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We use ab initio density functional calculations to determine the interactionof a graphene monolayer with the Si(111) surface. We found that graphene formsstrong bonds to the bare substrate and accommodates the 12% lattice mismatch byforming a wavy structure consisting of free-standing conductive ridges that areconnected by ribbon-shaped regions of graphene, which bond covalently to thesubstrate. We perform quantum transport calculations for different geometriesto study changes in the transport properties of graphene introduced by the wavystructure and bonding to the Si substrate. Our results suggest that wavygraphene combines high mobility along the ridges with efficient carrierinjection into Si in the contact regions.

Optimizing electronic structure and quantum transport at the graphene-Si(111) interface: An ab-initio density-functional study