Size-dependent Interface Adhesion Of Graphene Membranes

Graphene, a monolayer sheet structure which consists of carbon atoms, has shown unique physical and chemical properties from both fundamental scientific issues and potentially technological applications, including biosensors, nanomechanical and nanoelectronic devices, etc. Supported on a substrate, the interfacial interaction between graphene and its underlying substrate has been one of the key questions from both the preparation and application of graphene. However, the epitaxial graphene membrane has a high surface-to-volume ratio, and edge atoms with high coordination deficiencies. As a result, the graphene membrane will be in self-equilibrium state, and the lattice strain will take place and further affect the related performances. Thus, the properties of graphene are different from that of the bulk graphite. In addition, as the discrepancies of lattice constant and thermal expansion coefficient in graphene and its underlying substrate, the mismatch strain will occur at the interface and will perturb the total energy of the system. Therefore, the existence of the defect on surface and interface has a significant effect on the adhesion property in the graphene membranes.In this paper, based on the continuum mechanics and atomic-bond-relaxation consideration, we develop a quantitative analytical method that describes the effects original from surface relaxation and interface misfit to explore the adhesion property between graphene and the underlying substrate. First of all, we study the size-dependent adhesion energy and interface separation of graphene membranes containing simple and complex interfaces. Then, we explore the effect of stepped substrate on the interface adhesion properties of graphene membranes. The achievements are shown as follows:(1) We address the underlying physical mechanism regarding interaction and adhesion between graphene and its substrate in simple interface, and establish a theoretical relationship between interface adhesion energy and graphene thickness based on the atomic-bond-relaxation consideration. It is found that the coupling role from spontaneous shrink of surface atoms and lattice mismatch at interface can be responsible for the change of interface adhesion. Also, the thickness-dependent interface separation in graphene/substrate in equilibrium state is attributed to the interface and surface effects.(2) We investigate the interface adhesion properties between graphene and its substrate in complex interface. Taking C/Cu/Ni and Cu/C/Ni as two typical examples, we develop a theoretical method to elaborate the relationship between the thickness of graphene membrane and complex interface adhesion energy based on the atomic-bond-relaxation consideration. Our results indicate that the thicknesses of graphene and Cu, and the site of Cu layer (adlayer on a simple graphene/substrate system either on top or between graphene and substrate) determine the adhesion energy and the interface separation in the self-equilibrium state. Our theoretical results are well consistent with the available evidences.(3) We further explore the adhesion property between graphene and its underlying stepped substrate. Taking the step height, terrace width and the configurations with different stacking modes into account, we find that the competition original from the graphene deformation energy stored in the stepped edge, the van der Waals interaction, and the strain energy determines the adhesion property of the stepped system. Moreover, we predict the debond phenomenon will be appearance in the stepped system, which is exceedingly well agreement with experimental measurements.