The deposition of Fe or Co clusters on Cu substrate by molecular dynamic simulation

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The deposition of Fe or Co clusters on Cu substrate by molecular dynamic simulation

Zheng-Han Hong

a

_{, Shun-Fa Hwang}

b,

⁎

_{, Te-Hua Fang}

a

Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan 807, ROC

b

Department of Mechanical Engineering, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliu, Taiwan 640, ROC

a b s t r a c t

a r t i c l e i n f o

Article history: Received 16 June 2010 Accepted 29 September 2010 Available online 7 October 2010 Keywords:

Molecular dynamic

Ionized cluster beam deposition Atomic stress

Surface roughness Tight-binding potential

A molecular dynamic method is used to simulate theﬁlm growth process of Fe or Co clusters depositing on Cu substrate with low energy. The tight-binding (TB-SMA) many-body potential is used to simulate the interaction between atoms. The effects of different incident energies and/or substrate temperatures on the surface roughness, layer coverage function, radial distribution function (RDF), and residual stress are investigated. From the simulation results, as the substrate temperature and/or incident energy is increased, the surface roughness of the grownﬁlm could be reduced, and the interface intermixing is increased. Also, as compared to Co–Cu system, Fe–Cu system has better surface roughness, less interface intermixing, and similar radial distribution function as well as average stresses.

1. Introduction

Cluster beam or ion beam sputtering deposition (IBS) is a conventionally adopted approach for producing a thinﬁlm on a substrate

[1–3]. The IBS process is applied with two purposes. Thefirst is to enhance the mobility of the deposited atoms and to promote thefilm growth. The other is to bombard the surface of a solid substrate and to remove its atoms for further deposition[1]. These two processes depend on adjusting the incident energy of the ions, the incident angle of ions, and the ion assisted ratio, which is the ratio of ions to neutral atoms. These parameters of IBS process influence the quality and morphology of the deposited thinfilm. Under different parameter combinations of IBS process, variousfilm growth processes, such as epitaxy[4,5],film mixing

[6–8]that refers to the mixing of the deposition atoms and the substrate atoms, and sputtering [9,10], can occur. Among them, epitaxy and mixing are interesting subjects for thinﬁlm of metallic multilayer system because the interfacial alloy formation resulted from atomistic mixing has effects on the electromagnetic properties of the system[11]. These nanoscale magnetic thinﬁlms (Fe–Cu, Co–Cu, or Ni–Cu) consisting of ferromagnetic/non-ferromagnetic multilayers for giant magnetoresis-tance (GMR) could be applied in magnetic sensors and hard disk devices. In these applications, the structural and compositional variation at the metal–metal interface is concerned[12–15].

Jeng et al.[16]experimentally showed the electronic structures and magnetocrystalline anisotropy (MCA) energies of Fe–Co–Ni binary alloy monolayers on Cu substrate using the generalized gradient approxima-tion. The results were found that in-plane magnetization showed for pure

Co and Ni monolayers and the perpendicular magnetization observed for pure Fe. Fonda et al.[17]experimentally investigated the interface mixing of the sputter-deposited Fe atoms on Al substrate at 300 K by metal vapor deposition. They found that a mixing interface was formed at the interface below the deposited ironﬁlm of 0.9 nm thickness. Molecular dynamic (MD) simulations are preferable to experiments in describing the morphology of the deposited thinﬁlm in detail and understanding the growing mechanisms. Chen et al.[18]discovered the morphology and behavior of Fe clusters depositing on the Fe substrate under different cluster sizes. Also, oscillations in the activation energy of surface diffusion were largely dependent on the cluster size. Kim et al.[19]simulated the multilayer structure using spontaneous intermixing of Co and Al in epitaxial Co/CoAl/Co structures. They observed that Al was deposited on Co substrate without any intermixing as incident energy of 0.1 eV and the deposition rate of 5 atom/ps were considered. Similar phenomenon was observed for surface intermixing of Co–Al system[20].

The stress associated with the IBS process in a deposited thinfilm on a substrate has been exploited for such applications as ultra-large scale integration (ULSI) in iron or iron-alloy interconnections. MD simulation is adopted to elucidate why stress evolution is critical to the reliability of a depositedfilm[21]. Zhang et al.[22]examined the mechanisms of generation of virial stresses at various incident energies using the Tersoff–Brenner potential to model the thin carbon film. The stress at the incident energy of 40 eV approached a steady-state value when the number of deposited atoms exceeded 600. A biaxial tensile stress was established in the depositedfilm when the incident energy was low, and a transition from tensile to compressive stress occurred at approximately 10 eV. This compressive stress began to drop as the incident energy was raised over 60 eV.

From the above discussion, it will be very interesting to discuss intermixing for metallic multilayer materials at the atomic level by

Surface Science 605 (2011) 46–53

⁎ Corresponding author. Tel.: +886 5 5342601x4143; fax: +886 5 5312062. E-mail address:[email protected](S.-F. Hwang).

Contents lists available atScienceDirect

Surface Science

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using MD simulation. In this study, the tight-binding (TB-SMA) many-body potential is chosen to model the atom interaction in the system of Fe–Cu or Co–Cu ﬁlm. The effects of different incident energies and/ or substrate temperatures on the surface roughness, layer coverage function, radial distribution function (RDF), and residual stress are investigated when epitaxial growth or interfacial intermixing is observed in the Fe–Cu or Co–Cu system.

2. Molecular dynamics method

In recent years, many-body potentials have been commonly adopted to accurately describe the interaction between metal atoms in MD. In this investigation, the TB-SMA many-body potential[23]is employed to model the atomic interactions between Fe and Cu atoms or between Co and Cu atoms, because it has been proved to be more accurate than Embedded-Atom Method (EAM) potential and it is easily applied in MD[24,25].

The TB-SMA potential energy U(rij) contains a repulsive pair potential

and a cohesive band energy term, and it could be expressed as

U rij = ∑N i = 1 − ∑j ξ 2 exp −2q rij r0−1 ! 1 2_{+ A exp} −p rij r0−1 " # ð1Þ where rijis the separation distance between atoms i and j,ξ is an effective

hopping integral, N is the number of atoms, and r0is theﬁrst-neighbor

distance. The parametersξ, A, q, p, and r0are obtained fromﬁtting to the

experimental values of cohesive energy, lattice parameter, bulk modulus, and two shear elastic constants [23]. The values of these parameters for Cu–Cu, Co–Cu, Fe–Cu, Co–Co, and Fe–Fe atoms are listed inTable 1. The parameters of the cross potential were obtained by using an interpolation scheme [26,27]. For the parameters ξ and A, the

harmonic mean,ξαβ=ξα+ξβ 1₌ 2_{and A} αβ= A α+ Aβ 1₌ 2_{, was used.}

The geometrical average was applied to the other three parameters as qαβ=(qα+ qβ)/2, pαβ= (pα+ pβ)/2, and r0αβ= (r0α+ r0β)/2.

The stress distribution of a thinﬁlm after deposition is sometimes important. The stress in a thinﬁlm can be evaluated as the atomic stress (also called BDT stress), which is calculated from the volume Vi

of atom i, and consists of two parts— the kinetic energy of the atom and the interatomic forces. The deﬁnition of BDT stress (σ) by Basinski, Duesbery, and Tayo[28]can be expressed as

σ = 1 Vi mivi⊗vi+ 1 2∑ N j≠i rij⊗fij " # ð2Þ

where miis the mass of the atom i, viis its velocity, fijis the interatomic

force, and⊗ denotes the tensor product of two vectors.

In this work, the substrate has the dimensions of 18a×18a×6a (a=lattice constant) from a face-centered-cubic (FCC) bulk crystal, as presented inFig. 1. The Cu(001) substrate perpendicular to the z-axis comprises 7776 Cu atoms. The lowest layer of the substrate isﬁxed to prevent the moving of the substrate by the incident atoms during deposition. The middle layers of the substrate are called the thermal control layers, and the atomic velocities of these layers are rescaled at every ten-time steps, based on the prescribed substrate temperature. Therefore, these thermal control layers could absorb the kinetic energy of the incident atoms during the deposition process. The velocities of the atoms of the thermal control layers are given by Maxwell–Boltzmann distribution[26]. The eighth to twelfth layers are free motion layers that simulate the interactions and motions of particles after the impacts of the deposited atoms. Periodic boundary conditions are imposed in the x and y directions and no periodic boundary condition is applied in the z direction. The incident atoms are randomly located in the x and y directions, and the z position of the incident atoms is at 40 fold-lattice length above the substrate surface.

In this work the time step is chosen as 1 fs. On considering the simulation stability, the deposition rate in this work is 1 cluster per ps during the simulation time of 500 ps because it is computationally inexpensive and has been used in several similar studies[6,7]. This deposition rate is signiﬁcantly higher than that in experiments. Recently, to have a more realistic deposition rate, an accelerated dynamics approach was applied to speed up the diffusive events and to reach time scales of seconds[29,30]. It is expected that the deposition rate used in Table 1

Parameters for TB-SMA potential.

Parameters A (eV) ξ (eV) p q r0(nm)

Cu–Cu 0.0855 1.224 10.96 2.278 0.255

Fe–Fe 0.1184 1.541 10.76 2.038 0.248

Co–Co 0.0950 1.488 11.604 2.286 0.250

Fe–Cu 0.0346 1.705 10.861 2.158 0.252

Co–Cu 0.0900 1.330 11.282 2.282 0.254

Fig. 1. Simulation model of the deposition process.

47 Z.-H. Hong et al. / Surface Science 605 (2011) 46–53

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3.3. Residual stress evolution

To observe the BDT stress at a layer, an average stress_σmnavgis

deﬁned for the layer as

σavg mn = 1 N∑ N i = 1 σ i mn ð4Þ

whereσmni is the BDT stress of the ith atom of the layer, m and n are

indices of the stress tensor, and N is the number of atoms of the layer. The average normal stressσzzavgand the average mean biaxial stress

σavg xx +σyyavg

2 are considered. The average mean biaxial stress is chosen because it is related to the residual stress of the layer.Fig. 7(a)–(d) presents the effects of different incident energies and different substrate temperatures on these two stresses of the deposited thinfilm for all layers in the Fe–Cu system. Here, the layers are numbered as inFig. 4. Since the bottom layer of the substrate isfixed, its average stress is excluded inFig. 7. Because the sign convention for force is positive for repulsion and negative for attraction, a positive stress is compressive while a negative stress is tensile. From thesefigures, both the average stresses of the substrate layers have oscillation, and it may result from the internal interaction between consecutive layers. On the other hand, there is no clear oscillation on both the average stresses of the deposited layers. When the incident energy is 1 eV/atom and the substrate temperature is 300 K, both the average stresses are compressive in both the substrate layer and the depositedfilm layer, as shown inFig. 7(a) and (b). Since the incident atoms are deposited on the substrate with little loss of kinetic energy, these compressive stresses may come from atomic impacting effect and the periodic boundary conditions in the x and y directions of the substrate

[35].

When the incident energy is increased to 5 eV/atom, both the average stresses are negative in the substrate layers. These tensile stresses may come from the island coalescence duringﬁlm nucleation and construction[35,36]. From Fig. 7(a), the average mean biaxial stresses of the deposited layers are still compressive and close to zero. FromFig. 7(b), the average normal stressesσzzavgof the deposited layers

numbered from 1 to 6 are still tensile while the stresses are compressive after layer number 7. These compressive stresses may come from atomic impacting effect and high atomic mobility. The abrupt transition from the compressive to the tensile state has been investigated theoretically and experimentally at the early stages of deposition[37]. When the substrate temperature is increased from 300 to 700 K at the incident energy of 5 eV/atom, both the average stresses have similar trends as shown inFig. 7(c)–(d). Increasing the substrate temperature leads to a gradual decrease on both the average stresses of the substrate layer. However, both the average stresses of the deposited layer increase as the substrate temperature is increased. Note that as the substrate temper-ature is increased, the oscillation of the averaged mean biaxial stress around the surface layer of the substrate may disappear as shown. This result may come from higher intermixing of the incident atom and the substrate atom occurring in these layers because of higher substrate temperature. FromFig. 7(a)–(b), it is also interesting to note that the σzzavgstresses are higher than the average mean biaxial stresses. On

comparing Co–Cu system and Fe–Cu system as shown inFig. 8(a)–(b), both the average stresses of Co–Cu system are very close to those of Fe–Cu system.

4. Conclusions

This study investigates in detail theﬁlm growth process of ionized cluster beam deposition (ICBD) for Fe clusters and Co clusters depositing on Cu substrate by using MD. Based on the above discussion, when the incident energy is 1 eV/atom and the substrate temperature is 300 K, the surface of the grownﬁlm is not smooth even under epitaxial growth. The

surface roughness of the grownﬁlm could be reduced as the substrate temperature and/or incident energy is increased. However, the interface intermixing between the incident atoms and the substrate atoms becomes clear. To compare between both cluster types, the surface roughness of Fe–Cu system is better than that of Co–Cu system, no matter the substrate temperature and/or incident energy is. In addition, the interface mixing of Co and Cu atoms is better than that of Fe and Cu atoms, even though their radial distribution functions are very close. Both the average stresses are compressive in both the substrate layer and the deposited ﬁlm layer as the incident energy of 1 eV/atom and substrate temperature of 300 K. However, when the incident energy is increased to 5 eV/atom, both the average stresses are negative in the substrate layers. As for the effect of the substrate temperature, increasing the substrate temperature leads to a gradual decrease on both average stresses of the substrate layer. However, both the average stresses of the deposited layer increase as the substrate temperature is increased. On comparing Co–Cu system and Fe–Cu system, both the average stresses of Co–Cu system are very close to those of Fe–Cu system.

Acknowledgement

This work was partially supported by the National Science Council of Taiwan under grants NSC 099-2811-E-151-001 and NSC 96-2628-E-151-004-MY3.

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