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Silicon carbide (SiC) is an excellent substrate for growth and manipulationof large scale, high quality epitaxial graphene. On the carbon face (the($\bar{1}\bar{1}\bar{1}$) or $(000\bar{1}$) face, depending on the polytype),the onset of graphene growth is intertwined with the formation of severalcompeting surface phases, among them a (3$\times$3) precursor phase suspectedto hinder the onset of controlled, near-equilibrium growth of graphene. Despitemore than two decades of research, the precise atomic structure of this phaseis still unclear. We present a new model of the(3$\times$3)-SiC-($\bar{1}\bar{1}\bar{1}$) reconstruction, derived from an {\itab initio} random structure search based on density functional theory includingvan der Waals effects. The structure consists of a simple pattern of five Siadatoms in bridging and on-top positions on an underlying, C-terminatedsubstrate layer, leaving one C atom per (3$\times$3) unit cell formallyunsaturated. Simulated scanning tunneling microscopy (STM) images are inexcellent agreement with previously reported experimental STM images.

The (3$\times$3)-SiC-($\bar{1}\bar{1}\bar{1}$) Reconstruction: Atomic  Structure of the Graphene Precursor Surface from a Large-Scale  First-Principles Structure Search