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Role of island corner rounding in the morphology transition of the submonolayers grown on metal (1 1 0) surfaces Z.-J. Liu, Y.G. Shen* Department of Manufacturing Engineering & Engineering Management, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China Received in revised form 11 March 2004; accepted 11 March 2004 Available online 6 May 2004

Abstract The role of island corner rounding in the temperature-dependent transition of one-dimensional (1D) monoatomic chain to two-dimensional (2D) island of the epitaixal submonolayers grown on metal (1 1 0) surfaces is studied. We show by Kinetic Monte Carlo simulations and a rate-equation analysis that for aggregation without detachment the anisotropy in corner rounding does play a decisive role in this morphology evolution, agreeing with a previous study where the one-way corner rounding controls the formation of 1D chain at intermediate temperatures and the two-way corner rounding is responsible for its transition to 2D island at high temperatures. However, for fully reversible aggregation, our simulation results reveal that the one-way corner rounding plays a minor role in the formation of 1D chain, even its activation energy can be significantly reduced. Instead, the capture of in-channel-diffusing adatoms by other adatoms or islands leading to the formation of in-channel bonds is responsible for the formation of 1D chain. With its hopping barrier normally less than that of the two-way corner rounding in metal (1 1 0) systems, the in-channel detachment by breaking one in-channel bond governs the transition of 1D chain to 2D island. Our simulation also shows that without the cross-channel atomic interaction the 2D island cannot be formed for fully reversible aggregation. # 2004 Elsevier B.V. All rights reserved. Keywords: Growth mechanism; Submonolayers; Monte Carlo simulation; Thin film

1. Introduction Diffusion of adatoms on metal surfaces is of great importance in the film growth. These fundamental surface processes determine the surface morphology and microstructure of resulting films. In epitaxial growth, many interesting surface patterns have been observed, e.g., pyramids in multilayers [1,2] and *

Corresponding author. Tel.: þ852-2784-4658; fax: þ852-2788-8423. E-mail address: [email protected] (Y.G. Shen).

dentritic or compact islands in submonolayers [3–5]. To explain the observed film morphology, the identification of the crucial surface processes responsible for the formed patterns has become one of the central tasks in this research field [6–8]. However, even in the relatively simple case of submonolayer growth, the understanding of the kinetics controlling the formed island shapes is still far from complete due to so many surface atomistic processes involved. In the past several years, the effects of island corner rounding on the change of island shape have drawn much attention. A typical example is the epitaxial growth

0169-4332/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2004.03.210

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Fig. 1. The illustration of a fcc metal (1 1 0) substrate with some relevant diffusion events.

on isotropic fcc metal (1 1 1) or (1 0 0) surfaces, where the corner rounding is believed to be the key process controlling the formation of fractal cluster at lower temperatures and its transition to compact island at higher temperatures [4,5,8]. For the growth on anisotropic substrates, e.g., metal (1 1 0) surfaces (see Fig. 1) where the atom terrace diffusion along the (1 1 0) channel (in-channel diffusion) is normally faster than that along the (0 0 1) direction (crosschannel diffusion) while the in-channel bonding is much stronger than the cross-channel bonding, the anisotropic corner rounding is also considered as the crucial factor responsible for the experimentally observed morphology transition of one-dimensional (1D) monoatomic chain at intermediate temperatures to two-dimensional island (2D) at high temperatures in the epitaxial growth of Cu/Pd (1 1 0) [9,10]. The central idea in [10] is that, the mass transport for the change of island shape is mainly through the perimeter diffusion by assuming that the hopping barrier of corner rounding can be significantly reduced. Based on this assumption, the authors concluded that the formation of 1D chain was due to the occurrence of the one-way island corner rounding and its transition to 2D compact island was generated by the two-way corner rounding. Although a detail simulation [11] based on a fully reversible model showed that on other growth systems, e.g., Ag/Ag (1 1 0) and Cu/Cu (1 1 0), this morphology transition was not controlled by the anisotropic corner rounding, the role of assumed reduction in hopping barrier of one-way corner rounding on the formation of 1D chain in fully reversible aggregation was not investigated. More-

over, an analysis of the effect of the corner rounding based on rate-equation theory for aggregation without detachment is still lacking. In this work, we present a detailed study on the role of corner rounding in such a temperature-dependent morphology during both fully reversible aggregation and aggregation without detachment by Kinetic Monte Carlo (KMC) simulations or rate-equation analysis. One of main goal of our study is to clarify the effect of one-way corner rounding with reduced hopping barrier on the formation of 1D chain during fully reversible aggregation, together with the importance of the existence of a weak cross-channel atomic interaction in the formation of 2D island.

2. Kinetic Monte Carlo simulation Our KMC simulation is carried out on a lattice of fcc (1 1 0) geometry (see Fig. 1). The randomly deposited atoms are allowed to stop on the top of underlying four substrate atoms but excluded to rest onto a preexisting island due to low coverage studied here (y ¼ 0:05). The permitted microscopic process is the adatom diffusion which falls into four classes (the signs shown in Fig. 1 denote both the diffusion event themselves and their hopping barriers): (1) terrace diffusion of isolated adatoms in x direction Et,x and y direction Et,y; (2) detachment of adatoms in x direction Ed,x and y direction Ed,y; (3) edge diffusion of adatoms in x direction Ee,x and y direction Ee,y; and (4) corner rounding of adatoms from x edge to y edge Ec,x and from y edge to x edge Ec,y. The adatom diffusion is modeled as a nearest-neighbor hopping process with the rate r ¼ v expðE=kB TÞ, where v ¼ 1012 Hz is an adatom attempt frequency, E the hopping barrier, T the substrate temperature, and kB the Boltzmann’s constant. The hopping barrier E is the sum of a term from the substrate whose value equals the barrier of terrace diffusion Et and a contribution from each lateral nearest neighbor Eb, namely, so called bond-breaking model which agrees well with the theoretical calculations [11]. Due to two-fold anisotropy considered here, both Et and Eb are direction-dependent and the hopping barrier for adatoms diffusing along X- or Y-axis can be calculated by Ex ¼ Et;x þ nx Eb;x þ ny Eb;y or Ey ¼ Et;y þ nx Eb;x þ ny Eb;y with nx and ny being the nearest

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neighbors in X and Y direction, respectively. The barriers for corner rounding, are determined through the method employed in [10,11]. For comparison, almost the same energy parameters used in [10] are adopted in our simulations, namely, Et;x ¼ 0:30 eV, Et;y ¼ 0:45 eV, Eb;x ¼ 0:20 eV, and Eb;y ¼ 0:02 eV. Note that we assign a small value Eb;y ¼ 0:02 eV to denote the weak cross-channel bonding, which is in contrast to Eb;y ¼ 0:0 eV used in [10]. As will shown later, without weak interaction between cross-channel atoms, the 2D island cannot form for fully reversible aggregation. To implement our simulations, we use an event-based binary tree algorithm [12–14] where every Monte Carlo step corresponds to a diffusion process selected according to its rate-dependent probability and the simulated time interval t is given by the probabilities of all possible processes Pi by t ¼ 1=SPi . A specially designed feature of our KMC algorithm is that the occurring frequencies of all events during the growth can be recorded, which allows readily determining the effect of corner rounding. Simulation is performed on a 64 64 lattice with periodic boundary conditions.

3. Results and discussion Fig. 2 shows the typical morphology of the submonolayers with a coverage y ¼ 0:05 and a deposition rate F ¼ 2 monolayers/min grown at different tem-

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peratures. Strongly temperature-dependent morphology evolution is evident. At low temperatures, small clusters slightly elongated to the in-channel direction can be observed (see Fig. 2(a)). With the rise in temperature, 1D monoatomic chains begin to appear (see Fig. 2(b)). When further increasing the growth temperature, 2D islands form (see Fig. 2(c)). From a thermodynamics point of view, the system for thin film growth tends to form an energetically most favorable configuration, while the kinetics determines the growth behavior of the film [15,16]. The temperature-dependent island morphology reflects the kinetically limited nature of surface processes. However, as long as the growth temperature is high enough to break the kinetic limitation, the energy favorable configuration, namely 2D compact islands, can form independent of the substrate systems, e.g., on metal (1 0 0) or (1 1 1) surfaces [3–5]. Therefore, the formation of 1D chain is the crucial step in this morphology transition. To characterize the morphology transition, we simply use the percentage of the number of in-channel bonds P[110]b with P½110b ¼ N½110b =ðN½110b =N½001b Þ where N[110]b or N[001]b is the number of formed in-channel bonds or cross-channel bonds. Apparently, for perfect 1D monoatomic chains P[110]b is equal to one while P[110]b should decrease when 2D islands begin to form. Fig. 3(a) shows the evolution of P[110]b as a function of deposition temperature, from which the temperature regime for the formation of 1D chain and

Fig. 2. The typical morphology of epitaxial submonolayers with a coverage y ¼ 0:05 grown at different temperatures: (a) T ¼ 170 K, (b) T ¼ 260 K, and (c) T ¼ 300 K.

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Fig. 3. The evolution of (a) P[110]b, (b) occurring frequencies of relevant events, and (c) PEc;x & PE in-channel as a function of deposition temperature.

its transition to 2D island can be clearly identified. To investigate the effect of corner rounding on the formation of 1D chain, we have made a detailed record of the occurring frequencies of the relevant events at different growth temperatures. The results are presented in Fig. 3(b), where Ed0 ;x is different from Ed,x and represents the in-channel detachment by breaking one cross-channel bond. Note that the occurring times of Ee,y are not shown due to rare occurrences. As can be seen from Fig. 3(b), in the temperature regime (around 230–260 K) where the 1D chains can form,

the one-way corner rounding Ec,x seldom occurs (less than 20 times) compared to other events such as Et,x, Ee,x, Ed0 ;x , and Et,y. To reasonably reflect the role of Ec,x in the formation of monoatomic 1D chain, we define a quantity PEc;x with PEc;x ¼ N½110b Ec;x = Ntotal ½110b where N½110b Ec;x is the number of in-channel bonds generated by Ec,x and Ntotal ½110b is the total number of formed in-channel bonds during the whole growth process (Ntotal ½110b includes two parts: the number of broken in-channel bonds during the growth N½110b broken and the number of formed in-channel bonds after growth N½110b ). Thus, PEc;x denotes the percentage of in-channel bonds generated by Ec,x. Fig. 3(c) shows the values of PEc;x in the temperature range 220–280 K. PEc;x is generally less than 0.04 at the temperature range studied where 1D chains can form, indicating that the direct one-way corner rounding Ec,x is almost negligible in the formation of 1D chain. Actually, we have found that the formation of in-channel bond is primarily through the capture of in-channel-diffusing adatoms by other adatoms or islands. Similarly, we define a quantity PEin-channel with PEin-channel ¼ N½110b Ein-channel =Ntotal ½110b where N½110b Ein-channel is the number of in-channel bonds produced by the capture of in-channel-diffusing adatoms. As can be seen from Fig. 3(c), 90% or even more of the in-channel bonds are produced by in-channel diffusion of adatoms. The results also reveals that the indirect oneway corner rounding, namely through two-step corner rounding (detachment through the event Ed0 ;x followed by terrace diffusion Et,y reattaching the island), contributes less to the formation of 1D chain. Note that the hopping barrier of Ec,x is not significantly reduced below Et;y þ Eb;y as assumed in [10]. We have also performed a simulation by letting Ec;x ¼ 0:42 eV (lower than Et;y þ Eb;y ¼ 0:47 eV) but keeping other energy parameters unchanged to meet the condition of ‘significantly reduced’. The results are presented in Fig. 4. Despite a rise in the occurring times of Ec,x due to the reduced barrier, no significant change in the value of PEc;x suggests that the barrier-reduced one-way corner rounding also plays a minor role in the formation of 1D chain, which is quite different from the assumption made in [10]. Recalling the analysis in [10], one of the main views is that, when the barrier of Ec,x is reduced, the perimeter diffusion can dominate over the terrace diffusion in the mass transport for the change of island shape, namely, the cross-channel bonds can be changed into the

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Fig. 4. The evolution of (a) P[110]b, (b) occurring frequencies of relevant events, and (c) PEc;x & PE in-channel as a function of deposition temperature obtained by assuming Ec;x ¼ 0:42 eV, lower than Et;y þ Eb;y ¼ 0:47 eV.

in-channel bonds through Ec,x. However, our above results demonstrates clearly that the system does not need frequent occurring of Ec,x to change the island shape, even in the case where the barrier of Ec,x is reduced below Et;y þ Eb;y. Instead, the picture for the formation of 1D chain should be as follows: when the deposited atoms randomly diffuse along the surface, they can be captured by other adatoms or islands. Once they are captured in the (1 1 0) direction, namely forming an in-channel bond, they become relatively stable due to high binding energy and relatively small occur-

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ring frequencies of the events involving the breaking of in-channel bonds at that growth temperature. If captured in the (0 0 1) direction, they can still move due to low binding energy, namely through the event Ee,x or Ed0 ;x. However, the cross-channel diffusion, e.g., Et,y and Ed,y, can let these moving adatoms cross this channel and diffuse on other channels, and hence, make it possible for them to be captured in the (1 1 0) direction again. Therefore, the high occurring times of Ee,x, Ed0 ;x , Et,y and Ed,y can prompt the formation of 1D chains. Normally, so long as the hopping barrier of the one-way corner rounding is not unreasonably low, it plays a minor role in the formation of 1D chain for fully reversible aggregation. For the transition from 1D chain to 2D island, one naturally expects that it will take place when the event associated with the breaking of in-channel bonds, e.g., Ed,x or Ec,y, begins to occur and thus, the transition temperature can be determined roughly according to the onset temperature of this event. In our case, the event Ed,x (0.50 eV), not Ec,y (0.65 eV), is expected to trigger this transition due to much lower hopping barrier than Ec,y. As can be seen in Fig. 3(b), compared with the in-channel detachment Ed,x, the two-way corner rounding Ec,y plays a minor role in this transition due to much smaller occurring times in the transition temperature regime. This observation is similar to the result obtained in [11]. However, it should be pointed out that although the in-channel detachment Ed,x controls the formation of 2D island, the existence of an interaction between cross-channel atoms, namely Eb,y, also plays an important role in the formation of 2D island. As shown in Eb,y Fig. 5, the transition temperature is Eb,y-dependent: small Eb,y can lead to a higher transition temperature. Because of the change in Eb,y having no impact on the values of Ed,x in the bond-breaking model, the result indicates that transition temperature for 1D chain to 2D island depends not only on Ed,x but also on the above-mentioned events involved in the formation of 1D chain, namely, Ee,x, Ed0 ;x , Et,y and Ed,y. Note that for Eb;y ¼ 0 this transition cannot be observed even the growth temperature reaches 330 K. This suggests that without the interaction between cross-channel atoms the 2D islands cannot form. The possible reason for this is that 2D compact islands cannot become the energy favorable configuration due to the lack of cross-channel atomic interaction. The result also implies that the

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v expðEc;y =kB TÞ. For td, when the terrace diffusion is significant, it is governed by the deposition rate F as td 1=F where the unit of F is atom/s. Thus, we have, c1 Ee;x c2 Ec;x tx ¼ exp þ exp (1) v kB T v kB T c3 Ee;y c4 Ec;y ty ¼ exp þ exp (2) v kB T v kB T and td v ¼ tx ðFc1 expðEe;x =kB TÞÞ þ ðFc2 expðEc;x =kB TÞÞ (3) ty ðc3 expðEe;y =kB TÞÞ þ ðc4 expðEc;y =kB TÞÞ ¼ tx ðc1 expðEe;x =kB TÞÞ þ ðc2 expðEc;x =kB TÞÞ Fig. 5. The evolution of P[110]b as a function of deposition temperature with different values of Eb,y.

assumption of Eb;y ¼ 0 is unreasonable for fully reversible aggregation. However, we note that the anisotropic corner rounding may be indeed needed for the formation of 1D chain and its transition to 2D island in the case of aggregation without detachment. For such a relatively simple case, we first give a brief analysis. Because the adatom detachment is not permitted in the growth, in principle, the mass transport responsible for the change of island shape is through the perimeter diffusion. We use three time scales in our analysis: the average interval (td) for two depositing adatoms to detach an island, the average time (tx) for an adatom to stay at x edge before it goes to y edge leading to a new in-channel bond, and the average time (ty) for an adatom to reside at y edge before it escapes to x edge resulting in a new cross-channel bond. Naturally, the formation of 1D chain is expected when the following two conditions are satisfied: td =tx @ 1 and ty =tx @ 1. As suggested by Zhong et al. [8], tx or ty can be approximated by the sum of two time lengths: the average time te,x or te,y cost by the adatom at x edge or y edge for reaching a corner and the average time tc,x or tc,y for the adatom to across the corner from x edge to y edge or from x edge to y edge. Obviously, te,x or te,y should be inversely proportional to the adatom edge hopping rate v expðEe;x =kB TÞ or v expðEe;y =kB TÞ. Similarly, tc,x or tc,y is inversely proportional to the adatom corner rounding rate v expðEc;x =kB TÞ or

(4)

where c1,, c2, c3, and c4 are approximately considered as constants for a given growth. Considering Ee,x normally smaller than Ec,x and Ee;y ¼ Ec;y in the bond-breaking model, we can simplify Eqs. (3) and (4) as td v Ec;x

exp (5) tx Fc2 kB T t y c3 þ c4 Ec;y Ec;x

exp (6) tx c2 kB T Eq. (5) indicates that at a given deposition rate, high temperature T or low Ec,x favors the formation of 1D chain, whereas Eq. (6) implies that high temperature T or weak anisotropy in corner rounding will prompt the formation of 2D island. Thus, the formation of 1D chain and its transition to 2D chain are controlled by corner rounding. The conditions for the formation of 1D chain are at a suitable growth temperature and the existence of a strong anisotropy in corner rounding. To check our analysis, we have firstly performed a KMC simulation with Et;x ¼ 0:30 eV, Et;y ¼ 0:45 eV, Eb;x ¼ 0:20 eV, and Eb;y ¼ 0:02 eV but suppressing all the possible detachment events. However, 1D chain-like configuration cannot be observed probably due to the possible weak anisotropy in corner rounding. Therefore, we reduce the value of Eb,y to 0.0 eV for raising the energy difference between Ec,x and Ec,y The results are presented in Fig. 6. The temperature-dependent value P[110]b shows clearly that strong anisotropy in corner rounding can generate this morphology evolution (see Fig. 6(a)). The significant rise in the value of

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the in-channel detachment, not the two-way corner rounding. We also reveal that the 2D island cannot become the energy favorable configuration and cannot form at high temperatures without the cross-channel atomic interaction. However, for aggregation without detachment, our analysis reveals that the anisotropy in corner rounding controls this temperature-dependent morphology evolution.

Acknowledgements The work described in this paper was supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region, China (Project No. City U 1097/02E).

References

Fig. 6. The evolution of (a) P[110]b and (b) PEc;x and PE in-channel as a function of deposition temperature for aggregation without detachment using the parameters Et;x ¼ 0:30 eV, Et;y ¼ 0:45 eV, Eb;x ¼ 0:20 eV, and Eb;y ¼ 0 eV.

PEc;x , which is generally larger than 0.85 in the temperature range 230–290 K (see Fig. 6(b)), reveals that Ec,x controls the formation of 1D chain.

4. Conclusion In conclusion, we have studied the role of island corner rounding in the morphology transition of 1D chain to 2D island of epitaxial submonolayers grown on metal (1 1 0) substrates. Our results show that, for fully reversible aggregation, the one-way corner rounding plays a minor role in the formation of 1D chain, and the transition to 2D island is governed by

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