First principles study of graphene related materials 2

Part II: Synthesis In this part, we discuss two methods for the synthesis of graphene-related materials In Chap 4, we use density-functional theory calculations to explain the experimental observations during the synthesis of graphene quantum dots from the decomposition of C60 on Ru(0001) surface, and also during the chemical vapor deposition growth of hexagonal boron nitride on Ru(0001) 64 Chapter Understanding the synthesis process of graphene-related materials Abstract: To utilize graphene-related materials in mass-produced devices, we need ways to synthesize these materials in large-scale, in good quality, and in the desired size and shape Computational studies can shed light on the observations made by experimentalists during the synthesis process of these materials, thus assisting the experimentalists to find better ways to synthesize these materials In this chapter, we use density-functional theory (DFT) calculations to investigate the process of synthesizing geometrically well-defined graphene quantum dots through the catalytic decomposition of C60 on the Ru(0001) surface, and also the nucleation and growth of a hexagonal boron nitride monolayer on the stepped Ru(0001) surface using chemical vapor deposition * Only the DFT simulations were conducted by the Ph.D candidate The experimental results were obtained by others and are included here for a coherent discussion of the topic 4.1 4.1.1 Graphene quantum dots from catalytic decomposition of C60 Introduction In Sec 1.2, we reviewed the current methods for synthesizing graphene and noted the promising method of chemical vapor deposition (CVD) on metal surfaces for producing macrosize graphene If we wish to use the CVD method to grow graphene nanoislands of smaller sizes, it is clear that we must limit the aggregation of carbon fragments on the metal surface, and there are two ways that this can be accomplished Firstly, the diffusion path length of a carbon fragment before meeting another fragment must be 65 CHAPTER SYNTHESIS OF GRAPHENE-RELATED MATERIALS 66 sufficiently long, which means that the amount of precursors deposited on the surface should be as little as possible Secondly, the diffusion velocity of the carbon fragments should be as low as possible, so it is advantageous to use metals that form strong bonds with carbon Furthermore, if we want the graphene nanoislands grown to have highly regular shapes, some thought has to be given to the choice of carbon precursors, since we want the resulting carbon fragments to be regular in shape and bond to each other in predictable ways For instance, Treier et al created regular-shape graphene nanoribbons and quantum dots through the cyclodehydrogenation of cyclic polyphenylene on the Cu(111) surface 100 Inspired by the metal-catalyzed cyclodehydrogenation of polyaromatic molecules to form C60 and the direct transformation of graphene to C60 , 171,172 we believe that the reverse process – which is the synthesis of regular-shape graphene quantum dots (GQDs) from the metal-catalyzed fragmentation of C60 – should be possible Thus far, there are only studies reporting the appearance of large graphitic domains generated from the decomposition of C60 on metal surfaces 173,174 We hypothesized that the fragmentation of C60 should produce uniform-size fragments, and by controlling the diffusion path length and velocity of the fragments as described above, GQDs with uniform geometries may be produced Herein, we report our experiments confirming the synthesis of well-defined GQDs from the cage-opening of C60 catalyzed by the Ru(0001) surface 175 4.1.2 Results and discussion 4.1.2.1 Experimental results: Graphene quantum dots from C60 decomposition Fig 4.1(a) shows the scanning tunneling microscope (STM) image of the infinite graphitic layer that is formed on Ru(0001) when 0.7 monolayer (ML) of C60 is deposited on the Ru surface and annealed at 1200 K for minutes Note that a monolayer of C60 film would produce five graphene layers if all the C atoms had remained on the surface Since a single layer of graphene was observed on the Ru(0001) surface after the annealing, substantial gasification of the decomposed carbon fragments must have occurred CHAPTER SYNTHESIS OF GRAPHENE-RELATED MATERIALS 67 Due to the lattice mismatch between the graphene layer and the Ru substrate, a graphene moiré structure with a lattice constant of ∼ 30 Å was formed Portions of the graphene structure sitting close to the Ru substrate (the ‘valleys’) show up as dim spots on the STM image, whereas areas of graphene that are buckled upwards from the metal surface (the ‘humps’) show up as bright spots For free-standing graphene, all C atoms in each hexagonal ring of graphene appear as individual bright spots under STM imaging 176 In cases where some of the atoms in the hexagonal ring are coupled to a substrate: for example in bernal-stacked graphene of a few layers, only atoms out of atoms that are not directly coupled to another carbon atom in the adjacent graphene layer are imaged under STM 177 For the infinite graphene layer on Ru(0001), we observed that all atoms of the hexagonal ring were imaged for the humps, whereas only out of atoms per hexagonal ring were imaged for the valleys When the C60 coverage is reduced to 0.03 ML and annealed to 500 − 600 K, the C60 molecules were observed to diffuse across the Ru surface and become embedded into the Ru surface [Fig 4.1(b–c)] The decrease in apparent height for the embedded C60 was ∼ 0.5 Å The embedding of C60 molecules adsorbed on metal surfaces have been observed before on Pd(110), 178 Pt(111), 179 Au(110), 180 and Ag(111) 181 The phenomenon has been attributed to the formation of metal-atom vacancies underneath the C60 molecules, which favorably enhances the C60 -metal adsorption enthalpy since C60 is able to form more bonds with the metal surface The increased adsorption enthalpy more than compensates for the unfavorable enthalpy in forming the metal-atom vacancy We hypothesize that such vacancies form under the C60 molecules on Ru(0001) too, and confirm this hypothesis through density-functional theory (DFT) calculations that will be shown later Upon flash annealing of the embedded C60 molecules to 725 K for minutes, numerous carbon clusters appear on the Ru surface, whose 2.7 Å apparent height is 60% lower than the 6.5 Å apparent height for C60 under a similar bias voltage About 23% of the CHAPTER SYNTHESIS OF GRAPHENE-RELATED MATERIALS 68 (a) (b) (d) (e) (c) (f) Figure 4.1: (a) STM image of the graphene moiré pattern formed from the decomposition of 1.2 ML of C60 molecules on Ru(0001) The 3-D constant current 24 × 20 nm2 STM images of C60 molecules diffusing on the Ru(0001) surface at (b) 500 K, and embedding into the surface at (c) 600 K (c inset) STM line contour showing the apparent height difference between the adsorbed C60 and the embedded C60 (d) Flower-shaped carbon clusters and (e) mushroom-shaped carbon clusters that are formed after the sample has been flash-annealed at 725 K for minutes; (f) carbon cluster with lateral diameter of 1.2 nm that appears when the annealing temperature is increased to 825 K (d–f inset) Magnified STM images of the carbon clusters (e inset) STM line contour showing the apparent height of the carbon clusters (white line) versus the C60 (green line) STM parameters: (a) V = 18 mV, I = 0.5 nA; (b–c) V = 1.25 V, I = 0.1 nA; (d) V = 0.3 V, I = 0.25 nA; (e) V = 0.3 V, I = 0.2 nA; (f) V = 0.3 V, I = 0.16 nA CHAPTER SYNTHESIS OF GRAPHENE-RELATED MATERIALS 69 decomposition fragments are flower-shaped clusters with a three-fold symmetry and lateral diameter of ∼ 0.7 nm [Fig 4.1(d)]; the other 67% are hexagonal mushroomshaped clusters with lateral diameter of ∼ 0.9 nm [Fig 4.1(e)] When the annealing temperature is increased to 825 K, larger clusters with lateral diameter of ∼ 1.2 nm are seen [Fig 4.1(f)] If the surface coverage of C60 on the surface is increased to 0.08 ML, large graphene quantum dots (GQDs) are seen in addition to the clusters described above, as shown in Fig 4.2(a) A minute annealing at 725 K results in a (15 ± 1)% yield of triangular GQDs with apparent lateral size of 2.7 nm [Fig 4.2(b)] Further annealing of the sample at 825 K for minute produces perfect hexagonal GQDs with lateral diameter of nm in a (30 ± 2)% yield [Fig 4.2(e)], while carbon clusters with diameters < nm completely disappear Other shapes with lower yields like parallelograms [Fig 4.2(c)], trapezoids [Fig 4.2(d)], and large hexagons [Fig 4.2(f)] are also seen These GQDs exhibit sizedependent band gaps; the differential conductance (dI/dV) characteristics of the GQDs obtained using scanning tunneling spectroscopy (STS) are shown in Fig 4.2(g), and the band gaps calculated from the analysis of the dI/dV curves are 0.8 eV, 0.6 eV, 0.4 eV and 0.25 eV for the triangular, parallelogram, hexagonal, and large hexagonal GQDs, respectively The triangular GQDs show the same moiré pattern and dim/bright contrast as infinite graphene on Ru(0001) Curiously, in contrast to the infinite graphene on Ru(0001), only out of atoms per hexagonal ring were imaged even for the humps (bright regions in the STM image) that are not strongly coupled to the Ru substrate This is likely due to the ‘topological frustration’ of the π-electron conjugation in finite-size graphene, as explained in Sec 1.1.1 We simulate the STM image using DFT calculations and the Tersoff-Hamann approximation for a triangular GQD that is similar in size and shape to Fig 4.1(e), to show that edge effects alone are responsible for the ‘3-out-of-6’ image CHAPTER SYNTHESIS OF GRAPHENE-RELATED MATERIALS (a) (b) (c) (d) (e) 70 (f) (g) Figure 4.2: (a) STM image of the graphene quantum dots (GQDs) and carbon clusters formed by the decomposition of 0.08 ML C60 on Ru(0001) (a inset) Magnified STM image of mushroom-shaped carbon clusters STM image of (b) triangular (2.7 nm), (c) parallelogram-shaped (2.7 × 4.2 nm), and (d) trapezoid-shaped (2.7 × 4.8 nm) GQDs (c inset) Line contour taken along the green line in (b) (e–f) Hexagon-shaped GQDs (5 nm and 10 nm) obtained after further annealing the sample at 825 K for minutes (g) STS data for the differential conductance (dI/dV) of the GQDs in b (I), c (II), e (III), f (IV), and for infinite monolayer graphene on Ru(0001) (V) STM parameters: (a,e) V = 0.5 V, I = 0.1 nA; (a,e inset) V = 0.3 V, I = 0.2 nA; (b–c) V = 0.3 V, I = 0.2 nA; (d,f) V = 0.3 V, I = 0.1 nA 4.1.2.2 DFT results: C60 adsorption and fragmentation mechanism To investigate if C60 adsorbs on the Ru surface with the formation of a metal atom vacancy, we calculate the adsorption energies of C60 on Ru(0001) at different adsorption sites using density-functional theory (DFT) Our simulation model consists of a 5-layer Ru(0001) periodic surface slab measuring 16.08 × 13.93 × 26.44 Å3 with a C60 molecule on the surface [Fig 4.3(a)] The third to fifth layer of Ru atoms are held fixed in position during any geometry optimizations The C60 molecules showed a ‘cloverleaf’ STM image with 3-fold rotational symmetry [Fig 4.3(b)], which indicates that the C60 molecule is oriented such that one of its hexagon rings is lying flat on the surface 182,183 Thus, we only consider configurations where the C60 molecule is oriented with a hexagon ring lying flat on the Ru surface for our simulations We conduct spin-polarized calculations based on DFT using the SIESTA code, 151 and use the local density approximation for the exchange-correlation functional 184 We apply Troullier-Martins pseudopotentials; 185 in the case of Ru, relativistic and non-linear CHAPTER SYNTHESIS OF GRAPHENE-RELATED MATERIALS (a) Ru atoms (1st layer) Ru atoms (2nd layer) 71 (b) C atoms Figure 4.3: (a) Periodic unit cell for the calculation of C60 adsorption energies on a 5-layer Ru(0001) surface slab (b) The ‘clover-leaf’ STM image of C60 which shows that it is adsorbed on Ru(0001) with one hexagon ring parallel to the surface Name 1) fcc 2) hcp 3) bridge 4) on-top 5) on-top_vac -7.695 -7.201 -7.793 -8.751 -9.077a 1.361b Geometry Adsorption Energy (eV) Table 4.1: The lowest-energy adsorption configurations of C60 on different locations on the Ru(0001) surface and their respective adsorption energies The top hemisphere of the C60 is not shown for clarity a Adsorption energy was calculated with respect to the energy of an Ru atom in the bulk metal, and b with respect to an isolated Ru atom (see text) core corrections are added Double-ζ plus polarization localized basis orbitals are used, with the C (2s, 2p) and Ru (4d, 5s) electrons treated as valence A meshcutoff of 300 Ry and a × × Monkhorst-Pack 186 sampling scheme are used Geometry optimizations are conducted using the conjugate gradient algorithm until the Hellmann-Feynman force on each atom is less than 0.05 eV/Å There are four different high-symmetry locations that the hexagon ring of C60 can sit on the Ru(0001) surface: the fcc, hcp, bridge and on-top locations (see Table 4.1) The center of the hexagon ring of C60 is sitting on the face-centered cubic (hexagonal closepacked) interstitial site of the Ru(0001) surface for the fcc (hcp) location, while the center of the hexagon ring is located between two Ru atoms in the bridge location The on-top location has the center of the hexagon ring on top of an Ru atom There is also another degree of freedom associated with the rotation of the C60 molecule along the CHAPTER SYNTHESIS OF GRAPHENE-RELATED MATERIALS 72 axis that is perpendicular to the Ru surface for each location, and we investigate the different high-symmetry configurations of C60 on the Ru surface based on the rotation of the C60 as well The adsorption energy of C60 on the Ru slab is calculated by Eads = ERu+C60 − ERu − EC60 , (4.1) where ERu+C60 is the energy of the system with C60 adsorbed on the Ru slab, and ERu (EC60 ) is the energy of the isolated Ru slab (C60 ) The adsorption energies of the most stable configurations are shown in Table 4.1, and the on-top configuration is the most stable Next, we investigate to see if the formation of a metal-atom vacancy underneath the C60 molecule, as was seen for some transition metal surfaces, 74,178–180 is energetically favorable for the Ru(0001) surface If we remove the central Ru atom in the on-top configuration to form a Ru vacancy site (on-top_vac configuration in Table 4.1), the adsorption energy of C60 is now calculated as follows: Eads = ERu+C60 − ERu − EC60 − µRu , (4.2) where µRu is the chemical potential of the Ru atom that has been removed The value of µRu is likely to be between that of the Ru atom in the bulk metal and atomic Ru Taking these two scenarios into account, the possible adsorption energy of the on-top_vac configuration ranges from −9.077 eV (bulk Ru) to 1.361 eV (atomic Ru) If we further consider the fact that vacancy formation is an entropically favorable process, the on-top_vac system is certainly the most energetically favorable configuration With the creation of the Ru vacancy, the interaction between the C60 molecule and the Ru substrate is enhanced The bond lengths between the C atoms of the bottom hexagon ring and the closest Ru atoms [grey-pink bonds in Fig 4.4(a)] are on average, 2.0% shorter in the on-top_vac than for the on-top configuration; while the bond lengths between the second-tier carbon atoms of C60 and the closest Ru atoms [black–pink bonds in Fig 4.4(a)] are on average 2.5% shorter in the on-top_vac configuration Correspondingly, certain C–C bonds in the C60 molecule are weakened due to the interaction CHAPTER SYNTHESIS OF GRAPHENE-RELATED MATERIALS (a) 73 (b) Figure 4.4: (a) on-top_vac configuration of the C60 molecule The green arrow indicates the top-down point of view, from which (b) is derived (b) C–C bond lengths (Å) of the bottom hemisphere of the C60 in (a) The top hemisphere is not shown for clarity between C60 and Ru Fig 4.4(b) shows the bond lengths of the bottom hemisphere of the optimized C60 of the on-top_vac configuration The C–C long bonds, which are between a hexagon and pentagon ring in C60 (numbers labeled in red) in Fig 4.4(b), have lengthened by 2.6% on average compared to the isolated C60 molecule, and the C–C short bonds between two hexagon rings in C60 (numbers labeled in blue) have been lengthened by 3.0% We surmise that these lengthened bonds constitute a fault line that causes the C60 to rupture upon heating into two asymmetrical hemispheres The surface-retained fragment [red structure in Fig 4.4(b)] derived from the bottom hemisphere of the ruptured C60 evolves eventually into the observed surface-stabilized clusters on the Ru surface [Fig 4.1(c–d)], while the top hemisphere of the C60 cage desorb into the gas phase 4.1.2.3 DFT results: ‘3-for-6’ STM image of triangular GQDs To address why only out of atoms per hexagonal ring of the triangular GQDs are imaged under STM, the local density of states of a 2.7 nm triangular GQD, similar in size to the the one in Fig 4.1(e), with and without H atoms attached to the edges, was calculated We simulate two cases because the dangling bonds at the edges of the GQD should be partially quenched by interactions with the Ru substrate This bonding situation is likely to be between the case of a GQD fully edge-terminated by H, and the Part III: Applications In this part, we investigate various applications of graphene-related materials In Chap 5, we look at how graphene may be used as a template for the self-assembly of C60 molecules In Chap and 7, we investigate how strain engineering can be used to modify the heat transport and thermoelectric properties of graphene-related materials 87 Chapter The graphene moiré pattern as a template for the self-assembly of C60 molecules Abstract: The graphene moiré superlattice on Ru(0001) presents a complex topological landscape of humps and valleys to molecules adsorbing and diffusing on it Using spherical C60 molecules as a model for hard-sphere close-packing assemblies, we examine its assembly and layered growth on this corrugated landscape The hierarchy of adsorption potential wells on the moiré superlattice causes diffusion-limited dendritic growth of C60 films, as opposed to the isotropic growth observed on smooth surfaces like graphite At one monolayer coverage of C60 , the molecular rotation of C60 trapped in certain valley sites is frozen at room temperature, resulting in the alignment of all similarly trapped C60 molecules Our findings point to the possibility of using periodically-corrugated graphene in molecular spintronics due to its ability to trap and align organic molecules at room temperature * Only the DFT simulations were conducted by the Ph.D candidate The experimental results were obtained by others and are included here for a coherent discussion of the topic 5.1 Introduction The ability to tailor the arrangement of organic nanostructures on graphene is important to realize graphene’s potential as a template for molecular electronics 201–205 The assembly mechanism of organic molecules on graphene is distinct from bulk graphite due to the low density of step edges on graphene grown by chemical vapor deposition, as well as the presence of periodic corrugations on graphene grown epitaxially on metal surfaces 175 A rich spectrum of growth mechanisms is possible in organic film growth because of the geometric anisotropy of organic molecules 203,205–207 Molecular 88 CHAPTER GRAPHENE MOIRÉ PATTERN AS MOLECULAR TEMPLATE 89 packing of organic molecules on an inert substrate is affected by the degrees of freedom in their geometric orientation 208 Steric and electronic interactions between the molecules, and between the molecules and the substrate, can result in polymorphism of the deposited molecular film One approach to form well-ordered molecular assemblies is to utilize intermolecular interactions such as hydrogen bonds, ionic bonds, and p − p stacking to enable high-symmetry ordering of the molecules with selectivity and directionality 202,206,207 However, the assembly of molecules such as C60 requires another strategy, since the molecules lack ligands for directional bonding and are highly symmetrical in their geometry In addition, C60 has low-energy barriers of surface migration on inert substrates, and its rotational energy barrier 209,210 is on the order of a few tenths of meV Thus it is highly mobile on flat and inert substrates such as graphite at room temperature (RT) and the isotropic growth of round and compact C60 islands is favored 211 It is well-known that the in-plane compressive stress arising from the lattice mismatch of a graphene monolayer grown on metal gives rise to a highly-corrugated graphene superlattice known as the moiré pattern 71 It is interesting to consider how a corrugated landscape affects the assembly and packing of a highly-symmetrical, spherical molecule such as C60 , which can be viewed as a model for a hard-sphere close-packing arrangement We discover that the moiré surface presents a unique diffusion barrier that restricts the surface mobility of C60 due to the presence of corrugations, and provides an elegant way to manipulate the growth morphologies of C60 5.2 5.2.1 Results and discussion STM studies of C60 deposition on graphene moiré pattern Graphene forms moiré patterns on a number of metal surfaces, resulting in a graphene landscape of periodic humps and valleys, as the scanning tunneling microscope (STM) image of graphene on Ru(0001) in Fig 5.1(a) shows CHAPTER GRAPHENE MOIRÉ PATTERN AS MOLECULAR TEMPLATE 90 The size of the unit cell for the graphene moiré pattern depends on the number of graphene primitive unit cells (nG × nG ) needed to match the Ru(0001) unit cells (nRu × nRu ) nG was found to be 10.8 ± 0.3, 212 11, 213 and 11.6 ± 0.2 214 from low-energy electron diffraction (LEED) studies, while atomically-resolved STM studies found values of 10 215 and 11 213 For all of these studies, nRu = 11 Surface x-ray diffraction (SXRD) results showed that the moiré pattern has a much larger periodicity with (nG = 25, nRu = 23); this moiré unit cell is × larger than the size of the unit cells found in the other studies 216 However, as Wang et al 217 noted, the four subunits in the (nG = 25, nRu = 23) supercell differ only slightly from each other, an argument they used to justify the studying of the much smaller single subunit (this fact is corroborated by our experimental evidence, as will be shown later) They simulated subunits of different sizes; (nG = 11, nRu = 10) , (nG = 12, nRu = 11), and (nG = 13, nRu = 12), and found that the (nG = 12, nRu = 11) one is the most stable Previous theoretical simulations of the graphene overlayer on Ru(0001) show that: 217–219 • The hump region consists of almost free-standing graphene with no interaction with the metal substrate • There are two different types of valley regions In the valley called the Chcp valley, three atoms in a hexagonal ring of graphene occupy the hexagonal-closepacked (hcp) interstitial sites (henceforth called the hcp C atoms), while the other three atoms sit directly on top of an Ru atom (top C atoms) In the Cfcc valley, three atoms in the hexagonal ring of graphene occupy the face-centered-cubic (fcc) interstitial sites of Ru(0001) (fcc C atoms), while the other three atoms sit directly on top of an Ru atom (top C atoms) The chemical hybridization between the graphene and Ru in the valley regions results in a back-donated charge transfer to graphene 220,221 We investigate the assembly of C60 molecules on the graphene moiré pattern using STM At a low coverage of 0.04 ML, an individual C60 molecule is found to be adsorbed CHAPTER GRAPHENE MOIRÉ PATTERN AS MOLECULAR TEMPLATE 91 (a) (b) Figure 5.1: (a) STM image of graphene moiré pattern on the Ru(0001) surface Symbol A indicates the Chcp valley, B indicates the Cfcc valley, and C indicates the hump region At low C60 coverage, C60 preferentially adsorbs on the Chcp valley, as shown by the location of the blue ball-and-stick model of a C60 molecule (a inset) STM image of a single C60 trapped in the Chcp valley (b) As coverage of C60 increases, six C60 molecules – represented by the yellow ball-and-stick models – surround the trapped C60 in the Chcp valley in all the Chcp valleys [see Fig 5.1(a)] At this stage, the trapped C60 molecule can rotate freely, as inferred from the rounded hemispherical protrusion in the STM image shown in the inset of Fig 5.1(a) Once the Chcp valley is populated by seven C60 molecules to form a heptamer [Fig 5.1(b)], the population of neighboring sites occurs, and these follow a hierarchical order, beginning with the occupation of the Cfcc sites, followed by adsorption on the humps, and finally the adsorption of six C60 molecules around the circumference of the C60 molecules on the humps When the coverage of C60 molecules is increased from 0.04 to 0.4 ML, highly-uniform dumbbell shapes are now imaged for all the C60 molecules occupying the Chcp valleys [Fig 5.2(a)] The dumbbell shape is due to the C60 molecules adopting a structure with its 6:6 bond (the C–C bond between two hexagons on C60 ) facing upwards, as shown in Fig 5.2(d) 222,223 This indicates that molecular rotations are frozen at RT once a ‘crowding effect’ by neighboring C60 occurs The in-plane orientational ordering of C60 molecules in the Chcp valleys is stable up to 350 K [Fig 5.2(b)], beyond which the two-dimensional rotation (spinning) is thermally excited and some in-plane disorder results Out-of-plane molecular rotation occurs at 420 K, as can be seen from the smearing out of the dumbbell shape into a hemisphere for the C60 molecules in the Chcp valleys [Fig 5.2(c)] As the ‘unit cell’ for the pattern of C60 coverage is (nG = 12, nRu = 11), the subtle differences between the subunits of the (nG = 25, nRu = 23) unit cell are not discernible by the C60 molecules CHAPTER GRAPHENE MOIRÉ PATTERN AS MOLECULAR TEMPLATE 92 a) (a)) c) (b) b) (d) d) (c) Figure 5.2: STM image of a monolayer of C60 deposited on the graphene-Ru(0001) surface at (a) 300 K, (b) 350 K and (c) 420 K (d) A close-up of the dumb-bell shape seen under STM, and a molecular model of C60 with the pentagon rings that are responsible for the dumb-bell image highlighted in green STM parameters: V = 1.2 V, I = 0.1 nA 5.2.2 Bonding mechanism of C60 on graphene moiré pattern: DFT results In this section, we shall examine the bonding characteristics between C60 and the graphene moiré surface using density-functional theory (DFT) calculations Due to the huge computational demands of simulating a C60 molecule on the (nG = 12, nRu = 11) moiré unit cell, we decided to break the graphene moiré surface into three separate systems: one graphene layer was placed on top of a three-layer Ru(0001) periodic surface slab, with three atoms of a hexagonal ring of graphene sitting on hcp (fcc) interstitial sites and the other three atoms directly on top of Ru atoms to mimic the Chcp(fcc) valleys, while the humps were represented by a periodic graphene surface slab [Fig 5.3] The lattice parameter of graphene was increased by ∼9% to match that of Ru We calculated the projected density of states (PDOS) for the graphene atoms to see how the Ru substrate has affected it C60 molecules were placed on top of the surface slabs with two pentagon rings facing upwards, as shown in Fig 5.2(d) The C60 was CHAPTER GRAPHENE MOIRÉ PATTERN AS MOLECULAR TEMPLATE 93 (a) Cfcc valley (b) Chcp valley Topview C Ru(1st layer) (c) Topview Sideview (d) Hump Topview Sideview Ru(2nd and 3rd layer) Figure 5.3: (a) & (b) Top-view of the surface slab for the Chcp/fcc valleys showing the orientation of the graphene layer with respect to the Ru(0001) substrate; (c) Side-view of the simulation cell with C60 for the Chcp/fcc valleys; (d) Top-view: the humps are represented by a periodic graphene sheet; side-view: simulation cell for C60 with the graphene sheet placed on different locations and with different rotations on the surface slabs to get the most stable configuration The lateral size of the simulation cell was ∼ 16 × 18 Å2 , and a vacuum of 15 Å was applied in the vertical direction to prevent the C60 molecule from interacting with its periodic images We conduct simulations based on density-functional theory using the SIESTA code, 151 with the local density approximation (LDA) exchange-correlation functional 133 LDA has been shown to be adequate in reproducing binding energies in physisorbed systems 139,140 Troullier-Martins pseudopotentials 185 is employed, and relativistic and nonlinear core corrections are added for Ru Double-ζ plus polarization localized basis orbitals are used, with the C (2s, 2p) and Ru (4d, 5s) electrons treated as valence A × × Monkhorst-Pack 186 k-point mesh is used for sampling, and the meshcutoff is 300 Ry The forces on C60 , graphene, and the top-most layer of Ru atoms are relaxed using the conjugate-gradient algorithm till the force on each atom is < 0.01 eV/Å The adsorption energy of C60 is calculated to be Eads = EC60 +SC − ESC − EC60 , (5.1) where EC60 +SC is the total energy of the supercell containing the C60 and graphene, including the Ru slab in the case of the Chcp/fcc valleys; ESC is the energy of the su- CHAPTER GRAPHENE MOIRÉ PATTERN AS MOLECULAR TEMPLATE 94 Cfcc valley Eads= -1.704 eV Chcp valley Eads= -1.744 eV Hump Eads= -1.581 eV Figure 5.4: The adsorption energies Eads and most stable configurations of C60 on the three different locations of the graphene moiré pattern Only the lower hemisphere of the C60 is shown for sake of clarity percell without the C60 , and EC60 is the energy an isolated C60 in a vacuum box The adsorption energies for the most stable configurations of C60 in the three different locations on the graphene moiré pattern are shown in Fig 5.4 The results show that the adsorption energies of these different sites are sufficiently distinct, with the lowest Eads (most exothermic) for C60 in the Chcp valleys (−1.744 eV) to the highest Eads for C60 at the humps (−1.581 eV) The adsorption energy variation on a flat graphite surface is 13 meV since all adsorption sites are more or less equivalent; this explains why C60 molecules are highly mobile on graphite at RT 209,210 In contrast, the energy variation between the hump and Chcp valley is 163 meV, which exceeds the kinetic energy (kB T ≈ 25.7 meV) at RT Therefore, the surface migration of C60 is inhibited at RT and C60 will be trapped in surface potential energy wells However, the trapped C60 still has a spinning motion (rotation about the axis perpendicular to the Ru surface) since the energy barrier of spinning is very small, on the order of a few meV 209 Additional binding energy of C60 is contributed by the intermolecular van der Waals’ interactions with the neighboring C60 molecules, which provides an additional binding energy of 0.22 eV per C60 neighbor 224 Therefore, the C60 adsorbed on the Chcp site gains ∼ 1.32 eV in binding energy when surrounded by six C60 , which significantly increases the energy barrier for molecular spinning at RT Interestingly, in metal vapor deposition studies on the graphene moiré pattern on Ru(0001), Co atoms nucleate in both valley regions, 225 while Rh, 226 Pt, 227,228 Pd, 226 and Ru 212 atoms preferentially deposit in the Cfcc valley, while Au 226 very quickly forms a mono- CHAPTER GRAPHENE MOIRÉ PATTERN AS MOLECULAR TEMPLATE 95 layer on top of the graphene Sutter et al studied Ru atoms deposited on the graphene moiré pattern of Ru(0001), and they concluded that the Cfcc valley is preferred because the fcc C atoms have half-filled density of states near the Fermi level, which are like unsaturated dangling bonds that will bind to the metal atoms [see the PDOS of the fcc C atoms in Fig 5.5(a)] No such states are present for the hcp C atoms [Fig 5.5(c)] 212 The reason for the difference in the PDOS can be explained through a crystal orbital overlap population (COOP) analysis, where the wavefunction is decomposed into contributions from the atomic orbitals Consider a bond made up of two orbitals: ψ = c1 φ1 + c2 φ2 (5.2) If ψ is normalized, then |ψ|2 dr = = |c1 φ1 + c2 φ2 |2 dr = c2 + c2 + 2c1 c2 S12 , (5.3) where S12 is the overlap integral which can always be taken as a positive value The magnitude of 2c1 c2 S12 is indicative of the extent of interaction between φ1 and φ2 ; the interaction is bonding if 2c1 c2 S12 is positive (i.e., c1 and c2 have the same sign), and anti-bonding otherwise This quantity 2c1 c2 S12 is called the COOP 229 Fig 5.5(b) [Fig 5.5(d)] shows the strength of the bonding between the pz orbital of a fcc (hcp) C atom and the d-orbitals of the three nearest-neighbor 1st layer Ru atoms We can see that the pz orbital of the fcc C atom interacts mainly with the d xz and d yz orbitals, whereas the hcp C atom interacts mainly with the d yz and d x2 −y2 orbitals CHAPTER GRAPHENE MOIRÉ PATTERN AS MOLECULAR TEMPLATE 96 (a) (b) top C atom fcc C atom (c) (d) top C atom hcp C atom Figure 5.5: (a) PDOS analysis for the pz orbitals of the fcc C atoms and top C atoms with the d-orbitals of the 1st layer nearest-neighbor Ru atoms for the Cfcc valley (b) COOP analysis of the pz orbitals of the fcc C atoms with the d-orbitals of the 1st layer nearest-neighbor Ru atoms (c) & (d) are the same as (a) and (b), but for the Chcp valley instead Ef denotes the Fermi level Obviously, a different bonding mechanism is at play here for the C60 molecules as compared to the metal clusters, since the Chcp valleys are preferred instead As C60 is a well-known electron acceptor, 230 the preference for one valley over another might be due to their different electron-donating abilities We found that the workfunction of the Cfcc valley is 3.28 eV, while that of Chcp is higher at 3.05 eV From a comparison of the PDOS of the C atoms of C60 adsorbed on the Cfcc (Chcp ) valley shown in Fig 5.6(a) [Fig 5.6(b)] with the PDOS of the isolated C60 shown in Fig 5.6(c), we see that the discrete states of C60 adsorbed in the valley regions are slightly broadened but not vastly different from that of the isolated C60 molecule Hence we can conclude that the interaction between C60 and the valleys is a physisorption interaction The only major difference between C60 in the Cfcc and Chcp valleys lies in the position of the lowest unoccupied molecular orbital (LUMO) of C60 ; it seems that the higher the workfunction of the surface, the stronger the adsorption energy of the C60 To confirm this hypothesis, CHAPTER GRAPHENE MOIRÉ PATTERN AS MOLECULAR TEMPLATE 97 we calculated the charge density difference (ρdiff ) upon adsorption of C60 on the two different valleys: ρdiff (r) = ρC60 +SC (r) − ρC60 (r) − ρSC (r), (5.4) where ρC60 +SC (r) is the total charge density at point r of the supercell with the geometryoptimized C60 on the graphene and Ru(0001) surface slab, and ρC60 (r) (ρSC (r)) is the recalculated charge density of the supercell without the surface slab (C60 ) The ρdiff (r) 3-D plot shows how the charge density in the system has rearranged when C60 comes in contact with the surface slab The ρdiff 3-D plots are shown in Fig 5.6(a,b), and in both cases, we can see that there is an increase in charge density in the regions between the C60 molecule and the surface slab To quantify the charge transferred to C60 upon adsorption on the surface slab, planar averages of the charge density difference along the vertical axis are computed The charge difference planar averages were summed up for the planes from the spatial mid-point between the C60 molecule and the surface slab, up until the vacuum level This is the charge gained or lost by the C60 molecule upon adsorption in the valley sites The amount of charge gained by C60 when it is located in the Chcp region is 0.210 e, while it is 0.134 e for the Cfcc region The charge transferred to the C60 molecule is the highest for the Chcp valley, demonstrating that the higher workfunction of the Chcp valley allowed it to donate more charges to the C60 , leading to enhanced interaction between the two 5.2.3 Dendritic nanostructures from hierarchical assembly of C60 on graphene moiré pattern On the smooth graphite surface, C60 islands are observed to grow in a compact manner 211 In contrast, C60 dendritic islands with lobes – which are characteristic of diffusionlimited growth – are observed to grow on the graphene moiré pattern on Ru(0001), as shown in Fig 5.7(a) The graphene moiré humps act as diffusion barriers, so the C60 molecules adsorb on the graphene surface and then diffuse to the valley regions ¯ with high binding energies, which are in the 0110 directions The dendritic branches ¯ are thus oriented along the 0110 directions and their edge boundaries are terminated CHAPTER GRAPHENE MOIRÉ PATTERN AS MOLECULAR TEMPLATE 98 (a) Cfcc valley (c) C60 (b) Chcp valley C Ru(1st layer) Ru(2nd layer) Figure 5.6: PDOS and charge density difference plots of C60 adsorbed on the (a) Cfcc valley, and (b) Chcp valley The blue-dotted volume is the +0.0005 e/bohr3 isosurface, while the red solid volume is the −0.0005 e/bohr3 isosurface (c) PDOS for an isolated C60 by the moiré hump regions, resulting in a zigzag-type edge configuration [Fig 5.7(b– d)] The first layer C60 film exhibits an apparent corrugation of 0.15 nm when the sample is biased at +1 V, similar to the topological variation of the graphene moiré hump and valley At −1 V, the bright-dim contrast is maintained, indicating that the bright-dim features are the result of topological corrugations and not electronic variations [Fig 5.8(a,d)] Nucleation of the second layer takes place when the first layer C60 islands exceed a critical size of 200 ± 20 nm The second layer islands exhibit the same anisotropic growth behavior as the first layer islands [Fig 5.8(b)], which implies that the growth of the first two layers is influenced by the topography of the substrate The preferred adsorption sites for the second layer of C60 molecules are the three interstitial sites next to the first-layer C60 that is sitting on the hump, so a bright C60 trimer is seen in the STM image of the second layer CHAPTER GRAPHENE MOIRÉ PATTERN AS MOLECULAR TEMPLATE 99 (a) (b) (c) (d) Figure 5.7: STM images of the dendritic growth of C60 islands on the graphene moiré pattern (a) The C60 islands at 0.4 ML coverage (b) The grain boundary of the first layer C60 has zigzag edges (c) At 1.8 ML coverage, second and third layer growth of C60 occurs The dendritic growth of the second-layer C60 islands is aligned with the first-layer C60 islands The growth of the third layer becomes compact (d) Magnified view of green-dotted region in (c) reveals that the growth front of the first-layer dendritic ¯ C60 islands are along the 0110 directions, which is rotated by 30◦ with respect to the ¯ 1120 translational directions of the graphene moiré superlattice STM parameters: V = 1.2 V, I = 0.1 nA (a) (b) (c) (d) Figure 5.8: High-resolution STM images of the (a) first, (b) second, and (c) third layer of C60 films showing the bright-dim contrast in the first and second layer, but not in third layer (d) The height profile analysis of the brightest (highest) and dimmest (lowest) points in the STM scan of the first, second, and third layer C60 islands There is a progressive decrease in the height differential between the highest and lowest points as the number of C60 layers is increased STM parameters: V = 1.2 V, I = 0.1 nA CHAPTER GRAPHENE MOIRÉ PATTERN AS MOLECULAR TEMPLATE 100 (a) (b) (c) (d) (e) (f ) Figure 5.9: (a–f) Transforming dendritic islands with different thickness to compact islands by thermal annealing at 423 K for 10 minutes The influence of the substrate weakens significantly when it comes to the growth of the third layer, where the formation of compact triangular islands reflect the 3-fold symmetry of C60 molecules in the close-packing arrangement [Fig 5.8(c)] The dimbright pattern observed for the first two layers of C60 is also not seen for the third layer When the substrate temperature is increased to 423 K, the edge and corner diffusion becomes thermally-activated and the dendritic islands transform into compact islands, as shown in Fig 5.9(a–f) The dendritic C60 nanostructures formed on the graphene moiré pattern could see applications in nanoelectronics and optoelectronics, since the electrical and optical properties of C60 s are influenced by their supramolecular geometries 231 5.3 Conclusion In summary, we have shown through DFT calculations that the adsorption energies of C60 molecules on the corrugated topology of the graphene moiré superlattice varies from −1.744 eV in the Chcp valleys, to −1.704 eV in the Cfcc valleys, and −1.581 eV at the hump regions The interaction between the C60 molecules and the graphene moiré superlattice is a physisorption interaction, and the preference for the Chcp valley CHAPTER GRAPHENE MOIRÉ PATTERN AS MOLECULAR TEMPLATE 101 is due to the higher workfunction of the Chcp valley, which donates more electrons to the electron-accepting C60 This is in contrast to the previous studies on metal atom deposition on the graphene moiré superlattice, where the metal atoms preferentially chemisorb in the Cfcc valleys, which have half-filled density of states at the Fermi level Due to the large adsorption energy at the moiré valleys, freezing of the molecular rotation and spatial alignment of individual C60 molecules can be attained at room temperature (RT) Such a highly-oriented molecular array that is stable at RT may be potentially useful for applications in molecular spintronics, especially when endohedral fullerenes with magnetic spins can be aligned ... the graphene moiré pattern on Ru(0001), Co atoms nucleate in both valley regions, 22 5 while Rh, 22 6 Pt, 22 7 ,22 8 Pd, 22 6 and Ru 21 2 atoms preferentially deposit in the Cfcc valley, while Au 22 6... orbitals Consider a bond made up of two orbitals: ψ = c1 φ1 + c2 ? ?2 (5 .2) If ψ is normalized, then |ψ |2 dr = = |c1 φ1 + c2 ? ?2 |2 dr = c2 + c2 + 2c1 c2 S 12 , (5.3) where S 12 is the overlap integral... About 23 % of the CHAPTER SYNTHESIS OF GRAPHENE- RELATED MATERIALS 68 (a) (b) (d) (e) (c) (f) Figure 4.1: (a) STM image of the graphene moiré pattern formed from the decomposition of 1 .2 ML of C60