Using classical molecular dynamics and a simulated annealing technique, we show that microscopic corrugations occur in monolayer and bilayer graphene on 6H-SiC substrates. From an analysis of the atomic configurations, two types of microscopic corrugations are identified, namely periodic ripples at room temperature and random ripples at high temperature. Two different kinds of ripple morphologies, each with a periodic structure, occur in the monolayer graphene due to the existence of a coincidence lattice between graphene and the SiC terminated surface （Si- or C-terminated surface）. The effect of temperature on microscopic ripple morphology is shown through analysing the roughness of the graphene. A temperature-dependent multiple bonding conjugation is also shown by the broad distribution of the carbon-carbon bond length and the bond angle in the rippled graphene on the SiC surface. These results provide atomic-level information about the rippled graphene layers or~ the two polar faces of the 6H-SiC substrate, which is useful not only for a better understanding of the stability and structural properties of graphene, but also for the study of the electronic properties of graphene-based devices.
