12 The Electronic Structure of Epitaxial Graphene on 3C-SiC(111)
12.3. The Silicon Dangling Bonds and their Effect on the Electronic Structure
3C-SiC has a band gap of 1.44 eV (PBE) and experimental gap of 2.2 eV [204] (see Tab. 7.3). For ZLG the band gap is reduced to 300 meV (STS measurements) [270,109]. In Section12.1, we discussed the theDOSclose to the Fermi level. However, we could not reproduce the opening of a small band gap.
Figure 12.7.: The bulk projected Kohn-Sham band structure and DOS of the √
3-MLG structure with the Si dangling bond satur-ated by an H atom. The full band structure andDOSof the slab used in the calculation is shown in red and the3C-SiCbulk states in grey.
In Chapter9, we found 19 unsatur-ated Si atoms – the Si dangling bonds – at the interface between the SiC substrate and theZLGlayer. Their influence on the electronic structure and how they effect the graphene electronic properties is not fully un-derstood. It is speculated that the difference in the electronic struc-ture between the ZLG- and MLG layer is due to partial hybridisation of the C atoms in the ZLG layer and the substrate Si atoms [83,263].
It is conceivable that for the ZLG the observed low DOS in the SiC bulk band gap are caused by the un-saturated Si atoms in the top SiC bilayer.
Figure 12.8.: Four times theZLGlayer coloured depending on the Hirshfeld charge of the C atom from blue for electron gain to red for electron loss. The position of the unsaturated Si atoms is shown in pink. TheSTMimage taken from Qi et al. [256] is shown for comparison.
To evaluate the influence of the Si dangling bond, we will use the√
3-ZLG model as introduced in Sec. 12.1. The advantage of this approximated structure over the true (6√
3×6√
3)-R30◦ is that the Si dangling bond can be clearly distinguished from the two covalently bounded Si atoms.
In Figure 12.2 the Fermi level was pinned by a flat surface state in all three phases, the√
3-ZLG,√
3-MLGand√
3-BLG. The main suspect is the unsaturated Si dangling bond in the top SiC-bilayer at the interface. To evaluate the origin of the flat surface band, we saturated the Si dangling bonds by one H atom. After optimising the atomic structure, we calculated the band structure and DOS. In the band structure (Fig. 12.7) the Dirac point coincides with the Fermi level, such that the surface is undoped.
The3C-SiC bulkCBm is shifted away from the Fermi level. The energy difference betweenEDand theCBmis slightly reduced to 0.51 eV compared to 0.63 eV in the √
3-MLG(see Sec. 12.1). The surface band at the Fermi level disappeared. From Fig.12.7, we can conclude that the doping of the MLGlayer is induced by the Si dangling bonds at the interface and that it indeed give rise to the flat surface state at the Fermi level.
Using the √
3-ZLG model, we found that the Fermi level is determined by the interface structure most likely induced by charge transfer from the dangling Si bonds at the interface. We marked the Si dangling bonds underneath the ZLGlayer in pink in Fig.12.8. On the basis of geometric position and bond length differences, we identified the Si dangling bonds
(for a detailed discussion see AppendixE). They form two different types of cluster: two triangular shaped clusters per unit cell and one hexagonal.
The hexagonal cluster is centered around the Si atom positioned exactly in the middle of a C hexagon of theZLGlayer (see Fig.12.8). The dangling bond cluster give rise to the characteristic corrugation of theZLGlayer as discussed in Sec.9.1.
We can assign every C atom in theZLGlayer a charge by using the Hirshfeld partitioning scheme [142]. The calculated charge partitioning is shown in Fig. 12.8. On average, a C atom in the ZLGlayer is negatively charged by 0.024 e−/atom, which is reduced to 0.021 if a additionalMLG-layer is adsorbed (see Tab.12.1). The charge transfer in theZLGlayer is maximal at C atoms with a Si atom right underneath forming a strong covalent bond (shown as blue C atoms in Fig.12.8). On the other hand, for C hexagons on top of a Si dangling bond the electrons disperse (indicated by red C atoms in Fig.12.8).
In 2010, Qi et al. [256] visualised theZLGsurface usingSTMwith a special iron treated tip. They found two differently shaped patterns in theirSTM images: one hexagonal and two triangular pattern (theSTMimage taken by Qi et al. [256] is shown in Fig. 12.8). They suggested the presence of C-rich hexagon-pentagon-heptagon (H5,6,7) defects at two different defect positions, “hollow” and “top” (see Fig.9.4). In Section9.2, we demonstrated that the formation energy for these defects make their presence at the interface unlikely.
Due to the two different types of cluster formed by the Si dangling bonds, the charge in theZLGlayer is redistributed. The resulting pattern of the Hirshfeld charge map of theZLGlayer looks similar to the pattern seen in STM. It is conceivable that Qi et al. [256] actually visualised the Si dangling bonds in their measurements.
12.4. Summary
In conclusion, we used density-functional approximation (DFA)HSE06+vdW and PBE+vdWcalculations to evaluate the origin of doping in epitaxial few-layer graphene on the Si face of SiC. The√
3-approximated interface structure features three Si atoms in the top layer of which two are covalently bonded and one is unsaturated. Because of the clear interface structure the dangling bond can be identified. We evaluated the influence of the dangling bond on theZLG-layer and few-layer graphene. We found that indeed the
Si dangling bond dopes theZLG,MLGandBLGby a interface state at the Fermi level. TheBLGstructure has a Kohn-Sham band gap of 0.33 eV using theHSE06functional. Saturating the Si dangling bond by a hydrogen atom shifts the graphene Dirac point to the Fermi energy resulting in an undoped epitaxial graphene layer. Evaluating the electron density ofMLGwe found a doping of 0.0019 e−/atom (experiment∼0.005 e−/atom [83,35,238]). The doping shifts the Dirac point to −0.22 eV (experiment−0.4 eV). However, the doping as well as the corrugation of the MLG layer hardly disturb the graphene π bands. In the case of the 6√
3-ZLGstructure, we found a very low DOSnear the Fermi level, which might be to low to be detec-ted experimentally. Evaluating the electron density of the 6√
3-ZLGwe found a pattern in the electron density ofZLGsimilar to theSTMimages from Qi et al. [256]. In the STM image as well as in the electron density plot two differently shaped patterns are found: one hexagonal and two triangular pattern per unit cell. Similar to the patterns visualised inSTM measurements by Qi et al. [256].