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Diffusion behavior of single adatoms near and at steps during growth of metallic thin films on Ni surfaces
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Surface Science 294 (1993) 197-210 North-Holland
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Diffusion behavior of single adatoms near and at steps during growth of metallic thin films on Ni surfaces Chun-Li
Liu ’ and James B. Adams
Department
of Materials Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801, USA
Received 19 January 1993; accepted for publication 4 May 1993
Diffusion of single adatoms approaching both descending and ascending steps on Ni(lll), (110) and (100) has been investigated with the embedded atom method (EAM) and molecular statics (MS). (1) It was found that there exists a “forbidden” region near both descending and ascending steps on Ni(ll1). Adatoms have to overcome a slightly higher energy barrier to get into the “forbidden” region, which extends 2-3 nearest-neighboring spacings from the steps. This is consistent with FIM experiments for incorporation of Ir adatoms into ascending steps of Ir clusters. (2) Detailed calculations for incorporation of adatoms over descending steps of type B on Ni(ll1) have revealed that exchange diffusion, in which an adatom replaces the position of an atom in the step and exchange their roles, is energetically favored over ordinary jumps and is the dominant diffusion mechanism at the descending steps. This is consistent with recent FIM experiments of W adatom diffusion at Ir cluster edges of type B on Ir(111). (3) Exchange diffusion was also found to be favored over direct jumps at the descending steps on Ni(ll0) and Ni(100).
1. Introduction Diffusion behavior of single adatoms near and at atomic steps is crucial for understanding physical and chemical processes occurring on surfaces during growth of thin films. It has been shown that limited migration across descending steps can change surface morphology dramatically during crystal growth from the vapor [l]. Adatom diffusion across steps was considered to play a vital role in annealing of surface defects during ion bombardment of metallic surfaces [2-41. It is also especially important for low temperature growth of thin films or growth of superlattice structures when a high density of steps is desired and thermal energies of diffusing elements are low. Understanding atomic events near and at steps can greatly enhance our knowledge of the insights into these phenomena. Also, the study of diffusion behavior of single adatoms is of substantial fundamental interest in materials science * Present address: Solid State Division, Oak Ridge National Lab, Oak Ridge, TN 37831, USA. 0039-6028/93/$06.00
since surface diffusion is very sensitive to the structure of a surface and its defects, and is of great significance in developing mass transport theory. Incorporation of single adatoms into step ledges from the vapor phase can be accomplished in several ways: (1) direct incorporation of atoms into step ledges upon impingement from the vapor phase; (2) diffusion of adatoms to ascending steps and incorporation into kink sites through diffusion of adatoms along the step ledges; (3) diffusion of adatoms to descending steps, over the descending steps, and incorporation into kink sites through diffusion of adatom along the step ledges. A schematic of these processes is shown in fig. 1. The incorporation of adatoms at ascending steps on impact has been observed experimentally using a field ion microscope (FIM) [5]. However, incorporation of adatoms into ascending and descending steps is far from being well understood, simply because of experimental difficulties and the lack of reliable theoretical models. Although FIM has been extensively used to study surface diffusion, most experiments were limited
0 1993 - Elsevier Science Publishers B.V. All rights reserved
C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni surfaces
198
b
They found that the Ir adatom wandered around the Ir cluster, staying at N 3 nearest-neighboring spacings away from the cluster edges, until it finally jumped into the cluster ledge. These results have raised some questions: Do these phenomena occur near and at steps, which are quite similar to cluster edges? Does a similar phenomenon of an adatom’s wandering near ascending steps also occur near descending steps? What is the physical origin for such behavior? Does exchange diffusion also occur for homogeneous diffusion during epitaxial growth of metallic thin films? Does exchange mechanism occur on other fee surfaces in addition to fee (11 l)? This work is intended to answer these questions. The binding energies of kink-site atoms of metals and alloys on stepped surfaces were measured using FIM and time-of-flight atom-probe techniques by Tsong and coworkers [21-231, instead of the traditional temperature programmed thermal desorption method [24]. They also measured the dissociation energy of plane edge atoms and the rate of 2D thermal desorption (layer rearrangement by surface diffusion). From that they estimated the binding energy of single Ir adatoms to Ir(100) terraces [25]. It would be interesting to know the change in the binding energy with distance from the steps. Recent at-
T
a
Fig. 1. Incorporation of adatoms into surface layer during growth of metallic films from the vapor phase. (a) Diffusion of adatoms to descending steps, over the descending steps, and incorporation into kink sites through diffusion of adatoms along the step ledges. (b) Direct incorporation of atoms into the step ledges upon impingement from the vapor. (cl Diffusion of adatoms to ascending steps and incorporation of the adatoms into kink sites through adatom diffusion along the step ledge.
to single adatom diffusion on flat terraces of metal surfaces 16-191. The situation has begun to change. Wang and Ehrlich have reported an investigation of the detailed diffusion behavior of a W adatom at a descending step of Ir clusters on Ir(ll1) using FIM [20]. They found that the W adatom exchanged position with an Ir atom in the descending step and the onset temperature for this exchange diffusion was found to be lower than that for direct jumps over the cluster edge. Recently, Wang and Ehrlich also studied the diffusion behavior of a single Ir adatom near an Ir cluster.
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C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni surfaces
tempts in studying diffusion of single tungsten adatoms along step ledges on tungsten surfaces have been made by Gomer and coworkers using the field-emission fluctuation method [26-281. Different behavior at steps from that on flat terraces was found. They found that atoms can cross (001) oriented steps only with much higher activation energy. Slow diffusion parallel to steps was attributed to kink motion and they believed that motion of different kink configurations could be involved. Slow diffusion perpendicular to steps
was also seen. However, complexity of the experiments made their results uncertain in nature. Another essential approach for resolving the complexities of surface diffusion is to examine theoretically the possible contributory atomic processes. Most of the theoretical studies on metal surfaces [29,301 involved the use of Morse or Lennard-Jones potentials and only diffusion of single adatoms on flat terraces was attempted. The results based on pair potentials are not usually satisfactory. For example, calculations with
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Fig. 3. Schematic diffusion paths and energy barriers for adatom diffusion near type B step on Ni(ll1). (a) Diffusion paths of a single adatom near both descending and ascending steps. (b) Schematic energy barriers for adatom diffusion along diffusion paths. (c) Numerical values of the energy barriers.
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/ Diffusion of single adatoms on Ni surfaces
Morse potentials yielded reasonable values of activation energies for Pt and Rh, but very poor data for Ni [291. However, a recent EAM (embedded atom method) study of surface self-diffusion of single adatoms of seven fee metals [31] showed that the calculated activation energies for Ni using the EAM potentials were in excellent quantitative agreement with FIM experimental
data [153. However, the EAM only yielded qualitative agreement with experiments for Pt and Al [311. The purpose of this work is to carry out a comprehensive theoretical investigation of diffusion behavior of single adatoms near and at steps on Ni surfaces using the EAM and molecular statics (MS). The computational method is briefly
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(cl Fig. 4. Schematic diffusion paths and energy barriers for adatom diffusion near type A step on Ni(ll1). (a) Diffusion paths of a single adatom near both descending and ascending steps. (b) Schematic energy barriers for adatom diffusion along diffusion paths. Cc)Numerical values of the energy barriers.
C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni surfaces
outlined in the next section. In section 3 the results and discussion are presented. A few conclusions will be drawn in the last section.
2. Computational
method
The EAM method developed by Daw and Baskes [32] was utilized to calculate the total energy of an arbitrary arrangements of atoms in a metal. The EAM functions developed by Adams, Foiles and Wolfer (AFW) [33] were used for all the calculations. These functions are nearly identical to the standard ones developed by Foiles et al. [34], but they are fit to more accurate estimates of the vacancy formation energy. The activation energies were computed using molecular statics (MS). Details of the procedure can be found in our previous papers [31,35]. All the atoms in the system were fully relaxed in all three directions. The step ledges on (1111, (1101, and (100) Ni surfaces were running in (110) directions, which are the close-packed directions. In order to avoid the effects of step-step interactions on the results very large computational cells were employed. These cells usually consist of 400 atoms for each layeroand the distance between two steps is about 40 A. Periodic boundary conditions were imposed in the two directions parallel to the free surfaces in the computational cells.
3. Results and discussion 3.1. Diffusion of single adatoms approaching descending and ascending steps on Ni(ll1)
There are two types of steps on Ni(lll), A and B, as illustrated in fig. 2. By their crystallographic orientation, type A step is a (lOO)-step and type B step is a (Ill)-step. We showed earlier that during molecular dynamics simulations (MD) a single adatom migrates on Ni(ll1) through a series of individual jumps between fee and hcp sites [35]. The difference in the binding energy at fee and hcp sites is very small. In order to calculate the energy barrier for adatom diffusion we let the adatom approach the step in the same fashion
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during molecular statics calculations. For each jump the adatom was moved from an fee site to an hcp site or vice versa in fine steps. The energy barrier was obtained from the difference in system’s total energy for an adatom at the saddle point and at the equilibrium ending site on the minimum energy path. We first consider the case where a single adatom diffuses towards the descending steps of type B. The results are shown in fig. 3. Far from the step the adatom behaves quite similarly as it diffuses on a flat terrace. The energy barrier is constant at a value of = 0.056 eV. At a distance of 3 nearest-neighboring spacings from the step, the energy barrier suddenly rises to 0.064 eV. The increase in the energy barrier creates a “forbidden” region near the descending steps. The adatom has to overcome the “extra” energy barrier to get into the “forbidden” region. This is a different picture from the traditional view of adatom incorporation into the steps, in which adatoms are usually thought to travel to the steps in a similar fashion to that far from the step. Once the adatom is within the “forbidden” region, the energy barrier falls slightly below the value on the flat terraces. However, for the jump close to the descending step, i.e., 2 + 1 jump as shown in fig. 3a, the energy barrier rises again. The results of calculations of binding energies showed that the adatom prefers the hcp site (site 2 in fig. 3a) instead of the fee site (site 1 in fig. 3a) at the descending step, since the binding energy at site 2 ( - 3.345 eV) is higher than that at site 1 ( - 3.306 eV). Basically similar behavior was also found for a single adatom approaching ascending steps of type B. The energy barrier rises again to 0.060 eV at a distance of 3 nearest-neighboring spacings from the ascending step. The energy barrier drops dramatically close to the ascending step, i.e., to 0.040 eV for the jump 3 + 2 in fig. 3a. The binding energy at site 3 (-- 3.345 eV) is higher compared to the binding energy to other sites (-3.336 eV) in this case. However, the adatom near the ascending step is not stable at the site one nearest-neighboring spacing from the ascending step and the adatom directly goes to site 1 from site 3 by a single
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C.-L. Liu, J.B. Adams
/ Difjksion of single adatoms on Ni surfaces
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The energy barriers for adatom diffusion near both descending and ascending steps of type A are schematically shown in fig. 3b and actual values for the energy barriers are given in fig. 3c. We will deal with the energy barrier for adatom diffusion over the descending steps later in this paper. Quite similar behavior of adatoms near both descending and ascending steps of type A was found, as shown in fig. 4. The only difference is the magnitude of the energy barriers. The adatom
double jump with lower activation energy, as seen in fig. 3. We found a similar phenomenon for cluster migration on Ni(ll1) in that a single adatom was not stable at the sites one nearestneighboring spacing away from the clusters (even for a dimer), so the small clusters of up to five adatoms on Ni(ll1) migrate in concerted jumps of the entire cluster [36]. Based on these observations, we can see that the local distortion caused by both clusters and steps on Ni(ll1) has allowed multiple jumps for single adatoms.
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C.-L. Liu, J.B. Adams / Dijjksion of single adatoms on Ni surfaces
cannot sit at the site one nearest-neighboring spacing away from the ascending step and the energy barrier for the jump 2 -+ 1 near the astending step is substantially decreased compared to that for adatom diffusion on a flat terrace, i.e., only - 0.022 eV. The energy barrier for adatom
203
to jump into the “forbidden” region is also 0.060 eV near both the ascending and descending steps; in other words, atoms near the step are attracted to it. A schematic of the lateral dispIacements of surface layer atoms near a step is shown in fig. 5.
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Fig. 7. Schematic diffusion paths and energy barriers for a single adatom diffusion near step on Ni(ll0). Two diffusion processes are shown: in-channel (solid line) and cross-channel (dashed line). Details of cross-channel diffusion are further illustrated within the dashed square. In all the cases the energy barriers for cross-channel diffusion are higher than that for in-channel diffusion. At the descending step the adatom exchange diffusion (solid line) is preferred over the direct jump.
204
C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni surfaces
As we can see in fig. 5, the lateral distance between the first two atoms in the first layer close to the descending step decreases and the lateral distance between second and third increases. The lateral distances after that remain close to that on a free surface. On the other hand, near the ascending steps the lateral distances between two atoms extending from second to third nearestneighboring spacings from the steps are all expanded compared to the normal lateral distance without the steps. We noticed that the boundary between the “forbidden” region and the normal surface is also the boundary between the expanded and normal regions near the steps. For adatoms to diffuse into the “forbidden” region they have to jump from a normal surface area outside the “forbidden” region into a less dense area of the “forbidden” region due to expanded lateral distance between atoms. Thus, at the saddle point, the adatom is in a particular low density environment. This presumably causes the slightly higher energy barriers for adatoms to diffuse into the “forbidden” region, Furthermore, it has been known that diffusion on strained surfaces can be enhanced and this point is supported by the lower energy barriers within the “forbidden” region compared to that on a flat surface. Given this, we can understand the diffusion behavior of single adatoms near the steps: Within the “forbidden” region the surface is highly distorted and diffusion on such a surface is enhanced. As shown in fig. 6, the lateral displacements of the atoms that surround the adatoms at sites 3 and 5 near the descending step are different: The two atoms in front of the adatom at site 3 were displaced farther from their original positions both vertically and laterally; while the displacement was smaller for the atoms in front of the adatom at site 5. As a result the adatom at site 5 requires a higher energy to jump straight ahead than that for the adatom at site 3. Remarkably similar phenomena have been observed in FIM experiments by Wang and Ehrlich [37]. At low temperature the Ir adatom stayed away form the Ir cluster on Ir(ll1) during diffusion; at slightly higher temperature incorporation does occur, and the Ir adatom moves from the outer periphery of the plane to the cluster edge
during a single heating interval. The distance of the boundary of the “forbidden” region from the Ir cluster steps was approximately three nearestneighbor spacings. This is exactly the same as we have found on Ni(ll1) near ascending steps. A clear explanation for the FIM observations have not been available from their experiments. However, our computer simulation results indicate that there is a slightly higher energy barrier for adatoms to get into the “forbidden” region, but once the adatoms are within the “forbidden” region adatoms diffuse quickly to the cluster edges due to the reduced energy barriers. This is why in the FIM experiments a single Ir atom was never observed within the “forbidden” region. 3.2. Diffusion descending Ni(lO0)
of single adatorns approaching and ascending steps on Ni(ll0) and
Since Ni(ll0) is a “channelled” surface, diffusion of single adatoms may involve both in-channel diffusion and cross-channel diffusion by an exchange mechanism. During cross-channel diffusion the adatom exchanges position with a wall atom and the wall atom becomes an adatom. Our previous calculations [311 showed that the energy barriers for the exchange cross-channel diffusion were slightly higher than those for in-channel diffusion. In order to compare diffusion behavior near steps with that on flat terraces we calculated the energy barriers for both in-channel and exchange cross-channel diffusion near steps. The results are shown in fig. 7. As we can see, the diffusion behavior of adatoms near both the descending and ascending steps on Ni(ll0) is quite similar to that on the flat terraces. There is no obvious change in the energy barrier for adatom diffusion near steps like that on Ni(ll1). The diffusion barriers are almost constant at the value of 0.41 and 0.49 eV for in-channel and cross-channel diffusion, respectively. Similarly, the binding energy essentially does not change near the steps (-4.09 eV>. We also noticed that the energy barrier for direct cross-channel diffusion, as shown by the jump 2 + 1 in fig. 7, is as high as - 1.30 eV. This value is very close to the energy barrier for adatom to directly jump over a
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C.-L. Liy J.B. Adams / Diffusion of single adatoms on Ni surfaces
tween two rows of channel wall atoms is quite large. The atom rows can actually be considered as “mini-steps”. As we will see later in this paper, diffusion behavior of adatoms along the step ledges also supports this point. Similar results on Ni(100) were found and are
descending step, which is 1.34 eV. From these arguments we conclude that the existence of steps on Ni(ll0) surface basically does not affect diffusion behavior of adatoms. The reason for this is probably due to the fact that Ni(ll0) is an open and channeled surface, where the distance be-
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Fig. 8. Schematic diffusion paths and energy barriers for adatom diffusion near step on Ni(100). In the direction perpendicular to the step the energy barriers near the step decrease slightly, but the magnitude is small compared to the energy barrier on a flat surface. In the direction parallel to the step the energy barriers near the step remain basically same as on a flat surface. There is no “forbidden” region found near the step on Ni(100). Exchange diffusion of adatom at the descending step on Ni(100) was found to be energetically favored over the direct jump.
C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni surfaces
206
shown in fig. 8. Diffusion of single adatoms in the direction parallel to the step ledges is essentially unchanged and is the same as on a perfect surface. However, the energy barriers, for diffusion close to both the descending and the ascending steps in the direction perpendicular to the step ledges, is slightly lower compared to adatom diffusion in the direction parallel to the step ledges and on a flat terrace. But the magnitude of the difference is small. The binding energies near the steps are almost constant at -3.65 eV. 3.3. Exchange mechanism for diffusion of adatoms over descending steps on Ni(ll1)
In our previous study [35] we showed that an adatom at the descending step has to overcome an “extra” potential barrier to directly jump over the descending step before it can incorporate into the step ledge. However, the diffusion process may be more complicated than we thought originally. As Bassett [36] pointed out earlier, an adatom may exchange position with a step atom at the descending step to accomplish the incorporation process. Preliminary results for adatoms at
descending steps on Cu(ll1) also suggested that incorporation may occur by an exchange mechanism [38]. However, direct information was not available until recently when Wang and Ehrlich performed a detailed study of a W adatom diffusing over an Ir cluster edge on Ir(ll1) [20]. At descending steps of type B on both small (12 Ir atoms) and large (33 Ir atoms) clusters, the W adatom exchanged position with an Ir atom in the descending step and the replaced Ir atom was found to be left at the step ledge. They believed that an Ir adatom would behave similarly, but there is no experimental evidence. A schematic of possible diffusion processes at descending steps of type B on Ni(ll1) is shown in fig. 9. Three possible diffusion paths for an adatom to incorporate into a step ledge are illustrated. On path C, the adatom simply jumps over the descending step into the step ledge. On path A, the adatom at site 2 pushes the step atom forward and occupies its position. On path B, the adatom at site 1 exchanges position with a nearby step atom. On both path A and B, the replaced atom then moves into the step ledge. These processes are usually referred to as exchange diffusion, in which the concerted motion of two atoms type on
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Fig. 9. Schematic of diffusion processes at the descending step of type B on Ni(ll1) and the energy barriers of different diffusion paths. The energy barriers for the exchange diffusion processes by path A and B are 0.191 and 0.169 eV, and are lower than that for direct jump (path C, 0.550 eV) by a factor of 3!
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C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni sur$aces is involved and the two atoms involved have exchanged their roles. The energy barriers for exchange diffusion illustrated by paths A and B (0.191 and 0.169 eV, respectively) are lower than that for direct jump over the step (0.550 eV) by a factor of 3! This clearly indicates that exchange diffusion is energetically preferred over the direct jump. To further show that the exchange diffusion is the dominant diffusion mechanism at the descending steps, we consider the binding energies of an adatom to different sites at the steps. The binding energy at site 2 at the descending steps (-3.345 eV) is higher than that at site 1 (- 3.306 eV), implying that the adatoms that approached the descending steps of type B on Ni(ll1) would occupy site 2 more often than they occupy site 1. This further suggests that exchange diffusion is the dominant mechanism for adatom motion across descending steps of type B on fee (111). However, exchange diffusion of adatoms at the descending steps of type A is much more difficult. Although the binding energy at site 2 (-3.345 eV) is still higher than that at site 1 (- 3.305 eV), exchange diffusion, through push-
ing the step atom at site 2, is unlikely since another atom in front of the step atom blocks its path. Three possible diffusion processes at the descending step of type A on Ni(ll1) are shown in fig. 10. On path A, the adatom simply jumps over the descending step into the step ledge. On path B, the adatom at site 1 pushes the nearby step atom and occupies its position. On path C, the adatom at site 2 replaces the position of a step atom. The energy barriers for paths A, B, and C are 0.550, 0.550, and 0.587 eV, respectively. Therefore, the paths are almost equally likely, which is quite different from the case for adatom diffusion across type B steps. Our results are quite consistent with Wang and Ehrlich’s observations for W adatom diffusion at Ir cluster edges on Ir(ll1). However, we further demonstrated here that the exchange diffusion can also occur for homogeneous diffusion during epitaxial growth of metallic thin films. Due to detailed atomic arrangements at the descending steps, exchange diffusion only occurs at the descending steps of type B, not type A, on NKlll). This may explain the triangle islands with type A steps (the (lOO)-steps) on Pt(ll1)
type
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of diffusion processes at the descending step of type A on Ni(ll1) and the energy barriers of different diffusion harriers for the three possible diffusion processes by path A, B and C are 0.550, 0.550 and 0.587 eV, respectively, i.e. almost the same value of - 0.55 eV. No preference for exchange diffusion was found.
C.-L. Liu, J.B. Adam
208
/ Diffusion of single adatoms on Ni surfaces
during homoepitaxial growth at moderate temperature due to a faster growth of type B steps (the (Ill&steps), observed by Comsa [39]. 3.4. Exchange mechanism for adatom diffusion over descending steps on Ni(ll0) and Ni(100) Exchange mechanisms for adatom diffusion at the descending steps on Ni(ll0) and Ni(100) were also investigated. The results are shown in figs. 11 and 12 for adatom diffusion at the descending steps on Ni(l10) and Ni(lOO), respectively. As we see in fig. 11, at_the descending steps on Ni(llO), there are two possible diffusion paths for adatom diffusion over the descending steps: Direct jump and exchange diffusion by replacing a neighboring substrate atom in the step. The energy barriers calculated as shown in fig. 11 indicate that exchange diffusion is energetically favored over direct jump, although the difference in the energy barriers is small. It is not surprising that the exchange diffusion is also favored on Ni(100) since the atomic arrangements at the descending steps on Ni(ll0) and NKlOO) are quite similar, as seen in fig. 12. The energy barrier for exchange diffusion on Ni(100) is lower than that for direct jump by 0.06 eV, the same amount for the difference in the energy barriers on NKllO).
To our best knowledge this is the first time that exchange mechanism for adatom diffusion at the descending steps on fee (110) and (100) is reported to be energetically favored. The reason for this can be easily seen by examining the atomic arrangements at the descending steps on the surfaces. If the adatom jumps from the binding site (site 1) over the step, a lower terrace atom in front of the adatom is sitting in the pathway for diffusion. The adatom is more likely to sneak over the step along a path with open gap in the step, as demonstrated in figs. 11 and 12 by the long arrows. Alternatively, if the adatom pushes one of the nearby underneath atoms in the step, the pushed atom can jump over the step through the open gap at the step. The distortion due to the relaxation by the adatom at the step may also make the exchange diffusion easier. It is also obvious that diffusion distance by the exchange mechanism is shorter compared to that for direct jump. Another important result from diffusion of adatoms at the descending steps is that the energy barriers for adatoms to diffuse over the descending steps, either by direct jump or exchange diffusion, are much higher than those for adatom diffusion on a flat surface. This is true for all the surfaces we studied. This may have signifi-
Step
0
0 0
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0 8
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8)
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of diffusion
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lower terrace step on Ni(ll0). Exchange diffusion (1.28 eV) at the descending favored over direct jump (1.34 eV).
step on
C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni surfaces
step
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Fig. 12. Schematic of diffusion processes at the descending step on Ni(100). We noticed that the atomic arrangement at the descending step on Ni(100) is quite similar to that on Ni(ll0). It is not surprising that exchange diffusion (0.85 eV) is also favored over direct jump (0.91 eV).
cant effects on growth of metallic thin films. The adatoms approaching descending steps during growth can be reflected back due to much higher energy barriers for them to get over the steps. This result is consistent with early FIM experiments [40]. Eaglesham [41] found that during growth of epitaxial layers of Si at low temperatures the surface roughness increases as the film thickness increases. It was believed that this is due to the higher energy barrier for adatoms to incorporate into the descending steps. Similar results were found in a Monte Carlo simulation of film growth [l].
4. Conclusions (1) Diffusion behavior of single adatoms approaching descending and ascending steps of both type A and B on NXlll) changes at a distance of approximately 2 to 3 nearest-neighboring spacings from the steps. A slightly higher energy (0.060-0.064 eV> compared to diffusion on a perfect surface far from the steps (0.056 eV) is required for adatoms to further reach the steps to get into the “forbidden” region. Once the
adatoms are in the “forbidden” region, the energy barriers for adatom diffusion actually decrease, and the nearest-neighboring positions are actually unstable. The physical origin for the existence of the “forbidden” region is the step-induced strain field near the steps and the resulting elastic interactions between steps and adatoms are responsible for the increase in the energy barriers for adatom diffusion near steps. (2) Diffusion behavior of single adatoms approaching descending and ascending steps on Ni(ll0) and NXlOO) surfaces is essentially similar to that on the corresponding flat terraces. No “forbidden” region was found. (3) Exchange diffusion for adatoms over the descending steps of type B on NKlll) was found to be energetically favored over direct jumps. The energy barriers for two exchange diffusion processes (0.191 and 0.169 eV> are lower than that for direct jump (0.550 eV) by a factor of - 3. However, such an exchange is not favored at type A steps on fee (111). This is exactly what Wang and Ehrlich found out in a recent FIM experiment [20], in which they found a W adatom at the Ir cluster edge of type B on Ir(ll1) exchanged position with an Ir adatom in the cluster edge,
210
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/ Diffusion of single adatoms on Ni surfaces
although the exact exchange mechanism was not clear at that time, but exchange did not occur at type A steps. (4) Diffusion at descending steps on Ni(ll0) and NKlOO) surfaces has been studied for the first time, and exchange diffusion has been found to be slightly favored over direct jumps. The energy barriers for exchange diffusion at descending steps on Ni(ll0) and Ni(100) are 1.280 and 0.850 eV; while the energy barriers for direct jumps are 1.340 and 0.910 eV, respectively. There is no experimental information available to compare with our predictions.
Acknowledgements
We gratefully acknowledge the financial support from the Department of Energy, Basic Energy Science, through the Materials Research Laboratory at the University of Illinois under grant DE-A(O)-76 ER01198. We wish to thank the National Center for Supercomputing Applications for providing time on their CRAY-YMP. We also wish to thank G. Ehrlich and S.C. Wang for sharing their latest FIM results with us before publication. Finally, we thank S. Foiles, M. Daw, and M. Baskes for sharing the EAM codes with us.
References
111E.
Chason and B.W. Dodson, J. Vat. Sci. Technol. A 9 (1991) 1545. 121R. Kunkel, B. Poelsema, L.K. Verheij and G. Comsa, Phys. Rev. Lett. 65 (1990) 733. R. Kunkel, L.K. Verheij and G. Comsa, [31 B. Poelsema, Phys. Rev. B 41 (1990) 11609. [41 T. Michely, K.H. Besocke and G. Comsa, Surf. Sci. Lett. 230 (1990) L135. University Munich, [51 H.W. Fink, PhD Thesis, Technical 1989. [61 G. Ehrhch and F.G. Hudda, J. Chem. Phys. 44 (1966) 1309.
[7] D.W. Bassett and M.J. Parsely, J. Phys. D (Appl. Phys.) 2 (1969) 13. [8] W.R. Graham and G. Ehrlich, Surf. Sci. 45 (1974) 530. [9] W.R. Graham and G. Ehrlich, Thin Solid Films 25 (1975) 85. [lo] T.T. Tsong, P.L. Cowan and G.L. Kellogg, Thin Solid Films 25 (1975) 97. [ll] P.L. Cowan and T.T. Tsong, Phys. Lett. A 53 (1975) 383. [12] G. Ayraut and G. Ehrlich, J. Chem. Phys. 60 (1974) 281. 1131 D.W. Bassett and P.R. Webber, Surf. Sci. 70 (1978) 520. 1141 D.W. Bassett, J. Phys. C (Solid State Phys.) 9 (1976) 2491. [15] T.T. Tung and W.R. Graham, Surf. Sci. 97 (1980) 73. [16] T.T. Tsong and G.L. Kellogg, Phys. Rev. B 12 (1975) 1343. [17] D.A. Reed and G. Ehrlich, Philos. Mag. 32 (1975) 1095. [18] S.C. Wang and G. Ehrlich, Phys. Rev. Lett. 62 (1989) 2297. [19] S.C. Wang and G. Ehrlich, Surf. Sci. 224 (1989) L997. [20] S.C. Wang and G. Ehrlich, Phys. Rev. Lett. 67 (1991) 2509. [21] J. Liu, C.W. Wu and T.T. Tsong, Phys. Rev. B 43 (1991) 11595. 1221T.T. Tsong, Surf. Sci. 231 (1990) 81. 1231T.T. Tsong, Phys. Rev. B 30 (1984) 4946. [241 C. Chen and T.T. Tsong, Phys. Rev. B 41 (1990) 12403. 1251B. Taylor and I. Langmuir, Phys. Rev. 44 (1933) 4236. 1261D.S. Choi, SK. Kim and R. Gomer, Surf. Sci. 234 (1990) 262. D71 Y.M. Gong and R. Gomer, J. Chem. Phys. 88 (1988) 1359. 1281Y.M. Gong and R. Gomer, J. Chem. Phys. 88 (1988) 1370. 1291P.G. Flahive and W.R. Graham, Surf. Sci. 91 (1980) 449. [301 A.F. Voter, Phys. Rev. B 34 (1986) 6819. 1311 C.L. Liu, J.M. Cohen, J.B. Adams and A.F. Voter, Surf. Sci. 253 (1991) 334. 1321M.S. Daw and M.I. Baskes, Phys. Rev. Lctt. 50 (1983) 1285. [331J.B. Adams, S.M. Foiles and W.G. Wolfer, J. Mater. Res. 4 (1989) 102. [341S.M. Foiles, M.I. Baskes and MS. Daw, Phys. Rev. B 33 (1986) 7983. [351C.-L. Liu and James B. Adams, Surf. Sci. 265 (1992) 262. [361D.W. Bassett, in: Surface Mobilities on Solid Materials, Ed. V.T. Binh (Plenum, New York, 1983) p. 63. [371S.C. Wang and G. Ehrlich, to be published. on Self-diffusion at Metal Sur1381J.K. Norskov, Workshop faces, Copenhagen, April 1991. [391G. Comsa, 39th AVS meeting, Chicago, 1992. [401C.-L. Liu and James B. Adams, Surf. Sci. 294 (1993) 211. AT&T Bell Laboratories, private com[411D.J. Eaglesham, munication.
.,...,.,... :.*:::::::*.::::y::.::::zy:: :.:.:,..._ .i..n :.:.: ........:.:.: ....:, :.:.: :.:.: :.::::,_::: :.::sj: . . . .. . . . ..i........:.:.:
.~.:‘:‘.w+.:.:.:.~.:.:.:.:
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Surface Science 294 (1993) 197-210 North-Holland
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Diffusion behavior of single adatoms near and at steps during growth of metallic thin films on Ni surfaces Chun-Li
Liu ’ and James B. Adams
Department
of Materials Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801, USA
Received 19 January 1993; accepted for publication 4 May 1993
Diffusion of single adatoms approaching both descending and ascending steps on Ni(lll), (110) and (100) has been investigated with the embedded atom method (EAM) and molecular statics (MS). (1) It was found that there exists a “forbidden” region near both descending and ascending steps on Ni(ll1). Adatoms have to overcome a slightly higher energy barrier to get into the “forbidden” region, which extends 2-3 nearest-neighboring spacings from the steps. This is consistent with FIM experiments for incorporation of Ir adatoms into ascending steps of Ir clusters. (2) Detailed calculations for incorporation of adatoms over descending steps of type B on Ni(ll1) have revealed that exchange diffusion, in which an adatom replaces the position of an atom in the step and exchange their roles, is energetically favored over ordinary jumps and is the dominant diffusion mechanism at the descending steps. This is consistent with recent FIM experiments of W adatom diffusion at Ir cluster edges of type B on Ir(111). (3) Exchange diffusion was also found to be favored over direct jumps at the descending steps on Ni(ll0) and Ni(100).
1. Introduction Diffusion behavior of single adatoms near and at atomic steps is crucial for understanding physical and chemical processes occurring on surfaces during growth of thin films. It has been shown that limited migration across descending steps can change surface morphology dramatically during crystal growth from the vapor [l]. Adatom diffusion across steps was considered to play a vital role in annealing of surface defects during ion bombardment of metallic surfaces [2-41. It is also especially important for low temperature growth of thin films or growth of superlattice structures when a high density of steps is desired and thermal energies of diffusing elements are low. Understanding atomic events near and at steps can greatly enhance our knowledge of the insights into these phenomena. Also, the study of diffusion behavior of single adatoms is of substantial fundamental interest in materials science * Present address: Solid State Division, Oak Ridge National Lab, Oak Ridge, TN 37831, USA. 0039-6028/93/$06.00
since surface diffusion is very sensitive to the structure of a surface and its defects, and is of great significance in developing mass transport theory. Incorporation of single adatoms into step ledges from the vapor phase can be accomplished in several ways: (1) direct incorporation of atoms into step ledges upon impingement from the vapor phase; (2) diffusion of adatoms to ascending steps and incorporation into kink sites through diffusion of adatoms along the step ledges; (3) diffusion of adatoms to descending steps, over the descending steps, and incorporation into kink sites through diffusion of adatom along the step ledges. A schematic of these processes is shown in fig. 1. The incorporation of adatoms at ascending steps on impact has been observed experimentally using a field ion microscope (FIM) [5]. However, incorporation of adatoms into ascending and descending steps is far from being well understood, simply because of experimental difficulties and the lack of reliable theoretical models. Although FIM has been extensively used to study surface diffusion, most experiments were limited
0 1993 - Elsevier Science Publishers B.V. All rights reserved
C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni surfaces
198
b
They found that the Ir adatom wandered around the Ir cluster, staying at N 3 nearest-neighboring spacings away from the cluster edges, until it finally jumped into the cluster ledge. These results have raised some questions: Do these phenomena occur near and at steps, which are quite similar to cluster edges? Does a similar phenomenon of an adatom’s wandering near ascending steps also occur near descending steps? What is the physical origin for such behavior? Does exchange diffusion also occur for homogeneous diffusion during epitaxial growth of metallic thin films? Does exchange mechanism occur on other fee surfaces in addition to fee (11 l)? This work is intended to answer these questions. The binding energies of kink-site atoms of metals and alloys on stepped surfaces were measured using FIM and time-of-flight atom-probe techniques by Tsong and coworkers [21-231, instead of the traditional temperature programmed thermal desorption method [24]. They also measured the dissociation energy of plane edge atoms and the rate of 2D thermal desorption (layer rearrangement by surface diffusion). From that they estimated the binding energy of single Ir adatoms to Ir(100) terraces [25]. It would be interesting to know the change in the binding energy with distance from the steps. Recent at-
T
a
Fig. 1. Incorporation of adatoms into surface layer during growth of metallic films from the vapor phase. (a) Diffusion of adatoms to descending steps, over the descending steps, and incorporation into kink sites through diffusion of adatoms along the step ledges. (b) Direct incorporation of atoms into the step ledges upon impingement from the vapor. (cl Diffusion of adatoms to ascending steps and incorporation of the adatoms into kink sites through adatom diffusion along the step ledge.
to single adatom diffusion on flat terraces of metal surfaces 16-191. The situation has begun to change. Wang and Ehrlich have reported an investigation of the detailed diffusion behavior of a W adatom at a descending step of Ir clusters on Ir(ll1) using FIM [20]. They found that the W adatom exchanged position with an Ir atom in the descending step and the onset temperature for this exchange diffusion was found to be lower than that for direct jumps over the cluster edge. Recently, Wang and Ehrlich also studied the diffusion behavior of a single Ir adatom near an Ir cluster.
type A step
type B step
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199
C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni surfaces
tempts in studying diffusion of single tungsten adatoms along step ledges on tungsten surfaces have been made by Gomer and coworkers using the field-emission fluctuation method [26-281. Different behavior at steps from that on flat terraces was found. They found that atoms can cross (001) oriented steps only with much higher activation energy. Slow diffusion parallel to steps was attributed to kink motion and they believed that motion of different kink configurations could be involved. Slow diffusion perpendicular to steps
was also seen. However, complexity of the experiments made their results uncertain in nature. Another essential approach for resolving the complexities of surface diffusion is to examine theoretically the possible contributory atomic processes. Most of the theoretical studies on metal surfaces [29,301 involved the use of Morse or Lennard-Jones potentials and only diffusion of single adatoms on flat terraces was attempted. The results based on pair potentials are not usually satisfactory. For example, calculations with
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Fig. 3. Schematic diffusion paths and energy barriers for adatom diffusion near type B step on Ni(ll1). (a) Diffusion paths of a single adatom near both descending and ascending steps. (b) Schematic energy barriers for adatom diffusion along diffusion paths. (c) Numerical values of the energy barriers.
200
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/ Diffusion of single adatoms on Ni surfaces
Morse potentials yielded reasonable values of activation energies for Pt and Rh, but very poor data for Ni [291. However, a recent EAM (embedded atom method) study of surface self-diffusion of single adatoms of seven fee metals [31] showed that the calculated activation energies for Ni using the EAM potentials were in excellent quantitative agreement with FIM experimental
data [153. However, the EAM only yielded qualitative agreement with experiments for Pt and Al [311. The purpose of this work is to carry out a comprehensive theoretical investigation of diffusion behavior of single adatoms near and at steps on Ni surfaces using the EAM and molecular statics (MS). The computational method is briefly
type
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(cl Fig. 4. Schematic diffusion paths and energy barriers for adatom diffusion near type A step on Ni(ll1). (a) Diffusion paths of a single adatom near both descending and ascending steps. (b) Schematic energy barriers for adatom diffusion along diffusion paths. Cc)Numerical values of the energy barriers.
C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni surfaces
outlined in the next section. In section 3 the results and discussion are presented. A few conclusions will be drawn in the last section.
2. Computational
method
The EAM method developed by Daw and Baskes [32] was utilized to calculate the total energy of an arbitrary arrangements of atoms in a metal. The EAM functions developed by Adams, Foiles and Wolfer (AFW) [33] were used for all the calculations. These functions are nearly identical to the standard ones developed by Foiles et al. [34], but they are fit to more accurate estimates of the vacancy formation energy. The activation energies were computed using molecular statics (MS). Details of the procedure can be found in our previous papers [31,35]. All the atoms in the system were fully relaxed in all three directions. The step ledges on (1111, (1101, and (100) Ni surfaces were running in (110) directions, which are the close-packed directions. In order to avoid the effects of step-step interactions on the results very large computational cells were employed. These cells usually consist of 400 atoms for each layeroand the distance between two steps is about 40 A. Periodic boundary conditions were imposed in the two directions parallel to the free surfaces in the computational cells.
3. Results and discussion 3.1. Diffusion of single adatoms approaching descending and ascending steps on Ni(ll1)
There are two types of steps on Ni(lll), A and B, as illustrated in fig. 2. By their crystallographic orientation, type A step is a (lOO)-step and type B step is a (Ill)-step. We showed earlier that during molecular dynamics simulations (MD) a single adatom migrates on Ni(ll1) through a series of individual jumps between fee and hcp sites [35]. The difference in the binding energy at fee and hcp sites is very small. In order to calculate the energy barrier for adatom diffusion we let the adatom approach the step in the same fashion
201
during molecular statics calculations. For each jump the adatom was moved from an fee site to an hcp site or vice versa in fine steps. The energy barrier was obtained from the difference in system’s total energy for an adatom at the saddle point and at the equilibrium ending site on the minimum energy path. We first consider the case where a single adatom diffuses towards the descending steps of type B. The results are shown in fig. 3. Far from the step the adatom behaves quite similarly as it diffuses on a flat terrace. The energy barrier is constant at a value of = 0.056 eV. At a distance of 3 nearest-neighboring spacings from the step, the energy barrier suddenly rises to 0.064 eV. The increase in the energy barrier creates a “forbidden” region near the descending steps. The adatom has to overcome the “extra” energy barrier to get into the “forbidden” region. This is a different picture from the traditional view of adatom incorporation into the steps, in which adatoms are usually thought to travel to the steps in a similar fashion to that far from the step. Once the adatom is within the “forbidden” region, the energy barrier falls slightly below the value on the flat terraces. However, for the jump close to the descending step, i.e., 2 + 1 jump as shown in fig. 3a, the energy barrier rises again. The results of calculations of binding energies showed that the adatom prefers the hcp site (site 2 in fig. 3a) instead of the fee site (site 1 in fig. 3a) at the descending step, since the binding energy at site 2 ( - 3.345 eV) is higher than that at site 1 ( - 3.306 eV). Basically similar behavior was also found for a single adatom approaching ascending steps of type B. The energy barrier rises again to 0.060 eV at a distance of 3 nearest-neighboring spacings from the ascending step. The energy barrier drops dramatically close to the ascending step, i.e., to 0.040 eV for the jump 3 + 2 in fig. 3a. The binding energy at site 3 (-- 3.345 eV) is higher compared to the binding energy to other sites (-3.336 eV) in this case. However, the adatom near the ascending step is not stable at the site one nearest-neighboring spacing from the ascending step and the adatom directly goes to site 1 from site 3 by a single
202
C.-L. Liu, J.B. Adams
/ Difjksion of single adatoms on Ni surfaces
Type
B step
on Ni(ll1)
contracted /
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,,.,a9 u
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u
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contracted normal Fig. 5. Schematic of the lateral displacement between surface layer atoms near steps and adatom diffusion into the “forbidden” region. The numbers are the percentage of the lateral displacements near a step relative to the normal displacements on a free surface. For adatom diffusion into the “forbidden” region it is actually diffusing from a denser into a less dense environment, which raises the saddle point energy.
The energy barriers for adatom diffusion near both descending and ascending steps of type A are schematically shown in fig. 3b and actual values for the energy barriers are given in fig. 3c. We will deal with the energy barrier for adatom diffusion over the descending steps later in this paper. Quite similar behavior of adatoms near both descending and ascending steps of type A was found, as shown in fig. 4. The only difference is the magnitude of the energy barriers. The adatom
double jump with lower activation energy, as seen in fig. 3. We found a similar phenomenon for cluster migration on Ni(ll1) in that a single adatom was not stable at the sites one nearestneighboring spacing away from the clusters (even for a dimer), so the small clusters of up to five adatoms on Ni(ll1) migrate in concerted jumps of the entire cluster [36]. Based on these observations, we can see that the local distortion caused by both clusters and steps on Ni(ll1) has allowed multiple jumps for single adatoms.
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Fig. 6. Top view of lateral displacements of atoms surrounding the adatoms at sites 3 and 5 near the descending step of type B. The magnitudes of the displacements are exaggerated to show adatom motion. The lateral displacements are quite similar for adatoms at sites 3 and 5, but the magnitude is different. Similar phenomena were found near the ascending step of type B and both descending and ascending steps of type A.
C.-L. Liu, J.B. Adams / Dijjksion of single adatoms on Ni surfaces
cannot sit at the site one nearest-neighboring spacing away from the ascending step and the energy barrier for the jump 2 -+ 1 near the astending step is substantially decreased compared to that for adatom diffusion on a flat terrace, i.e., only - 0.022 eV. The energy barrier for adatom
203
to jump into the “forbidden” region is also 0.060 eV near both the ascending and descending steps; in other words, atoms near the step are attracted to it. A schematic of the lateral dispIacements of surface layer atoms near a step is shown in fig. 5.
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Fig. 7. Schematic diffusion paths and energy barriers for a single adatom diffusion near step on Ni(ll0). Two diffusion processes are shown: in-channel (solid line) and cross-channel (dashed line). Details of cross-channel diffusion are further illustrated within the dashed square. In all the cases the energy barriers for cross-channel diffusion are higher than that for in-channel diffusion. At the descending step the adatom exchange diffusion (solid line) is preferred over the direct jump.
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C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni surfaces
As we can see in fig. 5, the lateral distance between the first two atoms in the first layer close to the descending step decreases and the lateral distance between second and third increases. The lateral distances after that remain close to that on a free surface. On the other hand, near the ascending steps the lateral distances between two atoms extending from second to third nearestneighboring spacings from the steps are all expanded compared to the normal lateral distance without the steps. We noticed that the boundary between the “forbidden” region and the normal surface is also the boundary between the expanded and normal regions near the steps. For adatoms to diffuse into the “forbidden” region they have to jump from a normal surface area outside the “forbidden” region into a less dense area of the “forbidden” region due to expanded lateral distance between atoms. Thus, at the saddle point, the adatom is in a particular low density environment. This presumably causes the slightly higher energy barriers for adatoms to diffuse into the “forbidden” region, Furthermore, it has been known that diffusion on strained surfaces can be enhanced and this point is supported by the lower energy barriers within the “forbidden” region compared to that on a flat surface. Given this, we can understand the diffusion behavior of single adatoms near the steps: Within the “forbidden” region the surface is highly distorted and diffusion on such a surface is enhanced. As shown in fig. 6, the lateral displacements of the atoms that surround the adatoms at sites 3 and 5 near the descending step are different: The two atoms in front of the adatom at site 3 were displaced farther from their original positions both vertically and laterally; while the displacement was smaller for the atoms in front of the adatom at site 5. As a result the adatom at site 5 requires a higher energy to jump straight ahead than that for the adatom at site 3. Remarkably similar phenomena have been observed in FIM experiments by Wang and Ehrlich [37]. At low temperature the Ir adatom stayed away form the Ir cluster on Ir(ll1) during diffusion; at slightly higher temperature incorporation does occur, and the Ir adatom moves from the outer periphery of the plane to the cluster edge
during a single heating interval. The distance of the boundary of the “forbidden” region from the Ir cluster steps was approximately three nearestneighbor spacings. This is exactly the same as we have found on Ni(ll1) near ascending steps. A clear explanation for the FIM observations have not been available from their experiments. However, our computer simulation results indicate that there is a slightly higher energy barrier for adatoms to get into the “forbidden” region, but once the adatoms are within the “forbidden” region adatoms diffuse quickly to the cluster edges due to the reduced energy barriers. This is why in the FIM experiments a single Ir atom was never observed within the “forbidden” region. 3.2. Diffusion descending Ni(lO0)
of single adatorns approaching and ascending steps on Ni(ll0) and
Since Ni(ll0) is a “channelled” surface, diffusion of single adatoms may involve both in-channel diffusion and cross-channel diffusion by an exchange mechanism. During cross-channel diffusion the adatom exchanges position with a wall atom and the wall atom becomes an adatom. Our previous calculations [311 showed that the energy barriers for the exchange cross-channel diffusion were slightly higher than those for in-channel diffusion. In order to compare diffusion behavior near steps with that on flat terraces we calculated the energy barriers for both in-channel and exchange cross-channel diffusion near steps. The results are shown in fig. 7. As we can see, the diffusion behavior of adatoms near both the descending and ascending steps on Ni(ll0) is quite similar to that on the flat terraces. There is no obvious change in the energy barrier for adatom diffusion near steps like that on Ni(ll1). The diffusion barriers are almost constant at the value of 0.41 and 0.49 eV for in-channel and cross-channel diffusion, respectively. Similarly, the binding energy essentially does not change near the steps (-4.09 eV>. We also noticed that the energy barrier for direct cross-channel diffusion, as shown by the jump 2 + 1 in fig. 7, is as high as - 1.30 eV. This value is very close to the energy barrier for adatom to directly jump over a
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tween two rows of channel wall atoms is quite large. The atom rows can actually be considered as “mini-steps”. As we will see later in this paper, diffusion behavior of adatoms along the step ledges also supports this point. Similar results on Ni(100) were found and are
descending step, which is 1.34 eV. From these arguments we conclude that the existence of steps on Ni(ll0) surface basically does not affect diffusion behavior of adatoms. The reason for this is probably due to the fact that Ni(ll0) is an open and channeled surface, where the distance be-
step on NitlOO)
4B
00
(II)
8
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0 0
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0
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0
8
8
8
8
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8
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(b)
Fig. 8. Schematic diffusion paths and energy barriers for adatom diffusion near step on Ni(100). In the direction perpendicular to the step the energy barriers near the step decrease slightly, but the magnitude is small compared to the energy barrier on a flat surface. In the direction parallel to the step the energy barriers near the step remain basically same as on a flat surface. There is no “forbidden” region found near the step on Ni(100). Exchange diffusion of adatom at the descending step on Ni(100) was found to be energetically favored over the direct jump.
C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni surfaces
206
shown in fig. 8. Diffusion of single adatoms in the direction parallel to the step ledges is essentially unchanged and is the same as on a perfect surface. However, the energy barriers, for diffusion close to both the descending and the ascending steps in the direction perpendicular to the step ledges, is slightly lower compared to adatom diffusion in the direction parallel to the step ledges and on a flat terrace. But the magnitude of the difference is small. The binding energies near the steps are almost constant at -3.65 eV. 3.3. Exchange mechanism for diffusion of adatoms over descending steps on Ni(ll1)
In our previous study [35] we showed that an adatom at the descending step has to overcome an “extra” potential barrier to directly jump over the descending step before it can incorporate into the step ledge. However, the diffusion process may be more complicated than we thought originally. As Bassett [36] pointed out earlier, an adatom may exchange position with a step atom at the descending step to accomplish the incorporation process. Preliminary results for adatoms at
descending steps on Cu(ll1) also suggested that incorporation may occur by an exchange mechanism [38]. However, direct information was not available until recently when Wang and Ehrlich performed a detailed study of a W adatom diffusing over an Ir cluster edge on Ir(ll1) [20]. At descending steps of type B on both small (12 Ir atoms) and large (33 Ir atoms) clusters, the W adatom exchanged position with an Ir atom in the descending step and the replaced Ir atom was found to be left at the step ledge. They believed that an Ir adatom would behave similarly, but there is no experimental evidence. A schematic of possible diffusion processes at descending steps of type B on Ni(ll1) is shown in fig. 9. Three possible diffusion paths for an adatom to incorporate into a step ledge are illustrated. On path C, the adatom simply jumps over the descending step into the step ledge. On path A, the adatom at site 2 pushes the step atom forward and occupies its position. On path B, the adatom at site 1 exchanges position with a nearby step atom. On both path A and B, the replaced atom then moves into the step ledge. These processes are usually referred to as exchange diffusion, in which the concerted motion of two atoms type on
0
8
B step Ni(lll) 0
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69
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Fig. 9. Schematic of diffusion processes at the descending step of type B on Ni(ll1) and the energy barriers of different diffusion paths. The energy barriers for the exchange diffusion processes by path A and B are 0.191 and 0.169 eV, and are lower than that for direct jump (path C, 0.550 eV) by a factor of 3!
207
C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni sur$aces is involved and the two atoms involved have exchanged their roles. The energy barriers for exchange diffusion illustrated by paths A and B (0.191 and 0.169 eV, respectively) are lower than that for direct jump over the step (0.550 eV) by a factor of 3! This clearly indicates that exchange diffusion is energetically preferred over the direct jump. To further show that the exchange diffusion is the dominant diffusion mechanism at the descending steps, we consider the binding energies of an adatom to different sites at the steps. The binding energy at site 2 at the descending steps (-3.345 eV) is higher than that at site 1 (- 3.306 eV), implying that the adatoms that approached the descending steps of type B on Ni(ll1) would occupy site 2 more often than they occupy site 1. This further suggests that exchange diffusion is the dominant mechanism for adatom motion across descending steps of type B on fee (111). However, exchange diffusion of adatoms at the descending steps of type A is much more difficult. Although the binding energy at site 2 (-3.345 eV) is still higher than that at site 1 (- 3.305 eV), exchange diffusion, through push-
ing the step atom at site 2, is unlikely since another atom in front of the step atom blocks its path. Three possible diffusion processes at the descending step of type A on Ni(ll1) are shown in fig. 10. On path A, the adatom simply jumps over the descending step into the step ledge. On path B, the adatom at site 1 pushes the nearby step atom and occupies its position. On path C, the adatom at site 2 replaces the position of a step atom. The energy barriers for paths A, B, and C are 0.550, 0.550, and 0.587 eV, respectively. Therefore, the paths are almost equally likely, which is quite different from the case for adatom diffusion across type B steps. Our results are quite consistent with Wang and Ehrlich’s observations for W adatom diffusion at Ir cluster edges on Ir(ll1). However, we further demonstrated here that the exchange diffusion can also occur for homogeneous diffusion during epitaxial growth of metallic thin films. Due to detailed atomic arrangements at the descending steps, exchange diffusion only occurs at the descending steps of type B, not type A, on NKlll). This may explain the triangle islands with type A steps (the (lOO)-steps) on Pt(ll1)
type
8
@?3 0
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Q
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@
0 B
9
0 @
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higher Fig. 10. Schematic paths. The energy
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of diffusion processes at the descending step of type A on Ni(ll1) and the energy barriers of different diffusion harriers for the three possible diffusion processes by path A, B and C are 0.550, 0.550 and 0.587 eV, respectively, i.e. almost the same value of - 0.55 eV. No preference for exchange diffusion was found.
C.-L. Liu, J.B. Adam
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/ Diffusion of single adatoms on Ni surfaces
during homoepitaxial growth at moderate temperature due to a faster growth of type B steps (the (Ill&steps), observed by Comsa [39]. 3.4. Exchange mechanism for adatom diffusion over descending steps on Ni(ll0) and Ni(100) Exchange mechanisms for adatom diffusion at the descending steps on Ni(ll0) and Ni(100) were also investigated. The results are shown in figs. 11 and 12 for adatom diffusion at the descending steps on Ni(l10) and Ni(lOO), respectively. As we see in fig. 11, at_the descending steps on Ni(llO), there are two possible diffusion paths for adatom diffusion over the descending steps: Direct jump and exchange diffusion by replacing a neighboring substrate atom in the step. The energy barriers calculated as shown in fig. 11 indicate that exchange diffusion is energetically favored over direct jump, although the difference in the energy barriers is small. It is not surprising that the exchange diffusion is also favored on Ni(100) since the atomic arrangements at the descending steps on Ni(ll0) and NKlOO) are quite similar, as seen in fig. 12. The energy barrier for exchange diffusion on Ni(100) is lower than that for direct jump by 0.06 eV, the same amount for the difference in the energy barriers on NKllO).
To our best knowledge this is the first time that exchange mechanism for adatom diffusion at the descending steps on fee (110) and (100) is reported to be energetically favored. The reason for this can be easily seen by examining the atomic arrangements at the descending steps on the surfaces. If the adatom jumps from the binding site (site 1) over the step, a lower terrace atom in front of the adatom is sitting in the pathway for diffusion. The adatom is more likely to sneak over the step along a path with open gap in the step, as demonstrated in figs. 11 and 12 by the long arrows. Alternatively, if the adatom pushes one of the nearby underneath atoms in the step, the pushed atom can jump over the step through the open gap at the step. The distortion due to the relaxation by the adatom at the step may also make the exchange diffusion easier. It is also obvious that diffusion distance by the exchange mechanism is shorter compared to that for direct jump. Another important result from diffusion of adatoms at the descending steps is that the energy barriers for adatoms to diffuse over the descending steps, either by direct jump or exchange diffusion, are much higher than those for adatom diffusion on a flat surface. This is true for all the surfaces we studied. This may have signifi-
Step
0
0 0
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0 8
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0 0 8 0
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8)
higher Fig. 11. Schematic
of diffusion
@ 0
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o
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processes at the descending Ni(ll0) is energetically
lower terrace step on Ni(ll0). Exchange diffusion (1.28 eV) at the descending favored over direct jump (1.34 eV).
step on
C.-L. Liu, J.B. Adams / Diffusion of single adatoms on Ni surfaces
step
@
@ 0
*
@ 0
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209
Ni(100)
0000000 exchange diffusion 0~0000000 0000000 direct jump 0000000 0000000 0000000
Q9r +
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Fig. 12. Schematic of diffusion processes at the descending step on Ni(100). We noticed that the atomic arrangement at the descending step on Ni(100) is quite similar to that on Ni(ll0). It is not surprising that exchange diffusion (0.85 eV) is also favored over direct jump (0.91 eV).
cant effects on growth of metallic thin films. The adatoms approaching descending steps during growth can be reflected back due to much higher energy barriers for them to get over the steps. This result is consistent with early FIM experiments [40]. Eaglesham [41] found that during growth of epitaxial layers of Si at low temperatures the surface roughness increases as the film thickness increases. It was believed that this is due to the higher energy barrier for adatoms to incorporate into the descending steps. Similar results were found in a Monte Carlo simulation of film growth [l].
4. Conclusions (1) Diffusion behavior of single adatoms approaching descending and ascending steps of both type A and B on NXlll) changes at a distance of approximately 2 to 3 nearest-neighboring spacings from the steps. A slightly higher energy (0.060-0.064 eV> compared to diffusion on a perfect surface far from the steps (0.056 eV) is required for adatoms to further reach the steps to get into the “forbidden” region. Once the
adatoms are in the “forbidden” region, the energy barriers for adatom diffusion actually decrease, and the nearest-neighboring positions are actually unstable. The physical origin for the existence of the “forbidden” region is the step-induced strain field near the steps and the resulting elastic interactions between steps and adatoms are responsible for the increase in the energy barriers for adatom diffusion near steps. (2) Diffusion behavior of single adatoms approaching descending and ascending steps on Ni(ll0) and NXlOO) surfaces is essentially similar to that on the corresponding flat terraces. No “forbidden” region was found. (3) Exchange diffusion for adatoms over the descending steps of type B on NKlll) was found to be energetically favored over direct jumps. The energy barriers for two exchange diffusion processes (0.191 and 0.169 eV> are lower than that for direct jump (0.550 eV) by a factor of - 3. However, such an exchange is not favored at type A steps on fee (111). This is exactly what Wang and Ehrlich found out in a recent FIM experiment [20], in which they found a W adatom at the Ir cluster edge of type B on Ir(ll1) exchanged position with an Ir adatom in the cluster edge,
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/ Diffusion of single adatoms on Ni surfaces
although the exact exchange mechanism was not clear at that time, but exchange did not occur at type A steps. (4) Diffusion at descending steps on Ni(ll0) and NKlOO) surfaces has been studied for the first time, and exchange diffusion has been found to be slightly favored over direct jumps. The energy barriers for exchange diffusion at descending steps on Ni(ll0) and Ni(100) are 1.280 and 0.850 eV; while the energy barriers for direct jumps are 1.340 and 0.910 eV, respectively. There is no experimental information available to compare with our predictions.
Acknowledgements
We gratefully acknowledge the financial support from the Department of Energy, Basic Energy Science, through the Materials Research Laboratory at the University of Illinois under grant DE-A(O)-76 ER01198. We wish to thank the National Center for Supercomputing Applications for providing time on their CRAY-YMP. We also wish to thank G. Ehrlich and S.C. Wang for sharing their latest FIM results with us before publication. Finally, we thank S. Foiles, M. Daw, and M. Baskes for sharing the EAM codes with us.
References
111E.
Chason and B.W. Dodson, J. Vat. Sci. Technol. A 9 (1991) 1545. 121R. Kunkel, B. Poelsema, L.K. Verheij and G. Comsa, Phys. Rev. Lett. 65 (1990) 733. R. Kunkel, L.K. Verheij and G. Comsa, [31 B. Poelsema, Phys. Rev. B 41 (1990) 11609. [41 T. Michely, K.H. Besocke and G. Comsa, Surf. Sci. Lett. 230 (1990) L135. University Munich, [51 H.W. Fink, PhD Thesis, Technical 1989. [61 G. Ehrhch and F.G. Hudda, J. Chem. Phys. 44 (1966) 1309.
[7] D.W. Bassett and M.J. Parsely, J. Phys. D (Appl. Phys.) 2 (1969) 13. [8] W.R. Graham and G. Ehrlich, Surf. Sci. 45 (1974) 530. [9] W.R. Graham and G. Ehrlich, Thin Solid Films 25 (1975) 85. [lo] T.T. Tsong, P.L. Cowan and G.L. Kellogg, Thin Solid Films 25 (1975) 97. [ll] P.L. Cowan and T.T. Tsong, Phys. Lett. A 53 (1975) 383. [12] G. Ayraut and G. Ehrlich, J. Chem. Phys. 60 (1974) 281. 1131 D.W. Bassett and P.R. Webber, Surf. Sci. 70 (1978) 520. 1141 D.W. Bassett, J. Phys. C (Solid State Phys.) 9 (1976) 2491. [15] T.T. Tung and W.R. Graham, Surf. Sci. 97 (1980) 73. [16] T.T. Tsong and G.L. Kellogg, Phys. Rev. B 12 (1975) 1343. [17] D.A. Reed and G. Ehrlich, Philos. Mag. 32 (1975) 1095. [18] S.C. Wang and G. Ehrlich, Phys. Rev. Lett. 62 (1989) 2297. [19] S.C. Wang and G. Ehrlich, Surf. Sci. 224 (1989) L997. [20] S.C. Wang and G. Ehrlich, Phys. Rev. Lett. 67 (1991) 2509. [21] J. Liu, C.W. Wu and T.T. Tsong, Phys. Rev. B 43 (1991) 11595. 1221T.T. Tsong, Surf. Sci. 231 (1990) 81. 1231T.T. Tsong, Phys. Rev. B 30 (1984) 4946. [241 C. Chen and T.T. Tsong, Phys. Rev. B 41 (1990) 12403. 1251B. Taylor and I. Langmuir, Phys. Rev. 44 (1933) 4236. 1261D.S. Choi, SK. Kim and R. Gomer, Surf. Sci. 234 (1990) 262. D71 Y.M. Gong and R. Gomer, J. Chem. Phys. 88 (1988) 1359. 1281Y.M. Gong and R. Gomer, J. Chem. Phys. 88 (1988) 1370. 1291P.G. Flahive and W.R. Graham, Surf. Sci. 91 (1980) 449. [301 A.F. Voter, Phys. Rev. B 34 (1986) 6819. 1311 C.L. Liu, J.M. Cohen, J.B. Adams and A.F. Voter, Surf. Sci. 253 (1991) 334. 1321M.S. Daw and M.I. Baskes, Phys. Rev. Lctt. 50 (1983) 1285. [331J.B. Adams, S.M. Foiles and W.G. Wolfer, J. Mater. Res. 4 (1989) 102. [341S.M. Foiles, M.I. Baskes and MS. Daw, Phys. Rev. B 33 (1986) 7983. [351C.-L. Liu and James B. Adams, Surf. Sci. 265 (1992) 262. [361D.W. Bassett, in: Surface Mobilities on Solid Materials, Ed. V.T. Binh (Plenum, New York, 1983) p. 63. [371S.C. Wang and G. Ehrlich, to be published. on Self-diffusion at Metal Sur1381J.K. Norskov, Workshop faces, Copenhagen, April 1991. [391G. Comsa, 39th AVS meeting, Chicago, 1992. [401C.-L. Liu and James B. Adams, Surf. Sci. 294 (1993) 211. AT&T Bell Laboratories, private com[411D.J. Eaglesham, munication.