Chemical vapor deposition is an affordable method for producing high-quality graphene. Microscopic defects in graphene grown on copper substrates, such as five- and seven-membered rings, degrade the quality of graphene. Therefore, it is essential to study the growth process and factors affecting the quality of graphene on copper surfaces. In this study, first-principles calculations based on density functional theory show that the four-step dehydrogenation reaction of methane is endothermic, with the energy barrier for the last dehydrogenation step being relatively high. Additionally, CH forms dimers on the copper surface with a lower energy barrier and trimers with a higher energy barrier, indicating that carbon dimers are the primary precursor species for graphene growth in the early stages. Subsequently, in molecular dynamics simulations, the analytical bond-order potential based on quantum mechanics is employed. The results reveal that the growth of graphene on the copper surface involves the diffusion and gradual nucleation of carbon dimers in the early stages, the gradual enlargement of graphene domains in the intermediate stages, and the gradual merging of graphene domain boundaries in the later stages. Moreover, the growth of graphene on the copper substrate follows a self-limiting growth mode. Increasing the deposition interval of carbon atoms and reducing the carbon atom deposition velocity contribute to enhancing the quality of graphene grown on the copper substrate.

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