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Cu foils play an important role in preparing high quality of graphene films by chemical vapor deposition. For the commonly used commercial Cu foil, the nucleation density of graphene is high due to the associated defects in the manufacturing process of Cu foil. In this work, different substrates containing polished aluminum plate, polished stainless steel plate, glass ceramics, and SiO2/Si were selected as substrates to prepare distinct Cu foils with different roughness by thermal evaporation method. Then the growth conditions of high flatness graphene films and the effect of Cu foils on graphene films were discussed in detail. The results show that Cu foils are predominantly (111) orientation, and keep the surface with nanometer-level flatness after separation from substrates. After the growth of graphene, the nucleation density of Cu foil peeled from SiO2/Si is the lowest among these four kinds of substrates. At the same time, its crystal structure has almost no change and has good crystallinity. There are nearly no Cu grain boundary defects on the surface of the Cu foil peeled from SiO2/Si. When the pressure is 3 000 Pa and the flow rates of hydrogen and methane are 300 mL/ min and 0.5 mL/ min, respectively, a graphene single crystal domain with a lateral dimension of about 1 mm can be obtained. [ABSTRACT FROM AUTHOR]