Surface Science 539 (2003) L560–L566

www.elsevier.com/locate/susc

Surface Science Letters

Dimer binding energies on fcc(111) metal surfaces

Carsten Busse a,*, Winfried Langenkamp a, Celia Polop a, Ansgar Petersen a,Henri Hansen a, Udo Linke b, Peter J. Feibelman c, Thomas Michely a

a I. Physikalisches Institut, RWTH Aachen, D-52056 Aachen, Germanyb ISG 3, Forschungszentrum J€uulich, D-52425 J€uulich, Germany

c Sandia National Laboratories, Albuquerque, NM 87185-1413, USA

Received 19 May 2003; accepted for publication 4 June 2003

Abstract

Analysis of island density vs. temperature, observed in scanning tunneling microscopy, implies that the binding

energy of a self-adsorbed dimer equals 0.11–0.12 of the cohesive energy on Ir(1 1 1), Al(1 1 1), and Pt(1 1 1). While

ab initio calculations scatter around the experimental results by about 20%, field ion microscopy of Ir(1 1 1) and

Pt(1 1 1) yields dimer binding energies nearly a factor of three smaller than the corresponding scanning tunneling

microscopy results. On the basis of ab initio calculations, these low values are attributed to the neglect of dimer dis-

sociation processes at step edges.

� 2003 Elsevier B.V. All rights reserved.

Keywords: Density functional calculations; Scanning tunneling microscopy; Iridium; Aluminum; Low index single crystal surfaces;

Adatoms

1 As an example, for homoepitaxial growth on Pt(1 1 1) the

activation energies of the relevant atomic growth processes are

reproduced with an accuracy of about 0.1 eV compared to the

available experimental and ab initio results by assuming an

The dimer binding energy Eb;2 is the energygained by bringing a distant pair of stably self-

adsorbed adatoms to nearest-neighbor sites, al-

lowing them to form their minimum energy

configuration on a terrace. Experimentally thisquantity is derived from the dimer dissociation

energy, which is to good approximation the sum of

the dimer binding energy Eb;2 and adatom diffu-

sion activation energy Ed;1 [1,2]. The dimer bindingenergy is a key quantity for understanding and

predicting epitaxial growth. It is a first order esti-

* Corresponding author. Tel.: +4-9241-8027209; fax: +4-

9241-8022331.

E-mail address: busse@physik.rwth-aachen.de (C. Busse).

0039-6028/03/$ - see front matter � 2003 Elsevier B.V. All rights res

doi:10.1016/S0039-6028(03)00814-8

mate of the average in-plane nearest-neighbor

bond strength in growth processes, which, together

with the corresponding kinetic barriers, determines

the hierarchy of onset temperatures for growth

phenomena. 1

average in-plane nearest-neighbor bond strength of 0.5 eV in a

modified nearest-neighbor model [3]. The value of 0.5 eV is in

reasonable agreement with the experimental and ab initio

results for Eb;2 (compare Table 1). Apparently the in-planenearest neighbor bond strength depends only weakly on the

coordination number in the range of interest.

erved.

Fig. 1. Top row: STM-topographs of Ir(1 1 1) with size 1200�AA· 1200 �AA after evaporation of H ¼ ð0:13� 0:01Þ ML withF ¼ ð1:3� 0:1Þ � 10�2 ML/s at (a) T ¼ 225 K, (b) T ¼ 300 K,(c) T ¼ 550 K. Bottom row: STM-topographs of Al(1 1 1), size1250 �AA· 1250 �AA,H ¼ ð0:11� 0:01ÞML, F ¼ ð7:2� 0:6Þ � 10�3ML/s, (d) T ¼ 91 K, (e) T ¼ 137 K, (f) T ¼ 251 K.

Fig. 2. Arrhenius representation of island density n for Ir(1 1 1)(j) and Al(1 1 1) (N). The temperature scale is normalized with

the respective cohesive energies Ecoh. Full lines: Best linear fitsto the data in the respective temperature intervals. Inset: n vs.deposition rate F for Ir(1 1 1) (j) and best linear fit to the data(full line). For further details see text. Error bars not shown are

smaller than symbols.

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In a nearest neighbor model, with the binding

energy of atoms proportional to their coordina-

tion, Eb;2 would be 1=6 Ecoh for an fcc crystal,where the cohesive energy Ecoh is the energy gainedper atom by formation of a crystal from distant

atoms. It is well known that the bond energies ofan atom actually depend on the total number of

bonds it forms, increasing with decreasing coor-

dination [4,5]. Nevertheless, for bond breaking in

equivalent geometrical environments but different

materials, it is natural to hypothesize that the en-

ergy needed scales with Ecoh.Nonetheless, such scaling behavior has not been

found on fcc(1 1 1) surfaces till now. On the con-trary, there is a large scatter of Eb;2=Ecoh valuesobtained using different experimental and theoret-

ical methods. For instance, ab initio density func-

tional theory (DFT) calculations predict Eb;2 ¼0:13� 0:17 Ecoh for Al(1 1 1) [6–8], while field ionmicroscopy (FIM) suggests Eb;2 ¼ 0:045 Ecoh forIr(1 1 1) [9]. We will show here that this scatter is

largely due to systematic errors. Therefore we haveperformed STM experiments on Al(1 1 1) and

Ir(1 1 1) and revisited our data for Pt(1 1 1) [2].

Based on the results, and comparison with new

ab initio calculations for Ir, we argue that Eb;2indeed scales with Ecoh for these materials. Thus weestablish a rule for the value of Eb;2 on fcc(1 1 1)metals suggestive of a universal physical behavior

of these systems. This guideline can be used totrack down cases of special interest which do not

obey this rule. These cases deserve special analysis

to pin down the roots of their deviating behavior.

In addition, our studies yield rate parameters for

adatom and dimer diffusion.

The experiments were performed in two similar

UHV chambers [10] with base pressures P < 3�10�11 mbar. Both samples were cleaned by repeatedcycles of sputtering and annealing. Prior to depo-

sition the samples were flashed to a temperature

ensuring desorption of all species that might have

adsorbed from the background gas. Special care

was exercised to ensure clean deposition conditions

(P < 1� 10�10 mbar). After deposition the islanddensity stayed constant. Nevertheless, the samples

were quenched to avoid changes of island shapes.The methods employed to obtain Eb;2 are based

on the analysis of the T -dependence of the satu-

rated island number density n. Fig. 1 shows STMtopographs of Ir(1 1 1) and Al(1 1 1) after deposi-

tion at various T . The island density data areshown in Fig. 2.

For Ir(1 1 1) (full squares) three scaling regimes

may be distinguished (labeled I, II, and III), in

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which the data are fitted by linear regression (full

lines in Fig. 2). In regime I at low T , only adatomsare mobile and dimers are stable. Application of

rate equation nucleation theory then states that

n ¼ jF 1=3m�1=30 eEd;1=3kT [11], where F is the deposi-tion rate and j is a numerical factor. A linear fit tothe data thus yields the activation energy Ed;1 ¼ð0:30� 0:01Þ eV from the best-fit slope and an

attempt frequency m0 ¼ 5� 1011�0:5 s�1 for adatomdiffusion from the y-axis intercept. Increasing Tleads to scaling regime II, where dimers are still

stable but mobile. With the knowledge of Ed;1 theslope here yields the activation energy of dimer

diffusion Ed;2 ¼ ð0:44� 0:05Þ eV according ton / F 2=5eðEd;1þEd;2Þ=5kT [12]. Eventually, in regime III

dimers are unstable, i.e., dissociate on the time

scale relevant for nucleation, and only trimers are

stable nuclei. Knowing Ed;1, the slope yields Eb;2 ¼ð0:9� 0:2Þ eV according to n / F 1=2eð2Ed;1þEb;2Þ=4kT

[11], neglecting cluster diffusion, however.

As the slope at high T has quite a large errorand is certainly influenced by cluster mobility, wealso employed the more robust transition temper-

ature method stating Eb;2 ¼ kTt lnðntm0;diss=F Þ � Ed;1[2]. Here Tt ¼ 562 K (Ecoh=kBT ¼ 143) is the tran-sition temperature where the neighboring linear

fits II and III intersect, nt the corresponding n, and

Table 1

Parameters for atomic processes on Ir(1 1 1), Pt(1 1 1), and Al(1 1 1), a

Ed;1 (eV) m0 (Hz)

Ir(1 1 1) STM 0.30(1) 5 · 1011:0ð5Þ

FIM 0.290(3) [25] 2.1 · 1012:0LDA 0.24 [27]

Al(1 1 1) STM 0.04 5 · 1011

LDA 0.04 [24,28,29]

GGA

Pt(1 1 1) STM 0.26(1) [31] 5 · 1012:0ð5Þ

FIM 0.260(3) [26] 1.0 · 1013:0LDA 0.29 [32]

0.33 [33]

Eab;2ðEbb;2Þ results by assuming m0;diss ¼ m0ðm0;diss ¼ kT=hÞ. The numbers6.90, 3.42, and 5.86 eV for Ir, Al, and Pt, respectively [34]. Numbers

m0;diss the attempt frequency of dissociation. Asnothing is known a priori of m0;diss two values arederived for Eb;2, (a) assuming m0;diss ¼ m0 resultingin Eab;2 ¼ 0:73 eV and (b) assuming m0;diss ¼ kT=hresulting in Ebb;2 ¼ 0:88 eV.As is apparent in Table 1, STM and FIM agree

perfectly for Ed;1, m0, and Ed;2, within the limits oferror, thus largely ruling out the relevance of ad-

atom–adatom interactions for nucleation [13]. The

two methods disagree strongly for Eb;2: The FIMvalue is only 0.31 eV, nearly three times smaller

than the STM value of 0.88 eV, assuming

m0;diss ¼ kT=h for both experiments. According toFIM, regime III of dimer instability should beentered already well below 300 K. We performed

an additional test on dimer stability at 330 K by

measuring the flux dependence of n (see inset inFig. 2). Scaling behavior is observed with an ex-

ponent 0.36 ± 0.02. This value is consistent with

dimer stability, for which values between 1/3 (di-

mer stable and immobile) and 2/5 (dimer stable

and mobile) are expected. It is inconsistent withdimer instability, for which a value of 1/2 should

result. Thus, this measurement also contradicts the

FIM result for Eb;2.Lastly, we performed DFT calculations for an

Ir ad-dimer on Ir(1 1 1), analogously to those re-

s derived by STM, FIM, and DFT (using GGA or LDA)

Ed;2 (eV) Eb;2 (eV) Eb;2=Ecoh

0.44(5) 0.73a 0.11a

0.88b 0.13b

ð2Þ [25] 0.45(1) [26] 0.31b [9] 0.045b [9]

0.73 0.11

0.08 0.34a 0.10a

0.37b 0.11b

0.08 [28] 0.52 [30] 0.15 [30]

0.13 [29] 0.49 [8] 0.14 [8]

0.58 [24] 0.17 [24]

0.45 [30] 0.13 [30]

[31] 0.34(4) 0.62a 0.11a [2]

0.64b 0.11b

ð2Þ [26] 0.37(2) [26] 0.23(1) [9] 0.039b [9]

0.37 [33] 0.50 [2] 0.085 [2]

0.48 [33] 0.082 [33]

marked by * are estimated, see text. The cohesive energy Ecoh isin parentheses give the error of the last digit.

Fig. 3. Rescaled island densities n for Ir(1 1 1) (j), Pt(1 1 1) (�),and Al(1 1 1) (N), see text. Vertical line at Eb;2 ¼ 0:11 Ecoh.Lines to guide the eye.

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ported earlier for Pt(1 1 1) [2]. By using the local

density approximation (LDA) known to be more

accurate for the 5d-transition metals than the

generalized gradient approximation (GGA) [14],

we obtained Eb;2 ¼ 0:73 eV for the dimer in thefavored hcp position, in good agreement with theSTM results but more than double the FIM value.

The calculations were performed using the

VASP [15–18] total-energy code, its ultrasoft

pseudopotentials [19–21], which make a 14.6 Ry

plane-wave cutoff sufficient for Ir, and the Ceper-

ley–Alder local exchange-correlation potential

[22]. We model Ir adsorption on Ir(1 1 1) by plac-

ing the adatoms on the upper surface of a 6-layerIr slab. The atoms of the lowermost three slab

layers are fixed at bulk relative positions and the

rest allowed to relax till forces on them are <0.03

eV/�AA. We set the slab lattice parameter to 3.82 �AA,the bulk LDA value for a 60 point sample of the

irreducible 48th of the Brillouin Zone (expt.¼ 3.84�AA). To accelerate electronic relaxation, we employMethfessel and Paxton�s Fermi-level smearingmethod (width¼ 0.2 eV) [23]. We obtain the Ir ad-dimer binding energy, by subtracting twice the

total energy of a Ir(1 1 1)-3� 2ffiffiffi

3pslab with one Ir

adatom per supercell from the sum of the total

energies of two 3� 4ffiffiffi

3p

slabs, one clean and one

supporting an ad-dimer with Ir adatoms in near-

est-neighbor threefold hollows. The calculations

were done using a 4 · 4 sample of the supercellSurface Brillouin Zone.

For Al(1 1 1) the situation is less clear cut. Ex-

perimentally the data at low T scatter a little moreand no clear distinction between regimes I and II is

possible. The naı̈ve interpretation of the slope

above Ecoh=kT ¼ 198 (below T ¼ 200 K) is that itsimply represents adatom diffusion. Thus, Ed;1 ¼ð0:07� 0:01Þ eV and m0 ¼ 5� 1011 s. However, allDFT calculations for Ed;2 [8,24] indicate efficientdimer mobility already at our lowest T . Thus thelow-T slope more likely belongs to regime II,

yielding Ed;1 þ Ed;2 ¼ ð0:12� 0:01Þ eV, in fair

agreement with the corresponding sum of the DFT

values [7,8,24] (compare Table 1). Therefore, we

use the DFT value of 0.04 eV as estimate for Ed;1.From the marked bend at 200 K, which we thenattribute to the transition between regimes II and

III, and using the transition temperature method,

we obtain the two estimates Eab;2 ¼ 0:34 eV andEbb;2 ¼ 0:37 eV. (Using the na€ııve value, Ed;1 ¼0:07� 0:01 eV, instead would only marginallychange these results.)

In Ref. [2] we published a data set for Pt(1 1 1),

similar in quality and completeness to that pre-

sented here for Ir(1 1 1). Ed;1 and m0 as well as thenewly derived value for Ed;2 (see Table 1) againagree with the corresponding FIM results to

within the experimental error. However, Eb;2 isagain nearly three times larger than the corre-

sponding FIM binding energy.

Comparing our STM results for Eab;2 to experi-mental values of Ecoh makes it plain (see Table 1)that Eab;2 ¼ ð0:11� 0:01Þ Ecoh. Using the unbiasedvalue m0;diss ¼ kT=h increases the scatter slightly butEbb;2 still scales quite well and is between 11% and13% of Ecoh.The STM island density analyses thus imply

that details of the Ir, Al, and Pt electronic struc-

tures little affect what fraction of Ecoh binds dimeratoms to each other. In fact, a universal T -dependence of n emerges when the x-axis in theisland density plot for each material is rescaled bya ¼ ½lnðm0nt=F Þ � Ed;1=kT ��1, leading at Tt to aEcoh=kTt ¼ Ecoh=Eab;2. Fig. 3 shows, that all three datasets then fall on a universal curve, which bends

down at approximately the same island density ntand aEcoh=kT 9, i.e., when Eb;2 0:11 Ecoh.

Fig. 4. Minimum energy path for dimer dissociation on Ir(1 1 1)

at a kink position of a {1 0 0}-microfacetted step. The dissoci-

ation process proceeds by concerted motion of dimer and step

atoms. The intermediate minimum corresponds to the step edge

atom in an hcp-site. The barrier amounts to 0.30 eV and the

process is exothermic by about 1.2 eV.

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How do ab initio calculations compare to the

STM results? The LDA value for Ir(1 1 1) is in

good agreement with the STM experiments, al-

though the exact numerical agreement with Eab;2 iscertainly fortuitous. For Pt(1 1 1), the LDA yields

Eb;2 smaller by more than 0.1 eV (20%) comparedto STM. The LDA values for Eb;2 on Al(1 1 1) areclearly much too large. The GGA result, however,

exceeds the STM value by 20%, comparable to the

error for Pt (though in the opposite direction).

Thus, DFT binding energies differ by ±20%

from our STM studies and scale less well. This

discrepancy is small, however, compared to the

disagreement of more than a factor of two betweenFIM values of Eb;2 and all other calculationsand measurements for Ir and Pt(1 1 1) (see Table

1).

In a previous publication on ad-dimer binding

on Pt(1 1 1) [2] we proposed an explanation of this

discrepancy, pointing out that FIM probably

measures dimer dissociation at step edges, where it

is facile, rather than on the terrace, where it ne-cessitates much higher activation energies (see also

[35,36]). This is likely, since the ad-dimers are

highly mobile at their temperature of ‘‘dissocia-

tion’’, and thus frequently encounter the edge of

an apex plane with a typical radius of only 15–20

nearest neighbors.

However Wang and Ehrlich (W&E) argue

otherwise [37], on the basis of dimer dissociationproducts observed on and around the apex plane

of an Ir(1 1 1) FIM tip. They point out that once

an Ir adatom reaches a step bounding the Ir(1 1 1)

plane, it never returns to the plane�s central region,nor does it move around the circumference. It

stays in its boundary site until, eventually, it dif-

fuses, or exchanges such that an atom finally ap-

pears at the bottom of the step. On this basis,W&E contend that if, following a dimer dissocia-

tion event the two adatom partners are found far

apart at the step bottom, the dissociation must

have occurred on the terrace. Had it taken place at

the step, the partners would have been found ad-

jacent to each other at the step bottom. Since they

saw not only paired adatoms at the step bottom

(indicative of dimer dissociation at the step edge),but also a large fraction of widely separated ada-

toms at the step bottom following dimer dissoci-

ation at 250 K, W&E concluded that dissociation

on the terrace is facile, and that their earlier de-

duction of an 0.31 eV dimer binding energy was

largely correct.

This conclusion seriously conflicts with our

STM results and our LDA calculations. As notedabove, the LDA value of Eb;2 is 0.73 eV, which,together with Boisvert et al.�s Ed;1 ¼ 0:24 eV im-plies an LDA dissociation barrier of 0.97 eV. This

is much larger than the activation energies, 0.33

and 0.35 eV, we estimate for dimer dissociation at

the two types (A-type and B-type) of dense packed

steps on the basis of calculations similar to those

we reported for Pt. W&E say that dissociation atsteps and on terraces are both facile at 250 K.

LDA and the STM measurements imply that only

dissociation at steps can be.

One way out of the quandary is to consider the

atomic step edge structure of a FIM apex plane. It

not only consists of dense-packed steps but also a

large number of kinks, as seen e.g. in Fig. 2a of

Ref. [37]. For dimers at kinks, using J�oonssonet al.�s Nudged Elastic Band method [38], we cal-culate small dissociation barrier values as well. An

example is shown in Fig. 4, where a dimer disso-

ciates from the initial hcp position at a kink of a

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{1 0 0}-microfacetted step with the calculated ac-

tivation energy of 0.30 eV. Taking into account

that the dimer in the initial state configuration is

disfavored by 0.07 eV compared to an hcp-terrace

dimer, an effective activation energy of about 0.37

eV results from our calculations, similar to thevalues at the straight steps. However, contrary to

the situation at the straight steps, the dissociation

process at a kink creates a terrace adatom, which is

not located at the step, but one lattice row behind

it. Therefore the adatom is not subject to step edge

trapping. It may diffuse on the apex plane terrace

and finally incorporate into the step far away.

Thus dimer dissociation at kinks is likely to ex-plain the post dissociation pattern, which W&E

attributed to terrace dissociation events.

In summary, Eb;2 scales with Ecoh for threefcc(1 1 1) surfaces, which implies that details of the

Ir, Al, and Pt electronic structures little affect what

fraction of Ecoh binds dimer atoms to each other.The DFT result for Ir(1 1 1) shows good agreement

with the value obtained by STM, while the resultsfor Pt and Al scatter around the experimental

values about 20% or more. The FIM values for

Eb;2, lower by at least a factor of two than thoseobtained with the other approaches, appear to be

due to enhanced ad-dimer dissociation probabili-

ties at the steps and kinks of the FIM apex plane

as clarified by our DFT calculations. For Eb;2 onfcc(1 1 1) only two more estimates exist: ForRh(1 1 1) Eb;2 ¼ ð0:10� 0:07Þ Ecoh [39] and appli-cation of the transition temperature method to the

data for Pd(1 1 1) [40] yields Ebb;2 ¼ 0:10 Ecoh. It isthus plausible that the relation Eb;2 0:11 Ecoh is asuitable guide to estimate Eb;2 on other fcc(1 1 1)metal surfaces as well.

Acknowledgements

This work was supported by the Deutsche

Forschungsgemeinschaft and the DOE Office of

Basic Energy Sciences, Division of Material Sci-

ences. Sandia is a multiprogram laboratory oper-

ated by Sandia Corporation, a Lockheed Martin

Company, for the United States Department ofEnergy under contract DE-AC04-94AL85000.

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