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.