In experiment, the first stage of graphitisation is the carbon rich surface structure, the so-called zero-layer graphene (ZLG) or ’buffer-layer’. The detailed atomic structure was debated for many years as there is conflicting experimental evidence in the literature. InSTMa (6×6) pattern is imaged [192, 210, 55, 307]. On the other hand, LEED measurements indicate a (6√
3×6√
3)-R30◦ periodicity [332,264]. Also, the detailed atomic structure of the carbon nano-mesh has been under debate until recently. Chenet al.
[55] suggested a nano-mesh structure with isolated carbon islands and Qi et al.[256] suggested an arrangement of C-rich hexagon-pentagon-heptagon (H5,6,7) defects in the ZLG (the defects are discussed in more detail in Sec. 9.2). In 2009, Riedl et al. [262] demonstrated that the ZLG can be converted intosp2bonded graphene layer, the so-called quasi-free-standing mono-layer graphene (QFMLG) (see Ch.13), by intercalation of hydrogen at the SiC-graphene interface. This was interpreted as a strong argument in favour of the hexagonal atomic arrangement in theZLG [109]. Goler et al.[109] clarified the atomic structure of theZLGby atomically-resolved STM imaging. They demonstrated that the ZLG is indeed topologically identical to a graphene monolayer and thus represents a true periodic carbon honeycomb structure. They could not observe any obvious atomic defects in theQFMLG and concluded that also the defect concentration in theZLGis most likely very low. Today, the general consensus is that the C atoms arrange in a hexagonal atomic lattice such as in free-standing graphene [264,83,335,166,183,263,109].
The (6√ 3×6√
3)-R30◦periodicity originates from the lattice mismatch be-tween the SiC and the graphene lattice parameter. The large, commensurate ZLGunit cell consists of a (6√
3×6√
3) SiC supercell (108 Si and 108 C atoms per bilayer) covered by a (13×13) honeycomb graphene-like supercell (338 C atoms) [264, 83, 335, 166, 263, 109, 227]. The lattice match is almost strain-free compared to a graphene plane in graphite (experiment: 0.2 % at T=0 K [195,9], PBE+vdW: 0.1 % Tab. 7.2, see Ch. 9). The C atoms in the ZLG-layer are partially covalently bonded to the top Si atoms of the substrate.
Continued heating and extended growth times detaches the C-plane of the ZLGfrom the substrate to formMLGand a newZLG-layer underneath [293, 125]. TheMLG-layer is asp2bonded graphene layer. Further heating leads to a successive formation ofBLG[238] and few-layer graphene films. In
the following, we address the C-rich surface phases in their experimentally observed, large commensurate (6√
3×6√
3)-R30◦ supercells, using slabs containing six SiC-bilayers under each reconstructed phase (1742 up to 2756 atoms forZLGup to three-layer graphene (3LG), respectively).
Figure 8.4.: Top view of the relaxedZLGstructure usingPBE+vdW. The unit cell in the x-y-plane is indicate by a grey rhombus. The C atoms in the ZLG layer are coloured according to theirz-coordinate (the colour scale reaches from yellow for atoms close to the substrate to blue for atoms away from it). The top Si-C bilayer is shown as well, here thez-coordinate scales from black to white, where black indicates that the atom is pushed towards bulk SiC. The ZLG hexagons furthest away from the substrate form a hexagonal pattern (marked in grey). The Si atom of the top Si-C bilayer in the middle of a ZLG carbon ring has the minimumz-coordinate (in the middle of the unit cell marked in light green).
Figure8.4shows the geometric structure of theZLG-layer and the top Si-C bilayer from a top view. The unit cell in the x-y-plane is indicate by a grey rhombus. The atoms in the structure are coloured depending on their position along thez-axis. The atoms of the top Si-C bilayer are coloured from black to white, where black indicates an atom position close to the substrate and white close to the ZLG-layer. The colour scale for the atoms in the ZLG-layer ranges from yellow for atom positions close to the substrate to blue for atoms away from it. In theZLG-layer, the atoms furthest away from the substrate (shown in blue) form a hexagonal pattern (marked in grey).
The corrugation of theZLG-layer is also observed inSTMexperiments [166, 335,263,68,80]. Riedlet al.[263] used atomically resolvedSTMimages to construct a model of the (6√
3×6√
3)-R30◦interface structure they found a quasi (6×6) periodicity in good agreement with the pattern in Fig.8.4(see Ref. [263] Figure 3.d). The Si atom of the top Si-C bilayer with the minimum z-coordinate is located in the middle of aZLGcarbon ring (in the center of the unit cell shown in Fig.8.4). The corrugation originates from an interplay
between C atoms covalently bonded to the substrate and sp2 hybridised ones.
The next C-rich phase consists of theZLGphase covered by a purelysp2 bonded graphene layer, theMLG. The MLGlayer is a (13×13) graphene cell stacked on top of the ZLG-layer in graphite-like AB stacking. The BLGphase consists of theZLGstructure covered by two graphene layer in graphite-likeABAstacking.
Figures8.5a-c show theZLG,MLGandBLGphases together with key geo-metry parameters predicted at the level ofPBE+vdW. To capture the extend of the corrugation shown in Fig.8.4and analyse its effect on the substrate and the adsorbed graphene layer, we plotted histograms for the atomic z-coordinates. For illustration purposes, we broadened the histogram lines using a Gaussian with a width of 0.05 Å.
The corrugation from the highest C atom to the lowest C atom in the ZLG-layer is 0.83 Å. Emery et al. [80] found a corrugation of 0.9 Å by x-ray standing-wave-enhanced x-ray photoemission spectroscopy (XSW-XPS) and x-ray reflectivity (XRR) measurements [80]. Few of the Si atoms of the top Si-C bilayer are pushed into the carbon layer of the top Si-C bilayer.
We highlighted the lowest Si atom in Fig.8.4, as pointed out above the Si atom is underneath the midpoint of a carbon hexagon in theZLG-layer. The dangling bond of this Si atom pushes against theπ-bonded parts of the C interface plane [334].
The addition of more graphene planes hardly affects the interface geometry.
The corrugation of the ZLG-layer transfers to the MLG phase, leading to a significant buckling of the topmost graphene layer (0.41 Å between top and bottom of the plane). This strong corrugation is qualitatively consistent with x-ray characterisation techniques (XSW-XPS, XRR) [80] and STMimages [55,65,21]. The corrugation is reduced in theBLGphase to 0.32 Å in the first graphene layer and 0.24 Å in the second one. This buckling reflects some coupling to the covalently bonded interface C-rich plane, which is much more corrugated (0.8 Å in our work, similar to experimental estimates [109,68]). The observed graphene interplanar distances near the interface are slightly expanded compared to experimental bulk graphite (3.34 Å [9]) and in good qualitative agreement with estimates fromSTM[21]
andTEM[230].
Figure 8.5.: Geometry and key geometric parameters determined by DFT-PBE+vdW for the three phases (a)ZLG, (b)MLGand (c)BLGon the Si face of3C-SiC(111) and histograms of the number of atoms (Na) versus the atomic coordinates (z) relative to the topmost Si layer (Gaussian broadening: 0.05 Å). Nais normalised by NSiC, the number of SiC unit cells. All values are given in Å. (Data published in Nemecet al.[227])
We compared our findings to geometries for the PBEfunctional without vdWcorrection, and forLDA(Fig.8.6). TheLDAandPBEfunctional show a similar trend for the interplanar bonding of theMLG-layer as for graphite (see Ch.6.2). InPBE, the interplanar distance between theZLGand MLG-layer is unphysically expanded to 4.42 Å. In contrast, theLDAgeometry of the carbon planes agrees qualitatively withPBE+vdW, althoughLDA incorporates no long-rangevdWinteractions. The first qualitative geometry difference between thePBE+vdWandLDAtreatments appears in the cor-rugation of the Si atoms in the top Si-C bilayer. InPBE+vdWthe distance between top an bottom Si atom is 0.76 Å, but inLDAit is reduced to 0.53 Å (PBE: 0.08 Å). The difference mainly originates from the central Si atom (shown in Fig.8.4), where the Si dangling bond pushs against theπ-bonded parts of the C interface plane.
Figure 8.6.: Histogramm of the number of atoms Na versus the atomic coordinates (z) relative to the topmost Si layer (Gaussian broadening: 0.05 Å). The key geometric parameter of theMLGon the Si face of3C-SiC(111) at the level of a)LDAand b)PBE. All values are given in Å.
The atomic density map derived from combined XSW-XPS and XRR ana-lysis [80], also shows a significant broadening for the Si atoms in the top Si-C bilayer. However, the corrugation in the top Si-C bilayer was not the focus of the experimental work [80] and therefore cannot clarify the observed difference in the geometry obtained by using theLDAandPBE+vdW func-tional. We will keep these subtle differences in mind, when discussing our results.
The Si-terminated surface of6H-SiCis widely used to achieve a controlled formation of high quality epitaxial graphene monolayers [95,82,307,263].
In the following, we discuss the structural difference between3C-SiC- and 6H-SiC-MLG. For the 6H-SiC-MLG, we use the S36H terminated surface (see Fig.8.1) and the lattice parameter listed in Tab.7.2. For the structure optimisation, we used thePBE+vdWexchange-correlation functional.
Figure 8.7:MLGon6H-SiC(0001) and histogram of the number of atoms Na versus the atomic co-ordinates (z) relative to the top-most Si layer (Gaussian broaden-ing: 0.05 Å). Nais normalised by NSiC, the number of SiC unit cells.
Dn,n+1 is the distance between the layer n and n+1, dn gives the Si-C distance within the SiC bilayern, andδnthe corrugation of the layer n. All values are given in Å. (Figure published in Ref. [294])
Overall, the atomic structure of3C-SiC-MLG(Fig.8.5b) and6H-SiC-MLG (Fig.8.7are very similar. For6H-SiC-MLG, the corrugation of theMLG-layer and of theZLG-layer is slightly increased to 0.45 Å and 0.86 Å, respectively.
However, the layer distances Dn,n+1 are the same for 6H-SiC-MLG and 3C-SiC-MLG. Overall, the changes with the polytype are minor, which is not surprising as the Si-C bilayer stacking order is identical for3C-SiCand S36Hterminated6H-SiC.