▎ 摘　　要

The performances of graphene sheets in nano-devices strongly depend on their morphology, which can be changed enormously by the nanoscale asperities of the substrate. Therefore, it is of great importance to predict morphologies of graphene supported by substrates with different rough surfaces and non-developable curved surfaces. To study the morphology of substrate-supported graphene, a novel methodology is proposed based on the mode-independent energy method (MIEM) and the theoretical analysis on the strain field of graphene. In the method, the morphology of the supported graphene is predicted by judging the stability of graphene in its hypothetical conforming state. Thus, there is no need to concern the complex morphology of graphene sheets, and accordingly, this method is applicable to the substrates with non-developable surfaces, of which the graphene morphologies are difficult to predict by conventional methods. Using this method, the critical condition for the morphology of graphene sheets supported by substrates with convex asperities is established, which agrees well with the results of molecular dynamics (MD) simulations. It is revealed that the shape of the convex asperity is the most important factor that affects the morphology. As long as the half-cone angle of the asperity is small enough, for example, below about 0.4 for silicon substrates, the graphene sheet that covers the convex can conform completely to the substrate. Otherwise, if the half-cone angle is larger, the sizes of the graphene and the asperity also affect the morphology. The shape and size effects on the graphene morphology is summarized in a phase diagram, which provides guidance for the design of graphene-based systems in advanced nano-devices. The methodology developed in this paper is applicable to other two-dimensional materials as well.