6.2 Structure of graphene nanoflakes on Au(111)
6.2.2 Atomic structure of graphene nanoflake edges on Au(111)
Apart from the general graphene-substrate interaction, the bonding between the edges of GNFs and the substrate is important. High resolution STM topographies yield infor-mation on the atomic arrangement of GNF edges and LDOS features at the edge allow for a derivation of a possible H-termination. In Figure 6.9 (a) the edge region of a float-ingGNF is depicted. The edge runs mainly parallel to the zigzag direction of graphene.
A closer inspection in Figure 6.9 (b) shows intermediate armchair segments that are in-corporated into the zigzag dominated edge. The apparent height of the zigzag regions features bright spots constituting arcs that begin at the flake edge and then bend into the
2Calculation details G/Au(111): The projector augmented plane wave method [223] is used with a plane wave basis set with a maximum kinetic energy of 500 eV and the PBE exchange-correlation potential [224]
implemented in the VASP program [225]. Long-range van der Waals interactions were included using a semi-empirical DFT-D2 approach proposed by Grimme [226]. Interactions between periodic images of the slab are avoided by using a dipole correction [227]. The surface Brillouin zone is sampled with a 3×3k-point mesh centered theΓpoint. The graphene/Au interface is modeled using supercells, which have a (6×6) lateral periodicity and contain one layer of (7×7) graphene on a four-layer slab of metal atoms. The slab replicas are separated by approximately 18 Å in the surface normal direction. STM images were generated according to Tersoff-Hamann formalism [149] as implemented in [228]. Calculations performed by E. N.
Voloshina, Humboldt Universität zu Berlin.
6.2 Structure of graphene nanoflakes on Au(111) 95
(a)
2 nm
b
5 Å
STM
(b) (c)
freestanding G / single H termination
DFT
Figure 6.9 | Atomic structure of GNF edges on Au(111).(a)Atomically resolved STM topography of the edge of a GNF. The inset shows the honeycomb lattice of graphene within the flake.(b) Magnifi-cation of the area marked in (a).(c)Simulated STM image of a freestanding graphene segment using the Tersoff-Hamann approximation. The simulation reproduces the experimentally observed apparent height well. DFT calculation and Tersoff-Hamann simulation was performed by E. N. Voloshina and L.
Hammerschmidt. Scanning parameters: (a-b)V=-0.3 V,I=1.2 nA,T=10 K; (c)E−EF= 0...-0.3 eV.
Reprinted with permission from [218]. Copyright 2014 American Chemical Society.→Online.
GNF interior. Since the apparent height is considerably influenced by the LDOS of the sample on top of a possible bending of graphene at the edges, a large apparent height of single atoms is predominantly connected to a large LDOS. Highest intensity in the topography in Figure 6.9 (b) is found in the vicinity of zigzag edges concentrated on one sublattice of graphene. Consequently graphene rings are represented by single atomic protrusions instead of carbon rings due to the LDOS variations close to edges. Further into the flake interior the increased apparent height of the edge sublattice decays and the honeycomb lattice is completely restored within several nanometers [see inset in Figure 6.9 (a)]. The observation of increased LDOS connected to one single sublattice close to the edge is possibly connected to the formation of edge states, which are expected also for rougher zigzag edges as discussed in section 2.2.1.
The experimentally extracted atomic arrangements of the edges were compared with the results of DFT including Tersoff-Hamann simulations3. The DFT calculation was car-ried out for a free-standing graphene sheet (neglecting a substrate influence) with unre-constructed and single H-terminated edges (one hydrogen atom per edge carbon atom).
3Calculation details freestanding G: The projector augmented plane wave method [223] is used with a plane wave basis set with a maximum kinetic energy of 500 eV and the PBE exchange-correlation potential [224] implemented in the VASP program [225]. The surface Brillouin zone is sampled with a 3×3k-point mesh centered theΓpoint. The slab replicas are separated by approximately 15 Å in the surface normal direction. C–C and C–H bond lengths were fixed to 1.442 Å and 1.084 Å, respectively. STM images were generated according to Tersoff-Hamann formalism [149] as implemented in [228]. Calculations performed by E. N. Voloshina, Humboldt Universität zu Berlin and L. Hammerschmidt, Freie Universität Berlin [218].
(a)
(b) i
without H termination with H termination
iii ii
Figure 6.10 | DFT calculations of graphene edges. (a) Simulated STM image of a single H-terminated free-standing graphene edge. (b)Simulated STM image of an unsaturated free-standing graphene edge. In both simulations no substrate is considered. Simulation of STM using Tersoff-Hamann approximation. DFT calculations and Tersoff-Tersoff-Hamann simulations were performed by E.
N. Voloshina and L. Hammerschmidt. E−EF = 0..+0.3 eV. Reprinted with permission from [218].
Copyright 2014 American Chemical Society.→Online.
A simulation of the STM image was performed using the Tersoff-Hamann approxima-tion. A H-termination is very likely in experiment due to ubiquitous residual hydrogen in UHV chambers and during the preparation procedure involving thermal decomposi-tion of hydrocarbons. In Figure 6.9 (c) the STM simuladecomposi-tion of the edge structure shows similar features as in the original STM image. The majority of the LDOS is localized at the C-H group of zigzag edges and the corresponding sublattice. Armchair segments incor-porated into the zigzag edge, or small zigzag segments lead to the reduction of LDOS on specific atoms in the bright edge sublattice. On the large scale these LDOS modulations are often recognized as the characteristic arc-like features in STM images. Good overall agreement is achieved despite the neglected substrate interactions.
In order to strengthen the assumption of single H-termination, further calculations on graphene edges with and without single H-termination and neglected substrate were performed. In Figure 6.10 (a-b) the simulated STM images in Tersoff-Hamann approx-imation obtained from the two DFT calculations on the same graphene edge, but with different termination is shown.
In the case of H-termination similar results as in Figure 6.9 (c) were obtained. Note the different tunneling voltage of−0.3 eV in Figure 6.9 (c) compared to 0.3 eV in Figure 6.10. Again the LDOS is mainly localized on the C-H groups of zigzag elements and the corresponding graphene lattice. The LDOS on the bright edge sublattice decays within
∼10 atomic rows into the flake neutralizing the sublattice asymmetry. A calculation of the same edge segment without H-termination, i.e. with dangling bonds in Figure 6.10 (b) yields diverse results. In this case the LDOS is smeared across several atoms of straight zigzag edges. The LDOS closer to the interior of the flake is distributed such that two
6.2 Structure of graphene nanoflakes on Au(111) 97
Figure 6.11 |Graphene nanoflake. STM topography of a small GNF. Scanning parameters: V=0.3 V, I=1.0 nA,T= 10 K. Reprinted with permission from [218]. Copyright 2014
American Chemical Society.→Online. 3 nm
zig-zag zig-zag
nearest neighbor atoms exhibit increased LDOS. Consequently, the LDOS modulation occurs in both sublattices in contrast to the calculations with H-termination, where only the edge sublattice shows increased LDOS modulations.
The comparison shows that the experimentally observed situation for GNFs/Au(111) is well described by single H-terminated graphene without consideration of the metal substrate. Consequently a negligible interaction between H-terminated graphene edges on Au(111) is inferred. Theoretically this conclusion is backed up by a DFT calculation on ZGNRs on Au(111) with and without H-termination including the metal substrate by Liet al.[229]. In this work the graphene edge is found to bind to the metal atoms leading to a strong bending of the graphene edge in the case of missing H-termination. In con-trast, the H-terminated ribbon is found virtually flat without edge-metal bonding formed [229]. The results presented here are furthermore in line with results on deliberately hydrogenated graphene ribbons on Au(111) [230] and with experiments on bottom-up fabricated graphene ribbons on Au(111) surfaces [231]. The observed LDOS variations of H-terminated graphene edges on Au(111) and the propagation of LDOS patterns into the flake is consistent with experiments performed on HOPG [62, 63] further underlining the negligible influence of the metal substrate.
In Figure 6.10 several characteristic zigzag and armchair combinations were intro-duced into the edge region in order to resemble frequently observed experimental con-figurations: i) A missing carbon atom is introduced into a long zigzag element, ii) a short armchair edge segment is connected to two parallel zigzag edges, iii) two parallel long zigzag edges are interrupted by a short zigzag segment running 60° to the main edge di-rection. The general appearance of long zigzag edges resembles an appearance where only the edge sublattice is bright with only little intensity modulation within the atomic rows close to the edge. Such LDOS patterns are depicted in the image by a rhombus connecting the atoms of a single sublattice of graphene. In contrast, the perturbations induced in i)-iii) commonly give rise to LDOS modulations showing intensity on six next-nearest neighbor carbon atoms constituting a hexagon. These superstructure
modula-10 nm
(e) (c)
(d) (b)
(a)
d
b c
B A
Figure 6.12 | Defects in G/Au(111). (a)GNF with a large number of defects. LDOS modulations are formed in the vicinity of defects.(b-c)Magnifications of two characteristic defects.(d)LDOS modula-tions giving rise to (p3×p3)R30◦features are also observed far away from defects.(e)FFT showing the reciprocal lattice of graphene including satellite peaks from moiré and herringbone reconstruction (A) and the (p3×p3)R30◦superstructure (B). Scanning parameters:V=-20 mV,I=0.5 nA,T=9.3 K.
Size: (a) 30.5×30.5 nm2; (b-e) 4.2×4.2 nm2.
tions are responsible for the (p 3×p
3)R30° features commonly observed in literature for HOPG and SiC [55, 62, 63, 74]. The calculation also shows that armchair edges (ii) of-ten show lower LDOS and especially one sublattice remainsdark. A similar loss of LDOS intensity is furthermore experienced for arrangements of short zigzag edges (iii).
The results show the importance of the LDOS for interpretations of STM topogra-phies and underline possible limitations for the determination of atomic edge configu-rations from STM images. In Figure 6.11 an example of a small GNF is presented, where the LDOS modulations due to the graphene edges define the edge appearance and prop-agate far into the flake interior. The left side of the flake consists of largely zigzag oriented edge segments and represents again LDOS modulation features similar to the calcula-tions in Figure 6.10. The right side on the other hand shows more complicated LDOS modulations which presumably arise due to a rougher edge termination with a larger amount of armchair segments [62, 75].