Surface energetics in a heteroepitaxial model system: Co/Cu(111

PHYSICAL REVIEW B 15 JULY 2000-IVOLUME 62, NUMBER 3

Surface energetics in a heteroepitaxial model system: CoÕCu„111…

J. E. Prieto,* J. de la Figuera,† and R. MirandaDepartamento de Fı´sica de la Materia Condensada and Instituto Universitario de Ciencia de Materiales ‘‘Nicola´s Cabrera,’’

Universidad Auto´noma de Madrid, Cantoblanco, E-28049 Madrid, Spain~Received 19 November 1999; revised manuscript received 10 March 2000!

The first stages of the growth of Co on Cu~111! are studied by means of scanning tunneling microscopy. Bymeasuring island densities for several deposition rates, information about the diffusion coefficient on theterraces is extracted. The barrier for edge diffusion is estimated from the shape of the islands. Finally, therelevant Ehrlich-Schwoebel barriers for interlayer mass transport are estimated from the onset of step-flowgrowth mode and top layer nucleation density. The barriers are determined by comparison with simple physicalmodels. The implications of the figures obtained for the heteroepitaxial Co/Cu~111! system are discussed.

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I. INTRODUCTION

With the advent of modern growth techniques limolecular-beam epitaxy~MBE! or chemical vapor deposition, classes of materials based on artificial structures ofduced dimensionality can be routinely fabricated. Theseterials have properties unknown in bulk solids. For examplayered heterostructures of semiconducting compoundsplay interesting optical and transport properties, while ultthin films and superlattices made of alternating layersmagnetic and nonmagnetic metals show exotic phenomlike oscillatory magnetic coupling~OMC! as a function ofthe thickness of the nonmagnetic material and the assocgiant magnetoresistance effect, that makes them usefuapplications such as reading heads of magnetic informati1

An understanding of the origin of these propertiesquires a detailed structural characterization of the systewhich become increasingly sensitive to structural defewith decreasing dimensionality.2 This puts stringent requirements on the structural quality of the samples. For examthe relevant length scale for the OMC in metallic hetestructures is of the order of a few interlayer distances. Thefore, a structural perfection down to this level is requiredthe effect to be observed.

The structure and morphology of ultrathin films are detmined by phenomena occurring during growth. Thereforeis of fundamental importance to characterize the growth pcess in order to achieve an efficient understanding ofrelevant parameters and to be able to control the strucand morphology of the growing films to obtain the desirproperties.

Crystal growth is a complex process in which, in additito thermodynamics, kinetic factors play decisive roles,cause it usually takes place in conditions far from equilrium. Several studies have been performed on homoepitasystems, where information about kinetics, i.e., diffusibarriers, can be obtained, free from the complications arisfrom the presence of two different materials. This informtion is very important in order to develop models to undstand the growth processes. But the films with interestapplications are always the heteroepitaxial ones. Althoseveral studies were recently performed@see, e.g., the im-

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pressive atomistic view of intermixing of Co on Pt~111!~Ref. 3!#, quantitative information on the diffusion barriersheteroepitaxial systems is rather scarce. Some of theexamples concerning fcc~111! surfaces are Ag/Pt~111!,4 andPt on Ni~111! and Rh~111!.5

Co/Cu has been considered as a model system foreroepitaxial growth, because the similarity of the lattice prameters ~mismatch amounts to 1.9%! should allow thegrowth of heterostructures with a high degree of perfectiThis is indeed the case for the~100! orientation, where layer-by-layer growth of Co~Ref. 6! and the formation of epitaxiafcc-Co films7 on Cu~100! have been observed. Accordingthese favorable structural characteristics, the films dispgood magnetic properties, as shown by unambiguous obvations of the OMC effect.8,9 However, MBE-grown sampleswith ~111! orientation show much worse magnetproperties,10–12although they are potentially more interestinbecause thin enough Co/Cu~111! films show perpendicularmagnetic anisotropy.13 The origin of these poor magnetiproperties has been traced back to the absence of layelayer growth in the Co/Cu~111! system.14 This is a clear casewhere a thorough knowledge of the surface processes taplace at epitaxial growth is highly desirable in order to uderstand the origin of the observed magnetic phenomeogy.

In this work, we attempt a characterization of the surfaprocesses taking place during the heteroepitaxy of CoCu~111! by means of a scanning tunneling microsco~STM! study at different stages of the growth and with dferent conditions. Deposition experiments were performedroom temperature~RT! or below, because, for higher temperatures, interdiffusion of the two elements becomesdominant process. In fact it is already apparent at RT,discussed below. Emphasis will be placed on the quantifition of the processes in terms of the relevant diffusion baers, whereby STM data will be analyzed in terms of simpphysical models. It is our aim to obtain reasonable estimafor the barriers involved in order to characterize the growprocess in a quantitative way, and to allow calculations tocompared with experimental results. Eventually, the relatibetween the numbers obtained and the observed morphoare discussed.

2126 ©2000 The American Physical Society

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PRB 62 2127SURFACE ENERGETICS IN A HETEROEPITAXIAL . . .

II. EXPERIMENT

Experiments were performed in a stainless-steel ultrahvacuum~UHV! chamber equipped with a home made SThead of the inertial approach type and a commercial review four-grid low-energy electron-diffraction~LEED! op-tics ~OMICRON Vakuumphysik, GmbH! also suitable forperforming Auger electron spectroscopy~AES!. TheCu~111! sample was cleaned by cycles of Ar1 sputtering andannealing until no contaminants were visible in Auger sptra; the LEED pattern was a sharp 131, and STM imagesshowed clean, several hundred-Å-wide terraces separatemonoatomic steps. Co was deposited by means of a hmade evaporator in which a Co rod is heated by electbombardment. Deposition rates ranged between 0.12.5 ML min21. Coverages were determined by measurfractions of covered area in the low-coverage regime andmeans of AES in the higher ones. All the films displayclear 131 LEED patterns with low background intensitieSTM images were recorded at RT in the constant currmode, with bias voltages up to 2–3 V in magnitude atypical currents of 1 nA. Tips were electrochemically cfrom polycrystalline W wires and used in UHV with no futher treatment. Images shown here have been only smooand, in some cases, a small part of its derivative has badded to the image data in order to enhance edge con~this is the reason they appear as if they were illuminafrom the left!.

III. RESULTS

A. CoÕCu„111… system

The main features of the surface morphology in the heroepitaxial system Co/Cu~111! at RT are qualitatively wellunderstood by the work of the authors’ group and otheSTM images of representative stages of the growthshown in Fig. 1. Our knowledge can be summarized infollowing points.

~i! From the lowest Co coverages studied@Figs. 1~a! and1~b!#, two main phenomena take place on the Cu~111! sur-face. The first is that the substrate monoatomic stepsdecorated by islands at both the lower and the upper sidethe steps.14 An almost continuous, but irregular, onedimensional structure consisting of a mixture of Cu andregions is formed along the steps@Fig. 1~c!#. This effect hasbeen used to grow magnetic quantum wires.15

~ii ! The second aspect is the nucleation observed onsubstrate terraces: islands are formed with a height cosponding to two atomic layers of Co@Fig. 1~b!#. In RT depo-sitions, they present a well-defined triangular shape whertwo different orientations, rotated by 60°, coexist on tsame terrace. The first Co bilayer has been shown to prepredominantly the same fcc stacking as the Cu substrateto contain a significant fraction of Cu.16 A more recentLEED analysis showed that a small amount of regions ctaining a stacking fault can be detected,17 which can be theorigin of the triangular islands of minority orientation seenSTM images. Spectroscopic STM data confirm thinterpretation.18

~iii ! In low-temperature depositions, islands develop ddritic shapes and have been shown to consist of adjacenand Cu regions.19

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~iv! The substrate etching taking place during and aCo deposition is further signaled by the presencemonoatomic-deep vacancy clusters in the substrate’slayer @Figs. 1~a! and 1~b!#, which are preferentially locatednear the substrate steps.20,21

~v! For higher Co coverages, a morphology consistingmany atomic levels simultaneously exposed can be obse@Figs. 1~d!, 1~e!, and 1~f!#, while the stacking sequence of thlayers in the film experiences a gradual transition tohexagonal-close-packed~hcp! structure.17

B. Island densities and surface diffusion barrier

We start with an estimate of the surface diffusion barrEs

Co/Cu for Co adatoms on the Cu~111! terraces. A measurable magnitude directly related with it is the island densNx , which increases with increasing deposition rate andcreasing diffusivity on the surface.Nx depends on the sizeiof the critical nucleus, defined as the island size~in numberof atoms! at a given temperature that turns into stable upcapture of one extra adatom. The classical nucleation thebased on a rate-equation approach predicts a powerrelationship22

FIG. 1. STM images corresponding to several coverages ofdeposited at RT on Cu~111!: ~a! 0.1 ML, 1503150 nm2; ~b! profilealong the line in~a!; ~c! 0.6 ML, 1003100 nm2; ~d! 2.0 ML, 80380 nm2; ~e! 5 ML, 50350 nm2; and ~f! histogram showing thefraction of exposed area of each of the atomic levels visible in~e!.The solid line is a fit to a Poisson distribution centered at 4.9 M

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2128 PRB 62J. E. PRIETO, J. de la FIGUERA, AND R. MIRANDA

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for complete condensation~i.e., when re-evaporation is negligible! of two-dimensional~2D! islands. For the case ocomplete three-dimensional~3D! condensation, the numberin the denominators of Eq.~2! has to be substituted by 2.~Ref. 22!. In these equations,nx is the island densityNxnormalized to the atomic densityN0 of the substrate, 1.831015 atoms cm22 for Cu~111!, Ei is the binding energy ofa cluster of sizei, Es is the surface diffusion barrier,n0 is therelevant atomic vibration frequency, andR is the depositionrate expressed in ML s21.

The most straightforward way to determine the size ofcritical nucleus is to measure the island densityNx as a func-tion of temperature and to extract the value ofi by fitting toEqs. ~1! and ~2!.23 However, the presence of interdiffusioeffects already at RT in Co/Cu~111! ~Refs. 20 and 24! pre-cludes the possibility of studies at higher temperatures.stead, the dependence ofNx on the deposition rateR wasanalyzed. To this end, both magnitudes are plotted in lorithmic scales in Fig. 2 from the data of Table I. The isladensities in the experiments considered correspond tosaturation regime, which, according to Ref. 4, takes placecoverages larger than about 0.05 ML.

FIG. 2. Plot of the island density, measured in STM imagesseveral Co depositions on Cu~111! at RT, as a function of the deposition rate.

TABLE I. Experimental values for the density of islandsNx inCo depositions on Cu~111! at different ratesR and coveragesu. Thearea exposed is one-half of the coverage, since the Co islandsML high.

R (ML s21) Nx (islands cm22) u ~ML !

(1.760.5)31023 (2.060.5)31011 0.360.1(8.361.7)31023 (3.060.3)31011 0.1060.020.02360.007 (3.660.4)31011 0.760.20.0460.008 (4.060.5)3 1011 0.660.1

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Figure 2 shows the validity of the power law relation~1!in the Co/Cu~111! system. The exponent turns out to bep50.2260.02. It is a first important result, since it allowcritical nucleus sizes larger than 1 to be safely excludedRT. Our value is closer to the exponents predicted by Eq.~2!for a critical nucleus of one atom (p50.33 for 2D nucleationand p50.29 for 3D nucleation! than to any larger sizewhich results in higher figures. Actually, it is lower thathese numbers, so that a fraction of nucleation with a critisize i 50 cannot be excluded, as discussed below. We cclude that the use of the expressions fori 51 is justified as afirst approximation.

From the prefactor in Eq.~1! one could in principle cal-culate the hopping coefficient. But this would require tknowledge of the functionh(u,i ) in Eq. ~1!, which can varybetween 1022 and 10~Ref. 23!, leading to an unacceptablhigh error inEs . We have two alternative ways to computhe diffusion barrier. The first is to assume that the lowcoverage studied,u50.1 ML, that corresponds to only 5% othe surface covered with bilayer-high islands@see Fig. 1~a!#,is not far from the transient regime in whichnx increaseswith coverageu. Then we can use the simple relation

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that follows from dimensional arguments applied to trandom-walk motion of adatoms in the nucleation procwith i 51 ~Ref. 25!. In that way we obtain a hopping frequencyD59.03107 s21. Assuming a vibration frequencyof n051012 s21, the relation

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Es

kTD ~4!

gives a diffusion barrier for Co atoms on Cu~111! EsCo/Cu

50.21 eV.The second option is to consider coverages clearly in

saturation regime, like the 0.6 ML shown in Fig. 1~c!. Forthose, we can use the relation of Villainet al.,26 also derivedfrom simple scaling assumptions, to estimate the diffusrateD in terms of the deposition rateR and the mean islandseparationl:

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The mean island separationl is easily calculable in terms othe island density by

l 5nx21/2, ~6!

when both magnitudes are expressed in units of the surlattice parameter. Using the values corresponding to 0.60.7 ML of Table I, we arrive atD54.3 and 3.53108 s21,respectively, for which Eq.~4! gives Es

Co/Cu50.17 eV, notfar from the previous value in view of the rough characterthe estimations, so that a diffusion barrier ofEs

Co/Cu50.1960.02 eV is a plausible result. Note that it is the exponendependence ofD on Es that ultimately justifies the use of thpreceding relations, which are correct only within factorsorder unity.

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C. Island shapes and barrier for edge diffusion

After nucleation has taken place, the next process affing surface morphology is atomic diffusion along the edgof the growing islands, a kinetic process that determines tshapes. It is well known that, if this mobility is significantlimited, islands develop characteristic ramified~dendritic!shapes, as for example, in the heteroepitaxial growth ofon Ru~0001!.27 If the edge mobility is strictly zero, adatomarriving at an island edge just stay in the place where tmade contact for all subsequent times. This ‘‘hit and sticgrowth mode corresponds to the mathematical model cadiffusion-limited aggregation, and leads to islands of dendritic shapes with an arm width of one atom.28 However, ifthe edge mobility is small but nonnegligible, the arm widof the dendritic islands is larger, and its measure allowsestimation of the barrier for edge diffusion.

A simple physical argument can be invoked29 for estab-lishing the needed relation: an island will develop a compshape if the timete required for an adatom to ‘‘explore’’ itsperimeter and find the highly coordinated, energeticallyvorable, sites is smaller than the average timet i between twoadatom impingement events on the same island. The timt ican be written as the inverse ofI, the average adatom arrivarate at one island, which in turn can be estimated by

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nx. ~7!

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with L the typical dimension of the island andhe the hoppingrate along the island edge. It follows that a small, compisland that grows by adatom capture will undergo a transitto a less compact form at a certain critical size. This happwhen the two characteristic times become comparable,29 sothat setting them equal leads to an expression

Lc;S he

I D 1/2

, ~9!

valid for Lc , the critical size for onset of shape instabilitMonte Carlo simulations by Bartelt and Evans29 have con-firmed this relationship, with a proportionality constantabout 1.7, to be valid over a wide range in thehe /I param-eter. They further show thatLc can be taken as either thtypical size of a growing island at which a departure frocompact shapes is first observed, or as the average arm wLw in the case of fully developed dendritic islands.

We now apply the preceeding relation to our case CCu~111!. In images like Fig. 3~a!, we can estimate about 20Å for the critical island size above which the sides of ttriangular islands become mesoscopically ‘‘kinked.’’ Thcorresponds toLc'80 atoms, and we obtain a value forhe /Iof about 23103 by applying Eq.~9! as illustrated in Fig. 3 ofRef. 29. On the other hand, withR50.04 ML s21 and Nx54.031011 islands cm22, relation ~7! gives a value ofI'180 atoms s21. From these two numbers, we estimatehe'3.63105 hops s21 at RT.

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In the low-temperature~210 K! dendritic islands of Fig.3~b!, we can measure an average arm width of about 45corresponding toLw'18 atoms. According to Ref. 29, thiimplies he /I'100. Here we have takenLw as the width ofthe double-layer-high parts of the islands, because the moatomic high ones are due to decoration with Cu atoms coing from the substrate.19 The deposition rate isR50.0083 ML s21 and the island density 3.831011 islands cm22, so the arrival rateI amounts to'36 atoms s21 and the edge adatom hopping ratehe has avalue of'3600 hops s21 at 210 K.

From the values for the hopping ratehe at the two tem-peratures, and using the expression

he5n0 exp$2Ee /kT%, ~10!

with n051012 s21, we obtain two close values for the edgdiffusion barrier of 0.38 eV at RT and 0.33 eV at 210 K,that a value forEe around 0.3560.03 eV seems a reasonabresult.

D. Processes at steps and Ehrlich-Schwoebel barriers

Not all the deposited material ends up in the islannucleated at the terraces. The original substrate steps alsas sinks for the Co adatoms. This can be seen in Figs. 1~a!,1~c!, and 4~a!.

FIG. 3. STM images showing effects of limited edge diffusio~a! 0.6-ML Co deposited at RT (70370 nm2); the edges of largeislands depart from the straight line, as shown by the arrows.~b!0.12 ML Co deposited at 210 K (1003100 nm2); the islands aredendritic, with measurable arm widths.

FIG. 4. Effect of Schwoebel barriers:~a! STM image (2003200 nm2) of 0.2-ML Co deposited at RT showing a stepperegion: only in the wider terraces can nucleation take place.~b!STM image (1003100 nm2) of a 1.5-ML Co film deposited at RTwhere the onset of nucleation of the third-layer level can beserved.

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Processes occurring at steps determine the mode in wgrowth proceeds and this, in turn, has a decisive impacthe film morphology. Under conditions where the growdoes not take place in the step flow mode, the film morphogy is determined by the efficiency at whichinterlayer masstransportproceeds across the steps, as compared to thefusion rate on the terraces.

An efficient interlayer mass transport is essentiallayer-by-layer growth to take place, because otherwise atoms landed on top of growing islands have no chancedescend the limiting step and fill up the holes that remainthe lower levels, so they are bound to stay on top ofisland and there nucleate islands of the next level. Withcreasing coverage, rough films develop where several atolevels are simultaneously exposed. It can easily be shthat in the absence of interlayer mass transport, the exparea of the different atomic levels of the deposited matefollows a Poisson distribution.30 This situation is commonlyencountered in the homoepitaxial growth on fcc~111! metalsurfaces like Cu and Ag.31 A very different morphology de-velops if interlayer mass transport is efficient, i.e., if adatohave a significant probability to descend the step and fillthe holes in the considered level before the next one ispreciably populated. This is the case in fcc~100! metal sur-faces like Cu~100!, where layer-by-layer growth isobserved.32

The presence of a barrierEES at the steps hinderinginter-layer mass transport from the upper to the lower terracalled the Ehrlich-Schwoebel~ES! barrier,33,34 has been pro-posed as a phenomenological explanation for the diffemodes of growth observed on solid surfaces.35 EES is definedas the increment respect to the terrace diffusion barrierEs .There is not yet a generally accepted picture of the physorigin of the ES barrier. The presence of atomic exchamechanisms in the step-down transport36 on some surfacesobscures a simple interpretation in terms of the reductionthe coordination of the adatom in its transit to the highcoordinated adsorption site at the lower side of the step.the other hand, a suggestive correlation of the ES barwith the occupation of surface states has been proposed37,38

We now proceed to determine the ES barriers relevantgrowth in the Co/Cu~111! system.

1. Co on Cu

If the nucleation probability is small, then the largest pof the deposited atoms will reach the lower edge of existsteps, where they will be incorporated. This mode of growis known as step flow. Since adatom diffusivity and alsosize of the critical nucleus are increasing functions oftemperature, a transition temperatureTcr exists separating3D growth below it and step flow above it. This temperatudepends on the mean terrace widthl in the substrate.Markov39 found expressions forTcr in terms of the deposi-tion rateR and the barriers for surface diffusionEs and in-terlayer transportEES. The relation for the case of high Ebarrier and critical island sizei 51 is

kTcr5Es12EES

lnS n

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As stated in Ref. 39, this expression is valid for ideal 3growth, so when comparing with experiments, the tempeture that has to be taken is the highest at which the growtstill ideally 3D. In diffraction experiments, ideal 3D growtis signaled by a dependence of the reflected intensity oncoverageu of the form I 5I 0 exp(24u). These experimentshave the drawback that it is very difficult to determine tpertinent terrace width, that can be significantly different,surfaces with high ES barrier, from the mean length giventhe sample miscut angle due to processes of step buncduring the thermal treatments usually employed to cleansurfaces.39

In our system, the presence of interdiffusion effectsroom temperature again precludes the possibility of increing the temperature to detect the end of perfect 3D growHowever, the local character of a microscopy technique lSTM allows us to study the transition in the growth mofrom 3D to step flow at a given temperature~RT! as a func-tion of the terrace widthinstead of the temperature.

For large values ofl the growth mode is 3D, which is therange of applicability of Eq.~11!. Therefore,l must be takenasthe value at which nucleation at steps begins to be signcant. This can be taken as the mean distance between neboring islandsl for the corresponding values of the islandensity and deposition rate, because for values of the mterrace widthl lower thanl, practically no nucleation willtake place at the terraces, as shown in Fig. 4~a!. Applyingrelation~11! with Tcr equal to RT to the images of Fig. 4~a!,for which a l of about 70 atoms can be determined, atakingn051012 s21, we arrive at a value of 0.44 eV for thsum Es12EES. With Es

Co/Cu50.19 eV from our previousanalysis, we obtainEES

Co/Cu50.13 eV.

2. Co on Co

As the growth proceeds and the Co coverage is increathe situation resembles more and more the homoepitagrowth of Co on a close-packed Co surface. Therefore,relevant barriers which determine the morphology of tgrowing Co films are theEs

Co/Co terrace diffusion andEESCo/Co

Ehrlich-Schwoebel barriers corresponding to the diffusionCo atoms on Co surfaces. The presence of a limiting barEES for interlayer mass transport implies that at a criticcoverageQc below 1 ML, nucleation on the upper level muset in. Thus the measurement ofQc allows the determinationof EES, while the island density in the higher level, in turallows the estimation of the surface diffusion barrier. Nothat the values forEs

Co/Co andEESCo/Co arrived at in this way

may differ somewhat from the barriers for Co diffusion oCo bulk material because the bulk hcp structure and latparameters are only reached by films of several Mthickness.17 Markov calculated the rates for growth of thfirst monolayer and for nucleation on top of it, and derivquantitative expressions relating the critical coverageQc andthe EES barrier.40 For a critical nucleus size of 1 atom, thcorresponding relation is

S5 expS EES

kT D51

2

lc

a F ~C120.2653!1/226

7G21, ~12!

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5p Nx lc2 ; a is the surface lattice parameter,Ds is the sur-

face diffusion coefficient, anda1 is the number of ways~sixin this case! an adatom can join the critical nucleus of size

The magnitudeQc can be accurately taken as the 0.ML of exposed surface of the coalesced bilayer islands inSTM image of Fig. 4~b!. For this coverage, Co islands of ththird atomic level, now only one layer high, are just begning to form~they occupy only 5% of the surface! on top ofthe first Co bilayer. It is interesting to note that it is necessto deposit a high amount of material in order to coversubstrate completely. For instance, in the 2-ML film of F1~d!, about 20% of the substrate is still visible. Using oexperimental values, from Eq.~12! we obtain a result of 0.14eV for EES

Co/Co , the Co-Co Ehrlich-Schwoebel barrier.We need an estimate for the surface diffusion barrier

Co adatoms on a Co close-packed surface. To this endfollow the same procedure as in the case of migrationCu~111!. We consider the incipient population of the thiatomic level~one above the initial bilayer!, for which a cov-erage of 0.05 ML and an island density of about 131011 cm22 can be determined from images like Fig. 4~b!.In a regime of such a low coverage, Eq.~3! is likely to hold.With a deposition rate of 0.05 ML s21, we arrive at a hop-ping frequency of 1.231010 s21 which, with the usual as-sumption n051012 s21 leads through Eq.~4! to Es

Co/Co

50.08 eV.

IV. DISCUSSION

The fair agreement of the data in Fig. 2 with a straigline indicates the validity of the power-law relation~1!, andthus the description of nucleation in the Co/Cu~111! het-eroepitaxial system in terms of the rate-equation approac22

The fact that the exponent retrieved from the fitp50.2260.02 is closer to that predicted for 3D nucleation~0.29!than for 2D nucleation~0.33!, with i 51 ~Ref. 22!, can bepartially attributed to the formation, in the earliest stagesthe growth, of bilayer Co islands, which can be consideredincipient 3D clusters. However, since our exponent is ssignificantly lower than 0.29, a fraction of nucleation withcritical size i 50 cannot be excluded. This has been assoated with nucleation mediated by interdiffusion41 and, infact, effects of substrate etching20,21and hints of exchange oCo adatoms16,17,19have been observed. Nevertheless, nucation with i 50 cannot be the predominant mechanism,cause it would lead to no dependence ofNx on R at all (p50). It is very likely that interdiffusion-mediated nucleatioevents take place mainly close to the steps, where etcand intermixing have been preferentially observed.15,21

We have determined a value of 0.1960.02 eV forEs

Co/Cu , the diffusion barrier of Co adatoms on Cu~111!,from the analysis of nucleation densities. Since, toknowledge, there are no calculations of this number, weonly compare it with values from other systems. It is high

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than the barriers for self-diffusion on close-packed nobmetal surfaces as measured in He scattering studies ofCu~111! ~Ref. 31! ~0.03 eV! and Ag/Ag~111! ~Ref. 42!~0.051 eV!. These values, on the other hand, compare wwith our estimate for the Co-on-Co surface diffusion barriEs

Co/Co50.08 eV, obtained from the island density on topthe first Co bilayer, when the higher cohesion energy otransition metal like Co is taken into account. Therefore,accuracy of our result might be questioned because thetribution of nucleation events withi 50 tends to underestimate the diffusion coefficient when calculated through E~3!, so that the actual value ofEs might be lower than 0.1960.02 eV. However, this value is very comparable to thoobtained by several methods in related systems contaitransition metals, for example, 0.25 eV in Pt/Pt~111!; 0.17eV in Rh/Rh~111!; less than 0.22 eV in Pt/Rh~111! and Pt/Ni~111!, measured by field ion microscopy~FIM! ~Ref. 5!;0.168 eV in Ag/Pt~111! ~Ref. 4!; and 0.26 eV in Pt/Pt~111!,43

determined by STM. With the mentioned cautions and inabsence of further results, it is thus reasonable to ass0.19 eV and 0.08 eV as effective values for the energbarriers for diffusion of Co adatoms on Cu and Co clospacked surfaces, respectively, as derived from nucleadata.

From the analysis of island shapes, we arrive at a valuEe50.3560.03 eV for the activation barrier for diffusion oCo atoms along the steps of the islands. This value is sigcantly higher than our estimates for eitherEs

Co/Cu or EsCo/Co ,

the barriers for Co adatom migration on Cu and Co clopacked surfaces, respectively, as expected from simple bcounting arguments. Again, we can compare it with valufound for other metals. Bartelt and Evans, who derived E~9!, applied it to several epitaxial systems,29 and arrived atthe following values: 0.4060.02 eV for Pt/Pt~111!, 0.2560.02 eV for Au/Ru~0001!, and 0.3060.05 eV for Co/Ru~0001!. We find that our value of 0.3560.03 eV is per-fectly comparable to these figures.

We estimate the Ehrlich-Schwoebel barrier for Co atoapproaching a Cu step,EES

Co/Cu , to be about 0.13 eV, a number of the same order as our value for the surface diffusbarrier Es

Co/Cu , 0.1960.02 eV. The Co-on-Co ES and suface diffusion barriers are more determinant of the morphogy of the system from the third atomic level on, whicbegins to be populated at a coverage of about 1.5 MLcording to Fig. 4~b!. Our estimates for those figures aEES

Co/Co50.14 eV andEsCo/Co50.08 eV, respectively.

It is instructive to compare with values found in othsystems. Markov estimated 0.08 eV forEES in the homoepi-taxial growth on Cu~111! from experimental results,39 whileSTM experiments give 0.22 eV~Ref. 44!. For Ag/Ag~111!,0.13 eV~Ref. 45! and 0.12 eV~Ref. 46! were determined forEES in two different STM measurements, while 0.15 eV westimated by Markov.39 The corresponding values forEs are0.03 and 0.051 eV for Cu~111! ~Ref. 31! and Ag~111! ~Ref.42! self-diffusion, respectively. In Pt/Pt~111!, recentexperimental47,48 and theoretical studies36 found values forEES of several hundredths of an eV, which together wEs50.25 eV estimated by FIM~Ref. 49! or 0.26 eV bySTM,43 offer an explanation for the layer-by-layer growththis system at low temperatures,35 in contrast to the 3D

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growth mode in homoepitaxy on Cu~111! and Ag~111!. Inthe Pt~111! case, however, there may be additional compcations: both the ability of Pt to adsorb CO at low tempetures and the presence of a surface reconstruction at hitemperatures have been shown to influence drasticallygrowth morphology.47,50

Our values compare very well with those cited. SinceES barrier represents the amount of energy required toscend a stepin addition to the surface diffusion barrier, ouhigh values determined forEES compared toEs , especiallyin the Co/Co case, imply a reduced interlayer diffusivity aare responsible for the Poisson distribution of expoatomic levels in films with thicknesses of several monolaers, as shown in Figs. 1~e! and 1~f!. As a consequence, thsurface roughness of Co/Cu~111! films, defined as the seconmoment of the height distribution, scales as the squareof the coverage. This morphology leads to Co/Cu filmsunhomogeneous thicknesses at the level of several monoers, and precludes the possibility of observing magneticfects that require structural order down to the atomic levsuch as the OMC. This explains the poor magnetic properof ~111! oriented, MBE-grown Co/Cu heterostructures.10–12

In summary, we have analyzed the morphology of ultthin deposits of Co on Cu~111! with STM and, through com-parison with simple physical models, have been able totain estimates of the relevant energetic barriers that con

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the diffusion processes and determine the morphology offilms. The barriers that limit diffusion on the terraces, alothe steps and between the different atomic levels have bestimated and discussed. Their values are compiled in TII. In particular, the values of the barriers for interlayer aintralayer diffusion offer an explanation for the observed 3morphology of thin Co/Cu~111! films that, in turn, deter-mines their magnetic properties.

ACKNOWLEDGMENTS

The authors thank J.M. Gallego for his critical readingthe manuscript. Financial support by the Spanish CICthrough Project Nos. PB97-0031 and MAT98-0965-C04-is gratefully aknowledged.

TABLE II. Compilation of the values estimated in the text fothe diffusion barriers relevant to the growth of Co on cleCu~111!. These are the surface diffusionEs and Ehrlich-SchwoebeEES barriers for Co adatoms diffusing both on Cu and Co clopacked surfaces, and the barrierEe for diffusion of a Co atom alonga step edge.

EsCo/Cu EES

Co/Cu EsCo/Co EES

Co/Co Ee

0.19 eV 0.13 eV 0.08 eV 0.14 eV 0.35 eV

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.

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.

.

*Corresponding author. FAX:~34! 91 397 39 61. Email:[email protected]

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Surface energetics in a heteroepitaxial model system: Co/Cu(111

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