Interatomic potential for the Cu-Ta system and its application to surface wetting and dewetting

An angle-dependent interatomic potential has been developed for the Cu-Ta system by crossing two existing potentials for pure Cu and Ta. The cross-interaction functions have been ﬁtted to ﬁrst-principles data generated in this work. The potential has been extensively tested against ﬁrst-principles energies not included in the ﬁtting database and applied to molecular dynamics simulations of wetting and dewetting of Cu on Ta. We ﬁnd that a Cu ﬁlm placed on a Ta (110) surface dewets from it, forming a Cu droplet on top of a stable Cu monolayer. We also observe that a drop of liquid Cu placed on a clean Ta (110) surface spreads over it as a stable monolayer while the extra Cu atoms remain in the drop. The stability of a Cu monolayer and instability of thicker Cu ﬁlms are consistent with recent experiments and ﬁrst-principles calculations. This agreement demonstrates the utility of the new potential for atomistic simulations of Cu-Ta interfaces


I. INTRODUCTION
Interfaces between different phases are of significant fundamental interest and play an important role in many areas of technology.This is particularly true for interfaces between highly dissimilar phases of very different chemical composition and atomic structure.The Cu-Ta system studied in this work is a good example of such dissimilar phases since Cu and Ta have practically zero mutual solid solubility, have different crystal structures (FCC Cu versus BCC Ta) as well as highly different melting temperatures, mechanical strength, chemical reactivity and many other properties.[3][4] It is well recognized that large-scale atomistic simulations can give new insights into many materials phenomena, particularly occurring at interfaces.A major impediment to their broader application is the lack of reliable interatomic potentials for many materials.
Most of the existing interatomic potentials for metallic systems are based on the Embedded-Atom Method (EAM). 5While accurate EAM potentials have been developed for a few FCC metals (see e.g.Ref. 6 for a review), the method is less reliable for BCC metals in which the interatomic forces include an angle-dependent component.The challenge becomes even greater when dealing with binary systems in which one or both of the main phases are BCC.Although EAM potentials have recently been constructed and applied to simulations of Cu-Ta interfaces, [7][8][9] a more reliable description of bonding in this highly disparate system involving a BCC metal requires a model reaching beyond the regular EAM formalism.
The goal of this paper is to develop an angle-dependent interatomic potential for the Cu-Ta system and to verify its applicability to Cu-Ta interfaces.We choose the functional form of the recently proposed Angular-Dependent Potential (ADP) method 10 and utilize the existing potentials for pure Cu and Ta. 11,12Given that the experimental Cu-Ta phase diagram 13 contains no intermediate solid phases, we fit the cross-interaction functions to firstprinciples data only.To enhance the transferability of the potential to interface simulations, the fitting and testing data include a number of layered crystal structures as well as energyseparation curves for coherent Cu-Ta interfaces.
The potential generation and testing procedures and results are presented in Section II.In Section III we apply the new potential to atomistic simulations of wetting and dewetting of Cu from a Ta substrate.We show that the results of these simulations are well consistent with recent experimental data and first-principles calculations, 14 which confirms the suitability of the potential for atomistic studies of Cu-Ta interfaces.

A. The angular-dependent potential method
To account for the covalent component of bonding in the Cu-Ta system, we apply the ADP method as proposed earlier for the Fe-Ni system. 10In the ADP method, the total energy E tot is written in the form where the Roman indices i and j refer to atoms and the Greek superscripts to Cartesian directions.The first two terms in Eq. (1) represent pair interactions between the atoms and their embedding energies, respectively.Together they constitute the functional form of the regular EAM potential. 5The pair-interaction potential Φ s i s j (r ij ) depends only on the scalar distance r ij between atoms i and j and on their chemical species s i and s j .The embedding energy F s i is a function of the host electron density ρi induced on atom i by all other atoms of the system, ρi = where the electron density ρ s j (r) assigned to atom j is a function of the scalar distance r ij .
Note that the first two terms in Eq. (1) have central-force character, i.e., do not depend on angles between interatomic bonds.
The non-central character of the bonding is represented by the rest of the terms in Eq. (1), which depend on dipole vectors and quadrupole tensors ν i being the trace of λ αβ i : In these expressions, u ss ′ (r) and w ss ′ (r) are the two additional pairwise functions introduced in the ADP method.The new terms depend on angles between interatomic bonds and penalize the total energy for deviations of atomic environments from cubic symmetry.For example, they make contributions to E tot when a cubic crystal is subject to non-hydrostatic strains, thus affecting the elastic constants.They also contribute to the formation energies of ordered compounds.The angular terms modify (generally, increase) the energy of lattice defects and can be especially important in atomically disordered alloys, amorphous solids and liquids.
An ADP description of the binary system Cu-Ta requires 13 functions: Φ CuCu (r), w T aT a (r) and w CuT a (r).In this work we employ the existing EAM potential for Cu 11 and the recently developed ADP potential for Ta. 12 Since the Cu potential is based on the regular EAM formalism, the functions u CuCu (r) and w CuCu (r) are set to zero.With the given Cu and Ta potentials, we only need to construct the cross interaction functions Φ CuT a (r), u CuT a (r) and w CuT a (r).The invariant transformation coefficients s T a , g Cu and g T a (see e.g.

Ref.
6,15 for their definition) are used as additional adjustable parameters.

B. The fitting and testing database
The database used for fitting and testing the Cu-Ta potential contains first-principles data only.For bulk crystal structures, such data have been generated by the plane-wave pseudopotential method as implemented in the CPMD program. 16For the sake of consistency, we kept the calculation parameters as similar to those used for generating the ADP potential for pure Ta 12 as possible.In brief, the calculations employ the local density approximation within the density functional framework.The core states of Ta and Cu are represented by norm-conserving Troullier-Martins pseudopotentials, relativistic for Ta and non-relativistic for Cu.The copper pseudopotential requires the plane-wave cutoff energy as high as 100 Ry, which is used throughout.The k-point sampling in all calculations is approximately equivalent to the 12 × 12 × 12 Monkhorst-Pack grid in 1 × 1 × 1 cubic cell.A specific feature of the Cu-Ta system is an interplay between FCC-and BCC-based structures.To further reduce the errors arising from the numerical integration over the Brillouin zone, all energies are referred to those of pure components having the same lattice, whereas the FCC-BCC energy differences for pure Cu and Ta are evaluated to high precision separately.More details on the numerical setup can be found in Ref. 12.
The phase diagram of the Cu-Ta system shows practically zero mutual solid solubility between Cu and Ta and does not contain any intermetallic compounds or other solid phases. 13We have, therefore, chosen to fit the potential to first-principles binding relations (energy versus atomic volume) for several artificial ordered compounds that do not exist in the phase diagram.Such compounds include L1 2 -Cu 3 Ta, L1 0 -CuTa, L1 1 -CuTa, B2-CuTa and L1 2 -Ta 3 Cu. 17They represent three different chemical compositions and different types of ordering on the FCC and BCC lattices, thus spanning a significant area of configuration space.In addition, an FCC supercell containing a stack of three (111) Cu layers followed by three (111) Ta layers has been constructed to represent coherent Cu-Ta interfaces.The formation energy ∆E of each crystal structure relative to the equilibrium FCC Cu and BCC Ta has been computed for several atomic volumes around the energy minimum.Note that these calculations do not include any relaxation with respect to relative dimensions of the supercells or any internal degrees of freedom.
Binding relations for a few other structures have also been computed but used only for testing the potential.They include artificial FCC-based layered structures containing stacking sequences of (111) CuCuTa and CuTaTa.Furthermore, considering that C11 compounds were found to have rather low energies in the Fe-Ni system, 10 their formation energies in the Cu-Ta system have also been computed for the Cu 2 Ta and Ta 2 Cu stoichiometries.The C11 structure can be thought of as formed from FCC by filling (002) layers in the sequence In addition to the crystal structures indicated above, energies of several 32-atom supercells containing liquid alloys with the CuTa composition have been computed at the potential testing stage.Details of these liquid structures will be explained later (Section II D 2).
For testing the chemical binding across Cu-Ta interfaces, the interface energy as a function of separation has also been included in the database.9][20][21][22][23] These calculations use a supercell composed of five (110) Ta The Cu layers are stretched in in-plane directions to coherency with Ta.There are four different ways of placing a Cu layer on top of Ta (110), referred to here as "on-top", "bridge", "BCC-type" and "FCC-type" (see Ref.

C. Potential parametrization and fitting
The pair-interaction function is chosen in the generalized Morse form, where ψ(x) is a cutoff function defined by if x < 0 and ψ(x) ≡ 0 if x ≥ 0. This cutoff function guarantees that Φ CuT a (r) and its first three derivatives turn smoothly to zero at a cutoff distance r c .Eq. ( 6) contains the fitting parameters A, q, b, r 0 , δ, r c and h.The dipole and quadrupole functions are postulated in the form where q i and d i are fitting parameters.Both functions are subject to the same cutoff as Φ CuT a (r).Together with the transformation coefficients mentioned above, this parametrization includes 16 fitting parameters.
The parameters have been optimized by minimizing the weighted mean-squared deviation of the ADP binding relations from the respective first-principles binding relations using a simulated annealing method.After the fit, the optimized Φ CuT a (r The agreement between the ADP and first-principles CPMD energies is very resonable for the L1 1 and L1 2 structures and excellent for L1 0 and B2.Overall, given the approximate character of the ADP model, the potential displays good transferability over the entire concentration range.The agreement between the ADP and first-principles calculations is good for the cubic compounds and layered structures but less accurate for the C11 compounds.There is notable disparity for the energies of the C11 f -Cu 2 Ta and C11 b -Ta 2 Cu compounds both with and without atomic relaxation.It should be emphasized that C11 structures were not included in the potential fit and that this is a very severe test of the potential that involves strong deformations along an extended path in the configuration space.In fact, the Bain path is a rather stringent test even for interatomic potentials for pure metals.
The relaxed impurity formation energies predicted by the potential are 0.962 eV for Cu in Ta and 1.027 eV for Ta in Cu.The corresponding first-principles numbers being 0.463 eV and 0.836 eV, respectively.These numbers were obtained in small supercells.Note that the impurity data were not included in the potential fit.After relaxation in large simulation blocks, the ADP impurity formation energies becomes 0.764 eV for Cu in Ta and 1.096 eV for Ta in Cu, which is in good agreement with the first-principles results.These numbers are high enough to secure the experimentally established 13 negligible solid solubility between Cu and Ta.
For the applications intended in this work, it is requisite to have a potential that does not produce any stable Cu-Ta compounds at any composition or temperature.As a check of this property, the potential has been applied to minimize the energies of all compounds listed in Table II  this potential, they do give reasonable confidence that this will be the case in atomistic simulations.

The liquid phase
To test liquid properties, we created a 32-atom supercell of a CuTa compound and heated it up to a high temperature using molecular dynamics (MD) with the new potential.After the supercell had melted, it was cooled down to the temperature of 2000 K and equilibrated by running an NPT MD simulation at zero pressure for a few nanoseconds.The simulation was then continued for 10 more nanoseconds and a snapshot was saved after each nanosecond.The energies of the 10 snapshots thus produced were determined with the ADP potential and by the first-principles methods discussed in Section II B.
In Fig. 3, the ADP formation energies of the liquid supercells are plotted against their first-principles counterparts.Although the first-principles numbers are systematically on the higher side of the perfect agreement line, there is a clear correlation between the two calculation methods.
As a further test, the position of the liquidus line on the phase diagram has been explored by semi-grand-canonical Monte Carlo simulations.The methodology was similar to the one used recently in Ref. 26 and involved a solid-liquid interface that can move by consuming one phase or the other, depending on whether the temperature and composition are below or above the liquidus.At a fixed temperature, the chemical potential difference ∆µ can be adjusted to approach the solid/liquid equilibrium (no interface motion during a long simulation run).The respective equilibrium phase compositions are then computed by separate runs on single-phase systems at the estimated equilibrium T and ∆µ values.An accurate phase diagram calculation by this method is a computationally extensive procedure and was not pursued in this work.However, a few points have been estimated and found to be in qualitative agreement with the liquidus line on the experimental phase diagram. 13This is enough to reassure that the potential can adequately represent interactions between liquid Cu and solid Ta.As a side observation, liquid alloys undercooled below the liquidus line underwent a separation into Cu-rich and Ta-rich liquid phases with a well-defined interface.
This observation is in encouraging agreement with the kinetic liquid separation line and a critical point shown on the experimental phase diagram. 13

Surface decohesion
In the context of future applications to Cu-Ta interfaces, it is important to verify that the ADP potential provides an adequate description of binding between the Cu and Ta surfaces.In Fig. 4 we compare the interface binding curves obtained on identical supercells by first-principles MBPP calculations and using the ADP potential.The curves have been computed for four types of relative translations of the adjacent Cu and Ta layers indicated in Section II B. The minimum on each curve corresponds to the equilibrium spacing of the Cu and Ta slabs while its depth gives the equilibrium work of separation W s .
While the potential tends to underbind the interfaces, the ranking of the W s values and the equilibrium separations corresponding to the different translational states are correct.
The potential produces a hump at separations of about 3.5 Å.This artefact of the potential, apparently arising from an interplay between different shapes of the potential functions, might affect atomistic simulations involving Cu and Ta surfaces separated by this distance.
This should be kept in mind in applications of this potential.For interface separations close to equilibrium, however, this hump is unlikely to produce artefacts.

III. APPLICATION TO WETTING AND THIN-FILM STABILITY
To further assess the ability of the ADP potential to reliably reproduce interface properties between Cu and Ta, we have examined the stability and wetting behavior of thin Cu films deposited on a Ta substrate.8][29][30] We will limit the discussion to a particular problem for which a controversy exists in the literature, namely, whether Cu completely dewets from a Ta substrate or whether it leaves a monolayer (ML) coverage. 8,14,29,30perimental studies by Kuhn et al. 27 have demonstrated that ultrathin Cu films deposited on Ta (110) substrates form a stable 2D film for coverages up to 1.22 ML, with a mismatch occurring along the [1 10] direction of the substrate.Additionally deposited Cu atoms form 3D clusters on top of the Cu film.Similar results are reported by Chen et al. 28 for Cu deposited on polycrystalline Ta substrates, which also demonstrate that for a sub-monolayer (2 Å) coverage, a pseudomorphic Cu monolayer is stable both at room temperature and after annealing at a temperature of 1000 K.However, for the coverage of 5 Å and higher, dewetting of Cu from Ta is observed. 28 Recently, the mechanical and thermodynamic stability of Cu thin films on Ta was investigated by the first-principles MBPP method. 14It was shown that a monolayer of Cu on Ta (110) should indeed be stable and that excess Cu should dewet from Ta and leave a Cu monolayer on Ta.
It is not our intention to conduct an atomistic simulation of a "deposition experiment" in this study.Instead, we seek to demonstrate that the new ADP potential is capable of reproducing the basic features of interaction of Cu films with Ta, particularly the stability of a Cu monolayer on Ta and instability of multilayer films, resulting in their dewetting from the monolayer.To this end, we examine two different initial configurations: (i) thin Cu film placed on a Ta (110) substrate, and (ii) liquid Cu drop placed on a Ta (110) surface.In both cases, the evolution of the system is studied by MD at a constant temperature of 1400 K, which is above the melting point of Cu (1327 K; 11 the experimental value is 1357 K 32 ) but below that of Ta (3960 K; 12 the experimental value is 3290K 32 ).The first case should indicate whether a multilayer film is stable, whereas the second case is a test of the wetting behavior of Cu on Ta.The simulations are performed using the ITAP MD software package (IMD). 33 the first case, the initial Cu film is composed of two FCC (111) layers placed on the (110) surface of BCC Ta as shown in Figure 5(a).The Kurdjumov-Sachs orientation relationship is applied, (111) FCC (110) BCC , and [0 11] FCC [ 11 1] BCC , which is obtained from the Nishiyama-Wasserman orientation by a 5.26 • rotation about the interface normal.The substrate is composed of eight Ta (110) layers, so that the system contains 24,000 Ta atoms and 8,064 Cu atoms.The system dimensions parallel to the interface are 14.3 nm by 16.2 nm, with the initial thickness of 23.12 nm.Periodic boundary conditions are applied parallel and free boundary conditions perpendicular to the interface.The bottom Ta layer is kept fixed throughout the simulation in order to mimic a semi-infinite substrate.After an MD run for about a nanosecond at 1400 K, the system is slowly cooled down to room temperature.
In the MD snapshots shown in Fig. 5 The drops form a wetting angle with the remaining Cu monolayer of approximately 56 • .It is expected that, in a much longer MD run, they would eventually coalesce into single drop.
After cooling down to 300 K, the drops solidify and the underlying monolayer becomes more ordered as shown in Fig. 5(h).The crystal structure inside the drops is FCC and their shape is faceted.The crystal planes parallel to the facets and to the underlying monolayer are found to be (111).The monolayer consists of regions with coherent, pseudomorphic structure that replicates the structure of the Ta substrate.Such pseudomorphic regions are separated by lines of mismatch which are aligned approximately parallel to the [001] direction of the Ta substrate.Both the structure of the monolayer and the direction of the misfit lines may depend on the initial condition and the annealing schedule (particularly, the cooling rate).More details regarding the monolayer structure will be published elsewhere.
The results displayed in Fig. 5 demonstrate clearly that a bilayer Cu film is unstable and dewets, forming Cu droplets on top of a stable Cu monolayer.Thus, the ADP potential reproduces the instability of thin Cu films demonstrated experimentally. 28,30,31 the second case, a liquid Cu drop composed of 3,344 atoms and separately equilibrated at 1400 K is brought in contact with a Ta (110) substrate of dimensions 9.92 nm by 11.2 nm parallel to the surface, as shown in Figure 6(a).The surface area of the substrate is chosen so that the number of the Cu atoms in the drop would be sufficient to completely cover the substrate with one monolayer and leave enough atoms to agglomerate on top of it.The thickness of the substrate is the same as in the previous case.
The system is then subject to an MD run at 1400 K for 0.55 nanoseconds.Fig. 6 shows a series of snapshots from the simulation, with the color coding similar to the previous case.At early stages of the simulation, a "skirt" forms around the drop [Fig.6(b)], which continues to spread over the Ta substrate until it completely covers it, producing a stable Cu monolayer.The rest of the Cu atoms remain in the drop, which becomes smaller than the initial one.This structure remains stable for the rest of the simulation.The wetting angle between the drop and the monolayer is close to the one found in the previous case.
This simulation provides further evidence that a stable Cu monolayer is formed regardless of the initial condition.It further confirms the ability of the new ADP potential to reproduce the wetting behavior of Cu on Ta.

IV. CONCLUSIONS
The angle-dependent Cu-Ta potential developed in this work utilizes existing potentials for pure Cu and Ta, thus focusing on the cross-interactions.The cross-interaction functions have been obtained by fitting to first-principles binding relations for a number of crystal structures with different symmetries and chemical compositions.The approach in which a binary potential is produced by fitting cross-interactions to first-principles information with only a few experimental numbers, if any, is relatively new.It essentially turns the potential generation process into a paramerization of first-principles data, see the discussion in Ref. 6 and recent examples of Ni-Al and Cu-Ag potentials. 15,26This approach is especially justified for the Cu-Ta system, which simply does not contain any intermediate solid phases of the experimental phase diagram.Thus, using first-principles calculations for artificial intermetallic compounds is the only way of generating a potential.
The first-principles database used here for both the fitting and testing of the new potential has been generated within the density-functional formalism using two different methods: CPMD and MBPP.Besides the energies of several well-known crystal structures, the database includes purely artificial layered structures representing possible atomic arrangements near coherent interfaces.It also includes energy-separation curves for several coherent interfaces, as well as a number of liquid supercells.All together, the database spans a large area of configuration space and present an ideal testing bed for an interatomic potential.
The tests indicate that the new potential is transferable to a wide range of chemical compositions and atomic environments.Some of the physical properties compare well with their first-principles counterparts while others are reproduced less accurately.Given the complex and highly dissimilar nature of the Cu-Ta system and the semi-empirical character of the ADP model, we conclude that the new potential is quite suitable for atomistic simulations of this system. We CuCuTaCuCuTa... (respectively, TaTaCuTaTaCu...) and then allowing the c/a ratio to vary.The calculations have been performed for a set of c/a ratios with volume relaxation at each c/a.The function ∆E versus c/a thus obtained (which is similar to the Bain path of the FCC-BCC transformation) has two special points corresponding to the FCC and BCCbased C11 structures, which are denoted as C11 f and C11 b , respectively.Their energy has been additionally relaxed by allowing local atomic displacements (full relaxation).Finally, isolated substitutional impurities are represented by a 2 × 2 × 2 (32 atoms) FCC Cu supercell with a single Ta impurity and a 3 × 3 × 3 (54 atoms) BCC Ta supercell with a single Cu impurity.In both cases, full relaxation of the supercell has been implemented and the impurity solubility energy has been computed relative to the equilibrium FCC Cu and BCC Ta crystals.
14 for details).All four have been tested in this work.After the construction, the supercell has been relaxed by varying its dimension normal to the interface and the spacings between individual Cu layers.The interface separation process is modeled by varying the interfacial spacing ∆ of the adjacent Cu and Ta layers across the interface (by the periodic boundary conditions, the supercell effectively contains two such interfaces, both of which are being separated).No relaxation is allowed in this process.The separation continues until we end up with isolated Cu and Ta slabs.At each step, the interface binding energy E sep is determined as the energy difference per unit interface area relative to the completely separated state.Thus, E sep → 0 at ∆ → ∞ by definition.The function E sep (∆) calculated in this manner characterizes the strength of the bonding across the Cu-Ta interface.
function has been modified by adding a term 10(r − r * ) 4 at r < r * = 0.27 nm to eliminate an unphysical feature at short atomic separations.The optimized values of the fitting parameters are summarized in Table I and the pair-interaction functions are shown in the effective-pair format 6 in Fig. 1.Tabulated forms of the potential functions are available from the authors on request.D. Testing the potential 1. Crystal structures The binding curves for the cubic compounds used in the potential fit are shown in Fig 2.
with respect to all possible supercell shape variations and local atomic displacements.Although this full relaxation does reduce the formation energy of some of the compounds, it remains always positive.Fully relaxed formation energies of a number of additional compounds have been computed and found to be positive as well, including B32-CuTa, D0 3 -Ta 3 Cu, D0 3 -Cu 3 Ta, D0 19 -Ta 3 Cu, D0 19 -Cu 3 Ta, D0 22 -Ta 3 Cu, D0 22 -Cu 3 Ta.Furthermore, extensive semi-grand-canonical Monte Carlo simulations 25 were performed at different temperatures and chemical-potential differences ∆µ = µ Ta − µ Cu starting from compositionally disordered configurations.The result was invariably either almost pure Cu or almost pure Ta.No other solid phases were observed in the simulations.Although these tests do not constitute a rigorous proof that no intermediate phases can exist with , the Ta atoms are represented by the dark-blue color while the color of the Cu atoms reflects their potential energy according to the energy scale indicated in the Figure.During the first 50 ps, the Cu film maintains its integrity across the entire substrate as seen in Fig.5(b).After about 60 ps, the top Cu layer breaks up and forms a number of voids that expose the underlying Cu layer [Fig.5(c)].From the color of the Cu atoms in the top layer, it is evident that they have a higher potential energy than the atoms underneath.As the simulation progresses [Fig.5(d)-(g)], the atoms of the top layer agglomerate and form two liquid drops with comparable sizes and shapes.By the time t = 340 ps, the drops are completely formed and do not practically change for the rest of the simulation, aside from slight Brownian movements and small spontaneous rotations.

Cu-FIG. 1 :
FIG.1:The pair-interaction functions of the Cu-Ta ADP potential in the effective pair format.

2 3 FIG. 2 :
FIG. 2: Formation energy (per atom) versus atomic volume for ordered Cu-Ta compounds used for fitting the ADP potential.Points -first-principles CPMD calculations; dashed lines -ADP results.

FIG. 4 :
FIG. 4: Binding energy between Cu (111) and Ta (110) surfaces as a function of separation obtained (a) by first-principles MBPP calculations and (b) with the ADP potential.Different curves represent alternate translational states of the Cu-Ta interface.

FIG. 6 :
FIG.6:A sequence of snapshots from a molecular dynamics simulation of a Cu drop spreading on a Ta (110) substrate at 1400 K.A monolayer Cu spreads and a stable wetting drop forms on top of it.The color coding is the same as in Figure5.
24 (0.350 eV) compares well with the recent calculation by Gong et al. (0.357 eV).24 Table II summarizes the equilibrium formation energies of several compounds obtained by first-principles CPMD and ADP calculations.Note that the first-principles energy of L1 2 -Cu 3 30 instability of Cu films with thicknesses up to 50 Å deposited on Ta (110) and Ta (100) at room temperature was reported by Venugopal et al..31Upon heating, the films break up and agglomerate into islands, leaving one or two monolayer thick Cu films on the substrate.The remaining Cu forms µm-size islands with FCC crystal structure.The (111) planes of Cu are aligned parallel to the substrate surface and satisfy the Nishiyama-Wasserman orientation relationship.On the other hand, Kim et al.29report complete dewetting of Cu from Ta with a non-wetting contact angle of 123 ± 8.5 • and no evidence of a monolayer coverage.An additional experimental observation has recently been reported by Fillot et al.,30who found that thin Cu films are indeed unstable and dewet from Ta to form Cu clusters on top of a stable Cu monolayer on both BCC Ta and tetragonal β-Ta substrates.
9,8D simulations performed by Klaver and Thijsse7,8indicate that Cu atoms deposited on Ta (110) or (100) form a stable monolayer film with a "fish-bone" or "rippled" structure, with 3D Cu islands growing on top of it. Upther deposition, the islands coalesce and form an almost perfect FCC structure.However, no indication of Cu film dewetting has been given in that work.Similar conclusions have been reached in the MD simulations with an EAM Cu-Ta potential by Li et al..9 This work is part of our ongoing effort to create a fundamental understanding of * Electronic address: adham.hashibon@iwm.fraunhofer.de have applied the new potential in MD simulations of Cu wetting and dewetting on a Ta substrate.The simulations show that a Cu film placed on a Ta (110) surface dewets from it but leaves a stable Cu monolayer on the surface.The excess Cu atoms agglomerate into droplets on top of the monolayer, forming a relatively large wetting angle of about 56 • .Furthermore, if a droplet of Cu is placed on a clean Ta (110) substrate, exactly one monolayer spreads over the surface, while the excess Cu atoms remain in the droplet.Thus, we clearly observe high stability of a Cu monolayer on Ta and instability of thicker films.This finding is encouragingly consistent with our recent first-principles calculations, 14 of thermodynamics and mechanical properties of Cu-Ta interfaces.It is also in good agreement with experimental studies of thermal stability of Cu films deposited on Ta substrates. 2 B.-S. Kang, S.-M.Lee, J. S. Kwak, D.-S.Yoon, and H. K. Baik, J. Electrochem.Soc.144, 1807

TABLE I :
Optimized values of fitting parameters of the ADP Cu-Ta potential.

TABLE II :
Equilibrium formation energies (in eV per atom, relative to FCC Cu and BCC Ta) of