We use atom-tracking scanning tunneling microscopy to study the diffusion of Pd in the Pd/Cu(001) surface alloy. By following the motion of individual Pd atoms incorporated in the surface, we show that Pd diffuses by a vacancy-exchange, mechanism. We measure an effective activation energy for the diffusion of incorporated Pd atoms of 0.88 eV, which is consistent with an ab initio calculated barrier of 0.94 eV

Bartelt, Norman C.

Grant, M. L.

Hannon, J. B.

Swartzentruber, Brian S.

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t; IDiffusion Kinetics in the Pd/Cu(OOl) Surface AlloyM. L. Grantl, B. S. Swartzentruber2, N. C. Bartelt3, and J. B. HannonllDepartment of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-38902Sandia National Laboratories, Albuquerque, New Mexico 871853Sandia National Laboratories, Livermore, California 94551(Dated: November 17, 2000; received; revised; accepted; published)We use atom-tracking scanning tunneling microscopy to study the diffusion of Pd in thePd/Cu(OOl) surface alloy. By following the motion of individual Pd atoms incorporated inthe surface, we show that Pd diffusesby a vacancy-exchange,mechanism. We meaaurean effec-tive activation energy for the difision of incorporated Pd atoms of 0.88 eV, which is consistentwith an ab initio calculated barrier of 0.94 eV.PACS numbers: 68.35.Fx, 66.30.Jt, 05.40.Fb, 07.79.CZ.Whereas the stability of many alloy structures is un-derstood quantitatively, the kinetics of alloy formationand ordering are largely unknown. Characterizing theseprocesses is difficult because the local chemical and struc-tural environment is usually inhomogeneoue. In addition,determining the motion of individual atoms is challeng-ing experimentally, However, by choosing simple alloygeometries it is possible to characterize particular kheticprocesses in detail. In this letter, we investigate the or-dering Kketics of Pd/Cu alloys by following the motionof individual Pd atoms incorporated in the CU(OO1)sur-face, By measuring the time between diffusion eventsand the distribution of jump lengths, and comparing theresults to Monte Carlo simulations and first-principlestotal-energy calculations, we show that incorporated Pdatoms diiuse via lateral exchange with surface vacancies.Pd atoms are immediately incorporated into theCU(OO1) surface when deposited at room temperature.For coverages greater than 0.4 monolayer (ML), an or-dered c(2 x 2) alloy structure is observed [1]. The Pdatoms are confined to the top layer of the substrate ina checkerboard pattern characterized by Cu-Pd nearest-neighbors. First-principles electronic structure calcula-tions show that the tendency to form thk ordered sur-face alloy is particularly strong [2]. Annealing the alloystructure above 425 K results in Pd diffusion into thebulk [3]. The mechanism by which randomly incorpo-rated Pd atoms form the ordered c(2 x 2) alloy phaseremains unknown. Two possible ordering mechanismshave been considered in the literatme [4–6]. One possi-bility is that an incorporated Pd atom exchanges with aCu adatom. The Pd atom, now on the surface, diffusesrapidly and eventually incorporates at a new location.Schmid et al. found that thk mechanism is operative fora Cu/Co monolayer on Ru(OO1) [5]. An alternative mech-anism, originally proposed by Flores et al, in a study ofMn/Cu(OOl), is vacancy-mediated diffusion [4]. In thisscenario, an incorporated Pd atom diffuses via lateralexchange with a vacancy at the surface. In contrast toFIG. 1: STM Image (95x 85 ~2) of the CU(OO1)surfaceafter deposition of 0.01 ML of Pd at room temperature.The large protrusions are incorporated Pd atoms.adatom-mediated diffu.+on, the Pd atom remains incor-porated aa it dfises. Recent measurements show thatIn atoms incorporated in CU(OO1) diffuse via this mech-anism [6].We use atom-tratilng scanning tunneling microscopy(STM) [7] to follow the motion of incorporated Pd atomswith a time resolution of 1 ms. In atom tracking STM alateral feedback mechanism is used to lock the tip abovean incorporated Pd atom as it moves. By recording theposition of the atom as a function of time, we determinethe mechanism of diffusion. Specifically, by comparingthe measured distributions of residence times and jumplengths to Monte Carlo simulations, we show that incor-porated Pd atoms dfluse via vacancy exchange. Frommeasurements of the average hop rate as a function ofsubstrate temperature, we extract an activation energy?.DISCLAIMERThis report was prepared as an account of work sponsoredby an agency of the United States Government. Neitherthe United States Government nor any agency thereof, norany of their employees, make any warranty, express orimplied, or assumes any legal liability or responsibility forthe accuracy, completeness, or usefulness of anyinformation, apparatus, product, or process disclosed, orrepresents that its use would not infringe privately ownedrights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constituteor imply its endorsement, recommendation, or favoring bythe United States Government or any agency thereof. Theviews and opinions of authors expressed herein do notnecessarily state or reflect those of the United StatesGovernment or any agency thereof.Portions of this document may be iilegiblein electronic image products. Images areproduced from the best available originaldocument.tIi1.!“I![i,ib1I/[t~Ii!,$i!,~IIIItI{kI,IIi,$>I,.,tIIII[Ir[——— —.— .— .—,----- - . -a.. ... -. . - . ..—- ... .— ... .2for Pd diffusion of 0.88& 0.03 eV. Formally, this activa-tion energy is the sum of the vacancy formation energyand the vacancy-Pal exchange barrier.To compute configuration energies, we use theVASP (Vienna ah initio simulation package) [8] total-energy code, its ultrasoft pseudopotentials [9], and thePerdew-Wang ’91 version of the Generalized GradientApproximation[IO]. The computational unit cells are2fi x 2@ x 6 layers and the total energy is determinedfrom 8-10 k-points. We find that the large number oflc-points is critical to determine a properly convergedenergy, To compute the transition barrier energies, weuse J6nsson, Mills, and Jacobsen’s nudged elastic bandmethod[ll] within the VASP total-energy code.The experiments are performed in ultra-high vac-uum (base pressure 1 x 10–10 torr) using a variable-temperature STM. A clean CU(OO1) surface is obtainedby repeated cycles of sputtering for 15 minutes with lkVNel_ ions, followed by annealing at 800 ‘C for 5 min. Lowcoverages of Pd (< 0,01 ML) are deposited by heating atungsten filament wrapped with Pd wire. The STM im-ages and tracking data were recorded in constant currentmode with a tip-sample bias of-20 mV. Use of tunnelingbiases in the range -3 V to +3 V produced no measurableeffect on the measured kinetics or images.Upon deposition at room temperature, Pd atoms im-mediately place exchange with Cu atoms in the surfacelayer, forming a ultra-thin alloy. An image of the surfacefollowing deposition is shown in Fig. 1. The Pd atomsare imaged as large protrusions and are located on latticesites. A lateral feedback mechanism that continuouslymoves the tip ‘uphill’ is used to lock the tip above a Pdatom. The diffusion path of the Pd atom is determinedby recording the position of the tip as a function of time.Typically the tip position is recorded at a rate of 1 kHz.A two-dimensional map of the sites visited by a Pd atomat 62 ‘C is shown in Fig. 2. In this particular data set,the diffusing Pd hopped 71 times in 431 seconds (somesites are visited more than once).By analyzing the Pd coordinates as a function of timewe determine the residence time – the time between hops.The distribution of residence times for a Pd atom diRus-ing at 62 ‘C is shown in Fig. 3. In this data set, the atomhopped 853 times in a time interval of 5557s. If the timebetween Pd hops is uncorrelated, the distribution of resi-dence times should decay exponentially. The solid line inFig, 3 is an exponential decay with decay constant equalto the average residence time. The agreement betweenthe solid line and the data points indicates Pd dtilon isan activated process, and there is no correlation betweenPd diffusion events.An analysis of the temperature dependence of Pd dif-fusion shows that from 31 ‘C to 69 ‘C, the average res-idence time decreases from 145.3 s to 5.0 s. BecausePd diffusion is an activated process, the hopping ratesmeasured for this temperature range follow an A.rrheniusform with an activation energy of 0.88+ 0.03 eV (Fig.>LxFIG. 2: Site visitation map of a Pd atom at 62 “C, withthe CU(OO1)unit mesh superimposed.4).F!romthe experimental data taken at 62 ‘C, we compilethe distribution of jump lengths, as seen in Fig. 3 (darkbars). The distribution shows that many of the jumpsare longer than the CU(OO1) nearest-neighbor distance(a=, 2.55 ~). Thereis a 75.2% chance that the Pd atomappears to take a single hop, 17.0% for a diagonal (ma)hop, and 4.2% probability of a longer jump (2a). Withinthe statistical error, the distribution of jump lengths is in-dependent of temperature over the range 31 “C to 69 “C.Jumps greater than unit length are actually comprised ofa ‘burst’ of single hops in rapid succession. Because themotion of the Pd atom during the burst is too fast for theatom tracker to resolve, we cannot measure the details ofthe path during the long jump. Rather, we measure thetime between the short bursts of jumps.In the context of the two potential diffusion mecha-nisms, a burst has distinct meanings. For the adatom-exchange mechanism, the burst corresponds to the Pdadatom diffusion on the surface before reincorporationback into the surface. We would measure only the initialand final incorporated states. In this picture, the rate atwhich bursts occur is governed by the rate at which anincorporated Pd atom exchanges with the Cu adatoms.For vacancy-mediated diffusion, a burst corresponds to~E(xm!EDm 222000-. ---- .,, ,/, ..-.4, ........ .......,-~- .,,.,.,,-“x, ... .. . .. . . . . .. .. . . . . . . ... . . . ,,,.. . . .1 4 r3o 10 20 30 40Residence T ime (s)0,8‘ 1b),5°’6=a:0,4&lDLb-_J1 ‘1-z 2VT Tr3Ym r3Hop Length (latticeconstants)FIG, 3: (a) Residence time distribution (time betweenmeasured Pd hops) at 62 ‘C. The solid line is the ex-pected exponential decay if the time between hops is un-correlated. (b) Distribution of jump lengths at 62 “C.Dark bars represent experiment whereas the shaded barsare simulation.the repeated visitation of the Pd atom by a (rapidly) dif-fusing surface vacancy. The rate of Pd diffusion is deter-mined by the visitation rate of surface vacancies. Thesetwo rates are governed by very different energetic. First-principles calculations indicate the activation energy forPd-Cu adatom exchange is 1.16 eV, while the activationenergy for vacancy diffusion is only 0.466 eV.The distributions of jump lengths for the two mecha-nisms are also quite different. To see this, we consider thefraction of jumps of length @a. Since Pd atoms incorpo-rate randomly at room temperature, rather than at steps,the probability of incorporation must be comparable tothat of surface diffusion. In thk limit, a Pd atom thatexchanges with a Cu adatom will not diffuse far beforem-exchanging. The jump length distribution can be com-puted trivially if we assume the Pd atoms immediatelyre-exchange into the surface. The number of fia hopswill be half that of single hops. For vacancy-mediateddiffusion, the fraction of @a hops is much lower. Thereason for this is that the vacancy must execute a mini-mum of four coordinated hops in order to move the Pdatom diagonally. In our experiments, we measure a ratioof flu to single hops of about 0.23, significantly lowerthan the estimate for the adatorn-exchange mechanism-: \5SuE = 0.880.1~c1al(n r50.03 eV34 35 37 38I/k? (e~ )FIG. 4 Temperature dependence of the average hop rateof an incorporated Pd atom. The data follow an Ar-rhenius form with an activation energy of 0.88 eV andmeasured prefactor of 1012”4+0”4Hz.(0.5).These simple arguments can be made precise by simu-lating the two dtilon processes using Monte Carlo tech-niques. In the simulation for exchange diffusion there isone free parameter: the average number of hops com-pleted on the surface before re-incorporation. This pa-rameter is governed by the ratio of the surface hop rateto the incorporation rate. The best agreement with ex-periment is achieved when the incorporation rate is com-parable to the hop rate. However, even in this limit thecomputed jump length distribution does not describe ex-periment: there are far too few single hops, too manydiagonal hops (greater than 30%), and a long tail of hopsgreater than 2a. Consequently, the measured distributionof jump lengths can never be attained for the exchangedif&ion model, due to the consistently-high percentageof predicted diagonal hops.On the other hand, Monte Carlo simulations forvacancy-mediated diffusion accurately describe the data.In the simulation a vacancy executes a random walk on agrid with periodic boundary conditions. We initially as-sume no interaction between the vacancy and Pd. Sincethere is infinite time resolution in the simulation, onlysingle hops of the Pd are observed. We account for thefinite sampling time of the atom tracker (At= 1 ms) by‘binning’ the simulation data. The free parameter in thismodel is the ratio of the vacancy hop rate to the samp-ling rate. Once bimed, the simulation data exhibits theanticipated trend of a low probability of diagonal jumps.However, a small but significant discrepancy betweenthe simulation and measurement remains. Experimen-tally 75% of the hops are of unit length, whereas the va-cancy simulation predicts 62~0. Thk discrepancy arises~r.!,.,.,:, ,. .,... ‘.4from our initial assumption of negligible interaction be-tween the Pd atom and vacancy. A repulsion betweenthe vacancy and Pd reduces the number of long jumps.Intuitively, we expect a repdsion. Pd exchanges witha Cu atom in the first place due to its higher aflin-ity for Cu neighbors. Therefore, removing one of thoseneighbors through the presence of a vacancy results in ahigher energy configuration. Including a small nearestineighbor (< 50 meV) repuKlon between the vacancy andPd atom in the simulation leads to quantitative agree-ment between the measured and calculated jump lengthdistributions. This is seen in the shaded bars of Fig. 3,where a 40 meV repuk40n between the vacancy and Pdatom[12] results in a high percentage of single hops, withthe appropriate number of diagonal hops. Consequently,we conclude that the diffusion of the Pd in the surfacealloy proceeds via a vacancy mediated mechanism.Since the hop rate is not correlated, the rate shouldbe proportional to both the vacancy concentration andvacancy hop rate. Therefore, the activation energy forPd diffusion is equal to the sum of the vacancy formationenergy and the energy barrier associated with lateral Pd-vacancy exchange. The computed energies using VASPare 0.474 and 0.466 eV, respectively. The sum (0.94 eV)is consistent with the measured activation energy of 0.88eV, In the adatom-exchange model, the activation en-ergy corresponds to the sum of the Cu adatom formationenergy and the Pd-Cu exchange barrier. Within VASPthe sum of these barriers is 1.73 eV and is clearly in-consistent with the measured activation energy. Theseresults further support our conclusion that the diffusionof incorporated Pd atoms occurs via vacancy dtiusion.In summary, by measuring the motion of incorporatedPd atoms as a function of temperature, and compar-ing the results to Monte Carlo simulations and ilrst-principles total-energy calculations, we conclude that Pdatoms diffuse via a vacancy-mediated mechanism. Com-parison of the measured distribution of jump lengthsagrees well with Monte Carlo simulations of vacancy-exchange if a small repulsion between the Pd and va-cancy is assumed. The measured activation energy for Pddiffusion (0.88 eV) is consistent with the firstiprinciplescalculations of the sum of the vacancy formation energyand vacancy diffusion barrier. The experiments were per-formed at Sandia National Laboratories, a multiprogramlaboratory operated by Sandla Corporation, a LockheedMartin Company, for the US DOE under contract No.DEAC04-94AL85000.REFERENCES[I] S. H. Lu, Z. Q. Wang, S. C. Wu, C. K. C. Lok, J.Quinn, Y. S. Li, D. Tian, F. Jona, and P. M. Mar-cus, Phys. Rev. B 37, 4296 (1988); P. W. Murray,I. Stensgaard, E. Laegsgaard, and F. Besenbacher,Phys. Rev. B 52, R14 404 (1996); P. W. Murray,1. Stensgaard, E. Laegsgaard, and F. Besenbacher,[2][3][4][5][6][7][8][9][10][11][12]Surf. Sci. 365,591 (1996).J. Kudrnovsky, S. K. Bose, and V. Drchal, Phys.Rev. Lett. 69,308 (1992).A. R. Koymen, K. H. Lee, G. Yang, K. O. Jensen,and A. H. Weiss, Phys. Rev. B 48, 2020 (1993).T. Flores, S. Junghans, M. Wuttig, Surf. Sci. 371,14 (1997).A. K. Schmid, J. C. Hamilton, N. C. Bartelt, and R.Q. Hwang, Phys. Rev. Lett. 77,2977 (1996).R. van Gastel, E. Somfai, W. van Saarloos, and J.W. M. Frenken, (unpublished).B. S. Swartzentruber, Phys. Rev. Lett. 76, 459(1996).G. Kresse and J. Haber, Phys. Rev. B47, 558(1993); Phys. Rev. B49, 14251 (1994); G. Kresseand J. Furthmii.ller, Comput. Mat. Sci. 6, 15 (1996);Phys. Rev. B54, 11169 (1996).D. Vanderbilt, Phys. Rev. B41, 7892(1990); A.Pasquarello, K. Laasonen, R. Car, C. Lee and D.Vanderbilt, Phys. Rev. Lett. 69, 1982(1992); K. Laa-sonen, A. Pasquarello, R. Car. C. Lee and D. Van-derbilt, Phys. Rev. B47, 10142(1993); G. Kresse andJ. Hafner, J. Phys.: Cond. Mat. 6, 8245(1994).J. P. Perdew, in Electronic Structure of Solids ’912edited by P. Ziesche and H. Eschrig (Akademie Ver-lag, Berlin, 1991); J. P. Perdew and Y. Wang, un-published.H. J6nsson, G. Mills, and K. W. Jacobsen, in Clas-sical and Quantum Dynamics in Condensed PhaseSimulations, edited by B. J. Berne, G. Ciccotti, andD. F. Coker (World Scientific, Singapore, 1998).The VASP total-energy calculations yield a vacancy-Pd repulsion of 45 meV. ~

Diffusion Kinetics in the Pd/Cu(001) Surface Alloy

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Diffusion Kinetics in the Pd/Cu(001) Surface Alloy

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