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Structural study of Co and Au nanoclusters landed onto Cu
Nuclear Instruments and Methods in Physics Research B 267 (2009) 1447–1450
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Structural study of Co and Au nanoclusters landed onto Cu J.C. Jiménez-Sáez a, A.M.C. Pérez-Martín b, J.J. Jiménez-Rodríguez b,* a b
Dpto. de Física y Química Aplicadas a la Técnica Aeronáutica, E.U.I.T. Aeronáutica, Universidad Politécnica de Madrid (UPM), E-28040 Madrid, Spain Dpto. de Física Aplicada III (Electricidad y Electrónica), Facultad de Ciencias Físicas, Universidad Complutense de Madrid (UCM), E-28040 Madrid, Spain
a r t i c l e
i n f o
Article history: Available online 10 January 2009 PACS: 71.15.Pd 61.46.Bc 81.15.z Keywords: Molecular dynamics Cluster deposition Cluster epitaxy
a b s t r a c t The process in which nanoclusters of Co and Au at low energy (<1 eV/atom) impinge on a substrate of Cu (0 0 1) has been studied by molecular-dynamics (MD). Particularly our interest is focussed on the crystalline structure of the clusters and on whether the epitaxy is achieved. The atomic interactions are calculated by means of a many-body potential based on the second momentum approximation of tight-binding scheme. The size of the clusters ranges from a few tens to a few hundreds of atoms. Techniques such as the analysis of grains, the calculation of epitaxy factor and the common neighbour analysis (CNA) are methods of analysis, used in this work, capable to determine the crystalline orientation and resemblance of the clusters to the substrate once they have been deposited on it. The number of atoms with fcc structure is explicitly calculated. The high values found, for large clusters, corroborate that part of the original structure of the cluster remains intact. The results obtained can be summarized as follows: whenever epitaxy requires an expansion of the cluster structure to fit the substrate, the process is more effective than the opposite in which a compression is required. The size of the cluster plays an opposite role in the epitaxial process, i.e. the effectiveness to get epitaxy diminishes for large sizes. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The novel electronic, mechanical, catalytic, magnetic and optical properties and the related technological applications of the nanostructured surfaces obtained upon the deposition of clusters have motivated a great number of theoretical, simulation and experimental studies involving clusters in recent years [1]. An attractive method to prepare cluster-assembled materials is the low-energy cluster beam deposition (LECBD) technique [2]. Typical cluster sizes range from a few tens to a few thousands of atoms. Since the kinetic energy of the clusters never exceeds 10 eV no fragmentation of the cluster is expected upon impact on the substrate. Au, Cu and Co materials used in this work and their combination exhibit most of the main wanted properties in nanostructures. Just to mention a few examples, noble metal such as Au or Cu have important catalytic properties [3]; Au nanoparticles stand out due to of their biosensing capability [4]; Co nanoclusters show interesting magnetic properties [5], in fact, Co/Cu magnetic multilayers [6] or Co nanoclusters embedded in a non-magnetic metal such as a Cu matrix [7] exhibit the giant magnetoresistance (GMR) effect. In most cases, the fundamental characteristic is the size dependence of these properties. * Corresponding author. Tel.: +34 913944376; fax: +34 913945196. E-mail address: josejjr@fis.ucm.es (J.J. Jiménez-Rodríguez). 0168-583X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2009.01.154
The aim of this work is the study of the heteroepitaxy in largeand small-misfit systems by using Au, Co nanoclusters on Cu(0 0 1) substrates. The influence on epitaxy of the cluster size and initial structure has been researched in depositions at soft-landing conditions (<0.1 eV/atom). Properties of the material and lattice mismatch are also indispensable factors when it comes to explain epitaxy results. Let us not forget that the strain at the interface hinders notably the epitaxial growth. Similar results have been previously reported [8–10]. Palacios et al. studied small Cu and Au clusters (up to 55 atoms) landed on Cu substrates. We make emphasis, in this contribution, on the size of Co and Au nanoclusters for which transition from epitaxy (small clusters) to no epitaxy (large clusters) is produced. Most of the reported results here have been simulated up to 10 times varying slightly the initial position. The reproducibility is good for small and large clusters being more critical in the transition region. In this latter case, the most frequently results obtained are reported. 2. Computational and analysis methods Computation of atomic trajectories is essentially determined by the interatomic potential. For the Au–Cu interactions, we make use of the second moment approximation in the Friedel tight-binding theory, as first introduced by Ducastelle [11], later used by Finnis
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and Sinclair [12], and improved by Ackland et al. for this combination of metals [13]. The atomic interaction range is extended up to and including third nearest neighbours. The potential for the Co– Cu system is formulated in the second moment tight-binding approximation (TB-SMA) [14]. The atomic interaction range is extended up to and including the eight nearest neighbours in an hcp lattice for ensuring better stability of this phase [14]. More details about calculation method can be found elsewhere [9]. The simulation time was 150 ps and the time step 0.5 fs. Au/ Cu(0 0 1) and Co/Cu(0 0 1) with a lattice misfit of 12.8%, 1.96%, respectively, were the systems under study. The misfit is defined as d ¼ ðac as Þ=as , where ac and as are the lattice parameters of the cluster and the substrate, respectively [15]. Positive misfit corresponds to compressive strain and negative to tensile strain when the film is coherent with the substrate. The substrate had 45 45 15 unit cells and its number of atoms was 125,550. Periodic boundary conditions were used in the directions parallel to the (0 0 1) surface (x,y-plane), and non-periodic boundary conditions in the normal direction (z direction). Atoms in the bottom layer were left free. The inilayer were fixed and in the top (0 0 1) tial geometries of Au and Co clusters correspond to the most stable isomers for free closed-shell clusters of these materials [16–18]. The shape of the clusters were hexagonal faceted cuboctahedra (CO, also so-called Wulff polyhedra) of 38, 201, 586 and 1289 atoms (fcc phase) [19,20]; and Mackay icosahedra (IC) of 13, 55, 147, 309 and 561 atoms (assemblage of fcc sub-units by dislocations). Hence, the diameters range from 0.4 to 3.3 nm. An irregular hexagonal faceted cuboctahedron (iCO) of 116 atoms randomly rotated was also used. For Co, in bulk form, fcc phase is only stable above 693 K [21], however, nanoclusters of previous sizes show energetic preference for this phase [22]. After independent equilibration at a specific temperature of cluster and substrate, the former is placed close to the free surface of the latter over its centre. For the icosahedra, the fivefold axis is parallel to the normal to the substrate surface, ICp; and for the cuboctahedra, two configurations were chosen: one with a (0 0 1) face parallel to this surface in order to facilitate the epitaxy, and hence making the [0 0 1] direction of the cluster parallel to the normal to the substrate surface, COp; and another attempting to replicate the experimental conditions by rotating the cluster with a random angle, CO. The actual deposition was done by giving the cluster a velocity in the direction of the substrate with a kinetic energy of 17 meV/atom, which is of the order of the thermal energy (soft-landing conditions). This value minimizes plastic effects during the deposition of the largest clusters [23]. Different types of analysis were carried out to determine the clusters crystalline structure: first of all, we have characterized the cluster as a whole by means of a factor of epitaxy, fepi [9], which measures, on average, the grade of structural resemblance between the cluster and the substrate. Also CNA [24] were performed, in order to determine the kind of bonds, and therefore, to associate a lattice structure to each atom. By this method, the number of atoms into an fcc lattice Nfcc is determined although these atoms do not had the same orientation than in the substrate. Finally, the analysis of the grains [25] determines the number and orientation of the grains constituent of the cluster.
3. Results and discussion Our objective will be the study of the structure of the equilibrium state of heteroepitaxial systems after the deposition process. The perfect definition and parallelism of the (0 0 2) cluster planes with the substrate surface will be defined as ‘layer structure’, whereas the perfect linkage and prolongation of the (2 0 0) and (0 2 0) planes of the substrate inside the cluster shall be referred
to as coherent epitaxy. An imperfect linkage of these planes would be characteristic of semi-coherent epitaxy with existence of misfit dislocations, only possible in the largest Au or Cu clusters (contact diameters above 2 nm). In general, we will speak about alignment between cluster (or part of this) and substrate, if besides the perfect linkage and definition of the planes perpendicular to the substrate surface inside the cluster (or part of this), the layer structure is also present. In Fig. 1, the xz-projections of different deposited clusters are shown in order to assess the final alignment of the cluster. Represented sizes were chosen to show the transition from alignment to non-alignment. In Co (lattice misfit d < 0), the transition takes place in the range from 55 atoms to 309 atoms. This means that Co clusters with a number of atoms smaller than 309 get the linkage and definition of planes perpendicular to the substrate surface all over the cluster and besides a layer structure. Nevertheless, as the cluster size increases, clusters show these characteristics in an increasingly more imperfect way. In the case of the Co147 cluster, it shows alignment in most simulations, but a completely disordered structure also arises, although with lower probability, for the initial ICp orientation [9]. In Au (d > 0), the distinguishing of layers parallel to the substrate surface (i.e. layer structure) happens in the range from 55 to 309 atoms; however, the transition in the linkage and definition of perpendicular planes takes place in a narrower range, from 55 to 147 atoms (see Fig. 1). In the irregular-cuboctahedral (iCO) Au116 cluster, the definition of perpendicular planes is rather imperfect. In fact, the probability of obtaining a structure similar to the Au309 case is rather high. Therefore, perpendicular planes in CO clusters found more difficult to acquire substrate properties. In short, below 100 atoms alignment does not depend on the chemical element or the lattice mismatch. This behaviour is explained by the independence on the material of the shortrange reordering phenomena. This fact has been corroborated by Järvi et al. [26] in homoepitaxial systems. For larger sizes, but inferior to 300 atoms, hence still intermediate, both the material properties and the lattice misfit determine the end of the alignment: the larger misfit, the smaller limit size for alignment. Besides, cluster atoms find easier to carry out an expansion process (d < 0) to fit the substrate than a compression process (d < 0). Although not shown here, Nepi does not grow gradually, as a function of the simulation time, but by jumps on a scale of ps. The abrupt nature of this process suggests that its origin is, in general, in the activation of a cooperative movement hindered, among other factors, by the cluster size. In Co (low misfit), the influence of the cluster size during the reordering is smaller. Besides, the initial structure is also important: the Co55 cluster (initially IC: fcc phase with grain boundary dislocations, GBD) cannot acquire the epitaxial structure as fast as the Co116 cluster. Focusing on the dependence on the cluster size of the epitaxy in the equilibrium state, the degree of adaptation of the cluster to the substrate lattice and also the cluster size acquiring fcc structure have been studied. Fig. 2 shows, as a function of the cluster size, (a) the number of cluster atoms in the interior with fcc structure, Nfcc, normalized to the number of interior atoms and (b) the number of epitaxial atoms, Nepi. By Nfcc we mean those atoms with 12 neighbours, each characterized by the set of index 421, given by CNA. Fig. 2(b) shows clearly that large clusters do not get epitaxy (Nepi < 65%) and Co clusters accommodate better than Au clusters (smaller values of Nepi) to the substrate due to a smaller misfit lattice. Fig. 2(a) also depicts this latter fact and besides confirms that small clusters get epitaxy. However, the high Nfcc-values obtained for large clusters would correspond to the frequent situation in which a large cluster lands on the substrate, keeping its initial fcc structure but with a different orientation, as a whole, than the substrate. Both in Au and in Co, all the clusters below 100 atoms have all their atoms completely well placed. For intermediate-size clusters
J.C. Jiménez-Sáez et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1447–1450
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Fig. 1. xz projection of the deposited and quenched clusters of 55, 116, 147, 201 and 309 atoms for the Co/Cu and Au/Cu systems at 300 K and 17 meV/atom. Colours in cluster are assigned according to the fi-values: fi < 0.15 black (epitaxial atoms), 0.15 6 fi < 0.3 gray and fi P 0.3 light gray (fi in rad).
Fig. 2. (a) Number of interior atoms with fcc orientation Nfcc and (b) number of epitaxial atoms Nepi versus the cluster size (measured as N1/3) for the different Au/Cu and Co/ Cu systems.
(116–201 atoms), differences arise between both materials, specifically, between CO clusters: Co201 has a considerable number of epitaxial atoms, while Au201 has very few. This situation is explained by the difficulty of the CO Au clusters in distinguishing the planes perpendicular to the interface. We have verified that a value of the epitaxy factor, fepi, inferior to 0.5 is the limit for a completely epitaxial cluster [9]. This value would be roughly the same as the corresponding average value of fi = 0.9 used by Meinander et al. as upper limit for full contact epitaxy [27]. Values of fepi between 0.5 and 1 correspond to clusters with a large epitaxial grain and GBD, and besides an aligned structure throughout the cluster. Epitaxy in these clusters with a number of epitaxial atoms ranging from 65% to 80% approximately will be called incomplete [9]. To compare quantitatively the degree of epitaxy of our systems, we have plotted the epitaxy factor fepi as a function of the cluster size in Fig. 3. We have unfolded this graph in two to visualize the behaviour of CO, COp clusters (Fig. 3(a)) and ICp clusters (Fig. 3(b)). Only Au and Co clusters below 100 atoms are completely epitaxial since fepi < 0.5 [9,10]. Besides, Co116 and Co201 clusters have values of fepi ranging from 0.5 to 1, and therefore, show incomplete epitaxy due to the GBD (see Fig. 1) [9]. For large and intermediate clusters, values of fepi in Co are lower (better epitaxy) than in Au due to the lattice misfit. By comparison of the alignment in intermediate-size cluster, it is observed that Au clusters (d > 0), generally, fit the substrate more
difficulty. So, for example, the Au116 cluster does not turn out to be epitaxial. The explanation of this effect is found mainly in the positive misfit since minimum-energy paths and energy barriers are more unfavourable for dislocation nucleation in epitaxial layers with compressive (d > 0) strain [15]. This is also corroborated by comparison with the deposition of Cu on Au [10]. Besides, firstprinciples strain-energy calculations by using the local-density approximation (LDA) establish that, under biaxial compression, one of the hardest directions of deformation in Au is <0 0 1>. Meinander et al. [28] obtained a value of about 200 atoms as limit of epitaxy for CO, Cu clusters on Cu(0 0 1) with a criterion approximately equivalent to fepi < 0.5 [29]. Co116, Co147 and Co201 clusters have epitaxy factors slightly larger (see Fig. 3), therefore, they could fit into that limit. It is also interesting to analyze the modification of the results if the CO clusters are deposited with the same crystallographic orientation than the substrate, therefore, initially aligned with this (COp cases). Obviously, these clusters are found in the most favourable deposition conditions for epitaxy [9]. Epitaxy factors of COp and CO clusters were plotted in Fig. 3(a). The largest difference in degree of epitaxy between both types of cluster takes place in the case of the largest clusters. The COp clusters of this size show a good epitaxial behaviour due to the good positioning just after the landing of a large number of atoms far from the interface. Differences in fepi begin to be appreciable above 116 atoms for Au (with large misfit) and above 201 for Co (low misfit). Let us remind that one hundred
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Fig. 3. Epitaxial factor, fepi, versus cluster size. (a) and (b) show, results for rotated CO, parallel COp clusters and for ICp clusters, respectively.
atoms marks the limit from which the long-range coupling effects begin to take part in epitaxy [26]. Differences for smaller clusters correspond more to statistical fluctuations than to a real influence of the initial orientation of the cluster. It is noteworthy that the aligned Au116 case has an epitaxy factor larger than the random case. This is due to that the aligned system reaches more easily a layer structure without definition of perpendicular planes, similar to Au201 in Fig. 1 and characterized by a worse epitaxy. 4. Summary and conclusions Deposition at low energy (<1 eV/atom) of icosahedral (IC) and cuboctahedral (CO) nanoclusters (13–1289 atoms) has been studied by constant-temperature molecular-dynamics for Co/Cu(0 0 1) and Au/Cu(0 0 1) systems. The former has a negative lattice misfit and the latter has a large and positive misfit. At 300 K and 0.017 eV/atom, below 100 atoms alignment of the cluster lattice with the substrate does not depend on the material or misfit. This suggests the independence on both of the short-range reordering phenomena. Transition from alignment to non-alignment takes place between 55 and 309 atoms in low-misfit systems, Co, and between 55 and 201 in large-misfit systems, Au. For negative-misfit systems, icosahedral clusters in this range may show a disordered structure. For large- and positive-misfit systems, in intermediate cluster sizes the initial IC shape favours the alignment, whereas the CO shapes only facilities the layer structure. Thus, the upper limit for epitaxy is reduced down to 116 atoms in CO clusters, and on the contrary, the layer structure remains up to 309 atoms. The number of epitaxial atoms increases steeply with time approximately in one or two jumps. The abrupt nature of this process suggests that its origin is in the activation of a cooperative movement hindered by the cluster size. Epitaxy factor does not rise above around one in all epitaxial systems. Above 100 atoms, Au clusters fit the substrate with greater difficulty and Co clusters are aligned more easily due to the smaller lattice misfit. An aligned initial orientation of the cluster may give rise to very different final structures for all systems above approximately 200 atoms.
References [1] P. Jensen, Rev. Mod. Phys. 71 (1999) 1695. [2] G. Fuchs, P. Melinon, F. Santos Aires, M. Treilleux, B. Cabaud, A. Hoareau, Phys. Rev. B 44 (1991) 3926. [3] K. Mallick, M.J. Witcomb, M.S. Scurrell, Appl. Phys. A 80 (2005) 797. [4] H.-H. Chen, H. Suzuki, O. Sato, Z.-Z. Gu, Appl. Phys. A 81 (2005) 1127. [5] R. Morel, A. Brenac, C. Portemont, T. Deutsch, L. Notin, J. Magn. Mater. 308 (2007) 296. [6] A. Paul, T. Damm, D.E. Bürgler, S. Stein, H. Kohlstedt, P. Grünberg, J. Phys.: Condens. Matter 15 (2003) 2471. [7] A. García Prieto, M.L. Fdez-Gubieta, J. Chaboy, M.A. Laguna-Marco, T. Muro, T. Nakamura, Phys. Rev. B 72 (2005) 212403. [8] F.J. Palacios, M.P. Iniguez, M.J. Lopez, J.A. Alonso, Phys. Rev. B 60 (1999) 2908. [9] J.C. Jiménez-Sáez, A.M.C. Pérez-Martín, J.J. Jiménez-Rodríguez, Phys. Status Solidi A 205 (2008) 1330. [10] J.C. Jiménez-Sáez, A.M.C. Pérez-Martín, J.J. Jiménez-Rodríguez, Vacuum 81 (2007) 1515. [11] F. Ducastelle, J. Phys. 31 (1970) 133. [12] M.W. Finnis, J.E. Sinclair, Philos. Mag. A 50 (1984) 45. [13] G.J. Ackland, V. Vitek, Phys. Rev. B 41 (1990) 10324. [14] F. Cleri, V. Rosato, Phys. Rev. B 48 (1993) 22. [15] O. Trushin, E. Granato, S.C. Ying, P. Salo, T. Ala-Nissila, Phys. Rev. B 65 (2002) 241408(R). [16] G. Rossi, R. Ferrando, Nanotechnology 18 (2007) 225706. 6pp. [17] D. Reinhard, B.D. Hall, P. Berthoud, S. Valkealahti, Phys. Rev. B 58 (1998) 4917. [18] X.Q. Zhao, S. Veintemillas-Verdaguer, O. Bomati-Miguel, M.P. Morales, H.B. Xu, Phys. Rev. B 71 (2005) 024106. [19] S.C. Hendy, B.D. Hall, Phys. Rev. B 64 (2001) 085425. [20] A.L. Mackay, Acta Crystallogr. 15 (1962) 916. [21] M. Hansen, Constitution of Binary Alloys, McGraw-Hill, New York, 1958. [22] O. Kitakami, H. Sato, Y. Shimada, F. Sato, M. Tanaka, Phys. Rev. B 56 (1997) 13849. [23] J.C. Jiménez-Sáez, A.M.C. Pérez-Martín, J.J. Jiménez-Rodríguez, Nucl. Instr. and Meth. B 249 (2006) 816. [24] A.S. Clarke, H. Jonsson, Phys. Rev. E 47 (1994) 3975. [25] J.C. Jiménez-Sáez, A.M.C. Pérez-Martín, J.J. Jiménez-Rodríguez, Phys. Status Solidi A 203 (2006) 1229. [26] T.T. Järvi, A. Kuronen, K. Meinander, K. Nordlund, Phys. Rev. B 75 (2007) 115422. [27] K. Meinander, T.T. Järvi, K. Nordlund, Appl. Phys. Lett. 89 (2006) 253109. [28] K. Meinander, J. Frantz, K. Nordlund, J. Keinonen, Thin Solid Films 425 (2003) 297. [29] J.C. Jiménez-Sáez, A.M.C. Pérez-Martín, J.J. Jiménez-Rodríguez, in: E.V. Dirote (Ed.), New Developments in Nanotechnology Research, Nova Science Publishers, New York, 2006.
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Structural study of Co and Au nanoclusters landed onto Cu J.C. Jiménez-Sáez a, A.M.C. Pérez-Martín b, J.J. Jiménez-Rodríguez b,* a b
Dpto. de Física y Química Aplicadas a la Técnica Aeronáutica, E.U.I.T. Aeronáutica, Universidad Politécnica de Madrid (UPM), E-28040 Madrid, Spain Dpto. de Física Aplicada III (Electricidad y Electrónica), Facultad de Ciencias Físicas, Universidad Complutense de Madrid (UCM), E-28040 Madrid, Spain
a r t i c l e
i n f o
Article history: Available online 10 January 2009 PACS: 71.15.Pd 61.46.Bc 81.15.z Keywords: Molecular dynamics Cluster deposition Cluster epitaxy
a b s t r a c t The process in which nanoclusters of Co and Au at low energy (<1 eV/atom) impinge on a substrate of Cu (0 0 1) has been studied by molecular-dynamics (MD). Particularly our interest is focussed on the crystalline structure of the clusters and on whether the epitaxy is achieved. The atomic interactions are calculated by means of a many-body potential based on the second momentum approximation of tight-binding scheme. The size of the clusters ranges from a few tens to a few hundreds of atoms. Techniques such as the analysis of grains, the calculation of epitaxy factor and the common neighbour analysis (CNA) are methods of analysis, used in this work, capable to determine the crystalline orientation and resemblance of the clusters to the substrate once they have been deposited on it. The number of atoms with fcc structure is explicitly calculated. The high values found, for large clusters, corroborate that part of the original structure of the cluster remains intact. The results obtained can be summarized as follows: whenever epitaxy requires an expansion of the cluster structure to fit the substrate, the process is more effective than the opposite in which a compression is required. The size of the cluster plays an opposite role in the epitaxial process, i.e. the effectiveness to get epitaxy diminishes for large sizes. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The novel electronic, mechanical, catalytic, magnetic and optical properties and the related technological applications of the nanostructured surfaces obtained upon the deposition of clusters have motivated a great number of theoretical, simulation and experimental studies involving clusters in recent years [1]. An attractive method to prepare cluster-assembled materials is the low-energy cluster beam deposition (LECBD) technique [2]. Typical cluster sizes range from a few tens to a few thousands of atoms. Since the kinetic energy of the clusters never exceeds 10 eV no fragmentation of the cluster is expected upon impact on the substrate. Au, Cu and Co materials used in this work and their combination exhibit most of the main wanted properties in nanostructures. Just to mention a few examples, noble metal such as Au or Cu have important catalytic properties [3]; Au nanoparticles stand out due to of their biosensing capability [4]; Co nanoclusters show interesting magnetic properties [5], in fact, Co/Cu magnetic multilayers [6] or Co nanoclusters embedded in a non-magnetic metal such as a Cu matrix [7] exhibit the giant magnetoresistance (GMR) effect. In most cases, the fundamental characteristic is the size dependence of these properties. * Corresponding author. Tel.: +34 913944376; fax: +34 913945196. E-mail address: josejjr@fis.ucm.es (J.J. Jiménez-Rodríguez). 0168-583X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2009.01.154
The aim of this work is the study of the heteroepitaxy in largeand small-misfit systems by using Au, Co nanoclusters on Cu(0 0 1) substrates. The influence on epitaxy of the cluster size and initial structure has been researched in depositions at soft-landing conditions (<0.1 eV/atom). Properties of the material and lattice mismatch are also indispensable factors when it comes to explain epitaxy results. Let us not forget that the strain at the interface hinders notably the epitaxial growth. Similar results have been previously reported [8–10]. Palacios et al. studied small Cu and Au clusters (up to 55 atoms) landed on Cu substrates. We make emphasis, in this contribution, on the size of Co and Au nanoclusters for which transition from epitaxy (small clusters) to no epitaxy (large clusters) is produced. Most of the reported results here have been simulated up to 10 times varying slightly the initial position. The reproducibility is good for small and large clusters being more critical in the transition region. In this latter case, the most frequently results obtained are reported. 2. Computational and analysis methods Computation of atomic trajectories is essentially determined by the interatomic potential. For the Au–Cu interactions, we make use of the second moment approximation in the Friedel tight-binding theory, as first introduced by Ducastelle [11], later used by Finnis
1448
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and Sinclair [12], and improved by Ackland et al. for this combination of metals [13]. The atomic interaction range is extended up to and including third nearest neighbours. The potential for the Co– Cu system is formulated in the second moment tight-binding approximation (TB-SMA) [14]. The atomic interaction range is extended up to and including the eight nearest neighbours in an hcp lattice for ensuring better stability of this phase [14]. More details about calculation method can be found elsewhere [9]. The simulation time was 150 ps and the time step 0.5 fs. Au/ Cu(0 0 1) and Co/Cu(0 0 1) with a lattice misfit of 12.8%, 1.96%, respectively, were the systems under study. The misfit is defined as d ¼ ðac as Þ=as , where ac and as are the lattice parameters of the cluster and the substrate, respectively [15]. Positive misfit corresponds to compressive strain and negative to tensile strain when the film is coherent with the substrate. The substrate had 45 45 15 unit cells and its number of atoms was 125,550. Periodic boundary conditions were used in the directions parallel to the (0 0 1) surface (x,y-plane), and non-periodic boundary conditions in the normal direction (z direction). Atoms in the bottom layer were left free. The inilayer were fixed and in the top (0 0 1) tial geometries of Au and Co clusters correspond to the most stable isomers for free closed-shell clusters of these materials [16–18]. The shape of the clusters were hexagonal faceted cuboctahedra (CO, also so-called Wulff polyhedra) of 38, 201, 586 and 1289 atoms (fcc phase) [19,20]; and Mackay icosahedra (IC) of 13, 55, 147, 309 and 561 atoms (assemblage of fcc sub-units by dislocations). Hence, the diameters range from 0.4 to 3.3 nm. An irregular hexagonal faceted cuboctahedron (iCO) of 116 atoms randomly rotated was also used. For Co, in bulk form, fcc phase is only stable above 693 K [21], however, nanoclusters of previous sizes show energetic preference for this phase [22]. After independent equilibration at a specific temperature of cluster and substrate, the former is placed close to the free surface of the latter over its centre. For the icosahedra, the fivefold axis is parallel to the normal to the substrate surface, ICp; and for the cuboctahedra, two configurations were chosen: one with a (0 0 1) face parallel to this surface in order to facilitate the epitaxy, and hence making the [0 0 1] direction of the cluster parallel to the normal to the substrate surface, COp; and another attempting to replicate the experimental conditions by rotating the cluster with a random angle, CO. The actual deposition was done by giving the cluster a velocity in the direction of the substrate with a kinetic energy of 17 meV/atom, which is of the order of the thermal energy (soft-landing conditions). This value minimizes plastic effects during the deposition of the largest clusters [23]. Different types of analysis were carried out to determine the clusters crystalline structure: first of all, we have characterized the cluster as a whole by means of a factor of epitaxy, fepi [9], which measures, on average, the grade of structural resemblance between the cluster and the substrate. Also CNA [24] were performed, in order to determine the kind of bonds, and therefore, to associate a lattice structure to each atom. By this method, the number of atoms into an fcc lattice Nfcc is determined although these atoms do not had the same orientation than in the substrate. Finally, the analysis of the grains [25] determines the number and orientation of the grains constituent of the cluster.
3. Results and discussion Our objective will be the study of the structure of the equilibrium state of heteroepitaxial systems after the deposition process. The perfect definition and parallelism of the (0 0 2) cluster planes with the substrate surface will be defined as ‘layer structure’, whereas the perfect linkage and prolongation of the (2 0 0) and (0 2 0) planes of the substrate inside the cluster shall be referred
to as coherent epitaxy. An imperfect linkage of these planes would be characteristic of semi-coherent epitaxy with existence of misfit dislocations, only possible in the largest Au or Cu clusters (contact diameters above 2 nm). In general, we will speak about alignment between cluster (or part of this) and substrate, if besides the perfect linkage and definition of the planes perpendicular to the substrate surface inside the cluster (or part of this), the layer structure is also present. In Fig. 1, the xz-projections of different deposited clusters are shown in order to assess the final alignment of the cluster. Represented sizes were chosen to show the transition from alignment to non-alignment. In Co (lattice misfit d < 0), the transition takes place in the range from 55 atoms to 309 atoms. This means that Co clusters with a number of atoms smaller than 309 get the linkage and definition of planes perpendicular to the substrate surface all over the cluster and besides a layer structure. Nevertheless, as the cluster size increases, clusters show these characteristics in an increasingly more imperfect way. In the case of the Co147 cluster, it shows alignment in most simulations, but a completely disordered structure also arises, although with lower probability, for the initial ICp orientation [9]. In Au (d > 0), the distinguishing of layers parallel to the substrate surface (i.e. layer structure) happens in the range from 55 to 309 atoms; however, the transition in the linkage and definition of perpendicular planes takes place in a narrower range, from 55 to 147 atoms (see Fig. 1). In the irregular-cuboctahedral (iCO) Au116 cluster, the definition of perpendicular planes is rather imperfect. In fact, the probability of obtaining a structure similar to the Au309 case is rather high. Therefore, perpendicular planes in CO clusters found more difficult to acquire substrate properties. In short, below 100 atoms alignment does not depend on the chemical element or the lattice mismatch. This behaviour is explained by the independence on the material of the shortrange reordering phenomena. This fact has been corroborated by Järvi et al. [26] in homoepitaxial systems. For larger sizes, but inferior to 300 atoms, hence still intermediate, both the material properties and the lattice misfit determine the end of the alignment: the larger misfit, the smaller limit size for alignment. Besides, cluster atoms find easier to carry out an expansion process (d < 0) to fit the substrate than a compression process (d < 0). Although not shown here, Nepi does not grow gradually, as a function of the simulation time, but by jumps on a scale of ps. The abrupt nature of this process suggests that its origin is, in general, in the activation of a cooperative movement hindered, among other factors, by the cluster size. In Co (low misfit), the influence of the cluster size during the reordering is smaller. Besides, the initial structure is also important: the Co55 cluster (initially IC: fcc phase with grain boundary dislocations, GBD) cannot acquire the epitaxial structure as fast as the Co116 cluster. Focusing on the dependence on the cluster size of the epitaxy in the equilibrium state, the degree of adaptation of the cluster to the substrate lattice and also the cluster size acquiring fcc structure have been studied. Fig. 2 shows, as a function of the cluster size, (a) the number of cluster atoms in the interior with fcc structure, Nfcc, normalized to the number of interior atoms and (b) the number of epitaxial atoms, Nepi. By Nfcc we mean those atoms with 12 neighbours, each characterized by the set of index 421, given by CNA. Fig. 2(b) shows clearly that large clusters do not get epitaxy (Nepi < 65%) and Co clusters accommodate better than Au clusters (smaller values of Nepi) to the substrate due to a smaller misfit lattice. Fig. 2(a) also depicts this latter fact and besides confirms that small clusters get epitaxy. However, the high Nfcc-values obtained for large clusters would correspond to the frequent situation in which a large cluster lands on the substrate, keeping its initial fcc structure but with a different orientation, as a whole, than the substrate. Both in Au and in Co, all the clusters below 100 atoms have all their atoms completely well placed. For intermediate-size clusters
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Fig. 1. xz projection of the deposited and quenched clusters of 55, 116, 147, 201 and 309 atoms for the Co/Cu and Au/Cu systems at 300 K and 17 meV/atom. Colours in cluster are assigned according to the fi-values: fi < 0.15 black (epitaxial atoms), 0.15 6 fi < 0.3 gray and fi P 0.3 light gray (fi in rad).
Fig. 2. (a) Number of interior atoms with fcc orientation Nfcc and (b) number of epitaxial atoms Nepi versus the cluster size (measured as N1/3) for the different Au/Cu and Co/ Cu systems.
(116–201 atoms), differences arise between both materials, specifically, between CO clusters: Co201 has a considerable number of epitaxial atoms, while Au201 has very few. This situation is explained by the difficulty of the CO Au clusters in distinguishing the planes perpendicular to the interface. We have verified that a value of the epitaxy factor, fepi, inferior to 0.5 is the limit for a completely epitaxial cluster [9]. This value would be roughly the same as the corresponding average value of fi = 0.9 used by Meinander et al. as upper limit for full contact epitaxy [27]. Values of fepi between 0.5 and 1 correspond to clusters with a large epitaxial grain and GBD, and besides an aligned structure throughout the cluster. Epitaxy in these clusters with a number of epitaxial atoms ranging from 65% to 80% approximately will be called incomplete [9]. To compare quantitatively the degree of epitaxy of our systems, we have plotted the epitaxy factor fepi as a function of the cluster size in Fig. 3. We have unfolded this graph in two to visualize the behaviour of CO, COp clusters (Fig. 3(a)) and ICp clusters (Fig. 3(b)). Only Au and Co clusters below 100 atoms are completely epitaxial since fepi < 0.5 [9,10]. Besides, Co116 and Co201 clusters have values of fepi ranging from 0.5 to 1, and therefore, show incomplete epitaxy due to the GBD (see Fig. 1) [9]. For large and intermediate clusters, values of fepi in Co are lower (better epitaxy) than in Au due to the lattice misfit. By comparison of the alignment in intermediate-size cluster, it is observed that Au clusters (d > 0), generally, fit the substrate more
difficulty. So, for example, the Au116 cluster does not turn out to be epitaxial. The explanation of this effect is found mainly in the positive misfit since minimum-energy paths and energy barriers are more unfavourable for dislocation nucleation in epitaxial layers with compressive (d > 0) strain [15]. This is also corroborated by comparison with the deposition of Cu on Au [10]. Besides, firstprinciples strain-energy calculations by using the local-density approximation (LDA) establish that, under biaxial compression, one of the hardest directions of deformation in Au is <0 0 1>. Meinander et al. [28] obtained a value of about 200 atoms as limit of epitaxy for CO, Cu clusters on Cu(0 0 1) with a criterion approximately equivalent to fepi < 0.5 [29]. Co116, Co147 and Co201 clusters have epitaxy factors slightly larger (see Fig. 3), therefore, they could fit into that limit. It is also interesting to analyze the modification of the results if the CO clusters are deposited with the same crystallographic orientation than the substrate, therefore, initially aligned with this (COp cases). Obviously, these clusters are found in the most favourable deposition conditions for epitaxy [9]. Epitaxy factors of COp and CO clusters were plotted in Fig. 3(a). The largest difference in degree of epitaxy between both types of cluster takes place in the case of the largest clusters. The COp clusters of this size show a good epitaxial behaviour due to the good positioning just after the landing of a large number of atoms far from the interface. Differences in fepi begin to be appreciable above 116 atoms for Au (with large misfit) and above 201 for Co (low misfit). Let us remind that one hundred
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Fig. 3. Epitaxial factor, fepi, versus cluster size. (a) and (b) show, results for rotated CO, parallel COp clusters and for ICp clusters, respectively.
atoms marks the limit from which the long-range coupling effects begin to take part in epitaxy [26]. Differences for smaller clusters correspond more to statistical fluctuations than to a real influence of the initial orientation of the cluster. It is noteworthy that the aligned Au116 case has an epitaxy factor larger than the random case. This is due to that the aligned system reaches more easily a layer structure without definition of perpendicular planes, similar to Au201 in Fig. 1 and characterized by a worse epitaxy. 4. Summary and conclusions Deposition at low energy (<1 eV/atom) of icosahedral (IC) and cuboctahedral (CO) nanoclusters (13–1289 atoms) has been studied by constant-temperature molecular-dynamics for Co/Cu(0 0 1) and Au/Cu(0 0 1) systems. The former has a negative lattice misfit and the latter has a large and positive misfit. At 300 K and 0.017 eV/atom, below 100 atoms alignment of the cluster lattice with the substrate does not depend on the material or misfit. This suggests the independence on both of the short-range reordering phenomena. Transition from alignment to non-alignment takes place between 55 and 309 atoms in low-misfit systems, Co, and between 55 and 201 in large-misfit systems, Au. For negative-misfit systems, icosahedral clusters in this range may show a disordered structure. For large- and positive-misfit systems, in intermediate cluster sizes the initial IC shape favours the alignment, whereas the CO shapes only facilities the layer structure. Thus, the upper limit for epitaxy is reduced down to 116 atoms in CO clusters, and on the contrary, the layer structure remains up to 309 atoms. The number of epitaxial atoms increases steeply with time approximately in one or two jumps. The abrupt nature of this process suggests that its origin is in the activation of a cooperative movement hindered by the cluster size. Epitaxy factor does not rise above around one in all epitaxial systems. Above 100 atoms, Au clusters fit the substrate with greater difficulty and Co clusters are aligned more easily due to the smaller lattice misfit. An aligned initial orientation of the cluster may give rise to very different final structures for all systems above approximately 200 atoms.
References [1] P. Jensen, Rev. Mod. Phys. 71 (1999) 1695. [2] G. Fuchs, P. Melinon, F. Santos Aires, M. Treilleux, B. Cabaud, A. Hoareau, Phys. Rev. B 44 (1991) 3926. [3] K. Mallick, M.J. Witcomb, M.S. Scurrell, Appl. Phys. A 80 (2005) 797. [4] H.-H. Chen, H. Suzuki, O. Sato, Z.-Z. Gu, Appl. Phys. A 81 (2005) 1127. [5] R. Morel, A. Brenac, C. Portemont, T. Deutsch, L. Notin, J. Magn. Mater. 308 (2007) 296. [6] A. Paul, T. Damm, D.E. Bürgler, S. Stein, H. Kohlstedt, P. Grünberg, J. Phys.: Condens. Matter 15 (2003) 2471. [7] A. García Prieto, M.L. Fdez-Gubieta, J. Chaboy, M.A. Laguna-Marco, T. Muro, T. Nakamura, Phys. Rev. B 72 (2005) 212403. [8] F.J. Palacios, M.P. Iniguez, M.J. Lopez, J.A. Alonso, Phys. Rev. B 60 (1999) 2908. [9] J.C. Jiménez-Sáez, A.M.C. Pérez-Martín, J.J. Jiménez-Rodríguez, Phys. Status Solidi A 205 (2008) 1330. [10] J.C. Jiménez-Sáez, A.M.C. Pérez-Martín, J.J. Jiménez-Rodríguez, Vacuum 81 (2007) 1515. [11] F. Ducastelle, J. Phys. 31 (1970) 133. [12] M.W. Finnis, J.E. Sinclair, Philos. Mag. A 50 (1984) 45. [13] G.J. Ackland, V. Vitek, Phys. Rev. B 41 (1990) 10324. [14] F. Cleri, V. Rosato, Phys. Rev. B 48 (1993) 22. [15] O. Trushin, E. Granato, S.C. Ying, P. Salo, T. Ala-Nissila, Phys. Rev. B 65 (2002) 241408(R). [16] G. Rossi, R. Ferrando, Nanotechnology 18 (2007) 225706. 6pp. [17] D. Reinhard, B.D. Hall, P. Berthoud, S. Valkealahti, Phys. Rev. B 58 (1998) 4917. [18] X.Q. Zhao, S. Veintemillas-Verdaguer, O. Bomati-Miguel, M.P. Morales, H.B. Xu, Phys. Rev. B 71 (2005) 024106. [19] S.C. Hendy, B.D. Hall, Phys. Rev. B 64 (2001) 085425. [20] A.L. Mackay, Acta Crystallogr. 15 (1962) 916. [21] M. Hansen, Constitution of Binary Alloys, McGraw-Hill, New York, 1958. [22] O. Kitakami, H. Sato, Y. Shimada, F. Sato, M. Tanaka, Phys. Rev. B 56 (1997) 13849. [23] J.C. Jiménez-Sáez, A.M.C. Pérez-Martín, J.J. Jiménez-Rodríguez, Nucl. Instr. and Meth. B 249 (2006) 816. [24] A.S. Clarke, H. Jonsson, Phys. Rev. E 47 (1994) 3975. [25] J.C. Jiménez-Sáez, A.M.C. Pérez-Martín, J.J. Jiménez-Rodríguez, Phys. Status Solidi A 203 (2006) 1229. [26] T.T. Järvi, A. Kuronen, K. Meinander, K. Nordlund, Phys. Rev. B 75 (2007) 115422. [27] K. Meinander, T.T. Järvi, K. Nordlund, Appl. Phys. Lett. 89 (2006) 253109. [28] K. Meinander, J. Frantz, K. Nordlund, J. Keinonen, Thin Solid Films 425 (2003) 297. [29] J.C. Jiménez-Sáez, A.M.C. Pérez-Martín, J.J. Jiménez-Rodríguez, in: E.V. Dirote (Ed.), New Developments in Nanotechnology Research, Nova Science Publishers, New York, 2006.