Abstract: Graphene has attracted great attention owing to its excellent physical and chemical properties and potential applications. Presently, we can grow large-scale single-crystal graphene on transition metal substrates, especially Cu(111) or CuNi(111) surfaces, using the chemical vapor deposition (CVD) method. To optimize graphene synthesis for large-scale production, understanding the growth mechanism at the atomic scale is critical. Herein, we summarize the theoretical studies on the roles of the metal substrate in graphene CVD growth and the related mechanisms. Firstly, the metal substrate catalyzes the carbon feedstock decomposition. The dissociation of CH₄, absorption, and diffusion of active carbon species on various metal surfaces are discussed. Secondly, the substrate facilitates graphene nucleation with controllable nucleation density. The dissociation and diffusion of carbon atoms on the CuNi alloy surface with different Ni compositions are revealed. The metal substrate also catalyzes the growth of graphene by incorporating C atoms from the substrate into the edge of graphene and repairing possible defects. On the most used Cu(111), each armchair site on the edge of graphene is intended to be passivated by a Cu atom and lowers the barrier of incorporating C atoms into the graphene edge. The potential route of healing the defects during graphene CVD growth is summarized. Moreover, the substrate controls the orientation of the epitaxial graphene. The graphene edge-catalyst interaction is strong and is responsible for the orientation determination of a small graphene island in the early nucleation stage. There are three modes for graphene growth on metal substrate, i.e. embedded mode, step-attached mode and on-terrace mode, and the preferred growth modes are not all alike but vary from metal to metal. On a soft metal like Cu(111), graphene tends to grow in step-attached or embedded modes and therefore has a fixed orientation relative to the metal crystal lattice. Finally, the formation of wrinkles and step bunches in graphene because of the difference in thermal expansion coefficients between graphene and the metal substrate is discussed. The large friction force and strong interaction between graphene and the substrate make it energetically unfavorable for the formation of wrinkles. Different from the formation of wrinkles, the main driving force behind metal surface step-bunching in CVD graphene growth, even in the absence of a compression strain is revealed. Although significant effort is still required to adequately understand graphene catalytic growth, these theoretical studies offer guidelines for experimental designs. Furthermore, we provide the key issues to be explored in the future.

Key words: Graphene, Chemical vapor deposition, Epitaxy, Catalysis, First-principle calculations