Interface structure for growth of epitaxial graphene on SiC(0001)

In spite of the enormous effort devoted to the study of the epitaxial growth of graphene on SiC, there is not yet a consensus regarding the structure of the interface between graphene and the substrate. There have been a long standing discrepancy between low energy electron diffraction (LEED) and STM patterns regarding the periodicity of graphene on SiC(0001); the theoretical studies of the of $6\sqrt{3}\times6\sqrt{3}$ \footnote{S. Kim, J. Ihm, H. J. Choi, and Y. W. Son, Phys. Rev. Lett. {\bf 100}, 176802 (2008).} or $\sqrt{3}\times\sqrt{3}$ \footnote{F. Varchon {\em et al}, Phys. Rev. Lett. {\bf 99}, 126805 (2007); A. Mattausch and O. Pankratov, Phys. Rev. Lett. {\bf 99}, 076802 (2007} periodicity, while describing some aspects, disagree in important details with scanning tunneling microscopy (STM) images. We present a combined theoretical and experimental study, employing density functional calculations and STM, to investigate this issue. We propose the formation of a defected graphene layer at the interface, and then subsequent growth of graphene. The calculated bias-dependent STM images are in good agreement with our STM images, and provide insight into the details of the interface structure.