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The understanding of the formation of graphene at the atomic scale on Si-terminated 3C-SiC for obtaining high-quality graphene sheets remains elusive, although epitaxial graphene growth has been shown to be a well-known method for economical mass production of graphene/SiC heterojunctions. In this paper, the atomic behavior of carbon atoms on a Si removed 3C-SiC (111) surface for the formation of graphene buffer layer during the early stage of epitaxial graphene growth was investigated using a molecular dynamics simulation. Observation of the behavior of the remaining carbon atoms on the Si-terminated 3C-SiC (111) surface after removal of the silicon atoms revealed that graphene clusters, which were formed by sp2-bonded carbon atoms, start to appear at annealing temperatures higher than 1300 K. Our simulations indicated that the structural stability of the whole system increased as the number of sp2-bonded carbon atoms on the Si-terminated 3C-SiC (111) surface increased. It was also found that the diffusion energy barrier for the migration of carbon atoms from the on-top site to the bridge site on the Si-terminated 3C-SiC (111) surface mainly determines the critical temperature of graphene cluster formation.