a few

materials (refractory metals); for the rest, one still employing realistic potentials with STM anddiffraction experimental data; special attention hashas to rely on indirect techniques. Regarding theo-

retical methods, computer simulations are becom- been paid to the existence of ES barriers at theatomic steps, the mechanisms for step crossing anding increasingly popular. Improvements such as

the appearance of refined empirical atomic poten- the effect of a surfactant such as Pb.tials [5,6 ] and continuous advances in computertechnology are allowing us to treat a wider varietyof problems with ever-growing accuracy. 2. Computational detailsSimulations help us visualize elementary processesin detail and to correlate them with the resulting In this work we have used an MC technique in

which the atomic positions are treated as con-experimental features. In this way, the physicalorigin of relevant effects can be identified. tinuous variables. It must be stressed that our

method is different from the classical kinetic MCDiffusion across atomic steps is an interestingexample. In principle, one could think that a high which is usually performed on a discrete lattice.

In each step of our simulation, every atom in thein-plane mobility of the adatoms would suffice toensure the overall film quality, by allowing them sample is randomly displaced a fraction of a lattice

constant; the total energy of the resulting configu-to find the optimum position for attachment.However, other factors come into play during ration is then calculated, based on a set of intera-

tomic potentials similar to those used in MDgrowth that need be analysed with care. One ofthose aspects is the so-called ‘Ehrlich–Schwoebel simulations. Configurations are then accepted or

rejected in the usual way: those with an energy(ES) barrier’, the additional energy cost for adiffusing adatom to fall from an upper terrace to lower than the former are automatically adopted;

if the final energy is higher, the decision is takena lower one crossing a monatomic step [7,8].Obviously, the height of the ES barrier controls after comparing the Boltzmann factor of the

energy increment with a random number. In thisthe efficiency of interlayer mass transport, and istherefore a key parameter determining the rough- way, the simulation speed is considerably increased

at the expense of losing the deterministic characterness of epitaxial films and the quality of interfaces.For the preparation of artificial heterostructures it of MD. The direct relationship between the

number of iterations and the real elapsed time ismight be necessary to induce layer-by-layer growthin systems with poor interlayer diffusion. Different also lost: from our simulations we can identify

mechanisms and estimate the relative likelihood ofprocedures have been developed to assist andsomehow manipulate the growth process [9]. One different events, but we cannot calculate energy

barriers or diffusion rates. We use them, therefore,of the most promising methods is the use ofsurfactants. to gain insight into the relevant physical processes.

In any case, the reliability of the results dependsA surfactant is an additive whose presencemodifies the growth characteristics in a convenient fundamentally on the characteristics of the poten-

tials used.way [10]. Typically, low-surface-energy elementsare used as surfactants, so that they continuously The interaction potentials employed in our MC

simulations have been obtained using the second-segregate to the surface during deposition andmaintain their activity; in this way, also, no impuri- moment approximation of the tight-binding

scheme (TB-SMA) [18]. They include a short-ties are introduced into the growing film.Abundant reports of surfactant-induced layer-by- range, repulsive pair potential plus a long-range,

many-body contribution based on a tight-bindinglayer growth have appeared recently [11–15], anddifferent atomistic mechanisms have been pro- description of the electronic structure [19]. They

have been successfully used previously to studyposed to explain the observed behavior [16,17].In this paper we present a thorough study of the properties of transition metal surfaces [20,21],

137J. Ferron et al. / Surface Science 459 (2000) 135–148

noble metals [22] and microclusters [18,23,24]. not seem to affect the results in an essential way.With these potentials, the interaction at the ith Pb Furthermore, the main result reported in this paperatom is given by deals with atomic diffusion across the terraces,

which appears in our tests to be rather insensitiveV(ri)=A{∑

jU2

exp[−p2(rij−r

02

)]to minor modifications of the cut-off length.

The free parameters are determined in the+∑k

U1

exp[−p1(rik−r

01

)]}following way: p and q are related to the attractiveand repulsive parts of the potential, respectively.−{∑

jU22

exp[−2q2(rij−r

02

)]The behaviour of these terms is different at thesurface and in the bulk. Therefore, we have chosen+∑

kU21

exp[−2q1(rik−r

01

)]}1/2,(1) to use the values p

i=9/r0

i

and qi=3/r0

i

, that havebeen reported previously to be adequate to repro-while the interaction at the mth Cu atom is givenduce the surface characteristics of transition metalsby:[20]. A and U

iare found from fits to the properties

V(rm

)=A{∑k

U3

exp[−p3(rmk−r

03

)] of the pure metals. The value of A is obtained byminimizing the cohesive energy of the correspond-

+∑j

U1

exp[−p1(rmj−r

01

)]} ing bulk sample with r0i

as the nearest-neighbourdistance. U

iare determined then by fitting the

−{∑k

U23

exp[−2q3(rmk−r

03

] calculated bulk cohesive energy and the bulk mod-ulus to the experimental values. In the absence of

+∑j

U21

exp[−2q1(rmj−r

01

)]}1/2 , experimental data, the parameters describing the(2)Pb–Cu interaction are estimated by the average of

where index j runs over all Pb atoms and k over the corresponding values for Pb–Pb and Cu–CuCu ones. One should emphasize that these are not pairs. The validity of this approximation has beenpair potentials, because of the term containing the

tested in previous studies with this combination ofsquare root of the sum of the hopping integrals.

elements. The ordered structures and meltingThis term takes into account the essential bandbehaviour of Pb overlayers on Cu(100) have beencharacter of the metallic bonds [19,25,26 ]. Thesuccessfully reproduced [27]. In recent studies, theinteractions between the different types of atomsbulk properties of Pb, including the phononare determined by sets of three parametersspectrum, have been calculated giving excellent{U

i, p

i, q

i}; i=1 stands for Cu–Pb pairs, i=2 for

agreement with the experimental results [28,29].Pb–Pb and i=3 for Cu–Cu. r01

, r02

and r03

are theUnless otherwise stated, the Cu(111) samplebulk nearest-neighbour (nn) distances for Pb–Cu,

used in our calculations consisted of six layersPb–Pb and Cu–Cu, respectively. Then, rij

is thewith 128 Cu atoms in each; to study the surfactantdistance between two Pb atoms, r

mkbetween two

effect, a compact layer of 72 Pb atoms was addedCu atoms, and rik

, rmj

between a Pb atom and ato the upper surface of the slab. A probe adatomCu one. The sums are performed over all atomswas then deposited on the sample and its move-within a sphere of radius equal to 3.2 times the nnment monitored while the simulation progressed.distance of Cu, r0

3

. This size was chosen in orderThe two lowest Cu layers were frozen to simulateto include a full unit cell of the Pb-p(4×4) super-the bulk, while all the remaining atoms in thestructure for the study of the surfactant effect. Insample were allowed to move. The atomic posi-addition, we have also checked the effect of thistions were recorded in intervals of 10 MC steps.magnitude on the height of the ES barrier. WeThe slab representing the Cu(100) surface had sixfind that reducing this cut-off length leads tolayers of 10×10 atoms in a square lattice. Mostsignificant modifications of the step behavior; weof the calculations have been performed at acannot evaluate its impact on the ES barrier sincesample temperature of 540 K in order to speed upour technique does not allow us to determine

absolute energies. However, using larger radii does the diffusion processes and improve the statistics.


3. Self-diffusion on flat copper terraces trajectory over the surface is depicted in the lowerpanel. The adatom’s height z above the surfaceremains practically constant, because the electronicWe start our study with the simplest form of

atomic diffusion, that of a single adatom on a flat density of states at the (111) face of Cu is veryflat, with little corrugation and shallow adsorptionterrace. Our MC simulations show that, on the

(111) face, a Cu adatom diffuses from an adsorp- wells. Diffusion is easy under such circumstancesbecause the energy barrier that the adatoms havetion site to a neighbouring one hopping above a

bridge position, as shown in Fig. 1. There, the to overcome is very small.On the (100) face the situation is different; ourupper panel displays the time evolution (measured

in units of MC steps) of the three spatial coordi- MC results indicate that the predominant diffusionmechanism in this case, at 540 K, might be atomicnates of the diffusing adatom; a top view of itsexchange. This mechanism was proposed severalyears ago for the (100) face of Al [30], and it hasbeen confirmed later on other materials by FIMexperiments on refractory metals [31,32]. Similarresults have been obtained recently for a softelement such as Ag [33]. The process is graphicallydescribed in Fig. 2a, where four snapshots of oneof our simulations are displayed. These imagesshow how the adatom, sitting initially on a fourfoldhollow site of the (100) face, displaces a substrateatom and occupies its position; the ejected one,then, becomes a new adatom located at a differentposition on the surface, which results in an effectivediffusive displacement. Fig. 2b also shows thechanges in the coordinates of both atoms involved:the crossing of the graphs for the two z coordinatessignals the exchange. One should notice that thenet displacement of the atoms in this case is muchsmaller than on the (111) face. It is well knownthat diffusion on fcc (100) faces is considerablyslower than on (111) because the atomic structureof the former is less compact, and therefore thecharge density surface is much more corrugated.

Practically all the experimental observations ofatomic exchange to date have been obtained onopen-packed crystal faces, such as the fcc (100)and (110). Our finding points in the same direc-tion. This result, however, must be taken withcaution. There exists considerable debate in theliterature regarding the actual mechanism of sur-face self-diffusion on Cu(100); some calculationspredict diffusion by hopping [34,35] while othersfavour exchange [36–39]. Unfortunately, FIMexperiments cannot be performed on Cu tips to

Fig. 1. MC simulation of Cu self-diffusion on a (111) terrace.resolve this controversy. Our simulations also(a) Evolution of the adatom’s coordinates along its path: thereflect this puzzling situation. In fact, in analogousheight z remains constant, revealing a hopping mechanism. (b)

Top view of the adatom’s trajectory. MC runs performed on small samples (of just four


a coordinated displacement of at least two atoms.Owing to the random nature of the thermalvibrations, such a coordinated movement must bean unlikely event; therefore, it requires a relativelylong residence time of the Cu adatom at theadsorption site to succeed. As a rule of thumb,then, it could be said that hopping will dominateon fast-diffusing, close-packed surfaces, whereasexchange will take place most likely on the slow,open ones. The influence of the sample size on thediffusion mechanism can also be explained alongthese lines: the predominance of the hopping onsmall samples might be an artifact due to the effectof the periodic boundary conditions on the atomicvibrations and relaxations, because any factorcapable of affecting the displacements of the sur-face atoms can have a considerable effect on thelikelihood of the exchange process, while not somuch in the case of hopping. This hypothesis alsogives us a clue to understand the role of otheraspects that have been shown to influence thediffusion mechanism, such as strain [40].

4. Diffusion across monatomic steps:Ehrlich–Schwoebel barriers

The existence of a supplementary energy barrierat step edges was first observed in FIM experimentson refractory metals [7]; later experimental andtheoretical work demonstrated that this is acommon phenomenon [41]. This is also the case

Fig. 2. (a) Four snapshots during an MC run showing that aof Cu: Fig. 3 shows He scattering (TEAS) experi-Cu adatom prefers to diffuse by exchange on Cu(100). (b) Timements for the homoepitaxial growth of Cu on (a)evolution of the coordinates of the two highlighted atoms: the

crossing of the graphs for z signals their site exchange. the (100) and (b) the (111) faces. The monotonicdecrease of the specularly reflected intensityobserved during growth on Cu(111) indicates thatatoms on a side), hopping becomes the preferred

mode of diffusion. the film roughness is steadily increasing, as a resultof poor interlayer diffusion [42]; the inset is anOur interpretation of these contradictory theo-

retical results is the following. The two mechanisms STM image showing the surface morphology afterhaving grown a Cu film 5 ML thick. On Cu(100),of diffusion are not mutually exclusive, but rather

competing processes, each one with its own rate. in contrast, clear intensity oscillations can be seenduring deposition, implying layer-by-layer growthIt appears that for Cu(100) both processes might

have relatively similar probabilities. In that case, with good interlayer mass transport [43]. The samebehaviour has been observed during heteroepitaxysmall differences between calculations could have

a strong effect on the final result. In particular, of Co on Cu: efficient layer-by-layer growth onthe (100) face [44] as opposed to rough, statisticalthe exchange mechanism must be very sensitive to

the sample conditions. Atomic exchange involves growth on Cu(111) [45]. Clearly then, this out-


Fig. 3. Thermal energy atom scattering (TEAS) experiments showing the different types of homoepitaxial growth of Cu. (a) OnCu(111) interlayer diffusion is suppressed, resulting in multilayer growth, as demonstrated by the monotonic decrease of the specularintensity and also by the STM image presented in the inset (for a Cu thickness of 5 ML). (b) On Cu(100) interlayer diffusion is easyand the film grows layer by layer.

come must result from intrinsic characteristics of a step atom out of its position and replacing it.Similarly, we also find exchange diffusion acrossthe two crystal faces employed in the experiments;

similar results are to be expected for other fcc the [111]-oriented steps on Cu(100). The MCsimulations do not allow us to evaluate quantita-substrates. A comprehensive review of growth

modes on fcc (111) and (100) metallic surfaces tively the barrier heights and time intervals, andfor this reason we cannot establish significantcan be found in Ref. [46 ].

We have studied the crossing of steps by single distinctions between the different types of stepsregarding interlayer diffusion.adatoms by generating samples such as that shown

in Fig. 4, with a central terrace bounded by straight From these results we conclude that the domi-nant mechanism of diffusion across steps is atomicsteps on both sides. In this way, on Cu(111) we

have simultaneously present during the simulations exchange, for both faces of Cu, namely (100) and(111). The close similarity between those processesthe two types of low-energy steps that can be

found on this surface, oriented as [100] and [111] at the atomic scale also suggests that the heightsof the different ES barriers should not be veryfacets. Adatoms placed on the upper terrace diffuse

across the plane by hopping, as described above. different on both faces. This hypothesis is sup-ported by computer simulations of single-atomStep crossing, however, works in a different way:

after reaching the edge, the adatom eventually self-diffusion on Cu [47]. The energies reported inthat work for interlayer diffusion by atomicdescends to the lower terrace by exchange, pushing


alone: other factors come into play that need betaken into account. We believe that intralayerdiffusion also plays an important role, in a varietyof ways. For a fixed value of EES, interlayer diffu-sion is easier when Ed (the barrier for in-planediffusion) is higher. First of all, limited surfacediffusion results in the formation of a higherdensity of 2D islands of smaller average size;nucleation of second-layer islands on top of themis more difficult, since a minimum flat area isrequired for that to occur [48,49]. In addition,irregular step shapes and higher densities of kinksare also to be expected; the energy barrier for stepcrossing at those sites is considerably reduced [41],which also contributes to enhancing interlayerdiffusion. On the other hand, surface diffusion onCu(111) is easy, so that the islands formed duringgrowth are large and bounded by smooth stepswhich are more difficult to cross. Atoms landedon top of those islands during deposition willtherefore stay longer there and have a higherprobability of being joined by other adatoms toform stable nuclei; this process results in multi-layer growth.

5. Surfactant effect of lead

The use of surfactants to enhance interlayerdiffusion has been shown to be an effective methodto improve the quality of epitaxial films [11–15,50]. Pb is the element that we used as surfactantin this case. Pb grows on Cu(111) in the Stranski–Krastanov mode [51] forming first a dense mono-

Fig. 4. MC simulations of interlayer diffusion. (a) Top view of layer followed by the nucleation of 3D islandsthe sample surface used in the calculation, showing the adatom

with an average separation of several microns.(black circle) approaching the step and its exchange with anThese islands do not participate in the surfactantedge atom (marked with an arrow); (b) Evolution of the adatom

coordinates: The jump in z signals its descent to the lower effect; therefore, we will concentrate on the firstterrace. layer. Owing to the larger atomic size of the Pb

atoms, a (1×1) lattice cannot be formed; after aninitial stage at submonolayer coverage, where someexchange are EES(100)=0.03 eV and EES(111)=

0.057 eV. These calculations employed EAM surface alloying of Pb and Cu takes place [52,53],a saturation structure is reached consisting in ainteratomic potentials, and although the numerical

results must be considered approximate, they compact hexagonal arrangement producing ap(4×4) LEED pattern; the equivalent coverageillustrate well the subtleties involved in epitaxy.

Thus the existence of good layer-by-layer growth then is 9/16 (0.5625) of the Cu surface density[50,53,54]. Other experiments have found a slightlyfor Cu/Cu(100) and not for Cu/Cu(111) cannot

be explained in terms of different ES barriers different, incommensurate structure with a Pb cov-


erage of 0.53 [55]. Nevertheless, this discrepancy effect of the ES barrier in Cu(111). This surfac-tant-induced layer-by-layer growth can be main-is not relevant for the purpose of this paper, sincetained indefinitely, because the Pb layerthe surfactant effect of the Pb layer does notcontinuously segregates to the surface of the grow-appear to be linked to its superstructure. In fact,ing film. The Pb LEED pattern (shown in Fig. 5b)similar effects have been observed with othercan be observed at all times during and after Cuagents such as Sb, In or O [11–15]. The effec-deposition, indicating that the Pb superstructuretiveness of the Pb layer as a surfactant is demon-remains ordered during the segregation process.strated by the experimental results depicted inFig. 5c shows a STM image of the surface afterFig. 5a. These TEAS data were obtained deposit-having grown 5 ML of Cu. The film is very flating Cu on a Cu(111) surface that had been pre-with no more than three different atomic levelsviously covered with one monolayer of Pb. Theexposed per terrace, which implies a very efficientoscillations of the specular He intensity closelyinterlayer diffusion; and also, the hexagonal Pbresemble those presented in Fig. 3 for the homoepi-superstructure can be seen perfectly ordered ontaxy on Cu(100). This means that the presence oftop of the freshly deposited Cu layer. In thePb during Cu deposition practically suppresses thefollowing, we will apply our MC method to studyin detail the structure of the Pb layer, its effect onthe Cu substrate and the atomic mechanisms ofits surfactant behaviour.

5.1. Formation of the Pb-p(4×4) superstructureon Cu(111)

Starting with a random distribution of Pb atomson the Cu(111) surface, the simulation correctlypredicts the appearance of the p(4×4) structure;the only requirements are to have the right Pbcoverage and a sample large enough to accommo-date several unit cells. The in-plane distribution ofatoms is shown in Fig. 6a. This arrangement canbe characterized by its radial distribution function,presented in part (b) of the same figure.

The structure that comes out of the simulationagrees well with recent experimental results [56,57].It has a highly buckled unit cell, as it was to beexpected given the large lateral compression (ca.4% of the bulk lattice constant) that the Pb atomsare suffering. However, this large amount of buck-ling is not limited to the Pb layer, but affectsseveral Cu layers as well. Fig. 6c depicts a histo-gram of the atomic heights of all the atoms con-tained in the sample. The atoms in the two deepestCu layers are frozen at their bulk equilibrium

Fig. 5. (a) Surfactant-assisted growth of Cu on Cu(111) moni- positions; all the other layers show broadenedtored by TEAS. The presence of a full monolayer of Pb prede- distributions of heights, with maximum disorderposited on the substrate suppresses the effect of the ES barrier in the two uppermost layers. The corrugationand induces layer-by-layer growth. (b) p(4×4) LEED pattern

amplitude in the Cu substrate slowly decreasesof the Pb layer, continuously visible during and after deposition.with increasing depth; however, it is still non-(c) STM image for a 5 ML Cu film: no more than three atomic

levels are exposed, covered by the well-ordered Pb layer. negligible for the fourth Cu layer. It so appears


adsorbed Pb layer, and follow its evolution. TheCu adatom feels the sample’s attractive potentialand falls to the surface; this accounts for thecondensation energy. This energy is quickly dissi-pated at the surface, and does not influence theadatom’s diffusion. Some test runs performed withadatoms deposited at the sample surface with zeroenergy have shown essentially the same results.Immediately after its arrival at the surface, the Cuadatom exchanges positions with a Pb atom andgets inserted into the surfactant layer. Before doingso, the Cu atom moves laterally on top of the Pbonly by a fraction of a lattice constant, in orderto reach the nearest high-symmetry adsorptionsite. We have never observed the Cu atom diffusingby hopping above the Pb layer or popping out ofit after the initial exchange. This process isextremely fast, in terms of simulation steps: Fig. 7ashows the change in the height of the Cu atomafter deposition, for different temperatures; eachcurve is the average of at least 20 MC runs. Thehorizontal scale demonstrates that the Pb–Cuexchange process takes always place as soon asthe Cu atom has accommodated at the surface.From our data, the onset of the Pb–Cu exchangeseems to be independent of the substrate temper-ature; it is interesting to notice, however, that theprocess is executed more rapidly at low temper-ature, apparently because the reduced thermaldisorder of the Pb atoms interferes less with themovement of the two atoms involved in theexchange. The process of Cu burial and Pb segre-gation is thus extremely efficient, even at 50 K, theFig. 6. MC simulation of the Pb-p(4×4) superstructure. (a)

Top view of the sample surface, showing the atomic arrange- lowest temperature that we have studied.ment obtained after starting from a random distribution of Pb Subsequent simulations have been performed atatoms. (b) Radial correlation function used to characterize the 540 K in order to speed up the growth kinetics.degree of in-plane ordering. (c) The histogram of atomic heights Deposition of additional Cu atoms follows thereveals the strong buckling induced by the Pb in several Cu

same trend. Eventually, the Cu atoms embeddedlayers beneath the surface.within the Pb layer might nucleate to form anisland, also covered with Pb. We wanted to deter-

that the adsorption of Pb causes strong structural mine the effect that the formation of Cu islandsperturbations on the Cu surface; this might be a beneath the Pb has on the p-(4×4) superstructure.crucial point for the understanding of the surfac- With this purpose, we have also performed simula-tant effect and its influence on diffusion. tions depositing the Pb layer on a surface with a

Cu island previously grown on it. The result can be5.2. Surface segregation of Pb during Cu deposition seen in Fig. 7b; for clarity, the positions of the Pb

atoms have been marked with small crossed circles.We then simulate growth by depositing a Cu The p-(4×4) structure is clearly visible both on top

of the island and on the remaining terrace. Theadatom at a random position several A above the


the Pb layer. Nevertheless, our TEAS and STMexperiments (Fig. 5) reveal that Cu grows layer-by-layer in the presence of Pb. This growth moderequires considerable in-plane and interlayerdiffusion. One is then forced to assume that theCu atoms diffuse below the Pb layer. We havechecked this hypothesis by extending the MCsimulations well beyond the initial Pb–Cuexchange, and monitoring continuously the posi-tion of the deposited Cu atom. The results aresummarized in Fig. 8a: the graph depicts the evolu-tion of the height of a Cu adatom deposited on aflat Cu surface fully covered with Pb, for severaldifferent MC runs. The first height drop corres-

Fig. 7. Surface segregation of Pb upon Cu deposition. (a)Evolution of the height of a Cu atom deposited on top of thePb layer, for several temperatures. The Cu–Pb exchange is fasterat low sample temperature. (b) The p-(4×4) superstructure ofPb (small crossed circles) is maintained even on top of a Cuisland formed at the interface, as demonstrated by the in-planecorrelation function (c).

high degree of structural ordering is demonstratedby the radial correlation function (Fig. 7c), whichis hardly distinguishable from that shown in Fig. 6for a Pb layer grown on a flat, infinite surface.Apparently the presence of monatomic Cu steps Fig. 8. Exchange diffusion of Cu atoms below the Pb layer. (a)does not significantly alter the ordering of the Pb Different MC runs showing the variation of the height of a Cu

atom deposited on a Pb-covered Cu terrace; the drops in zstructure, at least at its saturation coverage.indicate first the initial Pb–Cu exchange and then (when appli-cable) Cu–Cu exchanges. (b) Top views showing the Cu–Pb5.3. Effect of the surfactant layer on Cu diffusionexchange (above) and the Cu–Cu one (below). The Cu atompulled out of the surface is a next-nearest neighbour of the

The findings presented in the previous section adatom; the Pb atoms are not shown in the last two framesfor clarity.suggest that Cu does not diffuse at all on top of


ponds to the Pb–Cu exchange described above;this one appears in all runs within a similar numberof MC steps. After that, some additional dropscan be seen. In these events, the Cu adatom entersthe Cu surface layer while at the same time anotherCu atom is expelled from it; one of these processesis displayed in successive frames in Fig. 8b.Resulting from this site exchange, we have a Cuatom that has effectively diffused from its originalposition to a new one.

Several points about this result deserve somediscussion. Firstly, it is remarkable that the Cuatom ejected from the surface is not one of theclosest to the adatom, but a next-nearest neigh-bour. This could be so for purely geometricalreasons, because the first neighbours are partlyblocked by the adatom sitting on top of them.This type of long exchanges has been reportedpreviously for the (100) face [58]. The secondpoint has to do with the relative rates of theseprocesses. The statistics accumulated from manydifferent runs show that the Cu–Cu exchange ismuch less likely than the Pb–Cu one, and alsostrongly temperature dependent. Several runs per-formed at 200 K have failed to show a singleexchange event for reasonable simulation times. It Fig. 9. Growth and dissolution of Cu islands covered by Pb.must be stressed that this is the only mechanism (a) The formation of 2D Cu islands below the Pb layer is

detected by the drop of the TEAS intensity during growth ofof atomic diffusion produced by the simulation forCu; upon annealing, the islands dissolve and the initial reflectiv-the Cu atoms in the presence of the surfactant;ity is recovered. (b) and (c): STM images showing the islandsunder no circumstances have we observed hoppingformed after Cu deposition and the terraces free of islands afteracross or above the Pb layer. We conclude, thus, annealing. These experiments support the idea that Cu atoms

that the in-plane diffusion of Cu on the Pb-covered are mobile below the surfactant.surface must be considerably retarded with respectto clean Cu(111).

hand side of the graph in Fig. 9a presents theTo prove this mechanism experimentally is veryevolution of the TEAS intensity, once correcteddifficult, because it would be necessary to observefor the Debye–Waller behaviour. The intensityindividual atoms diffuse below the Pb layer.recovery above 400 K reveals the disappearance ofExcluding this possibility, we designed an experi-defects from the surface. When the process isment to try to make sure that Cu atoms coveredcompleted, the specular intensity nearly reacheswith Pb can indeed move [59]. We start by growingthe same level of the initial surface. STM imagesa full monolayer of Pb on Cu(111) and depositingsuch as that shown in Fig. 9c demonstrate that thethen a submonolayer amount of Cu at roomislands have dissolved, their Cu atoms havetemperature. Under such conditions Cu forms 2Ddiffused to the substrate steps and disappeared,islands, as signalled by the decreasing intensity ofwhile the Pb superstructure is still visible on thethe specular He beam depicted in Fig. 9a; at thesurface. Obviously, we cannot be sure that thesesame time, Pb segregates to the surface as pre-atoms have moved below the Pb layer; however,viously described. After deposition the islands canin view of our previous results this hypothesisbe observed with STM, covered with Pb as shown

in Fig. 9b. We then anneal the sample: the right- seems the most plausible.


To complete our study, there is one last issue strates that the process takes place in essentiallythe same manner as described above. A roughregarding surfactant-induced layer-by-layerestimate based on the statistics obtained aftergrowth that has to be examined: the effect of themany different runs indicates that the rates ofsurfactant on atomic diffusion across steps. Ourexchange at the steps are not much affected by thesimulations did already show (see Fig. 4) that sitesurfactant, although this is something that weexchange with a step atom is the preferred mecha-cannot determine very accurately. We conclude,nism for interlayer diffusion on the clean Cuthen, that at least in the case under study thesurface; therefore, it is not surprising to find theappearance of surfactant-induced layer-by-layersame result in the presence of Pb. Fig. 10 summa-growth is due to the changes provoked by therizes the outcome of our calculation and demon-surfactant on the basic mechanism and rate ofin-plane diffusion, rather than to modifications ofthe step barriers themselves.

6. Discussion

Our simulations have demonstrated their abilityto reproduce the basic features of epitaxial growthand diffusion at the atomic level, thus allowing usto gain a deeper understanding of the underlyingphysics. From our study we have obtained severalconclusions. The first point has to do with the twomechanisms of diffusion on flat terraces, namelyhopping and exchange. These two processes areessentially different because in the first one a singleatom intervenes, whereas the second one involvesat least two of them. The activation energy forhopping is relatively easy to calculate with moderntechniques, since it depends solely on the actualatomic configuration of the sample. For exchange,in contrast, the situation is not so clear. Therequirement for a correlated displacement of sev-eral atoms is frequently overlooked, because in asense, calculations of barrier energies initiate theexchange by specifying the atomic positions alongthe most favorable trajectory; comments about theprobability of reaching that path are scarcely given.In the real case, however, the Cu adatom has towait a relatively long time at its position until therandom vibrations of the surrounding atoms pro-duce a favourable configuration that triggers theexchange process. This can explain why exchangediffusion is usually detected on relatively open andslow-diffusing surfaces such as the fcc (100) and

Fig. 10. MC simulations of diffusion across the two types of (110). In contrast, on clean Cu(111) exchange ismonatomic steps of the Cu(111) surface, in the presence of Pb.

extremely unlikely, because the small surface cor-In both cases, the exchange mechanism remains dominant, asrugation makes hopping diffusion very easy andfor the clean surface. (a) Evolution of the coordinates of the

diffusing Cu adatom. (b) Top view of the diffusion process. the residence time of the adatom at any given


position will be correspondingly short. Besides, the an in-depth understanding of the influence of theenergy cost of pulling an atom out of the compact ES barrier on layer-by-layer growth and the effect(111) surface is higher. of surfactants. The quality of growth is determined

The surfactant layer alters this situation in a by the balance between diffusion on the terracestwofold way: firstly, the Cu surface is greatly and across the steps. On fcc (111) surfaces, thestrained and distorted and this can facilitate the former takes place by hopping and is very fast,extraction of surface atoms. However, most impor- creating large islands with smooth borders. Undertantly, hopping diffusion is inhibited by the pres- such conditions, the effect of ES barriers is mostence of the surrounding Pb atoms, and therefore noticeable: after a few frustrated attempts to crossthe Cu adatom is forced to stay at its position the steps, diffusing adatoms can easily drift awayalmost indefinitely. The extended residence time from the edge and meet other atoms to form aincreases the probabilities to complete a site nucleus, thus causing multilayer growth. In con-exchange successfully, which is now left as the trast, on fcc (100) faces in-plane diffusion is muchonly possible mechanism of diffusion. slower and proceeds mainly by exchange; islands

The same idea allows us to explain the effect of have smaller average sizes and adatoms landed onthe surfactant on interlayer diffusion. When a top of them have more opportunities to fall to thediffusing adatom tries to descend a step in the lower level. Accordingly, the effect of the ESpresence of a ES barrier, the number of failed barrier is more important on fcc (111) surfacesattempts to jump across it will be large. If the than on the (100). Similarly, the role of theenergy for in-plane diffusion is small, then the surfactant could be to slow down terrace diffusionatom will most probably move away from the step by hindering hopping and promoting exchange.and back towards the island centre. During Our MC simulations using realistic empiricalgrowth, new atoms are continuously deposited potentials indicate that Cu atoms deposited on toponto the surface; eventually, the average time of a Cu(111) surface covered by a compact surfac-needed for nucleation will become shorter than tant (Pb) layer immediately get buried underneaththat required to cross the steps and 3D, multilayer it and eventually diffuse by exchanging positionsgrowth will occur. This is the case for the fast- with other Cu atoms from the substrate surface.diffusing Cu(111) face. On the other hand, as This process is slower than surface diffusion ondiscussed in Section 4, a moderately reduced clean Cu(111) and as a result interlayer diffusionin-plane mobility such as is the case for the is favored. The simulations do not reveal anyCu(100) face or for Pb-covered Cu(111) favours significant modifications in the crossings of steps,interlayer crossings by reducing the average size which takes place by atomic exchange both withof the islands and increasing the roughness of their and without surfactant.borders. The main effect of the surfactant, thus,would not necessarily be exerted on the steps buton the terraces. Similar ideas have been put for- Acknowledgementsward previously [48,49,60]; we believe that theresults of our simulations confirm the viability of Work by the Spanish group has been supportedthis mechanism and help visualize it. To summarize by the CICyT under Grant MAT98-0965-C04-02.the message of this paper in an intuitive way, one J. Ferron thanks Fundacion Antorchas for finan-could say that a Cu(111) surface covered with Pb cial support. V. Cros thanks the EU for aacquires most of the characteristics of the (100) scholarship.face for diffusion and growth.

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Influence of surfactants on atomic diffusion