Effects of mismatch strain and substrate surface corrugation on morphology of supported monolayer graphene

In a previous work, substrate-modulated morphology of graphene was analyzed using a numerical Monte Carlo method. Here we present an analytical approach that explicitly relates the van der Waals interaction energy to the surface corrugation and the interfacial properties. Moreover, the effect of mismatch strain is considered, which predicts a strain-induced instability under a compressive strain and reduced corrugation under a tensile strain.

Abstract: Graphene monolayers supported on oxide substrates have been demonstrated with superior charge mobility and thermal transport for potential device applications. Morphological corrugation can strongly influence the transport properties of the supported graphene. In this paper, we theoretically analyze the morphological stability of a graphene monolayer on an oxide substrate, subject to van der Waals interactions and in-plane mismatch strains. First, we define the equilibrium separation and the interfacial adhesion energy as the two key parameters that characterize the van der Waals interaction between a flat monolayer and a flat substrate surface. By a perturbation analysis, a critical compressive mismatch strain is predicted, beyond which the graphene monolayer undergoes strain-induced instability, forming corrugations with increasing amplitude and decreasing wavelength on a perfectly flat surface. When the substrate surface is not perfectly flat, the morphology of graphene depends on both the amplitude and the wavelength of the surface corrugation. A transition from conformal (corrugated) to non-conformal (flat) morphology is predicted. The effects of substrate surface corrugation on the equilibrium mean thickness of the supported graphene and the interfacial adhesion energy are analyzed. Furthermore, by considering both the substrate surface corrugation and the mismatch strain, it is found that, while a tensile mismatch strain reduces the corrugation amplitude of graphene, a corrugated substrate surface promotes strain-induced instability under a compressive strain. These theoretical results suggest possible means to control the morphology of graphene monolayer on oxide substrates by surface patterning and strain engineering.

The attached manuscript has been submitted for review. Comments and discussions are welcome.

Updated on May 26, 2010: This manuscript has been accepted for publication in Journal of Applied Physics.

Updated on July 15, 2010: This paper has been published in Journal of Applied Physics, vol. 107, 123531 (2010).