Molecular Dynamics Study of Ripples in Graphene and Bilayer Graphene

Transmission electron microscopy experiments have shown that suspended graphene is not perfectly flat, but displays ripples such that the surface normal of graphene varies by several degrees [1,2]. For multi-layered graphene, the ripples are suppressed with increasing numbers of layers. Recent experiments demonstrated that ripples in suspended graphene can also be controlled by mechanical and thermally induced strain [3]. Knowledge of and control over the ripples in graphene is desirable for fabricating and designing of strain-based devices. We show using molecular dynamics simulation that thermally induced ripples in suspended single and multi-layer graphene at room temperature result in deviations of the local surface normal by $\pm$ 7 $^{\circ}$ and $\pm$ 4 $^{\circ}$ for single and bilayer graphene, respectively. These angular deviations are in excellent agreement with transmission electron microscopy results [2] and confirm that these ripples can be dynamic and thermally induced. We also study how these angles change as a function of applied tensile and shear strain. [1] Meyer J. C., Geim A. K., et al. Solid State Communications, 143, 101 (2007). [2] Meyer J.C., Geim A.K., et al. Nature, 446, 60 (2007). [3] Bao W., Miao F., et al. Nature Nanotechnology, 4 (9), 562 (2009).