Step-Induced Oxygen Upward Diffusion on Stepped Cu(100) Surface

Nov 3, 2014 - Molecular dynamic simulations show that the adsorbed oxygen adatoms are unevenly distributed on the stepped surface, favoring the top te...
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Step-Induced Oxygen Upward Diffusion on Stepped Cu(100) Surface Qing Zhu,† Wissam A. Saidi,*,§ and Judith C. Yang†,‡ †

Department of Chemical and Petroleum Engineering, §Department of Mechanical Engineering and Materials Science, and Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States

‡

ABSTRACT: Surface defects such as step edges play an important role in determining the surface properties, affecting immensely the growth mechanisms and morphologies of the nanostructures in epitaxial film growth processes. Here, we probe the dynamics of the oxidation on stepped Cu(100) using molecular dynamic simulations in conjunction with a reactive force field, and we elucidate the mechanisms and energy barriers affecting the oxidation process. Molecular dynamic simulations show that the adsorbed oxygen adatoms are unevenly distributed on the stepped surface, favoring the top terrace. We show that this behavior is due to Ehrlich− Schwöbel (ES) barrier effect. However, differently from the reduced interlayer self-diffusion in descending a step as in a conventional ES barrier effect, we find instead that the ES barrier reduces the ascending diffusion barrier for oxygen, promoting its transport across the step edge and enhancing oxidation of the upper terrace. Additionally, we find that the ES barrier is stepheight dependent, where higher step edges reduce more the oxygen-ascending diffusion barrier and favor more oxidation of the upper terraces of stepped surfaces.

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INTRODUCTION

and promotes formation of 3D island structure in homoepitaxial and heteroepitaxial film growth.6−8 There are several factors affecting the magnitude of the ES barrier, such as crystalline facet types,12 step height,13 step width,14 and the chemistry/electronic environment.6 Additionally, the ES barrier can be of the inverse type, where the adatom is more stable on the top rather than the foot of the terrace.15 This is in contrast to the normal type where the opposite energy preference holds. For example, DFT calculations showed that the binding of O atoms to the lower side of step is weaker than on the upper side of step on Pt(111).16 Similar observations for Xe atoms on Pt (111) are inferred from STM experiments.17,18 In this case, it is expected that the interlayer mass exchange will be promoted, which favors the growth mode of 2D thin film structure. Despite the well-recognized notion that the ES barrier can reduce the adatom descending movement, recent experimental and theoretical work have revealed that the upward ascending diffusion of adatoms can also play an important role during film growth. Experimentally, it is found that 3D Al nanoclusters or islands grow on Al(110), which is attributed largely to the ascending adatom flux during Al deposition.8 The adatom ascending movement in the homoepitaxial deposition process has also been investigated by DFT calculations for several metal surfaces.19−21 However, the ascending dynamics in heteroepitaxial deposition processes has not been extensively investigated,

Self-assembly of nanostructures on thin films is of interest to several fields including catalysis, electronics, and information technology.1−3 For many experimental conditions it is often that nanostructure growth is far from equilibrium where kinetic effects are of key importance in determining the growth morphology.4 Depending on the nature of the supporting base and the deposited materials as well as the growth environment, nanostructures with different morphologies can self-assemble during homoepitaxial or heteroepitaxial film growth processes. Additionally, the existence of defects and, in particular, step edges on the substrate can have a profound effect on the self-assembly. For example, on copper, which is one of the best catalysts in heterogeneous catalysts, a recent in situ high-resolution transmission electron microscopy study showed that oxidation of stepped Cu(100) surfaces promotes formation of a flat metal− oxide interface through the Cu adatoms detachment from steps and diffusion across the terraces.5 For stepped surfaces, one key question is whether the surface growth process promotes formation of a smooth two-dimensional (2D) film or a three-dimensional (3D) island structure.6−9 In this respect, the Ehrlich−Schwöbel (ES) barrier at the interlayer interface10,11 has been shown to play an important role in determining the off-balance between these two growth mechanisms. The basic concept of the ES barrier is due to bond counting where an adatom approaching the ledge of a step sees less neighbors compared to the terrace, which in turn demotes the descending movement off a step edge. The ES barrier has been shown to reduce the interlayer mass exchange © 2014 American Chemical Society

Received: August 5, 2014 Revised: October 22, 2014 Published: November 3, 2014 251

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Figure 1. Models showing (a) S-L1, (b) S-L2, and (c) S-L3 Cu(100) surfaces.

°C, where the temperature is controlled using a Nosé−Hoover thermostat26−28 with a damping constant of 0.05 ps. The temperature choice was motived by recent experiments on stepped Cu surfaces that were conducted at a temperature of 350 °C.5 The Cu(100) surface slab is defined using an 8 × 8 surface supercell with a primitive lattice constant a = 3.71 Å. The slab has 12 layers; each layer has 128 Cu atoms. In the MD simulations as well as in the geometry optimizations, atomic coordinates in all directions are relaxed except the bottom 3 layers, which are kept fixed to minimize finite size effects in modeling the surface. It is expected that the 9 active layers in our slab model can describe adequately the oxidation up to 5 layers depth. This is because both experimental studies29 and DFT calculations19,30 have shown that the surface relaxation of Cu(100) mostly occurs within the first two layers, and thus, 4−6 Cu layers are sufficiently accurate to describe the Cu surface in most DFT calculations. Periodic boundary conditions are employed along the [010] and [001] crystallographic directions, while the interactions between images along the nonperiodic z direction are mitigated using a large vacuum space of 20 Å. Initially and prior to any product simulations, we used MD within NVT ensemble for 1 ps for thermalization to remove any bias due to the initial starting configuration. To gain more understanding of the effects of step height on the oxidation pattern, we use three different models for the step

especially in the case where the electronegativities of the deposited material and supporting base are appreciably different, such as in the process of metal oxidation. This knowledge gap is crucial in understanding the reactions on complex surfaces. In this paper, we use an atomistic molecular dynamics approach in conjunction with a reactive force field (ReaxFF) to provide an understanding of the dynamic process during oxidation of flat and stepped Cu(100) surface. We focus on the step-edge effect at the very early stages of surface oxidation investigating, in particular, its role in the oxidation dynamics. Additionally, we discuss the important role of adatom ascending diffusion during oxidation of the stepped surface and show that during the oxidation process the upper terraces are oxidized at a faster rate than the lower terraces of the step. We show that this oxidation trend is due to a reduction of the barrier of the upward diffusion from the ES effect, which enhances oxygen transport from the lower to the upper surface terraces.

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COMPUTATIONAL DETAILS Reactive molecular dynamic (RMD) calculations are carried out using the ReaxFF C++ module as implemented in Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS).22−25 All calculations are carried out using a relatively small time step of 0.5 fs to achieve stable molecular dynamic (MD) simulations for longer times up to 1 ns. MD simulations are carried out in the NVT ensemble with T = 350 252

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Figure 2. Cu+ and Cu2+ atom count during the oxidation process for (a) flat Cu(100) surface, (b) S-L1, (c) S-L2, and (d) S-L3 Cu(100) surfaces. Atoms are distinguished by their formal charge.

Figure 3. (a) Oxygen coverage during the oxidation process of the flat Cu(100) surface. The orange line corresponds to oxygen coverage on the first layer above the copper−vacuum interface, and the black line corresponds to coverage on the sublayers. (b−d) Oxygen coverage at the upper (red) and lower (blue) terraces. All atom counts are normalized with respect to the available adsorption sites. For example, for the 3-layer stepped surface S-L3, oxygen coverages at the upper and lower terraces are normalized to the 88 and 44 available hollow sites on the terrace, respectively.

nevertheless a good approximation for describing the early stages of oxidation, as we will discuss in the Results and Discussion. Specifically, the oxidation process is carried out by randomly depositing one oxygen atom every 2 ps at a distance 5 Å above the copper−vacuum interface. The choice for this time interval between oxygen depositions is motivated by experiments, which showed that oxygen atoms incident on the Cu(100) surface dissipate 75% of their available energy within 1 ps or 90% within 5 ps.31 Also, previous MD oxidation studies have utilized a similar setup.32,33 The velocity of the deposited oxygen atoms is chosen

defect corresponding to heights of one-, two-, and three-atomic layers for the Cu(100) surface, as shown in Figure 1. These models will be denoted by S-L1, S-L2, and S-L3, respectively. The upper terraces of these stepped surfaces have 64, 128, and 192 Cu atoms, respectively. The multilayer step models can be also regarded as representations of 3D mound structures. At standard temperatures and pressures, the oxidation process is initiated by the adsorption and dissociation of O2 molecules. However, in our simulations and for computational purposes we use atomic oxygen instead of O2 as the oxidation agent, which is 253

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heading toward the Cu surface along the normal direction and with a magnitude that is consistent with the average thermal velocity calculated from the Boltzmann distribution at T = 623.15 K (350 °C). To make the MD simulations more efficient, we remove oxygen atoms that are more than 20 Å above the top surface layer because these are less likely to interact with the surface within the relatively short time of the MD simulation and thus would only add to the overall simulation noise. To characterize the different stages during the oxidation process we monitor the oxidation state of Cu atoms where a charge of 0, +1, or +2 indicates that Cu belongs to the neutral, cuprous (Cu2O), or cupric (CuO) oxidation states, respectively. In practice, the formal charge for O2− is calculated to be −0.8e from the ReaxFF force field used in this work (e is the positive elementary charge). Thus, we choose 0.4e as the threshold for Cu+ counting and 0.8e for Cu2+, which is also consistent with the Mulliken charge analysis of 0.38e to 0.795e obtained using DFT.34 An equivalent understanding of the Cu oxidation state can also be gained by inspecting the number of bonds that each Cu makes, but this was not employed in our analysis. Additionally, we will quantify the oxygen coverage using ML to indicate that all of the hollow sites of Cu(100) are occupied by oxygen. For example, for the flat surface, this amounts to 128 oxygen atoms per 1 ML. We also conducted nudge-elastic band (NEB) calculations to compute the energy barriers for oxygen diffusion on flat and stepped surfaces. The climbing image budged elastic band (CINEB) method35−37 has been used to perform better search of the transition states. We use 10 images between two consecutive minima along the diffusion path to obtain a good resolution of the potential energy surface during the diffusion process.

Figure 4. Final configuration of the top two layers after 128 ps of oxidation on the flat Cu(100) surface. The gray sphere and black sphere represent Cu on the first and second layers, respectively, and the red sphere represents oxygen. The dashed yellow square depicts a c(2 × 2) Cu2O-like domain, and the solid yellow square depicts a c(1 × 1) CuOlike domain.

indicating that diffusion of the oxygen adatom into subsurface layers is an activated process. Previous DFT calculations by Lee and McGaughey39 showed that the diffusion barrier for embedding oxygen atoms into subsurface layers is strongly affected by the oxygen coverage of the first Cu(100) layer, where on the unreconstructed surface the barrier is as high as 2.65 eV at 0.25 ML but decreases to 0.49 eV at 0.75 ML coverage. Thermodynamically, subsurface embedment is also strongly affected by oxygen coverage of the top surface as shown in previous DFT calculations, e.g., subsurface embedded oxygen is energetically unfavorable by 0.08 eV on clean Cu(100) surface but favored by 1.40 eV if an oxygen adatom pre-exists on the surface.43 Additionally, from the MD simulations we observe that the surfaces become less susceptible to oxidation beyond the 1 ML limit due to the smaller oxygen adsorption probability on the surface compared to the low-coverage limit and the increase in the oxygen desorption probabilities. All of these factors combined together result in the reduced rate of subsurface oxidation. Overall our results are in agreement with the study of Jeon et al., which employed a similar computational framework and also reported formation of both CuO and Cu2O on Cu(100), Cu(110), and Cu(111) surfaces.33 In particular, for Cu(100) surface at 600 K (327 °C), initial oxidation quickly reaches saturation with both CuO and Cu2O existing in the end. This agrees with our findings as will be discussed more below. Additionally, Jeon et al. showed that further oxidation of the Cu surface is hindered because this requires significant surface reconstructions to enable deep-layer copper atom diffusion and transport to the interface layer. In contrast, in our simulations, we are able to confirm that a slow subsurface oxidation is feasible due to oxygen diffusion into deeper layers without the necessity of going through significant surface reconstructions. This difference with the previous study is likely because we are able to carry the simulations for longer simulation times (1000 vs 500 ps) owing to the smaller time step employed in our simulations (0.5 vs 1 fs). The small time step insures a stable MD simulation due to the

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RESULTS AND DISCUSSION 1. Oxidation of Flat Defect-Free Surface. We first study the flat step-free Cu surface to establish a reference to compare with the stepped surfaces. A complete understanding of the oxidation process can be gained by examining the number of Cu atoms in the cuprous Cu+ and cupric Cu2+ oxidation states as shown in Figure 2, in conjunction with the z location of the oxygen atoms as shown in Figure 3. Upon oxygen exposure, flat Cu(100) is oxidized first to Cu2O and then oxidized further to CuO, as seen from Figure 2a. We can classify the oxidation process into three stages. (1) Formation of Cu2O starts immediately on the Cu(100) surface and steadily increases with oxygen exposure up to ∼150 ps corresponding to ∼0.5 ML coverage. Figure 3a shows that almost all oxygen atoms occupy the first layer. (2) Cu2O is oxidized further to CuO starting from ∼64 ps (0.25 ML coverage) after the initial oxidation where at ∼360 ps the top layer is almost covered with pure CuO. (3) After 360 ps, oxidation of sublayers begins as seen from Figure 3a, albeit at a reduced rate, leading to slow growth of Cu2O and even CuO but at a much slower rate. Near the end of first stage, most of the Cu(100) surface is covered with oxygen adatoms occupying the hollow sites and leading to formation of c(2 × 2) reconstruction, as shown in the dashed yellow square depicted in Figure 4. This is consistent with the experimental observation that the Cu(100) surface oxidation starts from the unreconstructed c(2 × 2) phase38 as well as previous DFT simulations.39−42 A small region of c(1 × 1) CuOlike lattice structure is also observed, as depicted with the solid yellow square in Figure 4. Subsurface oxidation after 1.0 ML coverage proceeds in a similar fashion as the top layer, except at a much slower rate, 254

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Figure 5. Top view of the configurations after 1 ns of oxidation on (a) S-L1, (b) S-L2, and (c) S-L3 Cu(100) surfaces. Gray and black spheres represent Cu on the upper and lower terraces, and the red sphere represents oxygen. The dashed yellow line depicts the serration pattern on the 1-layer stepped surface.

oxidation does not proceed until the MRR structure is breached after a long period of higher pressure O2 exposure, after which the O2 dissociation is reactivated.38 2. Oxidation of Stepped Surfaces. Oxidation of the stepped surfaces follows similar trends as in the flat surface but with notable differences as we discuss below. Figure 2b−d shows that for all three different step-edge models Cu2O formation begins immediately after oxygen deposition and after about 100 ps (0.4 ML) CuO starts to emerge and increase steadily. In comparison, CuO oxidation of the flat surface happens at a faster rate where CuO formation commences at 64 ps. Figure 2b shows that for S-L1 the Cu2O coverage peaks at around 180 ps and then decreases slowly up to 560 ps, while concomitantly the CuO coverage increases steadily. This suggests that at this stage CuO formation takes place at the expense of Cu2O consumption but not to completion as Cu2O coverage does not drop to zero. After this period, Cu2O and CuO coverage keeps steady with a relatively slow increasing trend. For S-L2 shown in Figure 2c, the Cu2O coverage keeps increasing until around 360 ps and then the Cu2O coverage

decrease in the accumulative error in integrating the classical equations of motion. Experimentally, full oxidation of Cu to CuO was not reported in previous studies, where only Cu2O was shown to exist at 350 °C.44,45 This is in disagreement with our results and also with the previous simulation results,33 where in both studies full oxidation of Cu resulted in formation of CuO at the expense of the depletion of Cu2O. The main reason for this disagreement is due to the employed oxidation method where atomic oxygen is employed in the simulations as the oxidizing agent rather than O2 as in the experiments. Indeed, previous experimental and computational studies showed that O2 adsorbs on clean Cu(100) surface through a barrierless process that quickly leads to formation of monatomic oxygen adatoms that actively react with the surface.30 However, as the oxygen coverage increases on Cu(100), especially after formation of the missingrow reconstructions (MRR) structure, dissociation of O2 molecule at the copper surface becomes largely hindered by a barrier as high as 4 eV.46,47 This explains why the surface oxide structure is experimentally only oxidized to Cu2O. Further 255

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The most important result in our simulations is that the oxidation on the upper terrace of the step edge proceeds at a faster rate than on the lower terrace, as revealed from the oxygen coverage analysis in Figure 3b−d. This is also consistent for the three stepped surface models. For the 1-layer case, oxidation on both the upper and the lower terraces grows immediately after initial deposition of oxygen atoms with the oxygen coverage always larger for the upper terrace, as seen in Figure 3b. For S-L2 and S-L3, the oxygen coverage on the lower terrace remains negligible up to 50 ps after initial oxidation, as seen in Figure 3c and 3d. During this time, ∼0.20 ML of oxygen is deposited on the surface. These results suggest that there is oxygen transport from the lower to the upper terrace. To verify this, we examined the MD trajectory and counted the number of oxygen atoms that diffuse upward vs the number of oxygen atoms that diffuse downward. The trajectory analysis for the S-L3 model is shown in Figure 6, which supports this conclusion, namely, we can see that

decreases at a slow rate until 680 ps, indicating very little consumption of Cu2O whereas CuO coverage increases steadily. After 680 ps, Cu2O coverage increases again but only slightly, which is an indication for sublayer oxidation that leads to formation of new Cu2O domains. Compared to the 1-layer step oxidation, the Cu2O consumption ratio is even smaller, indicating that the subsurface oxidation is less hindered. For S-L3 shown in Figure 2d, Cu2O coverage increases in the first 150 ps similar to the flat surface but keeps steady thereafter instead of decreasing, indicating no Cu2O consumption takes place during formation of CuO. At about 340 ps, Cu2O coverage starts to increase again, indicating that subsurface oxidation of Cu atoms is similar to the flat surface model. After about 720 ps, the Cu2 O coverage peaks, after which it decreases with a concomitant increase in CuO coverage at an enhanced rate, indicating that CuO formation is at the cost of Cu2O consumption. After 920 ps, the CuO and Cu2O coverage keeps steady with small fluctuations. Overall, in contrast to the flat surface, formation of CuO domains on the three stepped surface models is not at the cost of depleting the Cu2O domains for most stages of the oxidation, and this trend is more apparent when the step height increases from 1 layer to 3 layers. This suggests that for the stepped models complete conversion from Cu2O to CuO on the surface layer is bypassed, and new Cu2O-like structures can be formed in the sublayers, whereas conversion to CuO-like structure on the interface layer only takes place at a reduced extent compared to the flat surface model. Thus, sublayer oxidation is significantly enhanced in the presence of a step-edge defect. Later we show that sublayer oxidation is mainly attributed to the oxidation on the top terrace of the step due to a reduction of the ascending oxygen diffusion barrier. The faster sublayer oxidation of the stepped surfaces compared to the flat surface that is seen in the MD results is likely because the Cu/O atoms are exposed to the open cut at the step edge, which makes the Cu(110)/O vicinal surface similar to the MRR Cu(100)/Cu configuration.48 Previously, Lee and McGaughey39 have shown that the barrier for sublayer oxygen embedment through the open groove of the MRR configuration is as low as 0.32 eV, which is significantly smaller than 1.21 eV on the unreconstructed surface, and the intralayer oxygen diffusion barrier on the sublayers is as low as 0.44 eV near the groove of MRR compared to 0.74 eV for surface diffusion. Thus, the Cu(110)/O vicinal surface may open a faster channel for subsurface oxygen incorporation in the vicinity of the step edge, which in turn explains the MD simulation results. Figure 5 shows the final configuration for the three different stepped surface models. For S-L1, the step edge shows a serration pattern, which is consistent with Lahtonen’s experimental observations.38 However, this snapshot could be depicting a singular effect, and we put no emphasis on this similarity. One common feature among all three step-edge models is that there exists an apparent Cu−Cu atom exchange where some of the sublayer Cu atoms enter the upper terrace of the step and vice versa. To show this more clearly, we use different colors to distinguish Cu atoms that belong originally to the step (gray) and those belonging to supporting base (black). This Cu−Cu atom exchange is especially apparent for S-L3, in which many of the second-layer Cu atoms at the step have entered the first layer, leading to expansion of the first layer in the lateral direction. This result indicates that active interlayer atom exchange takes place among Cu layers with a relatively smaller energy barrier.

Figure 6. Trajectory analysis for the oxygen thermal diffusion process on S-L3 Cu(100) surface analyzed every 50 ps. The red line represents the number of oxygen atoms that ascend from the lower terrace to the upper terrace, and the blue line represents the number of oxygen atoms that descend from the upper terrace to the lower terrace.

during the MD simulation the number of oxygen atoms diffusing upward is always more than that diffusing downward. Additionally, from Figure 3c and 3d we can see that oxygen diffusion to the upper terrace is less hindered on S-L2 and S-L3 compared to the S-L1 case. A detailed explanation of these diffusion trends is provided in the following section by computing the diffusion barriers. Finally, we note that the apparent noise in the data shown in Figure 3b and 3c for S-L1 and S-L2 is noticeably larger than that of Figure 3d for S-L3. This is because on stepped surfaces with small step heights there are smaller z-dimensional spans for the atom to be counted in the upper or lower terrace, resulting in larger fluctuations in atom counts. 3. Oxygen Diffusion Channel on Stepped Surfaces. Although oxygen diffusion on stepped surfaces has not been extensively investigated before in the computational framework, there have been nevertheless several experimental studies that shed light on this phenomenon. Previously, an STM study of the Al(111) surface oxidation showed that oxide formation has an uneven growth rate between the upper and the lower terraces of a step, where the upper terrace was favored.49 In another UVphotoelectron spectroscopy study of the mass diffusion of Ag on the Cu(110) surface, Goldmann et al. showed that there exists a 256

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flux channel for the oxygen adatoms to diffuse from the lower Cu terrace to the upper terrace of the Ag step.50 The enhanced oxidation of the upper terrace compared to the lower terrace can be because of either thermodynamic or kinetic factors. We argue below that differences in the kinetic barriers for diffusion of the oxygen adatom at the step edge is the cause of this behavior. When the oxygen adatom is in the vicinity of the step edge, surface diffusion will differ from that of the flat terrace due to the nature of the different number of neighboring Cu atoms and geometrical factors at the step edge. More specifically, we show next by employing NEB calculations that promotion of the oxidation toward the upper terrace of the step is attributed to the ES barrier effect.10,11 Before discussing the NEB results we examine first oxygen adsorption at the high-symmetry sites for step-free Cu (100). We find that the adsorption energies at the hollow, top, and bridge sites are −5.46, −2.19, and −3.45 eV. The order of the energies is in agreement with previous DFT results.30 However, in our ReaxFF calculations we find that the bridge site (I1 configuration in Figure 7) is a metastable local minimum structure, while

Figure 7. NEB profile for the T1−T2 diffusion on S-L3 stepped Cu(100) surface. Blue, black, and red cross signs represent the stable adsorption sites, intermediate configurations, and transition states, and the numbers in parentheses correspond to the relative adsorption energy of the configuration.

previous DFT calculations showed that the bridge site is a transition state.30 This somewhat affects our NEB results because in this case the diffusion barrier is not defined by the energy difference between the bridge and the hollow sites but between the highest energy transition state (saddle point) found in the NEB calculation and the hollow sites, which is higher than the bridge site configuration by ∼0.2 eV. The NEB calculations are employed to span the entire diffusion pathway for the three stepped models (Figure 8), where an oxygen adatom diffuses from the lower to the upper terraces. The entire diffusion path is broken into segments connecting two neighboring minima. For the flat (100) surface, the minima are located at hollow and bridge sites, and for the (110) surface, the intermediate configuration is the 3-fold hollow site shown schematically in the inset of Figure 8f and referred to as I4 and I5. Joen et al.33 previously concluded that the Cu/O force fields employed in this study can correctly represent the energy landscape of different oxygen on Cu configurations among all three low-index surfaces (100), (110), and (111). Thus, our

Figure 8. Top-view illustration for the oxygen diffusion process employed in NEB calculations for (a) S-L1, (b) S-L2, and (c) S-L3 Cu(100) surface. (d, e, and f) Corresponding side views, respectively. The gray sphere represents Cu on the upper terrace, the black sphere represents Cu on the first layer of the lower terrace, and the red sphere corresponds to oxygen. Red dotted circles represent neighboring diffusion sites.

approach should be able to describe energy differences during the diffusion process across the different surfaces. For an oxygen adatom ascending a 1-layer step edge, the adatom starts from a 4-fold hollow site on the lower terrace (site T1) and then hops to a neighbor 4-fold hollow site (site T2) so that the diffusion barrier between 4-fold hollow sites on a flat terrace can be obtained. Then the adatom diffuses toward the step foot (site L), from where the adatom climbs up the step edge to the step top (site H1). After that the adatom takes two diffusion processes from the step top to the final configuration at 257

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Figure 9. Energy profile along the oxygen diffusion process on (a) S-L1, (b) S-L2, and (c) S-L3 Cu(100) surfaces.

a 4-fold hollow site (site U2) on the upper terrace. The oxygen adatom ascending processes on S-L2 and S-L3 are very similar to the S-L1 case and only differ by including more hopping sites on

the (110) vicinal surface (H2 for 2-layer and H2 and H3 for 3layer models). 258

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the descending flux for the oxygen adatom, which explains the accumulation of oxygen adatoms at the upper terrace that is seen in the MD simulations of Figure 3b. Notice that under a negative ES barrier effect the energy barrier for the ascending diffusion is still a positive value but at a reduced amount compared to diffusion on a flat terrace. The results for the S-L2 and S-L3 stepped surfaces are fairly similar. The adsorption energy at the step foot (site L) is slightly weaker than the 4-fold hollow site on the flat terrace by ∼0.1 eV, while the energies along the step edge (110) vicinal surface (site H1 for 2-layer and sites H1 and H2 for 3-layer step) and at the step top (site H2 for 2-layer and site H3 for 3-layer) are approximately 0.62 eV weaker than the 4-fold hollow site. Here, the activation barrier of the oxygen adatom on the (110) vicinal surface through the “in-channel” hopping mechanism is around 1.40 (1.30) for S-L2 (S-L3), more than 0.80 eV lower than the diffusion barrier on the Cu(100) surface, suggesting a much quicker oxygen adatom diffusion flux along the step edge. Now the question is whether this flux favors the ascending or descending directions. As seen in Figure 9 b and 9c, the barrier for the adatom to reach the step-edge vicinal surface is 1.81 (1.76) eV from site L to H1. On the other hand, the adatom must overcome a larger barrier of 2.16 (2.14) eV to descend from site U1 to site H3. Compared to the 2.18 (2.15) eV barrier for O adatom diffusion on a flat Cu(100) terrace, here we have a negative ES barrier of −0.37 (−0.39) eV for the ascending diffusion and near zero ES barrier for descending diffusion. Overall, our results show that for oxygen diffusion along the step edge on the Cu(100) surface there is a negative ES barrier for the ascending movement even though the ES barrier for the descending movement is nearly zero. This effectively opens an enhanced ascending diffusion channel for oxygen transport and explains the faster oxidation rate of the upper terraces that are seen in the MD simulations. The ascending diffusion flux that is observed in our simulations is similar to what was found before for Al self-diffusion on the Al(110) surface.8 Also, it was shown that the barrier for the oxygen-ascending diffusion on stepped Pt(111) surface with A-type (100) microfacet is slightly lower than that of the descending barrier by ∼0.3 eV as well.16 Examining the energy barriers for thermal diffusion in the three plots of Figure 9, we see that oxygen diffuion on the flat terrace is the rate-limiting step for Cu diffuion. However, this process is activated by the relatively large energy provided by the initial adsorption of oxygen atoms on the terrace. In contrast, oxygen adsorption in the vicinity of the step edge is less likely given the limited number of available step edge adsorption sites, and thus, oxygen transport across the step edge is not predominantly due to the original oxygen adsorption but rather due to diffusion processes on a flat terrace. Additionally, the energy gained from initial adsorption dissipates quickly as discussed above; thus, less energy will be available when oxygen atoms approach the step edge after completing the diffusion process on flat terrace. As a result, the ES barrier effect, which alters the rate-limiting steps in cross-step-edge diffusion, will dominate the diffusion dynamics across the step edge even though the energy barrier at this vicinity is not as high as those on a flat terrace. Furthermore, the ES barrier showed a dependence on the step height, where it decreases from −0.30 to −0.39 eV when moving from S-L1 to S-L3. The increase in the magnitude of the ES barrier with step height is comparable to what is seen for Cu selfdiffusion on stepped Cu(111) using DFT before, although in that case the ES barrier is for diffusion down the step and has a

Figure 9 shows the potential energy surface profiles. Before discussing the activation barriers and their reduction due to stepedge defect, we note first that the adsorption energies for oxygen adatoms on the hollow sites of the lower terrace (T1) and higher terrace (U2) are almost identical for all three stepped models. This supports our argument before that the thermodynamic factor is not the cause of the oxygen diffusion trends that are inferred from the MD simulations. The activation energy barrier for oxygen atom to diffuse from one 4-fold hollow site to another one on the flat Cu(100) terrace is 2.15−2.18 eV among three stepped modes, and the energy difference between the bridge site and the hollow site is approximately 2 eV, as seen in Figure 7. For comparison, the energy difference between the bridge site and the hollow site is reported as 0.7430 and 0.89 eV51 in previous DFT calculations. To a large extent the discrepancy between our value and the two DFT results is because of the differences in the oxygen coverage, where our calculation is done at 1/128 ML oxygen coverage while the DFT calculations are performed at 1/4 (0.74 eV) or 1/ 6 ML (0.89 eV) oxygen coverage. To validate this, we note that we obtain a 1.51 eV energy difference between the bridge site and the hollow site at 1/4 ML and 1.67 eV at 1/6 ML oxygen coverage. In the low-coverage limit, the large oxygen diffusion barrier ΔE ≈ 2 eV can hinder oxygen diffusion on the surface in the 1 ns of MD simulation duration. This can be seen from transition state theory where the rate is given by k(T ) =

⎛ −ΔE ⎞ kBT exp⎜ ⎟ h ⎝ kBT ⎠

Here h is Planck’s constant, kB is the Boltzmann constant, and T is the temperature. For diffusion events to take place at T = 623.15 K within an approximately nanosecond time scale, ΔE should be less than 0.5 eV. However, the above estimation is only valid assuming an equilibrium Boltzmann distribution. In our MD approach, the deposited oxygen adatom gains ∼5 eV kinetic energy upon adsorption at a 4-fold hollow site, which is large enough to activate surface diffusion before this initial gained energy is dissipated in 1−5 ps.31 These arguments are corroborated in our MD simulations, where we observe that the main diffusion event of the oxygen adatom takes place right after the adsorption process. For larger oxygen coverage, the barriers become smaller and thus diffusion events are more observed during the simulations time. Figure 9a shows that for oxygen on S-L1 the adsorption energy at the step foot (site L) is slightly weaker than the 4-fold hollow site on the flat terrace by 0.07 eV, while the energy at the step top (sites H1) is 0.63 eV weaker than the 4-fold hollow site. Although the step-foot site is not showing enhanced binding energy for the diffusing oxygen adatom, possibly due to the nature of different coordination preference between the oxygen adatom and the supporting Cu atoms during the heterogeneous deposition, the unfavored less binding energy at the top of the step edge, on the other hand, is very apparent. As can be seen from Figure 9b, the barrier for the adatom to reach the step-edge vicinal surface is 1.88 eV from site L to H1. On the other hand, the adatom must overcome a larger barrier of 2.17 eV to descend from site U1 to site H1. Compared to the 2.18 eV barrier for O adatom diffusion on a flat Cu(100) terrace, here we have a larger negative ES barrier of −0.30 eV for the ascending diffusion and near-zero ES barrier for descending diffusion. Thus, the kinetic barrier difference suggests that the ascending flux is more favored than 259

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positive magnitude.13 Again, the dependence of the ES barrier on step height nicely explains our MD simulations. As seen in Figure 3, there is appreciable oxygen coverage on the lower terraces in the first 50 ps for S-L1 and nearly zero coverage for S-L2 and SL3. This shows that the barrier for oxygen transport from the low to the upper terraces for S-L2 and S-L3 is smaller than that of the S-L1, which is indeed what is obtained from the NEB calculations. Additionally, this dependence on step height explains the faster sublayer oxidation on stepped surfaces for SL2 and S-L3, as seen in Figure 2.

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CONCLUSION We probe the dynamics of the oxidation of stepped Cu(100) surface with different step heights using reactive MD simulations. As expected, the stepped surfaces show a faster rate of oxidation compared to the step-free surface and with a more enhanced subsurface oxidation. Additionally, the MD simulations show that the upper terrace of the step is oxidized at a faster rate compared to the lower terrace. To explain the MD results we employ nudged-elastic band (NEB) calculations to compute the oxygen diffusion barriers and the effect of the step defect on them. These calculations show that the oxidation pattern observed in the MD simulations can be explained by the existence of a negative Ehrlich−Schwöbel (ES) barrier that promotes oxygen-ascending diffusion across the step edge. Additionally, both the MD simulations and the NEB calculations show that ES barrier is step-height dependent where higher step edges lead to more enhanced ascending oxygen diffusion channels. Overall, our results explain the effects of step defects on the oxidation of Cu(100), which likely exist on other (100) metal surfaces too. Also, these results are valuable for larger scale simulations using a kinetic Monte Carlo framework as we employed previously.52

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Q.Z. and J. Y. are supported by the United States Department of Energy (DOE BES-ER46446 and DOE DE-FG02-03ER1547) and by internal funding through the Swanson School of Engineering, University of Pittsburgh. W.A.S. is supported by NSF under Grant No. DMR1410055. We are grateful for computing time provided in part by the University of Pittsburgh Center of Simulations and Modeling and by the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by the National Science Foundation (OCI-1053575).

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