This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 134.151.40.2

This content was downloaded on 28/08/2014 at 16:50

Please note that terms and conditions apply.

Molecular dynamics simulations of clusters and thin film growth in the context of plasma

sputtering deposition

View the table of contents for this issue, or go to the journal homepage for more

2014 J. Phys. D: Appl. Phys. 47 224004

(http://iopscience.iop.org/0022-3727/47/22/224004)

Home Search Collections Journals About Contact us My IOPscience

Journal of Physics D: Applied Physics

J. Phys. D: Appl. Phys. 47 (2014) 224004 (17pp) doi:10.1088/0022-3727/47/22/224004

Molecular dynamics simulations of clustersand thin film growth in the context ofplasma sputtering deposition

Lu Xie, Pascal Brault1, Jean-Marc Bauchire, Anne-Lise Thomann andLarbi Bedra

GREMI UMR7344 CNRS-Universite d’Orleans BP 6744 Orleans Cedex 2, France

E-mail: pascal.brault@univ-orleans.fr

Received 1 December 2013, revised 23 February 2014Accepted for publication 4 March 2014Published 14 May 2014

AbstractCarrying out molecular dynamics (MD) simulations is a relevant way to understand growthphenomena at the atomic scale. Initial conditions are defined for reproducing deposition conditionsof plasma sputtering experiments. Two case studies are developed to highlight the implementationof MD simulations in the context of plasma sputtering deposition: ZrxCu1−x metallic glass andAlCoCrCuFeNi high entropy alloy thin films deposited onto silicon. Effects of depositing atomkinetic energies and atomic composition are studied in order to predict the evolution ofmorphologies and atomic structure of MD grown thin films. Experimental and simulated x-raydiffraction patterns are compared.

Keywords: molecular dynamics, cluster growth, thin film growth, deposition, plasma sputtering

(Some figures may appear in colour only in the online journal)

1. Introduction

Plasma sputtering technology is widely used both in researchand in industry (Mattox 1989, Kelly 2000, Safi 2000,Musil 2005). Nevertheless, this fairly simple technology iscontinuously being improved (Helmersson 2006, Alami 2009,Sakarinos 2010). A first interest of magnetron sputtering isto build coatings with improved or complementary propertiescompared to the pristine bulk materials. Essentially, thinfilm properties are related to composition and microstructure,which in turn depend on the deposition conditions and thuson sputtering plasma properties. A second specific propertyof plasma sputtering and thus more specifically magnetronsputtering is that it acts as an atom source, able to interactwith an inert and/or reactive buffer gas, which contributesto the plasma ignition and properties. Such a source thusprovides a sputtered vapour (more or less directed) with well-defined composition, kinetic energy and angle distributions.Such ‘initial conditions’ determine the construction of thecoatings, for which a special initial stage is the growth ofsupported clusters, which may hold interest in themselves.Studying plasma sputter growth of supported clusters and thin

1 Author to whom any correspondence should be addressed.

films remains a challenging task for understanding currentproperties (film morphology, use properties) and predictingnew properties (Kelly 2000, Safi 2000, Musil 2005, Brault2011). Due to the atomic nature of this deposition process,an insight into the growth processes at the atomic scale isof paramount importance. In particular, molecular dynamics(MD) is a simulation technique that is well suited fordescribing materials at the atomic scale (Alder 1957, 1958,1959, Allen 1987, Haile 1992, Rapaport 1995, Frenkel 2001)and thus well suited for predicting clusters and thin filmcompositions and morphologies, as for example issued fromplasma deposition and growth experiments. Therefore,numerous approaches have been proposed for describingplasma–surface phenomena (Graves 2001, 2009, Wadley2001, Bogaerts 2009, 2010, 2012, Brault 2011). Focus onplasma sputter growth using MD is intended to illustrate thepower of MD and the capability of predicting morphology,structure and composition in agreement with experimentalresults (Georgieva 2010, 2011, Xie 2013a, 2013b). In thenext section, MD simulations are presented in the context ofplasma sputter deposition, with emphasis on initial conditions.This will be followed by two original case studies, whichhighlight the MD predictive capabilities for complex, far

0022-3727/14/224004+17$33.00 1 © 2014 IOP Publishing Ltd Printed in the UK

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

from equilibrium, systems: ZrxCu1−x metallic glass (MG) andAlCoCrCuFeNi high entropy alloy (HEA) thin film depositionand growth on silicon (1 0 0) substrate. Effects of depositingatom kinetic energies and atomic composition will be studiedin order to correlate with morphologies and atomic structure.

2. Implementing MD simulations in the context ofplasma sputtering deposition

2.1. Classical molecular dynamics

Classical MD is a method intended to numerically solve theNewton equations of motion for a given system of particles,for which the interactions are governed by a model describingthe forces between these particles. An advantage of MDsimulations is that systems can be studied with an atomicresolution at short time- and length-scales, down to fem toseconds and angstroms and up to nanoseconds, sometimesto microseconds, and a few hundred nanometres (Hansen2000). A very striking advantage in MD simulations is thatno assumption is made about the mechanisms operating in thesystem. MD simulations consist of tracking the solutions ofthe classical equations of motion, written as

�Fi = mi �ai = mi

d�vi

dt= mi

d2�ri

dt2(1)

where mi , �ri , �vi and �ai are the mass, position, velocityand acceleration of atom i in a defined coordinate system,respectively. The force F i acting on each atom i acceleratesthe particle i, which in turn leads to a new position, velocityand acceleration. Forces are derived as the negative gradientsof the potential energy (interaction potential) U with respectto atomic positions:

�Fi = −�∇riU (�r1, �r2, �r3, . . . , �rN) . (2)

The potential energy can be obtained using either empiricalpotential energy expressions, semi-empirical methods orab initio approaches. In MD simulations, the calculationsof the potential energy and force are the most computer timeconsuming parts. Once the initial conditions and interactionpotential are defined, equations (1) and (2) can be integratedto follow the time evolution of the atoms in response to theapplied forces. The trajectory of all atoms can be thus obtainedas solutions of equation (2), in the form of positions andvelocities of all the atoms at each time step. The velocityVerlet algorithm (Swope 1982) is used to integrate Newtonequations. To maintain the substrate at the desired temperature(Ts = 300 K in all simulations here) a Berendsen thermostat(Berendsen 1984) is applied for a specified duration: thethermal relaxation time. Typical thermal relaxation timesrange from 0.1 to 50 ps (Hou 2000) per impact on the surface.

2.2. Interaction potentials

In classical MD simulations, the forces between atoms inthe system are derived from a potential energy function; thisfunctional form is often based on a quantum mechanicaltreatment of the system. The more fundamental quantum

mechanical treatment is simplified by the use of variousapproximations, the values of which are taken either fromfirst principle calculations or from fits of the model toexperimental data.

In the present work, Lennard-Jones potentials areused to describe the interactions of the Si–(ZrCu) andSi–(AlCoCrCuFeNi) systems (Zhang 2002, Zhen 1983,Graves 2009). While pair potential parameters for thecorresponding compound materials are not directly avail-able, the Lorentz–Berthelot mixing rule is used (Allen 1987,Graves 2009). More generally, for any kind of potential that wecan use, in a first approximation, the following general rulescan be established: for length terms we consider arithmeticaveraging and for energy terms geometric averaging. Onecould guess that more precisely defined potentials were avail-able, which is not the case for all of these metal–silicon sub-strate interactions. Extracting ‘true’ potentials from ab initiosimulations is out of the scope of this article. Moreover,successful comparison with experiments (Xie 2013a, 2013b)allows use of this metal–substrate interaction potential forunderstanding effects of incoming atom kinetic energy andcomposition on morphology and structure of grown thin films.

Metal–atom interactions can be well described by the so-called embedded atom model (EAM) (Maisuradze 2003, Foiles2012). Such a potential, first introduced by Daw, Baskesand Foiles (Daw 1983, 1984, 1993, Foiles 1985, 1986), isnon-pairwise in the sense that it is based on concepts fromdensity functional theory, which stipulates, in general, that theenergy of a solid is a unique function of electron density. Theembedded-atom method uses the concept of electron (charge)density to describe metallic bonding. Essentially, each atomcontributes through a spherical, exponentially decaying fieldof electron charge, centred at its nucleus, to the overallcharge density of a system. Binding of atoms is modelledas embedding these atoms in this ‘pool’ of charge, where theenergy gained by embedding an atom at location r is somefunction of local density. The EAM parameters of Al, Co, Cr,Cu, Fe, Ni and Zr are given by Zhou et al (2001, 2004) andLin et al (2008).

The silicon substrate is described using the Tersoff semi-empirical three-body potential (Tersoff 1988a, 1988b, 1989).This potential has been successfully used to investigate thestructural, thermal vibration and surface properties of Si.

The EAM and Tersoff parameters are also implementedin the MDLAMMPS software (Plimpton 1995, 2012).

There exist many other semi-empirical analyticalpotentials. Also suited to metals are tight binding potentials(Rosato 1989, Sutton 1990, Cleri 1993, Treglia 1999,Goyhenex 2001). For covalent systems, reactive empiricalbond order potentials—REBO and adaptive intermolecularREBO (Brenner 1990, 2000, Stuart 2000, Ni 2002,Nikitin 2005)—are now widely used. A new reactive semi-empirical ReaxFF potential is growingly attracting attention(van Duin 2001, Nielson 2005, Neyts 2012).

2.3. Initial conditions for releasing sputtered atoms

Plasma sputtering deposition consists in producing an atomsource sputtered from biased solid targets by the created plasma

2

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

ions, typically argon. The sputtered atoms (or molecules,clusters) will lose energy through collisions with the gas phasealong the pathway to the substrate. We use a simple model ofparticle slowing down along straight-line trajectories, subjectto a continuous energy loss process, which allows calculationof the energy distributions of the particle flux as a functionof the distance from the source. The mean kinetic energy ofsputtered atoms is calculated according to a modification ofthe Thompson formula, as the sputtered atoms are travellingthrough a gaseous medium (Meyer 1981):

f (E) ∝1 −

(Ecoh+E

γEAr+

) 12

E2(1 + Ecoh

E

)3 (3)

EF = (E − kBTg

)exp [n ln (Ef/Ei)] + kBTg. (4)

EF is the final energy after n collisions. Ef/Ei = 1−γ /2 is theratio of energies after and before a collision (Gras-Marti 1983),with γ = 4

(mgms/(mg + ms)

2), where mg and ms stand for

plasma forming atom (argon here) and sputtered atom masses,respectively, and n = dpτ/kBTg. E is the energy of thesputtered particles as they leave the target, Tg is the sputteringgas temperature, n is the number of collisions that take placein the gas, d is the travelled distance, p is the sputteringgas pressure and τ is the collision cross section assuminghard core interactions. To calculate the energy loss (Ef) ofsputtered atoms with the gas atoms, a Maxwell–Boltzmann(MB) distribution at Tg is fixed for the gas (in our conditionsTg = 300 K, Eg = kBTg). Because we search for the completeenergy distribution of sputtered atoms, for each Eg in the MBgas distribution, the energy loss is calculated for a fixed valueof the kinetic energy E of a sputtered atom. This is repeatedfor each E in the Thompson distribution and weighted bythe collision probability, which is simply the convolution off (E) and the MB distribution at Tg (Meyer 1981). So, initialvelocities or equivalently kinetic energies can be obtained fromsuch a distribution using a rejection method (Press 1992). Thevelocities of the sputtered atoms can also be sampled froma Maxwell–Gaussian distribution with a mean kinetic energycorresponding to the energy loss calculated with equation (4)with randomly selected incident angles. Finally, Monte Carlosolvers such as SIMTRA (van Aeken 2008, Depla 2012) areable to calculate the energy and angle distribution function inthree dimensions in the real plasma sputtering system. Whenthe distribution function is found, a rejection method can beused to sample the kinetic energies and incidence angles of theparticles impinging on the substrate.

When initial velocities and incidence angles are known,initial positions in the horizontal plane are randomly sampledin a uniform distribution at a vertical position a little greaterthan the atom–surface and atom–atom cut-off distances. Theinitial vertical position can be gradually changed as the filmis growing to prevent the creation of a new position insidethe film. To mimic deposition the atoms should be releasedto the surface one after each other. The effect of argon ionsis neglected in the present simulations, so no argon ions arereleased to the surface during deposition.

2.4. Limitations and capabilities of MD deposition studies

The time interval between each released atom should bechosen greater than the energy relaxation of the substrateafter the collision, which ranges from 1 to a few tens ofpicoseconds (Hou 2000, Brault 2012). It is necessary tobe aware that atom fluxes in MD are unphysically largewhen comparing with experiment. When considering MDsimulations, sputtered atoms are released here every τ = 2 pson a 10 × 10 nm2 surface; this leads to a flux of 1024 atcm−2s−1. We have checked that increasing this time doesnot change the results. This should be compared to a typicalflux encountered in sputtering deposition: say, 1015 at cm−2 s−1

(around 1 µm h−1). The first and important consequenceis there is no possibility of predicting a deposition rate.Nevertheless, when recalling that excess energy is correctlydescribed using an appropriate thermostat, other informationsuch as sticking coefficient, structure, and morphology isattainable. Moreover, information as radial density functions(RDFs) and simulated x-ray diffraction (XRD) patterns can bereadily compared to experiments (Hansen 2000, Xie 2013a,2013b). The second main limitation is the possible longtime diffusion occurring in the growth process on the surface.Some strategies have recently been successfully carried out,including a Monte Carlo procedure coupled to MD simulations(Blackwell 2012, Neyts 2013). Such investigations are outof the scope of this article, because in the present studiesindividual atomic motions are very localized for HEA andMGs. Indeed, we have the chance that the atom size differenceacts to prevent high diffusion leading to the (near)-amorphousphase. The used potentials have the effect of normally leadingto crystalline phase for individual atoms (see ZrCu with largeCu or Zr content) Moreover, in the present simulations, wehave carried out simulations on 100 and 17 Å substrate widthswithout any significant differences. We think this comesfrom the size difference between atoms. For atom–substrateinteraction, the cut-off length is always less than half the boxsize: this prevents the size effects when applying periodicboundary conditions. More precise description of the metal–silicon will require ab initio determination of the interactionpotentials.

3. Case study 1. ZrxCu100−x (10 � x � 90) thin filmsdeposited on a silicon (1 0 0) substrate: effect of thedeposited atom kinetic energy

Recently, there has been a huge interest in the atomic-level structure and structure–property relationship in MGs.These materials have been studied for 40 years because oftheir promising properties belonging to both metals (electron,heat conductivity, ductility, etc) and glasses (hardness, etc)(Li 2007, Masumoto 1994).To stabilize an amorphous phase inmetallic alloys, atomic diffusion must be prevented. This couldbe achieved by setting up the chemical composition (mixingof elements with different atomic sizes) or by freezing a loworder phase during the synthesis process (Kawamura 1997). Ithas been shown that deposition of thin films by condensationonto cold substrates allows stabilization of low order structurein such systems.

3

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

Table 1. The calculated mean kinetic energies of incoming Zr and Cu atoms corresponding to three different experimental conditions.

Sets of Zr Cusimulations (eV) (eV) Corresponding magnetron sputtering experimental conditions

1 0.13 0.34 dT−S = 7 cm, P = 3 Pa, target bias (Zr) = 460 V, target bias (Cu) = 490 V2 7.65 6.67 dT−S = 9 cm, P = 0.25 Pa, target bias = 300 V3 12.6 9.61 dT−S = 7 cm, P = 0.03 Pa, target bias (Zr) = 460 V, target bias (Cu) = 490 V

Figure 1. Snapshots of Zr–Cu coatings deposited on Si(1 0 0) substrate at different ratios of Zr and Cu atoms (the numbers in brackets arethe Zr and Cu atom numbers respectively, leading to sticking coefficients around 90%). • Zr, • Cu, • Si. Mean kinetic energies are〈EZr〉 = 0.13 eV and 〈ECu〉 = 0.34 eV.

As an example, ZrCu alloys have attracted interest inrecent years, due to their bulk MG properties (Mei-Bo 2004,Wang 2004, Yu 2006, Paduraru 2007, Cheng 2011), andas amorphous alloy films for their mechanical (Musil 2003,Xu 2004, Das 2005) and superconductivity properties

(Karpe 1996). Dudonis et al (1996) prepared thin filmswith Zr composition in the range of 5 � x � 95by using high working power (490 W and 1380 W onCu and Zr targets, respectively) during magnetron sputterdeposition.

4

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

Figure 2. Total RDFs for ZrxCu100−x alloys; individual curvescorresponding to different alloy compositions are displacedvertically for clarity.

Figure 3. Calculated x-ray intensity versus 2θ of ZrxCu100−x filmswith different compositions.

Table 2. Position of the main XRD peak for ZrCu alloy in thesimulation; unit: 2θ(◦).

Zr–Cu Zr10Cu90 Zr20Cu80 Zr30Cu70 Zr40Cu60 Zr50Cu50

Main peak 42.45 41.6 40.5 39.7 38.65Zr–Cu Zr60Cu40 Zr70Cu30 Zr80Cu20 Zr90Cu10

Main peak 37.8 37.0 36.25 35.7

Numerous theoretical studies have also been conductedon ZrCu systems. Sha et al (2010, 2011) employedatomistic methods (among them MD) for studying ZrCu MGforming conditions. Almyras et al (2010) investigated themicrostructure of Zr35Cu65 and Zr65Cu35 MGs and found thatthese systems consist of small touching and/or interpenetratingicosahedral-like clusters, which results in ‘superclusters’ (SCs)satisfying the system composition. They thus claimed thatseeking the equilibrium configuration for interpenetratingicosahedron-like clusters allows the prediction of the MG

Figure 4. Snapshot of sputtered Zr90Cu10 with the lowest energies(set 1); the blue outline shows its original cell in the MD simulationand the solid line shows the crystal lattice orientation. The atom sizeis reduced to highlight the two grain structures.

microstructure. While bulk amorphous structure is known tobe formed under specific synthesis conditions, the dynamicsof growth of ZrCu amorphous thin film has not been so wellstudied using MD. A better understanding of thin film growthcan be thus achieved via MD simulations.

Mean kinetic energies are determined using equations (3)and (4) and the corresponding averaging procedure summa-rized in section 2.3. The aim is to reproduce the three differentexperimental situations summarized in table 1, for which MDgrowth runs are simulated. This is intended to determine therole of both the composition and the deposited atom kineticenergy on the formation of the expected amorphous phase.

MD simulation was carried out in a three dimensionalcell, which was periodic only along x and y directions. Thedimensions of the silicon (1 0 0) substrate are 25×25×10 Å3.The first two bottom layers of the substrate are fixed, whilethe other layers are temperature controlled using a Berendsenthermostat. The Zr and Cu atoms with different ratios arerandomly deposited on the substrate (one atom is releasedevery 2 ps). The integration time step is chosen to be 1 fs.The total number of released atoms is 10 000, leading to a totalsimulation time of 20 ns. Each atom is placed in the vacuumslab at a random position from 5 to 7 Å above the surface.Zr with composition 3 < x < 95 is selected if a generatedrandom number ξ is less than x/100, else Cu is chosen. Thecomposition of the films is nearly the vapour composition andsticking coefficients for all compositions are close to 90%. Theinitial velocities are randomly sampled in a MB distributionwith the defined mean kinetic energy.

5

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

Figure 5. Snapshots of Zr–Cu coatings deposited on Si(1 0 0) substrate at different Zr/Cu ratios (the numbers in brackets are the Zr and Cuatom numbers respectively). • Zr, • Cu, • Si. Mean kinetic energies are 〈EZr〉 = 7.65 eV and 〈ECu〉 = 6.67 eV.

In the first set of simulations, the mean kinetic energiesof incoming atoms are low: 〈EZr〉 = 0.13 eV and 〈ECu〉 =0.34 eV. Snapshots of the films deposited on the Si(1 0 0) aredisplayed in figure 1. It is interesting to see that, as the Zrconcentration increases, the morphology goes through threedifferent stages: film–cluster–film. As we can see from figure1, Zr10Cu90 is deposited as a film with a thickness around 4 nm.Then, from Zr20Cu80 to Zr50Cu50 the deposited atoms grow asclusters with height ranging from 6.5 to 7.5 nm. Finally, forZr60Cu40 to Zr90Cu10 a film is formed with thickness rangingfrom 5 to 7.5 nm.

Figure 2 shows the total RDF of the all–all pair forthese simulation sets. For the Zr90Cu10 deposition RDF, fourpeaks arise in this plot, showing the well-crystallized structure,

which can also be clearly seen in figure 1. From Zr10Cu90 toZr80Cu20, the first peak shifts towards larger radial distance asthe concentration of Zr increases from 10% to 90%, because thefirst neighbour distance of Zr (3.23 Å) is larger than that of Cu(2.55 Å). With the increase of Zr concentration, the structureof the system is changed from a Cu predominant film to a Zrpredominant film presenting an amorphous structure.

Meanwhile, in the RDFs of Zr10Cu90 to Zr80Cu20, thefirst peak broadens and splits comparing with Zr90Cu10, whichhas pronounced peaks typical of a crystalline structure. Theamorphous nature of the alloys in the range 10–80% is clearlyshown in the snapshots presented in figure 1.

Figure 3 shows the intensity and position of the XRD θ–2θ

peaks as a function of the Zr metal content. Again at the Zr

6

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

concentration of 90%, ZrxCu100−x films are crystalline, whichagrees with the snapshot in figure 1. As the Zr concentrationincreases from 10% to 80%, a shift of the peaks towardssmall angles (table 2) is observed. At the same time, all ofthese patterns consist of broader peaks, indicating a low orderstructure. In Zr90Cu10 a Cu atom with its small diameter canenter the gap between the Zr atoms, which has no or only alittle effect on the overall structure, while for Zr10Cu90 evena small content of Zr, due to its larger diameter, disturbs thecrystalline structure of Cu.

For a deeper insight into the film growth mechanism ofZr90Cu10, a snapshot at the lowest kinetic energies is shown infigure 4. The black solid line underlines the crystal latticemis-orientation. Clearly, the film exhibits two grains: onein the orientation marked ‘A’ and the other in the orientationmarked ‘B’.

At the beginning of the deposition process, the formedstable nuclei are crystalline with a random orientationdistribution. As a result, the growth and coalescence of smallclusters leads to their coarsening. In this simulation the energyof the deposited atoms is not high enough to overcome thediffusion activation energy and restructuring between clusterscannot occur. Therefore, the boundary is immobile through allthe film thickness. As the deposition goes on, the clusters havea similar growth rate but with different growth directions; as aresult, two grains are formed with different lattice orientations.

For conditions 2 (medium–high energies, 〈EZr〉 =7.65 eV and 〈ECu〉 = 6.67 eV), the morphologies of filmsdeposited on Si(1 0 0) are displayed in figure 5. To preciselystudy the appearance of the amorphous phase, the range of Zrcomposition is varied between 3% and 95%. The films grewto approximately 4–9 nm when increasing Zr concentration.

Based on these simulations, the total RDFs for Zr metalcontents varying from 3% to 95% are presented in figure 6.Meanwhile, in the RDFs of Zr10Cu90 to Zr80Cu20, the peakbecomes broad and split as compared to Zr3Cu97, Zr90Cu10 andZr95Cu5, which have pronounced peaks typical of a crystallinestructure. The amorphous nature of the alloys in the range10–80% is clearly shown in the snapshots presented in figure 5.

The calculated x-ray intensities versus 2θ of ZrxCu100−x

simulated films are shown in figure 7 and peak positions intable 3. At high concentrations of Zr or Cu, i.e. for Zr3Cu97,Zr90Cu10 and Zr95Cu5, films show a crystalline XRD patternwhich agrees with the present RDF calculations reportedin figure 6. However, Zr10Cu90 can be considered as anexception to this. With the same concentration, Zr90Cu10 hasa crystalline structure, but Zr10Cu90 is amorphous, which isalso clearly shown from the snapshots of the films presentedin figure 5. This is again because of the atom size differencebetween Zr and Cu.

In this condition, for comparison with set 1 of thesimulations, there is no grain boundary, and the film is singlecrystalline for Zr90Cu10 and Zr95Cu5.

For the highest kinetic energies, 〈EZr〉 = 12.6 eV and〈ECu〉 = 9.61 eV, the films exhibit a more compact structurethan for previous conditions, with a thickness of approximately4–7.5 nm. Corresponding snapshots of the films deposited onSi(1 0 0) are displayed in figure 8.

Figure 6. Total RDFs for amorphous ZrxCu100−x alloys,3 < x < 95.

Figure 7. X-ray intensity versus 2θ of ZrxCu100−x films withdifferent compositions.

Table 3. Position of the main XRD peak for ZrCu alloy in thesimulation; unit: 2θ (◦).

Zr–Cu Zr3Cu97 Zr10Cu90 Zr20Cu80 Zr30Cu70 Zr40Cu60 Zr50Cu50

Main 42.1 42.1 41.7 40.35 39.4 38.4peak

Zr–Cu Zr60Cu40 Zr70Cu30 Zr80Cu20 Zr90Cu10 Zr95Cu5

Main 37.5 36.8 35.95 35.75 35.7peak

Based on these simulations, the total RDF is calculatedfor each case and is presented in figure 9. The sametrends as previously reported are observed when increasingZr concentrations. In the RDF of Zr90Cu10, four peaks arise,evidencing a good crystalline structure (figure 9). FromZr10Cu90 to Zr80Cu20, the peaks become broad and split,evidencing amorphous structures.

Figure 10 shows the intensity and position of the XRDθ–2θ peaks as a function of the Zr metal content. In thissimulation, at the Zr concentration of 90%, the XRD peak

7

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

Figure 8. Snapshots of Zr–Cu coatings deposited on Si(1 0 0) substrate at different ratios of Zr and Cu atoms (the numbers in brackets arethe Zr and Cu atom numbers respectively). • Zr, • Cu, • Si. Mean kinetic energies are 〈EZr〉 = 12.6 eV and 〈ECu〉 = 9.61 eV.

is sharp, showing the good crystalline state, which agreeswith the RDF presented in figure 9. As the Zr concentrationincreases from 10% to 80%, the peak broadens, indicatingan amorphous structure, and the peak position shifts towardssmall angles (table 4). When comparing these calculated XRDpatterns with lower deposition energy, it is seen that Zr90Cu10

in both sets shows a crystallized structure, while for the otherratios an amorphous structure is formed. This indicates that thephase and structure of alloy is not much affected by the metalatom kinetic energy in the ‘high energy’ domain. However,figure 11 shows a specific orientation of the crystal structureof Zr90Cu10 for simulation sets 2 (A) and 3 (B). It can beseen that snapshot (A) displays a well crystallized structure,while snapshot (B) exhibits a crystalline structure capped byan amorphous structure, 1.5 nm high, on the film top.

During the deposition process, the impinging atoms makeimpacts with the growing film at the surface. The kineticenergy of depositing atoms is transferred to the atoms near theimpact site and the temperature of the system will locally rise.In order to mimic isothermal growth conditions, the Berendsenthermostat was used in an intermediate region above the fixedSi(1 0 0) substrate, for energy dissipation and maintainingthe substrate at a desired temperature. For set 2, the largekinetic energy of depositing atoms can be properly dissipated,facilitating the atoms hopping to the sites of stronger bindingand forming a continuous crystalline structure, while for set 3,with a higher kinetic energy, the excess energy of the incomingatoms perturbs the lattice and physically destroys the lattice,limiting the reconstruction.

8

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

Figure 9. Total RDFs for ZrxCu100−x alloys.

Figure 10. Calculated x-ray intensity versus 2θ of ZrxCu100−x filmswith different compositions.

4. Case study 2. Molecular dynamics simulation ofAlCoCrCuFeNi HEA thin film deposition onto silicon

HEAs are metallic compounds containing six to 13 elementswith a concentration in the range 5–35% for each element(Yeh 2006, Zhang 2014). In these alloys, because of the highentropy of mixing, formation of brittle intermetallic phases isavoided and multielement solid solutions are stabilized (fccand/or bcc) (Yang 2012). The combination of numerousmetallic elements with different sizes induces a sluggishatomic diffusion, leading to nanocrystalline or amorphousstructures. Bulk HEAs have been extensively studied for theirexcellent properties and performance, including outstandingstrength and resistance to oxidation at high temperatures,anti-adhesion, corrosion resistance, high temperature stability,hydrophobicity, high stiffness, strength and toughness, highhardness and high strain rate superplasticity (Wu 2006, Hsu2007, Lin 2011). However, HEAs are quite difficult to

Table 4. Position of the main XRD peak for ZrCu alloy in thesimulation; unit: 2θ(◦).

Zr–Cu Zr10Cu90 Zr20Cu80 Zr30Cu70 Zr40Cu60 Zr50Cu50

Main peak 41.85 41.3 40.2 39.15 38.2Zr–Cu Zr60Cu40 Zr70Cu30 Zr80Cu20 Zr90Cu10

Main peak 37.55 36.75 35.7 35.65

synthesize as bulk materials and, for many applications,transferring their exceptional properties to a bare material maybe of interest. A few studies on HEA thin films depositedby magnetron sputtering have been published (Chen 2004,2005, Yeh 2004, Chang 2008, Tsai 2008, Dolique 2009,2010), starting from alloyed targets formed by melting orcasting, or from mosaic ones (Dolique 2009, 2010). HEAscan be viewed as atomic-scale composites. Their finalproperties come from (1) the combination of properties oftheir constituting elements and (2) the stabilized solid solutionsand structures. Thus, for the design of new alloys dedicatedto a given application, prediction of structural features ofthe thin film would be of particular interest. Despite thisapplicative goal, understanding of the growth mode of suchcomplex multielement films is a challenging research subject.Available literature on metallic alloy thin film growth allowsthus carrying out simulation of the process at the atomic level.

The present section is devoted to MD simulations forstudying the growth of complex HEA thin films. Theintegration time step is chosen to be 1 fs. The HEA atomsimpinge on the Si(1 0 0) substrate with velocities sampled in aMB distribution leading to an incident mean kinetic energyof 1 eV. Two substrate sizes are chosen for the subsequentsimulations: (1) Si(1 0 0) with dimensions 100 × 100 × 20 Å3,(2) Si(1 0 0) with dimensions 17×17×20 Å3. The depositionmodel of the six atoms is shown in figure 12.

Three sets of MD simulations of AlCoCrCuFeNi HEA thinfilms with different element compositions are made, accordingto dc magnetron sputtering experimental conditions. XRDanalysis (Cu Kα radiation, λ = 0.154 05 nm, Bragg–Brentanogeometry) was performed.

During MD simulation, 10 000 atoms are released to theSi surface to realize three deposition sets. A random numberx is generated to select the nature of the atom to be released,where 0 � x < 100. Taking Al2Co9Cr32Cu39Fe12Ni6 as anexample, Al is chosen if 0 � x < 2, Co if 3 � x < 11, Cr if11 � x < 433 and so on. With this method the desired numberof different atom types can be properly selected according tothe expected film composition. The outputs of simulations willindicate whether the targeted composition is reached. Table 5gives the number of atoms really existing in the simulatedfilm and its composition. The compositions of the simulatedsamples are close to the targeted ones.

5. MD simulation of HEA deposition on large Si(1 0 0)

Sample simulation snapshots for Al2Co9Cr32Cu39Fe12Ni6,Al3Co26Cr15Cu18Fe20Ni18 and Al39Co10Cr14Cu18Fe13Ni6 thinfilms are reported in figure 13. In all cases, there is nocontinuous film growth and the deposits grow as various sized

9

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

Figure 11. Snapshots of Zr90Cu10 with conditions 2 (A) and 3 (B) grown on Si(1 0 0) substrate with their specific orientation showing thecrystal structure. The solid line in (B) is used to separate the amorphous and crystalline zones.

Figure 12. Schematic picture of the initial HEA deposition model.• Al, • Co, • Cr, • Cu, • Fe, • Ni, • Si.

clusters, more or less meandering, due to the limited number ofimpinging atoms and the large simulation cell size. The clustermean height is around 3–3.5 nm for 10 000 released atoms.

The RDF for the three samples was then calculated andis plotted in figure 14. The peaks represent the successiveneighbour distances of the atoms, which can be compared withthe corresponding values in crystalline phases of each element(see table 6).

As displayed in table 7, the average values are calculatedfrom

⟨rneighbour

⟩ = ∑i=1,n ciRi according to the element crystal

values presented in table 6, where ci is the atomic percentageof the ith component and Ri is the neighbour distance of theith HEA element in the pure crystal. By analysing the averageneighbour distance value of HEA in table 7, we can see that

Table 5. Targeted and simulated deposited alloy compositions.

Atoms Al Co Cr Cu Fe Ni

Sample S1 Al2Co9Cr32Cu39Fe12Ni6 (8630/10 000)

Deposited number 151 956 2835 3211 1023 454

Simulation 1.7 11.1 32.9 37.2 11.9 5.3composition (%)

Targeted 2 9 32 39 11 6composition (%)

Sample S2 Al3Co26Cr15Cu18Fe20Ni18 (8466/10 000)

Deposited number 237 2154 1214 1550 1692 1619

Simulation 2.8 25.4 14.3 18.3 20.0 19.1composition (%)

Targeted 3 26 15 18 20 18composition (%)

Sample S3 Al39Co10Cr14Cu18Fe13Ni6 (8680/10 000)

Deposited number 2977 1084 1222 1688 1146 563

Simulation 34.3 12.5 14.1 19.4 13.2 6.5composition (%)

Targeted 39 10 14 18 13 6composition (%)

the first neighbour distance is almost the same in these threesamples and around 2.45 Å. The expected second neighbourdistance does not appear in the simulated thin film. This can beexplained by the hard ball model (Kao 2008) and attributed tothe effect of mixing numerous elements with different atomicsizes as depicted in figure 15. The circles represent the first,second, third, fourth and fifth shells, respectively. Becausethe system is compact, the first shell will be stable or onlychange a little due to the presence of neighbour atoms withdifferent atomic radii. However, the second and third shells areindistinguishable because of the large fluctuation in occupationof different sites. This introduces the disappearance of thesecond peak in the RDFs.

10

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

Figure 13. Snapshots of HEA films deposited on Si(1 0 0) substratewith large substrate: • Al, • Co, • Cr, • Cu, • Fe, • Ni, • Si.

Figure 14. Total RDF of the HEA deposit at different compositions.

A further insight can be achieved by comparingexperimental XRD patterns with those calculated in thesimulation. The recorded XRD θ–2θ peaks are shown infigure 16, where the corresponding diffraction spectra (limitedto the θ–2θ range where the main peak of fcc and bcc phaseslies) are given. The following peak positions are observed:2θ = 43.77◦ for sample 3 and 2θ = 43.81◦ for sample 1,

attributed to the fcc(1 1 1)β structure; 2θ = 44.41◦ for sample2, attributed to the bcc(1 1 0)α structure. However, the broadand low intensity sample 2 peaks could indicate a mixture ofsolid solutions and a less ordered phase.

The calculated x-ray intensities versus 2θ of HEA samplesare shown in figure 17. By comparing the two XRD plot sets, itcan be observed that the peak positions in the simulated XRDare close to those detected in the experimental XRD patterns(see table 8).

As can be seen from figures 16 and 17, the peak intensitiesare very different between simulations and experiments.However, the three experimental peak intensities are notcomparable with one another, due to the different sets ofXRD measurements. Thus no conclusion on experimental andsimulated peak intensity evolution can be drawn. This showsthat such comparison can only be qualitative.

5.1. MD simulations of HEA film growth on a reduced sizeSi(1 0 0) substrate

In the previous section, we found that HEA clusters are formedafter 10 000 HEA atoms are released onto the substrate. Ifwe increase the number of deposited atoms, we can expect toevolve towards a continuous film morphology. But this willcost too much calculation time. Another method is to reducethe width of the box: the width of the new substrate cell isthus set to dimensions 17 × 17 Å2. The length in the x andy directions is thus one-sixth of the previous size. In otherwords, if the same height is reached, the volume of the newsimulation box is one-36th of the previous size box.

The interaction cut-off distances are set to 8 Å. The widthof the system was thus chosen in such a way that eachdimension would be at least twice the cut-off, so boundaryeffects are expected to be limited. With this smaller width, ifthe velocity of the deposited atom is too large along the x andy directions, it will pass through the periodic boundary severaltimes. This will affect the whole system and may introduceartefacts in the morphology. Figure 18 displays the trajectoryof a typical Cu atom in the process of deposition in sample 1.The small blue balls and the blue line represent the positionhistory of the moving Cu atom. Each position is separatedby a 4 ps travel time and the Cu atom can be captured bythe nearby surface atoms with a fast relaxation. This typicaltrajectory shows that this small substrate size can be used forthe MD simulations of HEA film growth without any effectof the periodic boundary condition. It can also be concludedthat such systems (HEA) are expected not to form large rangeorder, due to size differences preventing long range diffusion,leading to segregation.

During MD simulation, 2000 atoms are released to realizethree deposition sets with the same compositions as in theprevious section. These sets of calculation are equivalentto releasing 70 000 atoms onto the previous larger surface(100 × 100 Å2), so this is equivalent to observing the filmat a deposition time approximately seven times larger. Table 9gives the real composition of the HEA thin film in theexperiments, the number of atoms really existing in thesimulated film and its composition.

11

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

Table 6. The neighbour distances in single element crystals.

Lattice parameter 1st neighbour 2nd neighbour 3rd neighbour 4th neighbourElements (Å) (Å) (Å) (Å) (Å)

Al (fcc) aAl = 4.05 aAl√2

= 2.86 aAl = 4.05√

32 aAl = 4.96

√2 aAl = 5.73

Co (hcp) aCo = 2.51 aCo = 2.51√

2 aCo = 3.09 cCo = 4.07√

2 cCo = 5.76cCo = 4.07

Cu (fcc) aCu = 3.61 aCu√2

= 2.55 aCu = 3.61√

32 aCu = 4.42

√2 aCu = 5.10

Cr (bcc) aCr = 2.88√

32 aCr = 2.49 aCr = 2.88

√2 aCr = 4.07

√114 aCr = 4.78

Fe (bcc) aFe = 2.87√

32 aFe = 2.49 aFe = 2.87

√2 aFe = 4.06

√114 aFe = 4.76

Ni (fcc) aNi = 3.52 aNi√2

= 2.49 aNi = 3.52√

32 aNi = 4.31

√2 aNi = 4.98

Table 7. Average neighbour distances in the HEA.

1st neighbour 2nd neighbour 3rd neighbour 4th neighbourElements (Å) (Å) (Å) (Å)

Al2Co9Cr32Cu39Fe12Ni6 2.52 3.19 4.32 4.99(average)

Sample 1 2.44 — 4.27 4.79

Al3Co26Cr15Cu18Fe20Ni18 2.52 3.19 4.19 5.14(average)

Sample 2 2.45 — 4.30 4.83

Al39Co10Cr14Cu18Fe13Ni6 2.64 3.49 4.48 5.3(average)

Sample 3 2.46 — 4.35 —

The films grew to approximately 10 nm. Snapshots of thefilms with three different compositions deposited on Si(1 0 0)are presented in figure 19. It can be clearly seen that acrystalline structure is formed in samples 1 and 2 abovean amorphous HEA layer, while for sample 3 an amorphousstructure is formed on the overall thickness.

Actually, throughout the process of atom deposition,there exists a competition between the dense packing (tolower enthalpy) and the randomness of atoms (to increasethe configurational entropy) driven by thermal energy. Ineach step during simulation, each jumping atom or in situshaking is to seek its minimum energy position under therule of minimizing energy. However, at the same time, thekinetic energy or momentum also drives atoms to jump, whichis against the tendency towards the minimum energy. With thesame simulation conditions, the ‘engine’ of this competition,enthalpy and entropy, is determined by the only variedparameter, the composition of the HEA. In samples 1 and 2,the dense packing becomes dominant in making the atomicconfiguration more ordered: this occurs for low Al content (2%and 3%). In contrast, in sample 3 a disordered or amorphousphase tends to stabilize: this occurs for large Al content (39%).This can be interpreted as the high entropy effect.

Figure 20 shows the RDF of the three samples and table 10gives the four simulated neighbour distances and the corre-sponding theoretical crystal average values. In these threesamples, the disappearance of the second neighbour distancecomes from the disordered arrangement of the atoms prevent-ing stacking order growth. In samples 1 and 2, the RDFs show

Figure 15. Hard ball model for HEA (reprinted with permissionfrom Kao (2008), Copyright 2008 IOP).

pronounced peaks that can be attributed to a crystalline struc-ture, in agreement with the results presented in figure 19. Insample 3, it is shown that the intensity of the RDF is lower.Moreover, the first and second peaks become broad and fadeaway quickly. All of this indicates that sample 3 exhibits a loworder structure. This is also in agreement with the snapshot

12

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

Figure 16. Experimental XRD patterns of HEA film sputtered at300 K with different compositions.

Figure 17. The simulated XRD patterns at different compositions.

of sample 3 in figure 19. From a comparison among RDFpatterns in figure 20 versus figure 14, it is seen that, as thecontinuous film grows, the RDF patterns change very little foralloys of sample 3, showing amorphous state, but significantlyfor samples 1 and 2. For the continuous film the first four peaksbecome clearer and narrower and a fifth peak around 7.36 Åarises, showing the crystal-like structure formed.

Figure 21 shows the intensity of the calculated x-rayintensities versus 2θ of the HEA samples. The number ofatoms in this set of simulations is low, thus it is hard to get anXRD pattern corresponding to the experiment. To circumventthis, we have repeated the original HEA25 times, according tothe periodic boundary condition in the x and y directions. Asystem with around 50 000 atoms was built for calculating theXRD patterns more precisely. The peak positions are shownin table 11.

The simulated peaks at positions 2θ = 42.85◦, 43.6◦ and44.3◦ correspond to samples S3, S1 and S2, respectively, S2being close to the bcc(1 1 0)α structure while the S3 peak isfairly consistent with fcc(1 1 1)β (Xie 2013b). In this lattercase, because the peak is broader than for S1 and S2, the

Figure 18. Projected Cu atom during deposition (cross section of thecell along z). The trajectory time elapsed between positions is 4 ps.

structure has much shorter range order. These values are closeto the experiment, with a small shift towards smaller angles,which may be caused by the limited size of the simulationbox. Besides, with the same number of deposited atoms, asalready noticed, the XRD peak of sample 3 is broader than theothers. This is consistent with the disordered structure shownin figure 19. In contrast, samples 1 and 2 have narrow peaksand the well crystallized structure arises with thicknesses ofaround 4 nm and 5 nm respectively in figure 19. The width ofthe simulated XRD peak is proportional to the ‘amorphous’or crystallized phase in the simulation. Nevertheless, inexperiments (figure 16) S2 displays the broader peak, whilein the present simulations it is S3. This discrepancy is notwell explained. Due to the limited number of atoms in thesimulation compared to experiment, the comparison can onlybe qualitative. One has to keep in mind that the other atomsin the expanded film are just duplications of the same unitcell. This is the limitation of this model. Nevertheless, wecan use this procedure to get some information about thecrystalline or amorphous nature of the films, depending onthe composition of the HEA, to compare with the experiment.What is interesting in using small cells is thus to study thestructure for larger thicknesses.

6. Conclusion

The maturity of semi-empirical analytic interaction potentialdetermination allows extensive (parallel) implementation ofclassical MD simulations for handling complex systems,among them thin film growth phenomena. Plasma sputteringdeposition being a widely use technology, predictingstructures, morphologies and properties at atomic scales ischallenging for factories of the future, where integratingcomputational materials science will help in saving costlyexperimental tests. The initial steps in particular ofgrowth driving the final microstructure are reachable byMD simulation provided the deposition conditions can betranslated as inputs for MD simulations. The energetics of the

13

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

Table 8. 2θ positions of first XRD peaks for HEA in the experiment and simulation; unit: 2θ(◦).

HEA Al39Co10Cr14Cu18Fe13Ni6 Al2Co9Cr32Cu39Fe12Ni6 Al3Co26Cr15Cu18Fe20Ni18

ExperimentMain peak 43.77 43.81 44.41

SimulationMain peak 43.95 44.1 44.7

Table 9. Simulated deposited alloy composition in the smallsize cell.

Atoms Al Co Cr Cu Fe Ni

Sample 1 Al2Co9Cr32Cu39Fe12Ni6 (1660/2000)

Deposited number 37 165 523 643 189 103

Simulation 2.2 9.9 31.5 38.7 11.4 6.2composition (%)

Targeted 2 9 32 39 11 6composition (%)

Sample 2 Al3Co26Cr15Cu18Fe20Ni18 (1670/2000)

Deposited number 59 456 250 282 313 310

Simulation 3.5 27.3 15.0 16.9 18.7 18.6composition (%)

Targeted 3 26 15 18 20 18composition (%)

Sample 3 Al39Co10Cr14Cu18Fe13Ni6 (1656/2000)

Deposited number 634 186 218 305 208 105

Simulation 38.3 11.2 13.2 18.4 12.6 6.3composition (%)

Targeted 39 10 14 18 13 6composition (%)

deposition, i.e. how to correctly describe the energy dissipationthrough the substrate, can be handled with ad hoc velocityrescaling, provided that relaxation times are known. Thedefinitive unreachable information is the deposition rate dueto the unphysical large incoming particle fluxes compared tosputtering experiments. The present work, and the numerousothers previously published or being published, constantlydemonstrate that the compositions, structure, morphologiesand sometimes thin film properties are correctly describedusing MD simulations.

Case studies proposed here should be seen as highlightinghow MD is able to predict or to be compared toexperiments. First, ZrxCu100−x thin film growth is studiedby MD simulations using initial conditions consistent with amagnetron co-sputtering process. The crystallinity of the filmsis analysed by calculated RDFs and XRD patterns. The resultsshow that films containing large amounts of one of the elements(higher than 80%) are crystallized, whereas for intermediatecompositions a low order phase is evidenced. This trend is dueto chemical disorder, since the two types of atom seem to beincorporated in the same lattice (solid solution), which inducesdistortion of the lattice parameter. Results also show that themorphology of the films is dependent on the mean kineticenergy of the incoming atoms. With higher deposition energy,a compact and uniform film is likely to form. When the kineticenergies of the atoms are above a threshold a top amorphouszone grows, whereas at lower energy the morphology is in the

Figure 19. Snapshots of HEA films deposited on Si(1 0 0) substratewith small substrate; the dashed line separates the crystalline andamorphous structures. • Al, • Co, • Cr, • Cu, • Fe, • Ni, • Si.

Figure 20. Total RDF of the HEA deposits at the differentcompositions of figure 21.

form of clusters or film depending on the atomic composition.The more crystalline Zr90Cu10 evolves from a polycrystallinestate at low impinging kinetic energy to a pure crystalline oneat higher energy.

14

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

Table 10. Average neighbour distances in the HEA compared to element crystal values.

1st neighbour 2nd neighbour 3rd neighbour 4th neighbourElements (Å) (Å) (Å) (Å)

Al2Co9Cr32Cu39Fe12Ni6 2.52 3.19 4.32 4.99(average)

Sample 1 2.48 — 4.08 4.83

Al3Co26Cr15Cu18Fe20Ni18 2.52 3.19 4.19 5.14(average)

Sample 2 2.49 — 4.15 4.88

Al39Co10Cr14Cu18Fe13Ni6 2.64 3.49 4.48 5.3(average)

Sample 3 2.52 — 4.42 —

Figure 21. The simulated XRD patterns at different compositions.

Table 11. 2θ position of main XRD peak for HEA alloy in theexperiment and simulation; unit: 2θ(◦).

Al2Co9Cr32 Al3Co26Cr15 Al39Co10Cr14

HEA Cu39Fe12Ni6 Cu18Fe20Ni18 Cu18Fe13Ni6

ExperimentMain peak 43.81 44.41 43.77

SimulationMain peak 43.6 44.3 42.85

Second, the growth of complex systems such as HEAclusters or thin films can be studied by MD simulations. Due tothe short diffusion range, thin film growth has been studied ona rather small simulation box while cluster growth was studiedon a larger simulation box. Thin film structures are shown to besensitive to the HEA composition. Amorphous films with a topcrystalline layer grow for low Al content (2% and 3%). Pureamorphous thin film is observed for the composition with thelargest Al content (39%). Clusters always remain amorphous,as RDFs display broad peaks. Tentative comparison withexperimental XRD patterns is limited to the agreement of thepeak positions. Unfortunately, no comparison with the peakintensity is possible due to a too high experimental thickness.Certainly comparison between MD simulations and an ultra-thin deposited layer would be more fruitful, provided XRD θ–2θ measurements are possible with a very low film thickness(around 10 nm).

Acknowledgment

The China Scholarship Council is gratefully acknowledged forgrant 2009 60212.

References

Alami J, Bolz S and Sarakinos K 2009 High power pulsedmagnetron sputtering: fundamentals and applications J. AlloysCompounds 483 530–4

Alder B and Wainwright T 1957 Phase transition for a hard spheresystem J. Chem. Phys. 27 1208–9

Alder B and Wainwright T 1958 Transport Processes in StatisticalMechanics ed I Prigogine (New York: Wiley Interscience)pp 97–131

Alder B J and Wainwright T E 1959 Studies in molecular dynamics.I. General method J. Chem. Phys. 31 459–66

Allen M P and Tildesley D J 1987 Computer Simulations of Liquids(New York: Oxford University Press)

Almyras C E, Lekka N, Mattern G A and Evangelakis 2010 On themicrostructure of the Cu65Zr35 and Cu35Zr65 metallic glassesScr. Mater. 62 33–6

Baguer N, Georgieva V, Calderin L, Todorov I T, VanGils S andBogaerts A 2009 Study of the nucleation and growth of TiO2

and ZnO thin films by means of molecular dynamicssimulations J. Cryst. Growth 311 4034–43

Berendsen H J C, Postma J P M, van Gunsteren W F, DiNola A andHaak H R 1984 Molecular dynamics with coupling to anexternal bath J. Chem. Phys. 81 3684–90

Blackwell S, Smith R, Kenny S D and Walls J M 2012 Modelingevaporation, ion-beam assist, and magnetron sputtering of thinmetal films over realistic time scales Phys. Rev. B 86 035416

Bogaerts A, Bultinck E, Eckert M, Georgieva V, Mao M, Neyts Eand Schwaederle L 2009 Computer modeling of plasmas andplasma–surface interactions Plasma Process. Polym. 6 295–307

Bogaerts A, De Bie C, Eckert M, Georgieva V, Martens T, Neyts Eand Tinck S 2010 Modeling of the plasma chemistry andplasma–surface interactions in reactive plasmas Pure Appl.Chem. 82 1283–99

Bogaerts A, Aerts R, Snoeckx R, Somers W, Van Gaens W,Yusupov M and Neyts E 2012 Modeling of plasma andplasma–surface interactions for medical, environmental andnano applications J. Phys.: Conf. Ser. 399 012011

Brault P 2011 Plasma deposition of catalytic thin films:experiments, applications, molecular modeling Surf. Coat.Technol. 205 S15–23

Brault P, Caillard A, Charles C, Boswell R and Graves D B 2012Platinum nanocluster growth on vertically aligned carbonnanofiber arrays: sputtering experiments and moleculardynamics simulations Appl. Surf. Sci. 263 352–6

15

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

Brenner D W 1990 Empirical potential for hydrocarbons for use insimulating the chemical vapor deposition of diamond filmsPhys. Rev. B 42 9458–71

Brenner D 2000 The art and science of an analytical potential Phys.Status Solidi b 217 23

Chang H-W, Huang P-K, Yeh J-W, Davison A, Tsau C-H andYang C-C 2008 Influence of substrate bias, depositiontemperature and post-deposition annealing on the structure andproperties of multi-principal-component (AlCrMoSiTi) Ncoatings Surf. Coat. Technol. 202 3360–6

Chen T K, Shun T T, Yeh J W and Wong M S 2004 Nanostructurednitride films of multi-element high-entropy alloys by reactivedc sputtering Surf. Coat. Technol. 188–189 193–200

Chen T K, Wong M S, Shun T T and Yeh J W 2005 Nanostructurednitride films of multi-element high-entropy alloys by reactivedc sputtering Surf. Coat. Technol. 200 1361–65

Cheng Y Q and Ma E 2011 Atomic-level structure andstructure–property relationship in metallic glasses Prog. Mater.Sci. 56 379–473

Cleri F and Rosato V 1993 Tight-binding potentials for transitionmetals and alloys Phys. Rev. B 48 22

Coronell D G, Hansen D E, Voter A F, Liu C F, Liu X Y andKress J D 1998 Molecular dynamics-based ion-surfaceinteraction models for ionized physical vapordeposition featurescale simulations Appl. Phys. Lett. 73 3860

Das J, Tang M B, Kim K B, Theissmann R, Baier F, Wang W H andEckert J 2005 ‘Work-hardenable’ ductile bulk metallic glassPhys. Rev. Lett. 94 205501

Daw M S and Baskes M I 1983 Semiempirical, quantum mechanicalcalculation of hydrogen embrittlement in metals Phys. Rev.Lett. 50 1285

Daw M S and Baskes M I 1984 Embedded-atom method: derivationand application to impurities, surfaces, and other defects inmetals Phys. Rev. B 29 6443

Daw M S, Foiles S M and Baskes M I 1993 The embedded-atommethod: a review of theory and applications Mater. Sci. Rep.9 251–310

Depla D and Leroy W P 2012 Magnetron sputter deposition asvisualized by Monte Carlo modeling Thin Solid Films520 6337

Dolique V, Thomann A L, Brault P, Tessier Y and Gillon P 2009Complex structure/composition relationship in thin films ofAlCoCrCuFeNi high entropy alloy Mater. Chem. Phys.117 142–7

Dolique V, Thomann A L, Brault P, Tessier Y and Gillon P 2010Thermal stability of AlCoCrCuFeNi high entropy alloy thinfilms studied by in situ XRD analysis Surf. Coat. Technol.204 1989–92

Dudonis J, Brucas R and Miniotas A 1996 Synthesis of amorphousZr–Cu alloys by magnetron co-sputtering Thin Solid Films275 164–7

Finnis M W and Sinclair J E 1984 A simple empirical N -bodypotential for transition metals Phil. Mag. A 50 45–55

Foiles S M 1985 Application of the embedded-atom method toliquid transition metals Phys. Rev. B 32 3409

Foiles S M and Baskes M I 2012 Contributions of theembedded-atom method to materials science and engineeringMRS Bull. 37 485–91

Foiles S M, Baskes M I and Daw M S 1986Embedded-atom-method functions for the fcc metals Cu, Ag,Au, Ni, Pd, Pt, and their alloys Phys. Rev. B 33 7983

Foiles S M, Baskes M I and Daw M S 1988 Phys. Rev. B 37 10378(erratum)

Frenkel D and Smit B 2001 Understanding Molecular Simulation(Orlando, FL: Academic)

Girifalco L A and Weizer V G 1959 Application of the Morsepotential function to cubic metals Phys. Rev. 114 687

Georgieva V, Todorov I T and Bogaerts A 2010 Molecular dynamicssimulation of oxide thin film growth: importance of the

inter-atomic interaction potential Chem. Phys. Lett.485 315–319

Georgieva V, Voter A F and Bogaerts A 2011 Understanding thesurface diffusion processes during magnetronsputter-deposition of complex oxide Mg–Al–O thin filmsCryst. Growth Des. 11 2553–8

Gou F, Kleyn A W and Gleeson M A 2008 The application ofmolecular dynamics to the study of plasma–surfaceinteractions: CFx with silicon Int. Rev. Phys. Chem. 27 229–71

Goyhenex C and Bulou H 2001 Theoretical insight in the energeticsof Co adsorption on a reconstructed Au(1 1 1) substrate Phys.Rev. B 63 235404

Gras-Marti A and Valles-Abarca J A 1983 Slowing down andthermalization of sputtered particle fluxes: energy distributionsJ. Appl. Phys. 54 1071–5

Graves D B and Abrams C F 2001 Molecular dynamics simulationsof ion–surface interactions with applications to plasmaprocessing Adv. Chem. Eng. 28 149–202

Graves D B and Brault P 2009 Molecular dynamics for lowtemperature plasma–surface interaction studies J. Phys. D:Appl. Phys. 42 194011

Guo X Y and Brault P 2001 Early stages of silicon nitride filmgrowth studied by molecular dynamics simulations Surf. Sci.488 133–40

Haile J M 1992 Molecular Dynamics Simulations (New York:Wiley)

Hansen U, Rodgers S and Jensen K F 2000 Modeling of metal thinfilm growth: linking angstrom-scale molecular dynamicsresults to micron-scale film topographies Phys. Rev. B622869–78

Helmersson U, Lattemann M, Bohlmark J, Ehiasarian A P andGudmundsson J T 2006 Ionized physical vapor deposition(IPVD): a review of technology and applications Thin SolidFilms 513 1–24

Hou Q, Hou M, Bardotti L, Prevel B, Melinon P and Perez A 2000Deposition of AuN clusters on Au(1 1 1) surfaces: I.Atomic-scale modelling Phys. Rev. B 62 2825

Hsu U, Hung U, Yeh J, Chen S, Huang Y and Yang C 2007Alloying behavior of iron, gold and silver inAlCoCrCuNi-based equimolar high-entropy alloys Mater. Sci.Eng. A 460 403–8

Iftimie R, Minary P and Tuckerman M E 2005 Ab initio moleculardynamics: concepts, recent developments and future trendsProc. Natl Acad. Sci USA 102 6654–9

Jager H U and Yu Belov A 2003 ta-C deposition simulations: filmproperties and times-resolved dynamics of film formationPhys. Rev. B 68 024201

Kao S W, Yeh J W and Chin T S 2008 Rapidly solidified structureof alloys with up to eight equal-molar elements—asimulation by molecular dynamics J. Phys.: Condens. Matter20 145214

Karpe N, Bøttiger J, Krog J P, Nordstrom A and Rapp V 1996Influence of deposition conditions and ion irradiation on thinfilms of amorphous Cu–Zr superconductors Thin Solid Films275 82–6

Kawamura Y, Kato H, Inoue A and Masumoto T 1997 Fabricationof bulk amorphous alloys by powder consolidation Int. J.Powder Metall. 33 50–61

Li Y, Poon S J, Shiflet G J, Xu J, Kim D H and Loffler J F 2007Formation of bulk metallic glasses and their composites MRSBull. 32 624

Lin C M and Tsai H L 2011 Evolution of microstructure, hardness,and corrosion properties of high-entropy Al0.5CoCrFeNi alloyIntermetallics 19 288–94

Lin Z B, Johnson R A and Zhigilei L V 2008 Computational studyof the generation of crystal defects in a bcc metal targetirradiated by short laser pulses Phys. Rev. B 77 214108

Maizuradze G G, Thomson D L and Wagner A F 2003 Interpolatingmoving least squares methods for fitting potential energy

16

J. Phys. D: Appl. Phys. 47 (2014) 224004 L Xie et al

surfaces: detailed analysis of one-dimensional applicationsJ. Chem. Phys. 119 10002

Masumoto T 1994 Recent progress of amorphous metallic materialsSci. Rep. RITU A 39 91–102

Mei-Bo T, De-Qian Z, Ming-Xiang P and Wei-Hua W 2004 BinaryCu–Zr bulk metallic glasses Chin. Phys. Lett. 21 901

Meyer K, Schuller I K and Falco C M 1981 Thermalization ofsputtered atoms J. Appl. Phys. 52 5803–5

Musil J and Daniel R 2003 Structure and mechanical properties ofmagnetron sputtered Zr–Ti–Cu–N films Surf. Coat. Technol.166 243–53

Musil J, Baroch P, Vlck J, Nam K H and Han J G 2005 Reactivemagnetron sputtering of thin films: present status and trendsThin Solid Films 475 208–18

Neyts E C and Bogaerts A 2013 Combining molecular dynamicswith Monte Carlo simulations: implementations andapplications Theor. Chem. Acc. 132 1320

Neyts E, Khalilov U, Pourtois G and van Duin A C T 2012Hyperthermal oxidation of Si(1 0 0)2×1 surfaces: effect ofgrowth temperature J. Phys. Chem. C 116 8649–56

Ni B, Sinnott S B, Mikulski P T and Harrison J A 2002Compression of carbon nanotubes filled with C60, CH4, or Ne:predictions from molecular dynamics simulations Phys. Rev.Lett. 88 205505

Nielson K D, van Duin A C T, Oxgaard J, Deng W-Q andGoddard W A 2005 Development of the ReaxFF reactive forcefield for describing transition metal catalyzed reactions, withapplication to the initial stages of the catalytic formation ofcarbon nanotubes J. Phys. Chem. A 109 493–9

Nikitin A, Ogasawara H, Mann D, Deneck R, Zhang Z, Dai H,Cho K and Nilsson A 2005 Hydrogenation of single-walledcarbon nanotubes Phys. Rev. Lett. 95 225507

Paduraru A, Kenoufi A, Bailey N P and Schiøtz J 2007 Aninteratomic potential for studying CuZr bulk metallic glassesAdv. Eng. Mater. 9 505–8

Plimpton S J 1995 Fast parallel algorithms for short-rangemolecular dynamics J. Comput. Phys. 117 1–19(http://lammps.sandia.gov)

Plimpton S J and Thompson S P 2012 Computational aspects ofmany-body potentials MRS Bull. 37 513–21

Press W A, Teukolsky S A, Vetterling W T and Flannery B P 1992Numerical Recipes 2nd edn (Cambridge: CambridgeUniversity Press)

Rapaport D C 1995 The Art of Molecular Dynamics Simulations(Cambridge: Cambridge University Press)

Rosato V, Guillope M and Legrand B 1989 Thermodynamical andstructural properties of fcc transition metals using a simpletight-binding model Phil. Mag. A 59 321–36

Sarakinos K, Alami J and Konstantinidis S 2010 High power pulsedmagnetron sputtering: a review on scientific and engineeringstate of the art Surf. Coat. Technol. 204 1661–84

Sha Z, Feng Y and Li Y 2010 Statisticalcomposition–structure–property correlation and glass-formingability based on the full icosahedra in Cu–Zr metallic glassesAppl. Phys. Lett. 96 061903

Sha Z D, Zhang Y W, Feng Y P and Li Y 2011 Molecular dynamicsstudies of short to medium range order in Cu64Zr36 metallicglass J. Alloys Compounds 509 8319–22

Stuart S J, Tutein A B and Harrison J A 2000 A reactive potentialfor hydrocarbons with intermolecular interactions J. Chem.Phys. 112 6472

Sutton A P and Chen J 1990 Long-range Finnis–Sinclair potentialsPhil. Mag. Lett. 61 139

Swope W C, Andersen H C, Berens P H and Wilson K R 1982 Acomputer simulation method for the calculation of equilibriumconstants for the formation of physical clusters of molecules:application to small water clusters J. Chem. Phys. 76 637

Tersoff J 1988a New empirical approach for the structure and energyof covalent systems Phys. Rev. B 37 6991

Tersoff J 1988b Empirical interatomic potential for silicon withimproved elastic properties Phys. Rev. B 38 9902–5

Tersoff J 1989 Modeling solid-state chemistry: interatomicpotentials for multicomponent systems Phys. Rev. B 39 5566

Tersoff J 1990 Phys. Rev. B 41 3248 (erratum)Treglia G, Legrand B, Ducastelle F, Saul A, Gallis C, Meunier I,

Mottet C and Senhaji A 1999 Alloy surfaces: segregation,reconstruction and phase transitions Comput. Mater. Sci.15 196–235

Tsai M H, Yeh J W and Gan J Y 2008 Diffusion barrier properties ofAlMoNbSiTaTiVZr high-entropy alloy layer between copperand silicon Thin Solid Films 516 5527–30

van Duin A C T, Dasgupta S, Lorant F and Goddard W A 2001ReaxFF: a reactive force field for hydrocarbons J. Phys. Chem.A 105 9396–409

Van Aeken K, Mahieu S and Depla D 2008 The metal flux from arotating cylindrical magnetron: a Monte Carlo simulationJ. Phys. D.: Appl. Phys. 41 20530

Wadley H N G, Zhou X, Johnson R A and Neurock M 2001Mechanisms, models and methods of vapour deposition Prog.Mater. Sci. 46 329–77

Wang D, Li Y, Sun B, Sui M, Lu K and Ma E 2004 Bulk metallicglass formation in the binary Cu–Zr system Appl. Phys. Lett.84 4029–31

Wu J-M, Lin S-J, Yeh J-W, Chen S-K, Huang Y-S and Chen H-C2006 Adhesive wear behavior of AlxCoCrCuFeNi high-entropyalloys as a function of aluminum content Wear 261 513–19

Xie L, Brault P, Thomann A-L and Bedra L 2013a Moleculardynamics simulation of binary ZrxCu100−xmetallic glass thinfilm growth Appl. Surf. Sci. 274 164–70

Xie L, Brault P, Thomann A-L and Bauchire J-M 2013bAlCoCrCuFeNi high entropy alloy cluster growth andannealing on silicon: a classical molecular dynamicssimulation study Appl. Surf. Sci. 285P 810–16

Xu D, Lohwongwatana B, Duan G, Johnson W and Garland C 2004Bulk metallic glass formation in binary Cu-rich alloyseries—Cu100−xZrx (x = 34, 36, 38.2, 40 at%) and mechanicalproperties of bulk Cu64Zr36 glass Acta Mater. 52 2621–4

Yang X and Zhang Y 2012 Prediction of high-entropy stabilizedsolid-solution in multi-component alloys Mater. Chem. Phys.132 233–8

Yeh J 2006 Recent progress in high-entropy alloys Ann. Chim.31 633–48

Yeh J W, Chen S K, Lin S J, Gan J Y, Chin T S, Shun T T, Tsau C Hand Chang S Y 2004 Nanostructured high-entropy alloys withmultiple principal elements: novel alloy design concepts andoutcomes Adv. Eng. Mater. 6 299–303

Yu P, Bai H and Wang W 2006 Superior glass-forming ability ofCuZr alloys from minor additions J. Mater. Res. 21 1674–9

Zhang L and Jiang S 2002 Molecular simulation study of nanoscalefriction for alkyl monolayers on Si(1 1 1) J. Chem. Phys.117 1804

Zhang Y, Zuo T T, Tang Z, Gao M C, Dahmen K A, Liaw P K andLu Z P 2014 Microstructures and properties of high-entropyalloys Prog. Mater. Sci. 61 1–93

Zhen S and Davies G J 1983 Calculation of the Lennard-Jones n–mpotential energy parameters for metals Phys. Status Solidi a78 595–605

Zhou X, Wadley H, Johnson R A, Larson D, Tabat N, Cerezo A,Petford-Long A, Smith G, Clifton P and Martens R 2001Atomic scale structure of sputtered metal multilayers ActaMater. 49 4005–15

Zhou X, Johnson R and Wadley H 2004 Misfit-energy-increasingdislocations in vapor-deposited CoFe/NiFe multilayers Phys.Rev. B 69 144113

17