An effective medium theory study of Au islands on the Au(100) surface: reconstruction, adatom diffusion, and island formation

surface science ELSEVIER

Surface Science 365 (1996) 87-95

An effective medium theory study of Au islands on the Au(100) surface: reconstruction, adatom diffusion, and island formation Lutz B6nig, Shudun

Liu, Horia

Metiu

*

Departments of Physics and Chemistry and the Centerfor Quantized Electronic Structures (QUEST), University of California, Santa Barbara, CA 93106, USA Received 21 July 1995; accepted for publication 26 February 1996

Abstract We have used the effective medium theory to examine two kinetics phenomena related to the aggregation of the Au atoms deposited on a hex-reconstructed Au(100) surface. The island density can be analyzed by using scaling arguments derived from kinetic equations based on an assumed growth mechanism. The correct mechanism is still uncertain. The calculations reported here suggest that the diffusion of an isolated adsorbed atom is two-dimensional, the dimer is mobile, and the critical nucleus size is one. The scanning tunneling microscope experiments of GQnther, Kopatzki, Bartelt, Evans, and Behm have shown that the islands formed by the Au atoms are elongated rectangles and their widths are likely to be "quantized". Since the second surface layer has square symmetry and the top layer is hexagonal, the rectangular shape of the islands is not obvious. We suggest that this form appears because the atoms in the surface layer below the island are unreconstructed (i.e., revert to a square symmetry during island formation), while the atoms in the island have a hexagonal structure. Kinetics favors a six-atom-wide island: the diffusion of an atom along the long side of such an island is much faster than when the island width differs from six; the atoms sticking to the long side of a sixatom-wide island are rapidly transported to its short side, adding to the length and not to the width of the island. This transport is inefficient when the width differs from six. Keywords: Adatoms; Computer simulations; Epitaxy; Growth; Models of surface kinetics; Single crystal epitaxy; Surface diffusion; Surface relaxation and reconstruction

1. Introduction L o w - e n e r g y electron diffraction ( L E E D ) [ 1 ] , H e - i o n scattering [ 2 ] , scanning tunneling m i c r o s c o p y ( S T M ) [ 3 ] , t r a n s m i s s i o n electron m i c r o s c o p y ( T E M ) [4-], a n d X - r a y [ 5 ] m e a s u r e m e n t s have e s t a b l i s h e d t h a t the surface l a y e r of a A u ( 1 0 0 ) surface r e c o n s t r u c t s to form a q u a s i - h e x a g o n a l c l o s e - p a c k e d s t r u c t u r e r o t a t e d slightly with respect to the substrate. If the small r o t a t i o n is i g n o r e d * Corresponding author. Fax + 1 805 893 4120; e-mail: [email protected]

the surface unit cell is a p p r o x i m a t e l y (5 × 1). The a t o m density in the r e c o n s t r u c t e d layer is 20% larger t h a n in a layer in the bulk. C a l c u l a t i o n s b a s e d o n e m p i r i c a l m a n y - b o d y p o t e n t i a l s such as the "glue" m o d e l [ 6 ] a n d the e m b e d d e d a t o m m e t h o d [ 7 - 9 ] , o r on density functional t h e o r y [ 10,11] are able to r e p r o d u c e this surface structure. P t ( 1 0 0 ) [ 1 2 ] a n d Ir(100) [ 1 3 ] r e c o n s t r u c t in the s a m e way. G 0 n t h e r et al. ['14] used S T M to s t u d y the n u c l e a t i o n of A u islands on the r e c o n s t r u c t e d Au(100) surface, a n d f o u n d a n u m b e r of very interesting features. T h e d a t a on the island density

0039-6028/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PII S0039-6028 (96) 00679-6

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could be fitted only to scaling relationships that assumed one-dimensional (or extremely anisotropic) single atom diffusion, and a critical nucleus size of three atoms at low temperature and five atoms at high temperature. The latter assumption means that at low temperatures the trimer will dissociate rapidly and the quadrimer will not; and at higher temperatures the pentamer is kinetically stable and all the smaller clusters are not. Liu et al. [15] argued that the diffusion of an adsorbed atom, on a surface layer whose structure is very similar to that of a (111) surface, is not likely to be one-dimensional (i.e., it will not be strongly anisotropic). Moreover, the activation barrier preventing the motion of a dimer on the surface is likely to be smaller than the one preventing dimer dissociation; therefore, the kinetic equations used for deriving the scaling relationships should assume two-dimensional single-atom diffusion, mobile dimers, and a critical nucleus size equal to one. The scaling equations [ 16,17] corresponding to these assumptions [15] fit the data of Gt~nther et al. [ 14]. Since both models fit the data we need some additional information to help decide which one is correct. The effective medium calculations reported here support the model proposed by Liu et al. [15]. The measurements of Gianther et al. [ 14] show that the Au islands grown on the hex-reconstructed surface are rectangular. Considered from the point of view of symmetry alone this is somewhat surprising: the second surface layer has square symmetry, the atoms in the top layer form a hexagonal structure, and the islands grown on top of this layer are elongated rectangles. As if this were not enough, the width of the rectangles seems to be "quantized" [14]: most islands are 6, 12, or 18 atoms wide. Both the rectangular shape and the quantized width agree with a simple picture of island growth on this surface with the strip-like corrugation due to reconstruction. One of the aims of this paper is to provide a qualitative explanation for the kinetic stability of these islands under experimental growth conditions. For the clean reconstructed surface it is clear, based on experiments and computer simulations, that the second layer has a (100) structure. Therefore we assume that the atoms in the surface layer underneath the

island "unreconstruct" and take a square (100) structure, while the atoms forming the island have a hex reconstruction. As a result of this, six atoms in the island are commensurate with five atoms in the layer below; this commensuration also takes place for islands that are 12, 18, etc., atoms wide. This explains the energetic stability of these structures. We also find that the diffusion along the long island edges is much faster when the island is six atoms wide than for any other width. Because of this an atom reaching the long side of a rectangular island tends to be transported to the short edge rather than nucleate a new row that will form a seven-atom-wide island. The presence of the rectangular island shapes on the surface and the observed anisotropy of the denuded zones along steps, however, does not necessarily mean the diffusion of a single adatom is strongly anisotropic [ 14,15]. On the other hand, the island density data themselves can also be explained by a model with either anisotropic or isotropic diffusion of adatoms [ 14,15]. It is interesting to note that an STM study of the reconstructed Au(100) surface after sputtering [18] found that the "islands" formed by vacancies also have long rectangular shapes. One would naively think, in the spirit of a lattice gas model, that a vacancy is very similar to a particle and that vacancy islands ought to behave like particle islands. A little thought suggests that this is not the case. The kinetics of vacancy formation and migration is different from those of an adsorbed atom, and as a consequence both the kinetics and the thermodynamics of the vacancy islands may be quite different from that of the islands formed by the adsorbed atoms. The similarity in the shape of the two kinds of islands requires a deeper explanation than that which a lattice gas model would provide. There is no information regarding the migration of the Au atoms on the hex reconstruction of the Au(100) surface. An earlier embedded atom calculation of Liu et al. [19] used an unreconstructed Au(100) surface and the results are not relevant to the questions examined here. For this reason we have carried out extensive effective medium calculations of a variety of activation barriers for the kind of atomic motions that are most likely to be

L. B6niget al./Surface Science365 (1996) 87-95

involved in the kinetic processes discussed above. The effective medium theory (EMT) [20,21] is a semi-empirical scheme which includes many-body effects in total energy calculations for the transition metals. The parametrization was performed to provide good results for bulk properties. Nevertheless, it has been applied successfully to a number of surface phenomena such as surface reconstruction [22], diffusion on surfaces [23-26], the mechanism by which an island reaches a certain shape [27], and analysis of other kinetic phenomena such as re-entrant layer-by-layer growth [28]. We prefer the EMT for this particular study because the hex reconstruction resembles a (111) surface for which the embedded atom method dramatically underestimates the diffusion barrier while EMT seems to give more reasonable (but still too small) values. The size of the systems considered here and the number of energy evaluations required for finding the activation energies for all the relevant processes is too large to allow the use of ab initio methods. The qualitative nature of the questions asked in the present study make us believe that EMT is adequate for the present task.

2. A few details regarding the computations Typically, we use in our calculations a slab having 10 x 10 x 6 atoms, with periodic boundary conditions in the two dimensions along the slab. We allow the atoms in three layers nearest to the slab's surface to relax to their minimum energy position, and keep fixed the atoms in the three layers on the other side of the slab. When we calculate surface energies we allow all atoms to relax, so the sample has two equivalent surfaces. We make sure that the results are insensitive to the size of the slab by performing a few calculations with larger slabs. The potential cutoff in the EMT program is slightly larger than twice the nearestneighbor distance of the bulk fcc structure. In this case 54 neighboring atoms contribute to the energy of a single bulk atom. Increasing the cut-off distance further changes the cohesive energy by less than 1%. To find the equilibrium configuration we use a

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Metropolis algorithm [29]. This is run initially at room temperature, and then we gradually lower the temperature to 0.1 K to suppress the effect of thermal fluctuations.

3. Results 3.1. The stability of the reconstructed surface

Often the energy difference, per atom, between various surface structures is very small, and, given the unavoidable errors in an EMT calculation, we do not expect to find the correct absolute minimum. To perform calculations of interest to growth kinetics it is only necessary that the reconstructed surface corresponds to a sufficiently deep local minimum on the potential energy surface. We have arranged a quasi-hexagonal (5 × 1) layer on top of the square (100) surface of the fcc substrate (Fig. la). The atom density in the surface layer in the x-direction is that of the bulk; the density in the y-direction is higher: six surface atoms are commensurate with five atoms in the second layer. The atoms in the surface layer are compressed by 20% in the y-direction and have the same density as the bulk in the x-direction. In what follows we often refer to these two directions as the high density (y) and the bulk density (x) directions. The long edge of the rectangular islands observed by Gtinther et al. [ 14] is perpendicular to the high density direction: the density is high across the width of the island and is bulk-like along its length. If we start from a reconstructed surface-layer configuration and then let all atoms relax to reach a position of minimum energy, they maintain the hex reconstruction. As seen in previous calculations [6-8] and in STM measurements [3,14,18], the surface layer is buckled (see Fig. lb). For a system with an interlayer distance (in the bulk) of 2.04 ~,, the corrugation of 0.75 A found in our calculation is rather large. By shifting the surface layer by half a lattice constant in the x-direction we obtain a new type of stacking (see Fig. 2a), where the hexagonal layer takes the so-called top-center sites. The corrugation of this surface layer is 0.85 ,~, slightly larger than

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Fig. 1. (a) Top view of the hex surface layer. The surface atoms are on the bridge sites. (b) Side view. z is perpendicular to the surface and points towards vacuum.

Fig. 2. (a) Top view of the hex surface layer. The surface atoms are in the top-center sites. (b) Side view. z is perpendicular to the surface and points towards vacuum.

This energy is defined by in the previous arrangement. The energy difference between the two arrangements is so small that, considering the expected error of the E M T method, we cannot tell which one is more stable. It has been suggested [4] that the surface layer has a (28 x 5) unit cell. If one ignores the slight rotation, then 14 atoms in this unit cell are located approximately at two-bridge sites (see Fig. la) while the other fourteen are approximately on a top-site location. This may affect the structure of a long step perpendicular to the high density direction. We have not examined this structure here, as we believe that the difference between the (28 x 5) and the (5 × 1) structure will not influence significantly the island growth pattern that we are interested in. We have also calculated the energy per atom of the reconstructed and unreconstructed surfaces.

Es=(Et(N)-NEc)/Ns where Et(N ) is the total energy of a slab with N atoms, Ec is the cohesive energy of a bulk atom, and Ns is the number of surface atoms. We found that E~ for the unreconstructed surface is 0.31 eV and for the hex-reconstructed surface is 0.336 eV. According to E M T the unreconstructed surface is more stable, which is in disagreement with experiment. As we have already pointed out, the energy difference per atom between the two structures is very small and E M T does not have the accuracy needed to perform stability analysis of this kind. Furthermore, such a comparison is of questionable value since the reconstructed surface has 20% more surface atoms than the unreconstructed one. For this reason we have also calculated the surface energy of an unreconstructed surface which has an

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additional row of atoms on top of the surface for each five rows in the surface layer. For this, we obtain Es =0.282 eV. It is clear that a meaningful comparison can be made only if one knows exactly where to place the atoms produced when the surface unreconstructs. However, the calculations performed so far suggest that within E M T the reconstructed (5 x 1) surface is not the most stable phase at T = 0 K. Nevertheless, E M T provides a local minimum for the reconstructed surface, which allows us to find the positions of the surface atoms in this configuration. Unfortunately, the reconstructed surface is not very stable; we shall see that this causes some difficulties when we calculate some of the activation energies. 3.2. Diffusion o f a Au atom on a reconstructed Au surface

We can now address one of the questions asked in Section 1: is the diffusion of a single Au atom on the hex-reconstructed (100) surface so anisotropic that it can be considered one-dimensional? As we pointed out, the answer to this question is of importance to the scaling analysis of the island density. To calculate the barrier to diffusion we set up the reconstructed surface with one atom on it and then change the atomic positions in the whole system until we find the configuration giving the minimum energy. Then we drag the adatom from one minimum energy position to another. As we do this we relax the positions of the atoms along the "reaction path" (see Ref. [26]). Unfortunately, we find that the adsorbed atom being dragged from one binding site to another will pull with it an atom from the surface layer. The species moving is a diatomic and the displacement of the adatom creates a vacancy in the surface layer. There is no experimental evidence for the formation of such vacancies and therefore we assume that its formation is an artifact of the E M T interaction. This is consistent with the fact that within E M T the reconstructed surface does not have sufficiently high stability. To suppress this vacancy formation we force the surface atoms to maintain their position while the adsorbed atom is being moved from one binding site to another. This will affect the

magnitude of the diffusion barrier, but previous experimentation with the E M T method has shown that this effect is not large. For example, the diffusion barrier on the fiat unreconstructed Au(100) surface is 0.49 eV when all surface atoms are allowed to relax as the adsorbed atom moves along the reaction path, and it is 0.50 eV when the surface atoms are held in place; for the A u ( l l l ) surface the corresponding barriers are 0.102eV and 0.126 eV, respectively [21]. It is unlikely that keeping the surface rigid will substantially affect the activation energies of interest here. In Fig. 3 we show the low energy paths on which an adsorbed atom will move in the x and the ydirections. The energies along these paths are shown in Figs. 4 and 5. While the top layer has a hex geometry, the second layer is square. For this reason, various binding sites on the hex surface have different binding energies for the adsorbed atom, due to differences in the configuration of the atoms in the second layer. In one row along the x-direction (see Fig. 3) there are two types of binding sites, leading to two different diffusion barriers. All barriers in the x-direction, along other paths parallel to the one shown in Fig. 3, are between 0.15eV and 0.17eV (see Fig. 4). The diffusion along the y-direction is more complex and the largest barrier is 0.28 eV (see Fig. 5). At a temperature of 315 K, the anisotropy of diffusion = DffDx,

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Fig. 3. Single adatom diffusionpaths on the reconstructedsurface in the x- and in the y-direction

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3.3. Dimer mobility on the reconstructed surface

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We have also calculated the activation energy to move a dimer in the x-direction. As we drag the dimer along the reaction path the bond length remains practically unchanged; dimer motion does not take place through successive one-atom-afteranother-atom motion. The barrier is 0.2 eV (see Fig. 6). Small barriers have also been found for the Pt dimer on P t ( l l l ) [26,27,30], the Fe dimer on C u ( l l l ) [31], and the A1 dimer on A t ( l l l ) [32]. High dimer mobility has been observed by field ion microscopy [30,33,34] for surfaces other than Au. These calculations support the suggestion of Liu et al. [15] that in interpreting the island density measurements [ 14] one can use a two-dimensional model in which dimer motion is implicitly included. Moreover, as barriers to dissociation are generally much larger than those to diffusion, we believe that dimer dissociation is very slow at the temperatures at which the experiments were carried out and this process should not be included in the scaling analysis of the experimental data at lower temperature; therefore the critical nucleus size should be one [15].

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where Dp is the largest diffusion constant in the direction fl, is 1/58. At the temperature used in the experiments of Giinther et al. [14], the singleatom diffusion is not truly one-dimensional. A few words should be noted about the interpretation of the calculated barriers. We found previously [15] that an isotropic diffusion barrier of 0.35 eV together with substantial dimer mobility fits the experimental island density data very well. Here, the calculated barriers for monomer diffusion are substantially smaller than 0.35 eV. It is known that EMT can underestimate diffusion barriers on a (111)-like surface by as much as a factor of 2 [26,28 ] while the hierarchy of the calculated barri-

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L. B6nig et al./Surface Science 365 (1996) 87-95

3.4. Island shape and surface unreconstruction The deposition of Au atoms on the hex-reconstructed Au(100) surface leads to the formation of islands having an elongated rectangular shape [ 14], with the long side parallel to the x-direction (Fig. 1). Moreover, the aspect ratio of the islands depend on the deposition flux. This is an indication that island shape is controlled by the kinetics rather than thermodynamics. It is clear that, at some time in the deposition process during the formation of the top layer, the surface must "dereconstruct" and take the square (100) structure of the bulk. Otherwise, epitaxially grown Au would have 20% higher density and a different structure from Au obtained by other methods. Furthermore, the islands formed by deposition must take, at some time during the growth, the hex structure. The STM experiments on the grown islands do not have enough resolution to determine whether the island has the hex structure. However, Gauthier et al. [ 18 ] indicate that the bottom of the "vacancy islands" formed by sputtering do take the hex structure even when their area is small. It seems likely to us that a small island is hex-reconstructed and that the layer underneath it has the (100) structure. Since the unreconstruction of the second layer requires substantial atomic mobility (the layer must get rid of 20% of its atoms by sending them up to join the atoms deposited on the surface) it is reasonable to assume that this process takes place rather early during the island formation. In our simulations we added small hexagonal islands, three to six atoms wide in the y-direction, on top of a reconstructed surface. When we anneal this sample to high temperatures we observe that the surface atoms next to an island have a tendency to leave the surface layer and attach to the island. This suggests that the mechanism of"dereconstruction" involves a transfer of atoms from the covered surface layer to islands and a rearrangement of the atoms in the covered layer into a bulk structure. Since the density of a reconstructed area is 20% larger than an unreconstructed one, the "dereconstruction" provides excess atoms in addition to the deposited ones. Precise STM measurements of the difference between the number of atoms forming

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islands and the number of atoms deposited on the surface could test this scenario. We come now to the question of island width "quantization" suggested by GUnther et al. [14]. This follows from the assumptions made here: if the surface under the island is dereconstructed (i.e., has the (100) structure) and the island has a hex reconstruction, than the island atoms are in registry with the surface atoms exactly when the island is six atoms wide (see Fig. 1). One expects this registry to make the islands having 6, 12, etc., atoms along the y-direction more stable than any other islands. Note that in the x-direction the hex island is commensurate with the unreconstructed layer and there is no size preference. However, stability arguments have little kinetic value since they do not explain the mechanism through which the island arrives at the stable structure and maintains it. Moreover, the system reaches the most stable structure only under the right growth conditions. An understanding of the mechanism through which a given shape is reached comes from the properties of the diffusion processes. To find this mechanism we have created islands having a variety of widths in the y-direction (see Fig. 7) and then calculated the barrier to diffusion for an atom moving along the two long O

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Fig. 7. A six-atom-wide island on top of an "unreconstructed" area. We show the diffusion path for an atom rounding the corner to move away from the edge parallel to x. Note the structural differences between the upper and lower edge, which result in different diffusion rates along them.

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L. Brnig et al./Surface Science 365 (1996.) 87-95

edges (parallel to the x-direction). The structure of the two edges is slightly different and the diffusion barriers along them are different as well. Moreover, the activation energies depend on the width. The results are shown in Table 1. We see that an atom moves very rapidly along the edges of a six-atom-wide island. The diffusion of the atoms along an edge parallel to the ydirection is, on the other hand, always slow. We have also calculated the energy barrier that an atom has to overcome to go "around the corner" and leave the edge parallel to x (see Fig. 7). We found 0.51 eV for the upper edge and 0.24 eV for the lower one. These numbers suggest the following scenario: when an island is six atoms wide, the atoms that reach the edge parallel to x during deposition will move rapidly along it and then go around the corner, reach the other edge, and stop there. As a result, such an island grows predominately in the x-direction, getting longer and maintaining its six-atom width. If the island is less than six atoms wide the diffusion on at least one of the edges parallel to the x-direction is slow and the atoms have a high chance to meet on that edge and nucleate a new line of atoms to it: these islands become wider.

4. Summary We have used E M T calculations to answer two questions concerning the growth of Au islands on a hex-reconstructed Au(100) surface. The first question is what mechanism should be used in the scaling analysis of the number of islands formed during epitaxial deposition. The present calculations favor a model in which the adatom diffusion Table 1 The barrier to diffusionalong the long edges (parallel to the xdirection)whenthe island has an n-atomwidth in the y-direction Island width

Barrier eV (upper edge)

Barrier eV (lower edge)

3 4 5 6

0.52 0.16 0.56 0.24

0.47 0.45 0.47 0.04

is two-dimensional, the dimers are mobile, and the critical nucleus size is one. Liu et al. [15] have shown that such a model is consistent with the data. The second question is why the atoms form long rectangular islands on a surface layer with triangular symmetry laying on top of a layer with square symrnetry. We propose that during island formation there is particle transport from the surface layer into the island. The outcome of this transport is that the island has a hex reconstruction while the surface layer underneath unreconstructs to form a (100) layer. This change in reconstruction makes the islands having six atoms (or a multiple of six) in the y-direction commensurate with the substrate, which makes them more stable. We have also shown that the diffusion of atoms along the long edges (parallel to the x-direction) is very rapid when the island is six atoms wide (in the ydirection) and is slow otherwise. This renders the six-atom-wide island kinetically stable, while the atom landing on islands having a different width will nucleate new lines and become wider. This nucleation is more difficult on a six-atom-wide island. Once the seventh layer is nucleated, widening of the island continues until the island is 12 atoms wide, and so on. We have emphasized that the E M T calculations are not very precise. However the questions investigated here are of a qualitative nature and depend mostly on the relative magnitudes of different diffusion rates. There is a good chance that the conclusions reached here are correct and will be substantiated by further experiments.

Acknowledgements This work was supported in part by the Air Force Office of Scientific Research and by QUEST, an NSF Science and Technology Center for Quantized Electronic Structures (grant no. D M R 91-20007). We thank Per Stoltze and Jens Norskov for useful discussions.

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