Evolution of the morphology of small Co clusters grown on Au(1 1 1)

Evolution of the morphology of small Co clusters grown on Au(1 1 1)

Applied Surface Science 226 (2004) 178–184 Evolution of the morphology of small Co clusters grown on Au(1 1 1) I. Chado1, C. Goyhenex*, H. Bulou, J.P...

282KB Sizes 0 Downloads 2 Views

Applied Surface Science 226 (2004) 178–184

Evolution of the morphology of small Co clusters grown on Au(1 1 1) I. Chado1, C. Goyhenex*, H. Bulou, J.P. Bucher I.P.C.M.S., UMR 7504, 23 rue du Loess, B.P. 43, F-67034 Strasbourg Cedex 02, France

Abstract The evolution of the morphology of small clusters grown on a complex surface containing a regular network of defects is investigated in the case of Co on Au(1 1 1). On the basis of molecular dynamics calculations the existence of a critical size for the transition from mono- to bi-layer islands is inferred. Rather than strain effects, the final bilayer morphology of the deposit is conditionned by the demixtion tendency in the bulk (Co, Au) alloy, favoring Co–Co bonds against heteroatomic ones, and surface tension effects both going towards a prefered three-dimensional growth. # 2003 Elsevier B.V. All rights reserved. PACS: 61.50.Ah; 68.55.Jk; 71.15.Pd; 71.15.Fv Keywords: Cobalt; Gold; Growth morphology; Molecular dynamics simulation; Reconstruction; Relaxation

1. Introduction The Au(1 1 1) surface is well known for its herringbone reconstruction. The latter can be viewed as a periodic arrangement of point dislocations which may act as nucleation sites for atoms adsorbed from the gas phase. This reconstruction induces self organized growth of a variety of transition metals, such as Fe [1], Ni [2], Co [3], Pd [4] and Rh [5] while other metals, such as Al [6], Ag [7] and Au [8] seem insensitive to the point dislocations. Such an effect is related to a decrease of the hydrostatic pressure induced by the adsorption of atoms smaller than gold *

Corresponding author. Tel.: þ33-388-10-70-97; fax: þ33-388-10-72-48. E-mail address: [email protected] (C. Goyhenex). 1 Present address: Physikalisches Institut (EP3), Universita¨t Wu¨rzburg, Am Hubland, Wu¨rzburg, 97074 Wu¨rzburg, Germany.

on the reconstructed surface and is now well understood [9]. If an unified scheme has been put forward for the preferential nucleation, the origin of the various observed cluster morphologies is still unclear. Indeed, upon growth at room temperature, some metals like Fe and Ni form monolayer islands while Co is known to grow in bilayer islands [3]. In the case of Pd, the bilayer islands appear around 0.5 ML of coverage while for Rh a coexistence of both monolayer and bilayer is already observed at 0.2 ML. In the present work, we focus on the determination of possible critical sizes for the transition between different cluster morphologies using Molecular Dynamics simulations. Within the particular case of the Co/Au system, we show that considerations based on strain, surface energies (wetting criteria), and the corresponding bulk alloy behavior allow to explain the growth mode. In addition we discuss the effect of the surface inhomogeneity of the substrate.

0169-4332/$ – see front matter # 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2003.11.019

I. Chado et al. / Applied Surface Science 226 (2004) 178–184

2. The microscopic model If strain relaxation is often put forward to explain the early formation of bilayer islands in the case of Co/Au, chemical effects like the demixtion tendency in Co–Au alloys and wetting criteria can also influence the final structure of the deposit. In order to sort out the part of these different driving forces, a microscopic model is used. It is based on Quenched-Molecular-Dynamics (QMD) which is a relaxation procedure that allows one to determine the equilibrium positions of a finite number of atoms, at T ¼ 0 K, by integrating the equation of motion [10]. It requires the use of realistic N-body potentials from which the energy Ei of an atom at site i is calculated. In the tight-binding formalism [11], this energy is written as the sum of an attractive band energy Eib and a repulsive pair interaction Eir . Within the second-moment approximation [12] (SMA), one obtains for the attractive term: ( " !#)1=2 X rij 2 b Ei ¼  xXi Yj exp 2qXi Yj Xi Yj  1 r0 j;rij
179

X and Y indicate the chemical species (Co, Au). r0XX is the first-neighbor distance in the metal X and r0XY ¼ ðr0XX þ r0YY Þ=2. The repulsive term Eir is described by a sum of Born-Mayer ion-ion repulsions [13]: " !# X r ij AXi Yj exp pXi Yj Xi Yj  1 (2) Eir ¼ r0 j;rij
Fig. 1. Energy of the formation at 0 K of Co–Au alloy as a function of Co concentration.

180

I. Chado et al. / Applied Surface Science 226 (2004) 178–184

Table 1 Parameters values for the atomic interactions X

Y

A (eV)

p

q

x (eV)

Esol (X in Y) (eV/atom)

Esol (Y in X) (eV/atom)

Co Co Au

Au Co Au

0.141 0.106 0.189

10.633 10.87 10.40

3.113 2.36 3.87

1.614 1.597 1.744

0.50

0.75

Heteroatomic parameters are obtained by fitting the heats of solution Esol in order to reproduce the existence of the miscibility gap in a large range of concentration [16]. Homoatomic parameters taken from reference [14] are also reported.

from reference [16] in order to get a better representation of the miscibility gap. The main change is that the heats of solution for single substitutional impurities are larger than the calculated values of reference [15]. The miscibility gap is visualized on Fig. 1 representing the energy of formation of the (Co, Au) alloy at 0 K as a function of Co concentration. Experimental values can hardly be found in the litterature but we made the choice to follow at best the well known Hultgren values (see the left-hand side of the graphics) [16]. In this way, on each side of the curve (Fig. 1) the slope at the origin is greater than for the set of calculated values from reference [15] meaning that we take into account a larger miscibility gap. The heteroatomic parameters are reported on Table 1 together with the homoatomic parameters. In order to compare the relative stability of the different clusters, the adsorption energy Eads ðnCo Þ per

Co atom when nCo Co atoms are deposited onto a Au substrate is calculated as follows: Eads ðnCo Þ ¼

Etot ðCo=AuÞ  Etot ðAuÞ  nCo mðCoÞ ; nCo (3)

where Etot ðCo=AuÞ is the total energy (Au substrate and nCo adsorbed Co atoms), and Etot ðAuÞ is the energy of the bare substrate. mðCoÞ is the chemical potential of the Co vapor phase taken as the origin of energies. In the simulations the substrate is a slab of 15 (1 1 1) planes on the sides of which lateral periodical conditions are applied. The (1 1 1) bottom plane is always of bulk-type. The surface plane can be reconstructed or not depending on the purpose. In the most simple approach the adsorption energy is calculated successively for monolayer islands, for bilayer islands

Fig. 2. Three clusters used in the calculations, containing the same total number of Co atoms, N ¼ 37, but respectively monolayer (a), bilayer (b) and trilayer (c) in height.

I. Chado et al. / Applied Surface Science 226 (2004) 178–184

and for trilayer islands deposited onto a Au(1 1 1) unreconstructed substrate in order to get a situation of reference corresponding to the maximal lattice mismatch (14%). For a given size we always simulate the most isotropic compact shape, which is nearly hexagonal for obvious symmetry reasons on a (1 1 1) surface in agreement with experimental observations [17]. For bilayer islands, within the same criterion of compactness, we built islands with a ratio of first layer atoms over second layer atoms as close as possible to 1. The same procedure is applied for building the trilayer islands having then about the same number of atoms in each layer. In a further set of simulations, the

181

same clusters have been deposited on, or close to the elbows of the simulated herringbone reconstruction where the atomic structure is irregular and the interatomic distances smaller than on the coherent parts [9].

3. Critical cluster size: results and discussion Typical islands geometries used in the calculations are represented in Fig. 2. They contain the same number of Co atoms but are respectively monolayer, bilayer and trilayer in height. The values of the adsorption energies Eads as a function of the number

Fig. 3. Co/Au(1 1 1)-unreconstructed. (a) Adsorption energy as a function of the number of Co atoms for monolayer and bilayer and trilayer clusters respectively. (b) Mean interatomic Co–Co distances as a function of cluster size.

182

I. Chado et al. / Applied Surface Science 226 (2004) 178–184

N of Co atoms in the cluster are reported in Fig. 3a. From an energy point of view, a smooth transition appears between 10 and 20 atoms. Above 20 atoms, the bilayer morphology becomes more favorable. At low coverage, trilayer islands are rarely observed experimentally but it was interesting and complementary to evaluate if they could be a competitive structure at least at equilibrium. Indeed, as can be seen on Fig. 3a, for the size range 20–60 atoms, the associated adsorption energies are, although larger, very close to the values obtained for the bilayer islands. In the same way as for the mono-bilayer transition, a bi-trilayer transition is observed between 60 and 70 atoms from which the trilayer clusters becomes definitely more favorable. Therefore, on energy considerations only,

the overall growth is merely three-dimensional. The fact that the very small bilayer or trilayer islands are unfavorable can be roughly explained by simple coordination arguments. Indeed, in the very small bilayer and moreover in the small trilayer structures the proportion of very weakly coordinated Co adatoms is too high and it is more favorable to extend monolayer islands than to form directly three-dimensional clusters. In other words these three-dimensional clusters exhibit in the lower size range a too large proportion of surface leading to a large excess of surface energy in the total energy of the system. In the usual growth conditions where kinetics dominates, at low coverage, the bilayer clusters first extend laterally and the trilayer clusters are rarely observed. Thus, in the

Fig. 4. Co deposited on the bulge out type elbow. (a) Adsorption energy as a function of the number of Co atoms for monolayer and the bilayer clusters respectively. (b) Mean interatomic Co–Co distances as a function of cluster size. The inset shows a perspective view of the corrugated reconstructed (1 1 1) surface of gold.

I. Chado et al. / Applied Surface Science 226 (2004) 178–184

following, we focus on the experimentally [17] observed morphologies namely the mono- and bilayer ones. In order to evaluate the role of strain, the interatomic distances have been extracted from the relaxed structures. One sees in Fig. 3b that their value con˚ for 30 atoms. For verges to the Co bulk value 2.50 A the very small islands, the proportion of weakly coordinated atoms is more important leading to a strong contribution of the edge contraction to the overall distances distribution. Whatever the morphology or the size, the Co cluster always relax to the bulk lattice parameter; the mean distance in the islands is ˚ . Therefore any stress storage is prethen 2.50 A vented in the deposit. The effective lattice mismatch is reduced in the defective regions of the reconstruction, the elbows being the most compressed parts of it. The same islands as in the previous study on the unreconstructed Au(1 1 1) surface have been settled at different places on the complex zigzag substrate. The calculation of the adsorption energies for Co-islands deposited in the center of the hcp- or fcc-stacking regions leads to a behavior very similar to that obtained in the case of the Co on unreconstructed Au(1 1 1) surface. Actually, these regions of the substrate have a rather regular structure with a mean distance between nearest-neighbors atoms close to the bulk gold one. The maximal ˚ , is obtained in deviation from the bulk value, 2.88 A the hcp-stacking region where, with a mean distance ˚ [9], the effective lattice mismatch value of 2.82 A between Co and Au is reduced only from 14 to 12%. The next series of simulations has been performed for islands deposited on the most compressed region of the reconstruction namely on the bulge out elbow where the most important effect, if any, may be expected. In this region, the minimal mean atomic ˚ , at the in-plane nearest-neighbor distance is 2.68 A place where two discommensuration lines join to form a dislocation. The effective mismatch between Co and Au is estimated to be about 9%, taking into account the inhomogeneity of the distribution of distances in this defective region. The results are represented in Fig. 4a in the same form as for Co/Au(1 1 1)-unreconstructed. A perspective view of the bulge out elbow has been added as inset on the same figure. In fact, no real changes are found when going from the most strained (unreconstructed) to the most compressed (elbows)

183

substrate regions. The transition region remains between 10 and 20 atoms, above the bilayer morphology becomes definitely the most stable. The curves of the mean interatomic Co–Co distances in the islands of Fig. 4b reveal the same general tendency of the Co lattice to relax towards the bulk Co value. A slightly larger dispersion of the data points in both the energy curve and the mean Co–Co distance curve may be noticed. It is attributed to the influence of the perturbed underlying gold structure. This effect is important only for the monolayer islands and diminishes when they extend laterally meaning that the influence of the substrate is perceptible at very low coverage but disappears soon when the Co–Co bonds become enough numerous.

4. Conclusion In agreement with previous helium scattering measurements [18] and recent Scanning Tunneling Microscopy experiments [19], numerical simulations evidence a transition from monolayer to bilayer islands at very small cluster size (at about 20 atoms). The possible coexistence between monolayer and bilayer islands is also expected from the special shape of the adsorption energy curves (Fig. 3a) where the transition is smooth. An important conclusion is that the natural lattice mismatch between Au and Co is so strong that any stress storage is prevented and, from the early stages of growth, the Co lattice relaxes to its bulk value. The equilibrium deposit morphology is rather determined by the demixtion tendency, favoring Co–Co bonds against heteroatomic ones, and surface tension effects both going towards a prefered threedimensional growth. A real three-dimensional growth is prevented because of kinetics limitations.

References [1] J.A. Stroscio, D.T. Pierce, R.A. Dragoset, P.N. First, J. Vac. Sci. Technol. A 10 (1992) 1981. [2] D.D. Chambliss, R.J. Wilson, S. Chiang, Phys. Rev. Lett. 66 (1991) 1721. [3] B. Voigtlander, G. Meyer, N.M. Amer, Phys. Rev. B 44 (1991) 10354. [4] A.W. Stephenson, C.J. Baddeley, M.S. Tikhov, R.M. Lambert, Surf. Sci. 398 (1998) 172.

184

I. Chado et al. / Applied Surface Science 226 (2004) 178–184

[5] E.I. Altman, R.J. Colton, , Surf. Sci. 304 (1994) L400. [6] B. Fischer, H. Brune, J.V. Barth, A. Fricke, K. Kern, Phys. Rev. Lett. 82 (1999) 1732. [7] M.M. Dovek, C.A. Lang, J. Nogami, C.F. Quate, Phys. Rev. B 40 (1989) 11973. [8] D.D. Chambliss, R.J. Wilson, S. Chiang, J. Vac. Sci. Technol. B 9 (1991) 933. [9] H. Bulou, C. Goyhenex, , Phys. Rev. B 65 (2002) 045407. [10] C.H. Bennett, in: A.S. Nowick, J.J. Burton (Eds)., Diffusion in Solids, Recent developments, Academic, New York, 1975, p. 73. [11] J. Friedel, in: J.M. Ziman (Ed.), The Physics of Metals, Cambridge University Press, Cambridge, 1969, p. 340. [12] V. Rosato, M. Guillope´ , B. Legrand, Phil. Mag. A 59 (1989) 321.

[13] F. Ducastelle, J. Phys. (Paris) 31 (1970) 1055. [14] C. Goyhenex, H. Bulou, Phys. Rev. B 63 (2001) 235404. [15] F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema, A.K. Niessen, Cohesion in Metals, vol. 1, North Holland, Amsterdam, 1988. [16] R. Hultgren, P.D. Desay, D.T. Hawkins, M. Gleiser, K.K. Kelley, D.D. Wagman, in: Selected Values of Thermodynamic Properties of the Elements, American Society of Metals, Ohio, 1973. [17] S. Padovani, I. Chado, F. Scheurer, J.P. Bucher, Phys. Rev. B 61 (2000) 72. [18] C. Tolkes, P. Zeppenfeld, M.A. Krzyzowski, R. David, G. Comsa, Phys. Rev. B 55 (1997) 13932. [19] I. Chado, C. Goyhenex, H. Bulou, J.P. Bucher, submitted for publication.