Orientation-Dependent Growth Mechanisms of Graphene Islands on Ir

Nov 21, 2014 - Sandia National Laboratories, Livermore, California 94550, United States ... Graphene islands were nucleated by heating the Ir substrat...
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Orientation-Dependent Growth Mechanisms of Graphene Islands on Ir(111) P. C. Rogge,†,‡ S. Nie,§ K. F. McCarty,§ N. C. Bartelt,*,§ and O. D. Dubon*,†,‡ †

Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, California 94720, United States Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States § Sandia National Laboratories, Livermore, California 94550, United States ‡

S Supporting Information *

ABSTRACT: Using low-energy electron microscopy, we find that the mechanisms of graphene growth on Ir(111) depend sensitively on island orientation with respect to Ir. In the temperature range of 750−900 °C, we observe that growing rotated islands are more faceted than islands aligned with the substrate. Further, the growth velocity of rotated islands depends not only on the C adatom supersaturation but also on the geometry of the island edge. We deduce that the growth of rotated islands is kink-nucleation-limited, whereas aligned islands are kink-advancement-limited. These different growth mechanisms are attributed to differences in the graphene edge binding strength to the substrate. KEYWORDS: Graphene, rotational variants, crystal growth, kinks, low-energy electron microscopy

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kink density because orientation-dependent rebonding at the edges changes how kinks are created and how carbon attaches to them. To determine how the growth mechanisms change with orientation, it is crucial to compare islands with the same driving force for growth. Such a capability is provided by LEEM, where C adatom concentrations can be monitored in real time by measuring the electron reflectivity of the substrate.10,13,14 Thus, the effects of edge morphology and kink density can be isolated. Graphene on Ir(111) is an ideal system for such a study because growth is attachment-limited,10 which is also observed for graphene on Ru(0001),14 Pt(111),11 Pd(111),15 Cu(100),16 and Cu foils.17 In addition, adatom concentrations during growth are sufficiently large to be measured. Graphene islands were nucleated by heating the Ir substrate to 750−900 °C and introducing ethylene gas into the microscope. The flow was then shut off and sufficient time elapsed until the islands no longer grew. Figure 1a−b presents LEEM images of representative graphene islands. R0 islands are single domain and nucleate predominantly at lower temperatures (750−800 °C). With increasing temperature, the proportion of rotated islands increases. Individual rotated islands consist typically of multiple domains with different orientations relative to the Ir lattice, identified by selected-area low-energy electron diffraction (LEED). LEED patterns

o fully take advantage of the unique electronic and optical properties of two-dimensional (2D) materials,1−4 ways of growing large, defect-free crystals must be developed. The growth of 2D materials is classified as van der Waals epitaxy, which is characterized by weak out-of-plane bonding compared to strong in-plane bonding within the 2D layer.5,6 The growth of islands occurs by attachment at their edges. But because of the strong in-plane bonding for 2D materials, the energy of these edges may be high unless the edge atoms lower their energy, for example, by binding to the substrate.7−9 A key question is how does the structure of these edges affect the growth process. Here, we show that the structural changes in the edges induced by the relative orientation of graphene sheets with respect to the Ir substrate can fundamentally change the growth mechanism. Previous work has established that growth rates of graphene on Ir(111)10 and Pt(111)11 are orientation-dependent, but no explanation has been given. Presumably the edge structures are different. Recently, ex situ measurements of graphene growth on Pt foils suggest that the growth rate is proportional to how far the island edge is deviated from the zigzag, and the authors argue that this shows that the growth velocity is proportional to kink density as expected in the classic terrace-step-kink (TSK) model of crystal growth.12 So in the case of Ir(111), one would be tempted to account for the faster growth of islands rotated relative to the Ir substrate10 as due to increased concentrations of kinks. To test such ideas, we use low-energy electron microscopy (LEEM) to conduct in situ real-time measurements of graphene growth on Ir(111). Surprisingly, highly kinked edges can grow more slowly than edges with a lower kink density. Instead, orientation is a more important variable than © XXXX American Chemical Society

Received: August 30, 2014 Revised: October 26, 2014

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Figure 1. LEEM image of a rotated (a) and R0 (b) graphene island on Ir(111) at 850 °C. The vertical lines that traverse the LEEM images are Ir step bunches. The arrows depict the uphill direction of the staircase of Ir steps. FOV = 30 μm. (c−d) Thresholded LEEM images of (a) and (b), respectively. Zigzag termination denoted by the solid, exterior lines. The dashed, interior lines in (c) denote a domain boundary; each domain was rotated 14° oppositely to the Ir substrate (R14+, R14−). (e−f) Fourier transform (FT) of the rotated and R0 island, respectively. (g) FT intensity as a function of the polar angle; vertical lines denote the corresponding zigzag (the rotated domain polar angle was adjusted to align the zigzag terminations between R0 and R14+; the solid blue line corresponds to the zigzag for the single facet of R14−). (h) Comparison of the FT intensity within ±5° of the zigzag for R0 and rotated islands.

images taken over time that illustrate the growth of graphene islands at 850 °C. From the LEEM images, local step velocities were determined by measuring the step edge displacement with time. The adatom concentration was determined by monitoring the reflectivity of the Ir surface10,13,14 and was modified by changing the ethylene pressure, i.e., the C adatom concentration was changed from the value where the islands were not growing (ceq) via manipulation of the ethylene flow. Perhaps the most obvious difference between R0 and rotated islands is that the R0 growth is impeded in the uphill direction10,18seen by the compressed edge contours on the left side of the image stack in Figure 2awhile the uphill and downhill velocities of the rotated island in Figure 2b are comparable. To eliminate these substrate step effects on our analysis, local velocities of R0 and rotated islands were determined in similar directions relative to the substrate steps and are shown in Figure 2c−e. The comparisons highlight three distinct differences between rotated and R0 islands and show that the velocity of rotated islands is not simply a function of the C adatom concentration. First, the rotated island velocities display hysteresis with the C adatom concentration: the step velocity was faster as the C adatom concentration was increased. This hysteretic behavior was confirmed for the other two facets of this rotated island as well as for three other rotated islands. The hysteresis establishes that the growth rate is not simply a function of the C adatom concentration; instead, it also depends on how the C adatom concentration is varied. R0 islands did not exhibit hysteresis. Second, Figure 2d confirms that the growth velocity of rotated islands is relatively unaffected by uphill substrate steps in contrast to R0 islands. Third, as seen in Figure 2e, the velocity of an edge for the rotated island significantly increased at a constant adatom concentration (cad = 0.0065 ML). Further confirmation that the velocity is not simply a function of the C adatom concentration for rotated islands is gained by examining the image stack of the rotated island in Figure 3a. For this experiment, the C adatom concentration was increased and then held constant. During growth, a protrusion developed in the lower facet. The protrusion was tracked in time by applying the FT technique, and one sees in Figure 3b that the lower facet shifted further from the zigzag by 14° and

indicated high-quality graphene for both R0 and rotated domains. The vertical lines that traverse the LEEM images are Ir step bunches, where the average Ir terrace width is ∼100 nm. We first show that island morphology depends on orientation. Figure 1c−d shows thresholded LEEM images that highlight only the island shape. Differences in island shape are qualitatively apparent when compared to their respective zigzag terminations, which are denoted by the solid, exterior lines; i.e., a zigzag terminated edge would be parallel to the lines (see Supporting Information). The rotated island has faceted edges near the zigzag, whereas the R0 island has more rounded edges that do not necessarily align with the zigzag. This distinction can be quantified by taking the Fourier transform (FT) of the island images, shown in Figure 1e−f. The rotated island FT has coherent streaks that emanate from its center with an orientation perpendicular to the island step edges, whereas the R0 island has more diffuse streaks in its FT. The FT was converted to an intensity plot by integrating the pixel values along the radius as a function of the polar angle. In this form, the FT streaks are converted to peaks in the intensity plot shown in Figure 1g. With the corresponding zigzag termination denoted by the vertical lines, one clearly sees that the rotated island has prominent peaks centered near the zigzag, while the R0 intensity has less prominent features that do not correlate with the zigzag. To quantitatively compare island shapes, we use a metric in which the FT intensity is integrated ±5° about each known zigzag, summed, and then divided by the total integrated intensity. For the R0 island, 16% of its total intensity is within ±5° of its three zigzag terminations, whereas the rotated island has 41% within ±5° of its four zigzag terminations. After applying this FT analysis to 17 R0 islands and 12 rotated islands that spanned the temperature range of 750−900 °C, the results in Figure 1h clearly show that rotated islands have more of their perimeter within ±5° of the zigzag than R0 islands. To connect these differences in growth morphology with growth mechanisms, we measured growth velocities as a function of the C adatom concentration, cad, and correlated them with edge morphology. After nucleating graphene islands, selected islands were imaged while growing by further ethylene exposure. Figure 2a−b presents stacks of selected LEEM B

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Figure 3. (a) LEEM image stack of a rotated island grown at 950 °C. Zigzag termination denoted by the black lines. (b) Lower facet FT intensity during growth, zigzag termination denoted by the vertical, dashed line. (c) Local step velocity measured along the red line in (a) and the C adatom concentration as a function of time; markers (X) correspond to when the FT intensities in (b) were taken.

where a is the kink depth, ρk is the kink density, and vk is the kink velocity. The crucial issue is the rate at which kinks nucleate relative to the rate at which kinks advance by attachment. We consider the velocity measurement in Figure 2e and Figure 3c. At constant C adatom concentration, the step velocity of the rotated island increases significantly when the edge deviates from the zigzag. In the terrace-step-kink model, the step velocity at constant adatom concentration depends only on the kink density. As the edge deviates from the zigzag, the kink density increases, and the step velocity correspondingly increases. Because the roughness was kinetically unstable (i.e., fast growing edges are eliminated from growing crystals19), the edge flattens. This demonstrates that the edge grows faster if more kinks are present and places rotated islands in the regime where kink nucleation is relatively slow compared to kink advancement. The faceting we observe is presumably a consequence of slow kink nucleation and fast attachment to kinks: once a kink nucleates, it rapidly moves until it annihilates by colliding with other kinks or by reaching the crystal edge. The direction of the hysteresis in growth velocity for rotated islands indicates that increasing the C adatom concentration causes the step velocity to be above its steady-state value. We attribute this increase to differences in kink density: by increasing the C adatom concentration, more kinks are nucleated before their concentration reaches steady state by annihilation, resulting in a higher growth velocity.20 R0 islands behave differently. As seen in the image stack in Figure 2a, R0 edges can exhibit large deviations from the zigzag. In the context of the kink model, these deviations from the zigzag reflect a high kink density. However, the step velocity is independent of the edge deviation from the zigzag direction. For example, the R0 velocities taken along the green and black lines in Figure 2a and compared in Figure 2f are similar even though the green data are from an edge highly deviated from the zigzag. This result suggests that the R0 edge has a high kink density along the entire island perimeter (perhaps indicating that kink energies are on the order of the thermal energy, kT). This roughness occurs at a length scale smaller than our resolution limit of ∼10 nm; nonetheless, meandering R0 island edges on Ir(111) have been observed in scanning tunneling microscopy (STM).18 In this high-kink-density regime, the step

Figure 2. LEEM image stacks of a R0 (a) and a rotated (b) island grown at 850 °C. The innermost contour is the starting island; last contour is the final island after growth. Contours are not constant in time but are chosen only to illustrate edge morphology. Arrow depicts the direction of uphill Ir steps; zigzag represented by the exterior, black lines. (c−e) Comparison of local velocity measurements for R0 and the rotated island, where 1 monolayer (ML) equals the C atom density in a graphene sheet on Ir(111). Approximate directions relative to the substrate steps: downhill (c), uphill (d), and parallel (e). (f) Comparison of R0 local step edge velocities taken along the correspondingly colored lines in (a). Error bars in (c−f) denoted by the blue crosses next to each data set; error in (e) is less than the symbol size.

then returned to its original position. Correspondingly, the step velocity increased significantly (Figure 3c) when the protrusion was present despite a constant C adatom concentration. In contrast, R0 island growth velocity is independent of edge deviation from the zigzag. Five local R0 velocities were determined along the colored lines in Figure 2a and plotted together in Figure 2f. Except for the uphill substrate step direction, the R0 velocities are similar along the island’s entire perimeter, irrespective of the local edge deviation relative to the zigzag. Our observations indicate that the growth of the more faceted rotated islands is highly sensitive to the edge morphology. To explain why this is the case, we interpret these observations in terms of the standard terrace-step-kink model of crystal growth. In this model, growth species attach to kink sites at the crystal step edge. The step velocity is vs = aρk v k (1) C

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where B is a kinetic coefficient and n is the cluster size for attachment to a kink (Supporting Information). To determine the cluster size for attachment, first, ceq was determined directly by measurement of the Ir(111) surface reflectivity, which yields the C adatom concentration on the Ir surface in equilibrium with graphene islands.14 When the ceq data are plotted in the Arrhenius form, as in Figure 5a, the slope multiplied by the Boltzmann constant gives the enthalpy of adatom formation, Ef, i.e., the energy difference between a carbon atom in the graphene sheet and a carbon adatom. The data yield Ef = 0.50 ± 0.07 eV. This is in agreement with a previous first-principles result of Ef = 0.5 eV.10 Next, multiple local velocity measurements were taken for each R0 growth between 750 and 900 °C. Measurements taken parallel to the Ir substrate steps are plotted in Figure 5b to illustrate the R0 growth rate as a function of temperature. To determine the cluster size for growth, eq 2 was applied to each locally measured velocity. The experimentally obtained ceq values were placed into eq 2, and then B and n were optimized to fit the velocity data (Figure 5c). The average extracted value for n is 4.1 ± 1.0, where the error is the standard deviation. Interestingly, STM of graphene on Ir(111) observed the kink structure depicted for the R0 island in Figure 4.23 The same kink structure has also been attributed to carbon nanotube growth.24 Attachment of an even-numbered cluster (2, 4, 6 atoms) would not alter the kink morphology, i.e., the number of dangling bonds; thus, a four-atom cluster provides a simple interpretation of the cluster responsible for kink propagation. In general, the growth of islands that have large, isotropic kink densities, such as R0 islands, result in circular island shapes. However, Figure 2f shows that the R0 island velocity varies around its perimeter and results in a noncircular island. The plot in Figure 5d, however, indicates that this does not affect the cluster size analysis. One sees that all local R0 velocity measurements scale directly onto each other when multiplied by a chosen constant. The cluster size for attachment is reflected in the nonlinearity of the step velocity with the C adatom concentration, which is preserved for all local velocity measurements. Instead, the scaling only affects the value of the kinetic coefficient, B. An Arrhenius analysis of the kinetic coefficient gives the average activation barrier for growth and is 2.9 ± 0.1 eV for R0 domains (Supporting Information). Analysis of the kink-nucleation-limited regime for rotated domains is more challenging. Here, kinks nucleate by the attachment of clusters to the step edge,21,22 resulting in a kink

velocity is limited only by attachment kinetics to kinks, not kink nucleation. The absence of hysteresis and the lower degree of faceting along the zigzag for R0 islands support the scenario of a more kinked edge in which growth does not depend on kink nucleation kinetics. Thus, we arrive at a picture in which rotated and R0 islands grow in different kinetic regimes in the temperature range of 750−900 °C: kink-nucleation-limited and kink-advancementlimited, respectively, as depicted in Figure 4.

Figure 4. Orientation-dependent graphene growth model on Ir(111). Rotated domains are kink-nucleation-limited and result in faceted island shapes. The rounded R0 islands have a high kink density, and their growth is kink-advancement-limited. Growth of R0 domains occurs by attachment of a four-atom C cluster to kinks.

We now address why the velocities in Figure 2c−f are nonlinear functions of the C adatom concentration. This nonlinear dependence was previously reported for R0 islands on Ir(111)10 and graphene on Ru(0001).14 Such behavior would be expected for the kink nucleation kinetics of the rotated islandsthe cluster corresponds to the “critical size” for kink nucleation.21,22 However, for kink-advancementlimited kinetics, the nonlinearity suggests a critical size for kink propagation, i.e., the step velocity is proportional to the kink velocity in the high kink density limit (eq 1). We use a similar method as in ref 14 in which the nonlinear step velocity is modeled by how far out of equilibrium the attachment species is, given by the equation ⎡⎛ ⎞ n ⎤ c vs = B⎢⎜⎜ ad ⎟⎟ − 1⎥ ⎢⎣⎝ ceq ⎠ ⎥⎦

(2)

Figure 5. (a) Arrhenius plot of the experimentally determined ceq data. (b) Comparison of R0 local velocities taken in the direction parallel to substrate steps. Solid lines are fits using eq 2 with n = 4. (c) Select local velocity measurements from the 850 °C R0 island with best fits. Local velocities were taken in the directions relative to the substrate steps: parallel (green), downhill (red), and uphill (orange). Error bars in (b) and (c) are denoted by the crosses. (d) All five of the local velocity measurements for the 850 °C R0 island (Figure 2f) scale onto each other when multiplied by a chosen constant. D

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density that depends on the adatom concentration. In this regime, the step velocity is a convolution of the individual dependencies of the kink density and kink velocity on the adatom concentration. This increased complexity, coupled with our observations that the step edge velocity for rotated islands depends precisely on its morphology, which can vary during growth, prevents the application of a simple model to determine cluster sizes involved in kink nucleation and kink attachment for rotated islands. This, however, highlights the different factors that control the growth rate of R0 and rotated domains. Whereas the R0 growth rate depends on the attachment barrier to kinks and the density of four-atom clusters in the adatom sea, rotated domains depend on the energy barriers for kink nucleation and kink propagation, as well as the cluster sizes involved for each process. We ascribe the change of growth mechanism with graphene domain orientation to relative differences in the graphene edge binding strength to the substrate. Graphene edges can bind tightly to metal substrates.7−9 Furthermore, the moiré corrugations in the graphene sheet caused by interactions with the substrate change markedly with orientation.25 Given the large unit cells of the moirés, it is difficult to predict how bonding of the edges will depend on orientation, but it is reasonable to expect the change in bonding with orientation will also be large. This would cause kink energies and kink densities to depend on orientation. Further evidence that the edge binding strength depends on island orientation is revealed in the R0 LEEM image stack in Figure 2a; R0 growth is significantly slower in the uphill Ir step direction. This is because the R0 edge forms a stronger bond with an uphill substrate step due to the increased overlap of the graphene edge states and the metal step states than on the substrate terrace or at a downhill step.18,26,27 Rotated islands, on the other hand, grow both up and down Ir steps at the same rates (Figure 2b), reflecting that the R0 edge has a stronger interaction with substrate steps than rotated islands. In summary, we have shown that graphene exhibits distinct growth mechanisms that depend on its in-plane orientation relative to the Ir(111) lattice: kink-nucleation- and kinkadvancement-limited. This dependence is surprising given that the van der Waals interactions with the substrate presumably do not significantly depend on orientation. Instead, we propose that the graphene edge binding strength to the substrate is orientation-dependent and significantly affects the growth process. The relationship between growth shapes and edge binding strength that we observe here is consistent with observations of graphene on other substrates. Graphene islands on Ru(0001) are rounded, and their growth is strongly inhibited in the uphill substrate step direction,14,26 an indication of strong edge binding. Graphene islands on Pt(111),11 Ni(111),28 and Cu foils17 are faceted, and their growth is significantly less affected by substrate steps. The structure and properties of grain boundaries that form when grains coalesce will depend on these growth shapes. For example, growth limited by kink nucleation is expected to form flat interfaces between rotational variants. Thus, our work demonstrates that the optimal substrate for the growth of 2D materials can be dictated by how strongly island edges bind with the substrate, not just its interior.

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ASSOCIATED CONTENT

S Supporting Information *

Expanded discussion on the experimental methods, the Fourier transform shape analysis, and the cluster attachment analysis. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Director, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, of the U.S. Department of Energy Contract No. De-Ac04-94AL85000 (SNL), by the NSF under Grant No. DMR-1105541 (ODD, PCR), and by a DoD, Air Force Office of Scientific Research, NDSEG fellowship, 32 CFR 168a (PCR).

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(20) Because rough edges have a kink density, no hysteresis would be expected for the velocity of the facet measured in Figure 2e when it is rough, as observed at the higher C adatom concentrations. (21) Voronkov, V. Sov. Phys. Crystallogr. 1970, 15, 8−13. (22) Rashkovich, L. N.; De Yoreo, J. J.; Orme, C. A.; Chernov, A. A. Crystallogr. Rep. 2006, 51, 1063−1074. (23) Phark, S.-h.; Borme, J.; Vanegas, A. L.; Corbetta, M.; Sander, D.; Kirschner, J. Phys. Rev. B 2012, 86, 045442. (24) Ding, F.; Harutyunyan, A. R.; Yakobson, B. I. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 2506−2509. (25) Loginova, E.; Nie, S.; Thürmer, K.; Bartelt, N. C.; McCarty, K. F. Phys. Rev. B 2009, 80, 085430. (26) Sutter, P.; Flege, J.-I.; Sutter, E. Nat. Mater. 2008, 7, 406−411. (27) Thus, the Ir step density would affect how severely the R0 growth rate is suppressed in the uphill step direction. (28) Li, M.; Hannon, J. B.; Tromp, R. M.; Sun, J.; Li, J.; Shenoy, V. B.; Chason, E. Phys. Rev. B 2013, 88, 041402.

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