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Applied Surface Science 274 (2013) 164– 170

Contents lists available at SciVerse ScienceDirect

Applied Surface Science

jou rn al h omepa g e: www.elsev ier .com/ locate /apsusc

olecular dynamic simulation of binary ZrxCu100−x metallic glass thinlm growth

u Xie, Pascal Brault ∗, Anne-Lise Thomann, Larbi BedraREMI UMR7344 CNRS, Université d’Orléans, BP6744, 45067 Orleans Cedex 2, France

a r t i c l e i n f o

rticle history:eceived 5 February 2013eceived in revised form 4 March 2013ccepted 4 March 2013vailable online 14 March 2013

a b s t r a c t

In this work, we employed classical molecular dynamics simulations model to study ZrxCu100−x

(3 ≤ x ≤ 95) metallic glass films deposited on a silicon (1 0 0) substrate. Input data were chosen to fitwith the experimental operating conditions of a magnetron sputtering deposition system. The growthevolution is monitored with variable compositions of the incoming atom vapor. The Zr–Zr, Cu–Cu andZr–Cu interactions are modeled with the Embedded Atom Method (EAM), the Si–Si interaction with

eywords:olecular dynamics simulation

hin film growthetallic glass

lloyputtering deposition

Tersoff potential, the Zr–Si and Cu–Si interactions with Lennard-Jones (12-6) potential. Different filmmorphology and structure were detected and analyzed when the Zr to Cu ratio is varied. The results arecompared with X-ray diffraction and scanning electron microscopy analyses of experimentally depositedthin films by magnetron sputter deposition process. Both simulation and experiment results show thatthe structure of the ZrxCu100−x film varies from crystalline to amorphous depending on the elementalcomposition.

. Introduction

Recently, there has been a huge interest in the atomic-leveltructure and structure-property relationship in metallic glassesMGs). These materials have been studied for 40 years because ofheir promising properties belonging to both metals (electron, heatonductivity, ductility, etc.) and glasses (hardness, etc.) [1,2]. To sta-ilize an amorphous phase in metallic alloys, atomic diffusion muste prevented. This could be achieved by playing with the chemicalomposition (mixing of elements with different atomic sizes) or byreezing a low ordered phase during the synthesis process [3]. Itas been shown that deposition of thin films by condensation ontoold substrates allows stabilizing low ordered structure in metallicystems.

As an example, ZrCu alloys have attracted interest in recentears, due to its bulk metallic glass properties [4–8], and as amor-hous alloy films for its mechanical [9–11] and superconductivityroperties [12]. Dudonis et al. [13] prepared thin films with com-osition in the range of (5 ≤ x ≤ 95) by using high working power490 W and 1380 W on Cu and Zr targets, respectively) during mag-etron sputtering deposition.

Numerous theoretical studies have also been conducted onr–Cu systems. Sha et al. [14,15] employed atomistic methods fortudying Zr–Cu MGs forming conditions. Almyras et al. investigated

∗ Corresponding author.E-mail address: Pascal.Brault@univ-orleans.fr (P. Brault).

169-4332/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.apsusc.2013.03.004

© 2013 Elsevier B.V. All rights reserved.

the microstructure of Zr35Cu65 and Zr65Cu35 MGs and found thatthese systems consist of small touching and/or interpenetratingicosahedral-like clusters which results in “supercluster” (SCs) satis-fying the system composition [16]. They thus claimed that seekingthe equilibrium configuration for interpenetrating ICO-like clustersallows the prediction of the MG microstructure.

While bulk amorphous structure is known to be formed underspecific synthesis conditions, the ZrCu amorphous thin film growthhas not been so much studied. A better understanding of thin filmgrowth can be achieved via simulations and compared to availableexperimental data as X-ray diffraction patterns. Molecular dynam-ics (MD) has proven to be a very successful technique for a detailedunderstanding of growing processes of metal films, allowing us toexplore film forming evolution at the atomic level.

In this work we report on results of molecular dynamics simu-lations and on a structural study of ZrxCu100100−x metal alloy thinfilms grown by magnetron plasma sputter deposition. The maingoal is to investigate the relationship between the composition andthe structure.

2. Experimental

The ZrxCu100−x alloy films were prepared by DC magnetronsputter deposition in argon atmosphere (0.25 Pa) and at room

temperature. Two targets, pure Cu (purity, 99.999%) and pure Zr(purity, 99.999%), were used at the same time for co-depositionof the alloy films. The distance between the target and the sub-strate was set to 10 cm. By altering the sputtering power of both

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sipated with Berendsen thermostat in the course of simulation tokeep the whole temperature around 300 K (room temperature) cor-responding to the value in the experiment. The initial configurationof the deposition model is pictured in Fig. 1.

L. Xie et al. / Applied Surfa

argets, ZrxCu100−x thin films with different compositions wereynthesized on Si (1 0 0) wafers. Typical deposited thickness was00 nm. In order to study the structure of the ZrxCu100−x metalliclms X-ray diffraction analysis (Cu K� radiation, � = 0.15405 nm,regg–Brentano geometry) was performed. Microstructure of theeposits was observed on SEM images (Carl Zeiss-Supra40 – FEG-EM)

. Molecular dynamics simulation details

.1. Potential functions

MD is a simulation technique for computing the equilibriumnd transport properties of a classical many-body system. Givingn initial set of positions and velocities of a system of N atoms, eachtom is treated as a point mass and the atomic motion is solvedsing Newton’s equations [17].

The MD package LAMMPS [18] is used to simulate the depo-ition of atoms. A script driving the LAMMPS code was writtenor automating the deposition and the relaxation of the system.mplementing suitable interatomic potentials is certainly the mostmportant issue in molecular dynamics simulation. For describinghe interaction between Zr–Zr, Zr–Cu, Cu–Cu, we use the many-ody EAM potential [19–21]. Such a potential is non-pairwise in theense that it is based on concepts coming from density functionalheory, which stipulates in general that the energy of a solid is anique function of electron density. It is well adapted to simulatehe interaction between such metal atoms.

The total energy Etot of an atomic system can be expressed as:

tot =∑

i

Vi

i = 12

∑i

�ij(rij) + F(�ij)

i =∑i /= j

fi(rij)

i is the internal atom energy and �i is the electron density associ-ted with atom i due to the presence of other atoms in the system.(�i) is the energy required to ‘embed’ the atom i in the electronensity �i. �ij(rij) is a suitable pair potential.

Tersoff [20] Silicon empirical potential is used for describinghe interaction between the Si atoms. This potential has been suc-essfully used to investigate the structural, thermal vibration andurface properties of Si [20].

The Tersoff interatomic potential involves both two- and three-ody terms:

=∑

i

Vij

here Vij = fC(rij)[fR(rij) + bijfA(rij)]Here i and j are labels for the interacting atoms. The term fR

epresents a repulsive pair potential due to electron overlap, whileA represents an attractive pair potential associated with bonding.he function fC is merely a smooth cutoff function which limits theange of the potential. The coefficient bij (bond order) correspondso a many-body interaction of the form:

ij = �ij(1 + ˇnii �ni

ij )−1/2ni

niij =

∑k /= i,j

fC (rik)g(�ijk)

nce 274 (2013) 164– 170 165

where

g(�ijk) = 1 + c2i

d2i

− c2i

d2i

+ (hi − cos �ijk)2

And the constants �ij, ˇi, ni, ci, di and hi depend on the atomicspecies and �ijk is the angle between an i j bond and an i k bond.The EAM and Tersoff parameters are implemented in the LAMMPSsoftware.

We use a Lennard-Jones potential for the interactions betweendeposit atoms and substrate [17]:

Vij(rij) = 4ε

[(

rij

)12

−(

rij

)6]

The parameters and ε of LJ potentials of Zr, Cu and Si aresummarized in Table 1 [20,22]. is the distance canceling the LJpotential Vij() = 0 and −ε is the well depth of the LJ potential.

Species ε (eV) (Å)

Zr 0.7382 2.9318Cu 0.409 2.338Si 0.0175 3.826

When pair potential parameters for compound materials are notdirectly available, mixing rules can be used to make approximations[17]. As example, the Lorentz–Berthelot mixing rule is suitable forLennard-Jones potentials of species i and j, giving: εij = (εiεj)1/2 andij = (i + j)/2.

3.2. Computational model and analysis methods

MD simulation was carried out in a three dimensional cell,which was periodic only along x and y directions. The depositionof each particle is simulated at the NVE ensemble (i.e. the num-ber of particles N, the system volume V and the total energy E arekept constant). The dimensions of the Silicon (1 0 0) substrate are(25 × 25 × 10) Å3. The first two bottom layers of the substrate arefixed (red atoms in Fig. 1), while the other layers are temperature– controlled layers using a Berendsen thermostat [23].

When an atom is deposited, the system is in a non-equilibriumstate. The high energy of the deposited Zr and Cu atoms can be dis-

Fig. 1. Schematic picture of the deposition model. Gray atom is Zr, blue atom is Cu,yellow atoms are moving Si atoms, red atoms are Si fixed atoms.

166 L. Xie et al. / Applied Surface Science 274 (2013) 164– 170

Table 1The four nearest neighbor distances in Zr and Cu bulk crystals. Lattice constants for Zr and Cu are respectively aZr = 3.23 A, cZr = 5.15 A and aCu = 3.61 A.

Crystal name Structure First neighbor (Å) Second neighbor (Å) Third neighbor (Å) Fourth neighbor (Å)√

2 aZ

aCu = 3

dis

a

f

E

E[grtntccMotvbeTw[

detfebst

ceP

g

woabt

a

R

o

Zr hcp aZr = 3.23

Cu fcc aCu√2

= 2.55

The Zr and Cu atoms with the six different ratios are randomlyeposited on the substrate (one atom per 2 ps). Each atom is placed

n the vacuum slab at a random position from 5 to 7 A above theurface.

The mean kinetic energy of incoming atoms are calculatedccording to the modification of Thompson formula [24]:

(E) ∝ 1 − ((Ecoh + E)/EAr+ )1/2

E2(1 + Ecoh/E)3

F = (E − kBTg) exp[n ln(Ef /Ei)] + kBTg

f/Ei = 1 − /2 is the ratio of energies after and before a collision25], where = 4((mgms)/(mg + ms)2) where mg and ms stand foras atom (Argon here) and sputtered atom (Zr or Cu here) massesespectively, and n = dp�/kBTg. E is the energy of the sputtered par-icles as they leave the target, Tg is the sputtering gas temperature,

is the number of collisions that take place in the gas, d is theraveled distance, p is the sputtering gas pressure, and � is theollision cross section assuming hard core interactions. To cal-ulate the energy loss of sputtered atoms with the gas atoms, aaxwell–Boltzmann (MB) distribution at Tg is fixed for the gas (in

ur conditions Tg = 300 K). Because we search for the complete dis-ribution of sputtered atoms, we replace kBTg by Eg, a particularalue in the gas distribution. Thus for each Eg in the MB gas distri-ution, the energy loss is calculated for a fixed value of the kineticnergy E of a sputtered atom. This is repeated for each E in thehompson distribution and weighted by the collision probability,hich is simply the product of f(E) and the MB distribution at Tg.

24].At an argon pressure being of 0.25 Pa and a target to substrate

istance of 9 cm, the mean kinetic energy of Zr and Cu were foundqual to 7.65 eV and 6.67 eV, respectively. For the MD simulations,he velocities of the Zr/Cu deposited atoms are randomly sampledrom a Maxwell–Boltzmann distribution with the most probablenergy 7.65 eV and 6.67 eV separately. The timestep is chosen toe 1 fs. Every 10,000 timesteps, 5 atoms are released toward theurface, i.e. one atom per 2 ps on average. This time is enough forhermal relaxation to take place with Berendsen thermostat.

After simulation of Zr–Cu metallic film growth has beenompleted, the partial radial distribution functions (PRDF) weremployed to determine the correlation between the atoms. TheRDF can be expressed as

˛ˇ(r) = V

N˛Nˇ

⟨N∑i

N∑j /= i

ı(r − rij)

⟩

here V is the volume of the system, N˛ and Nˇ are the numberf atoms and ˇ, respectively, rij represents the distance betweentoms i and j, ı(r − rij) is the Dirac delta function, and the angularrackets represent the time average. The radial distribution func-ion RDF of atom i is denoted by gi(r) and is the sum of the PRDFs for

tom i to atom j, written as gi(r) =∑

j

gij(r). Similarly, the total

∑

DF for the whole system is computed as gtot(r) =

i

gi(r).

Finally, the simulated XRDs was employed to analyze the phasef Zr–Cu metallic film and to compare with the experiment data

r = 4.53 cZr = 5.15√

2 cZr = 5.57

.61√

32 aCu = 4.42

√3 aCu = 5.10

directly. In most radiation scattering experiments, the objective isto obtain information that characterizes either intramolecular orintermolecular structure. In such cases, variation of the scatteredintensity with angle is the quantity of main interest, whereas theabsolute intensity is of no concern. Thus, ignoring all intensity scalefactors and correction factors appropriate for the geometry of thescattering apparatus, the amplitude and intensity of radiation scat-tered coherently from an arbitrary set of n atoms may be writtenas:

F(Q) =n∑

j=1

fi exp(Q · rj)

I(Q ) = F(Q) ∗ F(Q) =n∑

j=1

n∑k=1

fifk cos (iQ · rjk)

Q = 2�

d= 2 sin �

n�

fi =∫

�ir exp(−2�iQr)d3r

where �i is the density of atom i, r is the position vector, and Q isthe scattering vector (Bragg’s law), fi is the atomic scattering factorsfor the radiation used, and rjk denotes the vector connecting atomsj and k.

4. Results and discussions

In order to study the influence of the elemental composition onthe crystallographic properties of the thin films, MD simulations ofZrxCu100−x metallic films grown on a crystalline Si (1 0 0) substratewere carried out at operating conditions similar to that describingmagnetron co-sputtering process. The Zr metal content in the filmranged from 3% (i.e. Zr3Cu97) to 95% (i.e. Zr95Cu5) which has beenfound by properly preparing the incoming vapor composition. Thefilm composition was found to be close to the vapor composition,which in turn means that sticking coefficients are close to eachother.

The films grew to approximately 5 ∼ 7.5 nm. Snapshots of thedeposited layers on the Si (1 0 0) substrate are presented in Fig. 2.

Based on these simulations, the partial radial distribution func-tion (PRDF) for the system ZrxCu100−x was calculated for each case.The Zr–Cu, Zr–Zr and Cu–Cu PRDFs at 3%, 20%, 46%, 55%, 73% and95% Zr metal contents are presented in Figs. 3–5 respectively.

At low or high concentrations of Zr, i.e. Zr3Cu97 or Zr95Cu5, thecalculated PRDFs show outstanding peaks which can be assumedas crystalline structure representing Cu and Zr separately, becausethe intensity and position of the peaks are very similar to thoseof the Cu and Zr crystals (Table 1). This is also clear from thesnapshots of the films at the corresponding Zr concentrations pre-sented in Fig. 2: the cross-sections of Zr3Cu97 and Zr95Cu5 havewell crystal structure. For the Zr contents between 3% and 95%,

the intensity of the PRDF peaks decreases dramatically. Especially,the first and second peaks become broader and split while theother peaks are fading away quickly, which represents an amor-phous structure. This is in agreement with the visual observation

L. Xie et al. / Applied Surface Science 274 (2013) 164– 170 167

F of Zr aT

itstti

ig. 2. Snapshot of Zr–Cu coatings deposited on Si (1 0 0) substrate at different ratios

he colors have the same meaning than in Fig. 1.

n Fig. 2 (from Zr20Cu80 to Zr73Cu27). Besides, The RDF of the sys-em exhibits a distinct first peak indicating that there exists a strong

hort-range order (SRO). We also observe that the first peak shiftsoward larger radial distance values when increasing Zr concen-rations. This was expected since the Zr–Zr first neighbor distances larger than that of Cu. The splitting of the peak is also visible

nd Cu atoms. The numbers in brackets are the Zr and Cu atom numbers respectively).

indicating a progressive change from a Zr predominant to Cu pre-dominant film.

Figs. 4 and 5 show the PRDFs for like bonds, Zr–Zr and Cu–Cuin these systems, respectively. As illustrated in Fig. 4, like bondsexhibit strong sensitivity to atomic concentrations. For example, inZr–Zr PRDFs, at low Zr concentration (Zr3Cu97), the PRDF does not

168 L. Xie et al. / Applied Surface Science 274 (2013) 164– 170

Fig. 3. Total RDFs for ZrxCu100−x alloys, individual curves corresponding to differentalloy compositions are displaced vertically for clarity.

Fd

edwcbiPcc

t2

Fd

that the peak positions in the simulated XRD are close to thatdetected in the experimental XRD patterns. For crystalline expected

ig. 4. PRDFs for Zr–Zr for ZrxCu100−x alloys, individual curves corresponding toifferent alloys are displaced vertically for clarity.

xhibited specific structure showing Zr atoms are well randomlyispersed in Cu background without correlations. This is confirmedhen looking at the corresponding snapshots. When the Zr con-

entration increases, the third and fourth peak slowly appears andecome “higher and narrower” indicating the Zr–Zr’s phase chang-

ng from amorphous state to crystalline. On the contrary, the Cu–CuRDF shows a stronger SRO in the Cu-rich film and a progressivehange from crystal to amorphous when the % of Cu decreases as it

an be seen in Figs. 4 and 5.

In summary, the PRDFs show that an amorphous structure ofhe films is observed in a wide compositional range i.e. when0 ≤ x ≤ 73.

ig. 5. PRDFs for Cu–Cu for ZrxCu100−x alloys, individual curves corresponding toifferent alloys are displaced vertically for clarity.

Fig. 6. XRD patterns of ZrxCu100−x film sputtered at 300 K with different composi-tions in the experiment.

For comparison with simulations, Fig. 6 shows the intensity ofthe XRD �–2� peaks as a function of the Zr metal content. At the Zrconcentration of 3% and 95%, ZrxCu100−x films are crystalline whichagrees with the present PRDF calculations reported in Figs. 3–5. Asthe Zr concentration increases from 20% to 73%, a shift of peakstoward small angles (2� = 41.8◦, 38.7◦ 37.4◦, and 35.9◦) is observed.Meanwhile, all of these patterns consist of a broad halo peak, indi-cating a low ordered structure. It seems that Zr and Cu atoms areinserted in the main element matrix and form a solid solution. Dis-tortion of the lattice parameter due to the different atomic sizeleads to a lowering of the crystallinity.

Three of the experimentally deposited films, i.e. at 3%, 72% and95% Zr metal content, were observed by SEM and the images ofthe films (surface and cross-section) are presented in Fig. 8(a)–(c),respectively. The films at 3% Zr and 95% (Fig. 8(a)–(d)) exhibit grainsof about 50 nm and columnar structure is visible on the cross-section micrographs. On the contrary Zr73Cu27 film (figure (c) and(d)) seems relatively dense and featureless which could correspondto an amorphous structure. SEM observations are thus in agreementwith XRD results.

Ignoring all intensity scale factors and correction factors appro-priate for the geometry of the scattering apparatus, the calculatedX-ray intensities vs. 2� of ZrxCu100−x simulated films are shown inFigs. 7 and 8. By comparing both XRD plot sets, it can be observed

conditions the peaks are broad due to finite size simulations. Also

Fig. 7. X-ray intensity vs. 2� of ZrxCu100−x film with different compositions in thesimulation.

L. Xie et al. / Applied Surface Science 274 (2013) 164– 170 169

Figure 8. SEM images of Zr–Cu films deposited on an Si(1 0 0) at 3% (a, b), 73% (c, b) and 95% (c, d) Zr metal content; image (a), (c), (e) is about the surface, image (b), (d), (f)is about cross section.

Table 2The 2� position of first XRD peak for ZrCu alloy in the experiment and simulation..

Zr–Cu Zr3Cu97 Zr20Cu80 Zr46Cu54 Zr55Cu45 Zr73Cu27 Zr95Cu5

Experiments: 2� (◦)First peak 43.2 41.8 38.7 37.4 35.9 34.5

Simulation 2� (◦)38.65

a(poutdc

5

ctwfi8osstfyrcdbetnd

[

[[

[[[

[

First peak 42.2 41.7

shift between experimental and simulated positions is observedTable 2) certainly due to finite size effects of the simulations, andossibly due to some layer strain in the experimental films. On thether hand, the peak intensities are very different between sim-lations and experiments. This is due to the difference in layerhickness, thus in the total atom number. And also the ratio ofifferent structural phases can be different too. At this stage, theomparison is only qualitative.

. Conclusions

ZrxCu100−x thin films grown by magnetron co-sputtering pro-ess were studied by MD simulations using initial conditions similaro the experimental operating ones. The crystallinity of the filmsas analyzed by calculated PRDFs and XRD. The results show thatlms containing large amount of one of the element (higher than0%) are crystallized, whereas for intermediate compositions lowrdered phase is evidenced. This trend is due to chemical disorder,ince both atoms seem to be incorporated in the same lattice (solidolution) which induces distortion of the parameter. The value ofhe later is found to lie between that of both pure metals. The resultsrom the MD simulations were compared with XRD and SEM anal-ses of the experimentally deposited thin films. The experimentalesults also showed that the structure of the films changes fromrystalline at a high or low Zr content to amorphous at interme-iate Zr contents, ranging from 20% to 75%. The good agreementetween experimental results and simulation is of particular inter-

st: it proves that modeling at the atomic level allows predictinghe structure of hundreds of nanometer thick films grown by mag-etron sputter deposition. MD may thus be a helpful tool for theesign of new alloys.

[

[[[

37.7 36.1 35.55

Acknowledgements

China Scolarship Council is acknowledged for grant #2009602124 to L. Xie.

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