Effect of stepped substrates on the interfacial adhesion properties of graphene membranes

In order to gain a comprehensive understanding of interface adhesion properties involved in adhesion energy and local interface separation between graphene membranes and underlying stepped substrates, we develop an analytic model by considering the total free energy originally from interfacial van der Waals interaction and elastic strain energy stored in the membranes based on an atomic-bond-relaxation consideration. It is found that the interface adhesion energy decreases with increasing membrane thickness. Moreover, as compared to the case of a flat substrate surface, the interface adhesion properties of graphene membranes on stepped surfaces are strongly affected by the substrate surface parameters, including step height, vicinal angle, membrane thickness, terrace width and orientation, etc., implying that the topographic fluctuation of graphene is attributed to the various interface separations at different substrate sites. Our predictions agree reasonably well with computer simulations and experimental observations, which suggest that the developed method can be regarded as an effective method to design the interface adhesion of graphene membranes in graphene-based functional device components.