First principles study of the graphene/Ru(0001) interface

Annealing the Ru metal that typically contains residual carbon impurities offers a facile way to grow graphene on Ru(0001) at the macroscopic scale. Two superstructures of the graphene/Ru(0001) interface with periodicities of 3.0-nm and 2.7-nm, respectively, have been previously observed by scanning tunneling microscopy. Using first-principles density functional theory, we optimized the observed superstructures and found interfacial C-Ru bonding of C atoms atop Ru atoms for both superstructures, which causes the graphene sheet to buckle and form periodic humps of ~1.7 A in height within the graphene sheet. The flat region of the graphene sheet, which is 2.2-2.3 A above the top Ru layer and has more C atoms occupying the atop sites, interacts more strongly with the substrate than does the hump region. We found that interfacial adhesion is much stronger for the 3.0-nm superstructure than for the 2.7-nm superstructure, suggesting that the former is the thermodynamically more stable phase. We explained the 3.0-nm superstructure's stability in terms of the interplay between C-Ru bonding and lattice matching.