VOLUME 93, NUMBER 8 P H Y S I C A L R E V I E W L E T T E R S week ending20 AUGUST 2004

Novel Local Free Energy Minimum on the Cu(001) Surface

Mikhail Ovsyanko, Georgiana Stoian, Herbert Wormeester,* and Bene PoelsemaMESA+ Research Institute, University of Twente, P. O. Box 217, 7500 AE Enschede, The Netherlands

(Received 15 December 2003; published 17 August 2004)

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High-resolution LEED (low-energy electron diffraction) data of Cu(001) reveal an uniaxial in-planelattice reconstruction by 1%. One-dimensional nanogrooves induced by ion bombardment involve thecreation of steps that enable this reconstruction. This is the first verification of van der Merwe’sprediction of step facilitated reconstruction. We confirm the predicted dependence on step orientation:h100i steps allow stress-relief and h110i steps do not, consistent with the known elastic anisotropy.Similar behavior is predicted for other nonreconstructed (001) surfaces of 3d and 4d metals.

DOI: 10.1103/PhysRevLett.93.086103 PACS numbers: 68.35.Md, 68.03.Cd, 68.35.Bs

4.90

4.95

5.00

5.05

-3 -2 -1 0 1 2 3

Sz

k// [%BZ]

FIG. 1 (color online). Plot of the specular beam profile alongthe [010] azimuth after 21600 s sputtering at 235 K forperpendicular scattering factor Sz between 4.92 and 5.10.Note that the intensity of the (0,0) spot is cut off (shown aswhite) in order to enhance the diffraction features.

The creation of a surface requires the breaking ofatomic bonds. The resulting lower coordination numbermakes the surface atoms strive for smaller interatomicdistances as noted first by Pauling [1]. This induces ingeneral an inward relaxation of the exposed layer andconsiderable tensile in-plane stress. Needs [2] calculatedthe tensile stresses for Al-metal surfaces as high as�10 GPa. Dodson [3] performed thin slab calculationsfor the (001)-surfaces of Ni, Ag, Cu, Pd, Au, and Pt. Heobtained a surface strain of several percents, increasingfrom Ni to Pt. Indeed, it has been found experimentally[4] that some (001)-surfaces of transition and noble met-als do reconstruct. Their termination is a (111)-like over-layer that periodically matches the (001)-bulk structure.The decision whether the (001)-surface does reconstructor not is quite subtle. The adsorption of small amounts ofatoms or molecules can lead to deconstruction [5,6]. In anab initio density-functional-theory study, Fiorentini et al.[7,8] investigated the tendency for (001)-transition metalsurfaces to reconstruct. They find that surfaces of themetals at the end of the 5d transition series such as Ir,Pt, and Au reconstruct, whereas their 4d counterparts Rh,Pd, and Ag do not. Reconstruction requires bond rear-rangements, leading to significant energy losses due to thedisruption or stretching of bonds between the mismatchedlayer and that underneath. The reconstruction results froma delicate balance between surface-substrate mismatchand strain related energy gain [7,8]. Their high strainenergy favors reconstruction for the 5d (001)-surfaces,while it is too small for their 4d and 3d counterparts. Thesurfaces of the 3d and 4d metals remain unreconstructedin agreement with experimental observations.

The claim by Muller et al.[9] of an in-plane reconstruc-tion of clean Cu(001) created a sensation. They found acontraction of about 1% from their LEED (low-energyelectron diffraction) I-V-analysis. Their finding provided anice framework for the contraction of 1% found for thepseudomorphic growth of Fe/Cu(001) [10–12]. TheCu(001) in-plane reconstruction was challenged both ex-perimentally [13,14] and theoretically [15]. Muller et al.[16] conceded and attributed their findings to either a

0031-9007=04=93(8)=086103(4)$22.50

‘‘lower lateral crystallinity’’ of their surface or ‘‘system-atic errors affecting the accuracy of their analysis.’’ In alater LEED-I-V-study, Walter et al.[17] indeed obtainedsmaller in-plane relaxation by introducing an energydependent inner potential.

We find experimental evidence for a new local mini-mum in the free energy of Cu(001). Indeed, Cu(001) has astrong tendency for an in-plane lattice contraction of 1%.It only prevails on surfaces with a finite amount of steps,when oriented along the h100i-azimuth. Note that h100i isthe soft direction with respect to deformation [18]. Thisgeometry permits to relieve tensile stress. This result is ofgeneral importance to the 3d and 4d (001)-metal surfaceswith implications for the creation of nanostructures on orin these surfaces and the structure of hetero-epitaxialislands.

Our method of choice to characterize the morphologyof surfaces is spot profile analysis low-energy electrondiffraction (SPA-LEED), with a resolution of �0:1% ofthe Brillouin Zone (BZ). All experiments have beenconducted in ultrahigh vacuum (pressure <10�10 mbar).

2004 The American Physical Society 086103-1

VOLUME 93, NUMBER 8 P H Y S I C A L R E V I E W L E T T E R S week ending20 AUGUST 2004

After a standard cleaning procedure, the flat Cu(001) sur-face has a mean terrace width of 80 nm, as derived fromthe FWHM of the (0,0)-beam in SPA-LEED. We haveextensively looked, but in accordance with Refs. [13–15],never found any indication for in-plane lattice recon-struction on the clean and flat Cu(001) surface.

The experiments that led to the observation of an in-plane reconstruction started by bombarding the Cu(001)surface at a selected temperature with 800 eV Ar� ions ata flux of 2� 1014 ions=m2s. The polar angle of incidenceis 80� and the azimuth direction chosen along [100].Under these conditions highly regular and only two layerdeep nanogrooves are formed, running parallel to theplane of incidence of the ions [19]. The distance betweenthe nanogrooves, or better, the periodicity of the one-dimensional nanopattern, depends on temperature, ionenergy, flux, and fluence. Figure 1 shows typical diffrac-tion features as a function of the parallel wave vector k==in SPA-LEED and the perpendicular scattering factor Szafter bombardment with a fluence of about 5�1018 ions=m2. The scattering factor Sz is defined by Sz �2d001=�, where d001 is the spacing between the atomplanes normal to (001) and � the electron wavelength.In these data, obtained with the substrate at 235 K, twoeye-catching features are visible next to the dominantspecular beam. One feature appears at a k==-value of about2.4% BZ. This feature is related to the periodicity of thenanogroove pattern, corresponding to 102 6 �A. Theother feature emerges at about 1% BZ, i.e., a periodicityof about 250 A. In similar experiments, performed at200 K and 175 K, the nanogroove pattern has a periodic-ity of about 71 A and 69 A, respectively. In all these caseswe observe a feature in the specular beam profile thatcorresponds to a much larger length scale of 250 25 �A.

-4 -2 0 2 41000

10000

100000

Inte

nsity

[ct

s/s]

k// [% BZ]

10000

100000

FIG. 2. SPA-LEED profile along [010] after sputtering for3600 s at 235 K (top) and subsequent annealing at 290 K for500 s (bottom).

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Within the accuracy, the latter feature coincides with thatobserved after bombardment at 235 K (Fig. 1). We em-phasize that the persistent feature appears at a fixed,temperature independent k==-value of 1% BZ, in spite ofthe clear temperature dependence of the nanogrooveperiodicity.

The specular beam profile obtained in a completelydifferent experiment is shown in Fig. 2. The upper panelshows data measured after bombarding Cu(001) again at235 K (cf. Fig. 1), but now after a six times smaller fluence(bombardment time 3600 s). The well-developed wingsindicate a nanogroove separation of 75 A. Subsequentlythe substrate is heated to 290 K. The evolution of thesurface morphology is illustrated by the specular beamprofile in the lower panel of Fig. 2, obtained after a 500 sanneal at 290 K. The initially clearly visible wings notonly decrease in intensity but also move toward thecentral peak, indicating an increase of the periodicityof the nanogroove pattern. Also, the intensity of themain peak increases, demonstrating substantial flatteningof the surface. We note that again, a small maximumfeature beside the main peak at �k== � 1% BZ emerges.This feature is persistent and its position does not dependon the annealing time. It remains present even afterleaving the sample at 290 K for as long as 10.000 s.Annealing of the initial structures at 250 K and at270 K leads to a similar appearance of small peaks,corresponding to 250 A.

The experiments described above show a very persis-tent feature emerging at �k== � 1% BZ. It corresponds toa length scale of 250 25 �A along [010], i.e., normal tothe nanogrooves. Its appearance is independent of thesubstantially varying thermal history. The diffractionfeature does not change its position even at temperatureswith many diffusion processes active on the surface.These combined observations demonstrate a thermo-dynamic origin of this feature.

The observations indicate an in-plane contraction ofthe lattice parameter of 1%. This phenomenon agrees withthe calculated tensile stress of (001)-faces of 3d, 4d, and5d metals [3,7,8]. The reconstruction results from a deli-cate balance between surface-substrate mismatch andstrain release [7,8,15]. We agree and reiterate that thisbalance does argue against reconstruction for smoothCu(001), with Cu being a 3d-metal. However, the actualsituation obtained after bombarding the Cu(001) sampleat grazing incidence along [100] deviates from this idealsituation. We do observe satellites along the [010]-azimuth but not along [100]. Instead of an isotropic in-plane surface plane contraction, the striped pattern onlyallows uniaxial in-plane contraction normal to thegrooves. The easier accommodation of lattice misfits inthe presence of atomic steps was predicted theoreticallyby van der Merwe [20].

We elaborate on the uniaxial in-plane contraction a bitfurther by considering a one-dimensional model.

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0.0 0.5 1.0 1.5

0.0

0.2

0.4

0.6

0.8

1.0

Inte

nsity

K// [%BZ]

FIG. 3. Simulated diffraction intensity at Sz � 4:97 of anatomic chain that only shows a height variation (dashed line)and an additional variation in lateral interatomic distanceaccording to the Frenkel-Kontorova model (solid line). Thecalculated results have been convoluted with the instrumentalresponse function.

VOLUME 93, NUMBER 8 P H Y S I C A L R E V I E W L E T T E R S week ending20 AUGUST 2004

Following van der Merwe [21–23], the periodic first-layeratom-substrate potential is approximated by a truncatedFourier series with an amplitude W. The underlying 1Dsubstrate is assumed completely rigid. The lateral inter-action in the first layer is modeled with springs, with aconstant �. The potential energy of a chain of N atoms,following the notation of Markov [24], given by

E��a2

2

XN�2

n�0

n�1 � n � f�2 �W2

XN�1

n�0

�1� cos2� n� :

(1)

In this, a is the bulk lattice constant, f � b� a�=a themisfit with b the lattice constant of the unstrained first-layer, and n the relative position of the nth first-layeratom with respect to the minimum of the potential well inunits of a. The first term accounts for residual strain dueto the different spacing between the first-layer atoms andb. The last term reflects the energy cost due to the misfitbetween the first layer and the substrate. The full energyminimum results then in a variation of the parallel latticeconstant for the first-layer atoms. In this case, the chainruns in the [010] azimuth. The energy W mimics theenergy difference between a Cu atom in the fourfoldhollow site and in the on-top position. We estimate thatW � 0:8 eV, about twice the activation energy for diffu-sion over the bridge site [25]. The strain relief energy hasbeen calculated using first principles by Fiorentini et al.[7,8,15]. For Cu(001), uniaxially contracted by 1%, theenergy gain amounts to 1.12 eV. This consideration doesnot incorporate the energy for the creation of dislocations,necessary to let the smooth surface reconstruct [7,8]. Thisdislocation energy clearly outweighs the strain reliefenergy, assuring that no reconstruction of the intact sur-face is observed [15]. However, the starting situation inour experiments is not the smooth but rather the nano-grooved surface. First we may consider the resultingsurface as a two-level system. In all situations of rele-vance here, the distance between the nanogrooves issmaller than 100 atomic spacings. The upper level cannow relax without a need for the incorporation of addi-tional dislocations. Obviously, the lower level remainsunreconstructed. The system can now fully profit fromthe energy gain predicted by the Frenkel-Kontorova ex-pression and the numbers quoted above: the presence ofatomic steps on the surface allows local in-plane contrac-tion. This holds even more if, as in our case, the stepsalternate from step-down to step-up. The atoms on thehigher of the two levels will lock in around the minimumenergy positions and the unfavorable positions are notoccupied. We assume first that both exposed levels occupy50% of the surface and that the periodicity of the step-upstep-down sequence equals 250 A. Then the upper levelallows an in-plane contraction at a much lower cost, ascompared to the smooth surface: the ‘‘expensive’’ posi-tions remain now unoccupied.

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The morphology of the real nanogrooved surface isquite complex, even within a simple two-level model inwhich only the upper level is reconstructed. To obtaininsight in the resulting beam profile we have simulatedtwo basic cases with different characteristics. The 1DFrenkel-Kontorova model (Eq. (1)) predicts that relaxa-tion of the upper level layer results in atomic positionsthat deviate laterally from the bulk lattice and undergo acorresponding variation in height. The latter is calledcorrugation and its amplitude amounts to a maximumof a

���2

p. To mimic the effect of corrugation we have

calculated the diffraction profile obtained from a chainof atoms with a periodicity of 100 a, their lateral posi-tions on bulk lattice positions and the vertical positionsvarying as a cosine with amplitude a

���2

p. The chain is

positioned on a 1D bulk crystal. The diffraction has beencalculated using the kinematic approximation and anelectron mean free path of 0.8 nm. This results in strongsymmetric features at 1%, with a FWHM correspondingto the instrumental resolution, see Fig. 3 (dashed line). Inaccordance with the Frenkel-Kontorova model (Eq. (1)),also the lateral position of the first-layer atoms in generaldeviate from the bulk position. This dispersion in lateralposition was also simulated within the same framework(solid line). The dispersion in lateral position leads to astrongly reduced feature compared to the intensity of the(0,0) beam. This intensity reduction can simply be ex-plained by the fact that the effective height distribution ofthe atoms is narrower. Additional calculations for variousfractions occupied by the upper level (coverage), varyingfrom 10 to 50%, show a small but persistent spectraldensity at 1% of the first Brillouin Zone. This spectraldensity remains rather constant with coverage. The lattercan be understood easily: for ‘‘low’’ coverage the atomscan fully relax and still remain quite near to the bottomof the potential wells. The effective upper layer lattice

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distance is then close to 0:99 a. For ‘‘high’’ coverage thesituation approaches the result for the second calculationdescribed above. In the latter case, the density at 1% BZ ismainly caused by the intrinsic length scale of 100 a of thecorrugation profile. Even with this simple model theobtained strength is of the order of the experimental data.

We note that Stepanyuk et al. [26,27] have calculatedin-plane (and out-of-plane) relaxation of lattice parame-ters near the edges of two-dimensional close packedadatom islands. In-plane contractions in the order ofalso 1% have been obtained, the actual value being de-pendent on the size of the islands. We note that our stablediffraction feature at �1% BZ has a distinctly differentorigin. Neither its position nor its magnitude do dependon the size of the structures.

van der Merwe and Kunert [28] also predicted thatrelief of the misfit energy facilitated by atomic stepsdoes depend on their orientation. We also confirm thisresult experimentally. We observe the feature at �k== �1% BZ only after bombarding the surface along h100i.Bombarding along the h110i azimuth never leadsto additional diffraction features. Relieving tensile stressis thus facilitated by preexisting h100i and not by h110ioriented steps. This observation is rationalized in termsof anisotropic elastic properties of the Cu(001) surface.Calculations by Ozolins et al.[18] show that h100i is thesoft direction with regard to lattice deformation. Incontrast, the h111i and the h110i directions are harddirections.

From the width of the diffraction patterns alongthe grooves, we estimate the average length of thegrooves at several hundred A. Reconstruction parallelto the grooves would thus involve accommodation ofa much higher mismatch energy. We also note that re-laxation of tensile stress normal to the grooves poses alocal minimum of the free energy. A relatively mildanneal at 400 K is sufficient to overcome the energybarrier separating the local minimum from the globalfree energy minimum leading to extended smooth (001)terraces.

In conclusion, we have observed an in-plane latticeparameter that is 1% smaller than the bulk lattice pa-rameter. This is due to the relief of the tensile stressinherent to (001)-surfaces of metals. The reconstruction,not observed for macroscopic (001)-terraces, is enabled bythe presence of h100i oriented atomic steps and not byh110i-steps. This is attributed to anisotropic resistanceagainst elastic deformations. The local free energy mini-mum, associated with the in-plane lattice contraction, isseparated from the global one, leading to unrecon-structed Cu(001) surface, by a relatively low-energy bar-rier, which can be overcome by a mild anneal at 400 K.Our results reconcile quite recent controversies in litera-ture. They are considered important for the delicate inter-play between mismatch and tensile stress energies onfcc(001) metal surfaces in general.

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This work is part of the research program of theStichting Fundamenteel Onderzoek der Materie (FOM),financially supported by the Nederlandse Organisatievoor Wetenschappelijk Onderzoek (NWO).

*Electronic address: Corresponding author:h.wormeester@utwente.nl

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