Wrinkling behavior of graphene on substrates with different surface morphologies

The wrinkling of graphene can strongly affect its stability and reliability in graphene-based nanodevices. However, it is still a tremendous challenge to accurately predict the wrinkling behavior of graphene on substrates with different surface morphologies. In this study, the wrinkling behavior of graphene on substrates with one-dimensional (1D) and two-dimensional (2D) sinusoidal surface morphologies is studied by continuum modeling and molecular dynamics (MD) simulations, where three deformation forms of graphene (non-conformal, transitional conformal and conformal) are theoretically determined. Our results show that the wrinkling behavior and interfacial shear force of graphene strongly depend on the wavelength and amplitude of the substrate surface and the elastic constants of the substrate, where the explicit expressions of the interfacial cohesive energy between graphene and the substrate are derived by using Gaussian quadrature based on interlayer van der Waals (vdW) interactions. The bistable state of the graphene wrinkling can be found when the wavelength and amplitude of the substrate surface are in a given range. Checking against our MD simulations shows that the present theoretical model has high accuracy. This study provides valuable physical insights for designing and assembling graphene-based flexible nanodevices on substrates.