Density functional study of graphene overlayers on SiC

Abstract

Despite the ongoing “graphene boom” of the last three years our understanding of epitaxial graphene grown on SiC substrate is only beginning to emerge. Along with experimental methods such as low energy electron diffraction (LEED), scanning tunneling microscopy (STM) and angle resolved photoemission spectroscopy (ARPES), ab initio calculations help to uncover the geometric and electronic structure of the graphene/SiC interface. In this chapter we describe the density‐functional calculations we performed for single and double graphene layers on Si‐ and C‐terminated 6H‐SiC surfaces. Experimental data reveal a pronounced difference between the two surface terminations. On a Si‐terminated surface the interface adopts a 6√3 × 6√3 unit cell whereas the C‐face supports misoriented (turbostratic) graphene layers. It has been recently realized that, on the Si‐face, the large commensurate cell is subdivided into patches of coherently matching to the substrate carbon atoms. In our calculations we assumed the “coherent match” geometry for the whole interface plane. This reduces the periodic unit to the √3 × √3R 30° cell but requires a substantial stretching of the graphene sheet. Although simplified, the model provides a qualitative picture of the bonding and of the interface electron energy spectrum. We find that the covalent bonding between the carbon layer and the substrate destroys the massless “relativistic” electron energy spectrum, the hallmark of a freestanding graphene. Hence the first carbon layer cannot be responsible for the graphene‐type electron spectrum observed by ARPES and rather plays a role of a buffer between the substrate and the subsequent carbon sheets. The “true” graphene spectrum appears with the second carbon layer which exhibits a weak van der Waals bonding to the underlying structure. For Si‐terminated substrate, we find that the Fermi level is pinned by the interface state at 0.45 eV above the graphene Dirac point, in agreement with experimental data. This renders the interface metallic. On the contrary, for a C‐face the “coherent match” model predicts the Fermi level exactly at the Dirac point. However, this does not necessarily apply to the turbostratic graphene layers that normally grow on the C‐terminated substrate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Contribution of the buffer layer to the Raman spectrum of epitaxial graphene on SiC(0001)

“…Since the unit cell of the (6 √ 3 × 6 √ 3)R30 • reconstruction (and even of the recently proposed (5 × 5) superstructure [35]) is prohibitively large for ab initio calculations of phonons, we have chosen to work with the ( √ 3 × √ 3)R30 • reconstruction which was also used in the electronic structure calculations of [26][27][28][29]. The model has been shown to lead to good qualitative agreement with experimental data.…”

Epitaxial graphene: a new material

“…For SiC(0001) pressing evidence is found for an interface carbon layer with graphene-like atomic arrangement bound covalently to the substrate forming the 6 3 reconstruction. A similar model was proposed in theoretical studies [84][85][86][87]. This model structure consists of a covalently bound stretched graphene layer, where the C-C distance had to be dilated by 8% in order to obtain a small enough unit cell that could be handled numerically.…”

“…This failure to describe the experimentally determined electronic structure correctly is most likely due to the simplified surface unit mesh which leads to too many dangling bonds. For the C-face the theoretical model [84][85][86][87] does not apply: the experimental data do not give any indication for a covalently bound graphene layer. Instead it is found that graphene is bound by weak dispersion forces to the SiC(000 1) surface.…”

Epitaxial Graphene: A New Material

“…As discussed elsewhere, this failure to describe the experimentally determined electronic structure correctly is most likely due to the wrong choice of surface unit mesh which leads to too many dangling bonds. On the C-face the model studied theoretically [63][64][65][66] does not apply at all: the experimental data do not give any indication for a covalently bound graphene layer. Instead it is found that graphene is bound by weak dispersion forces to the SiC(0001) surface.…”

“…For SiC(0001) pressing evidence is found for a graphene-like interface layer bound covalently to the substrate forming the 6 √ 3 reconstruction. A similar model was proposed in theoretical studies [63][64][65][66]. This model structure consists of a covalently bound stretched graphene layer, where the C-C distance had to be dilated by 8% in order to obtain a small enough unit cell that could be handled numerically.…”