Controlled ripple texturing of suspended graphene and ultrathin graphite membranes

Graphene is nature's thinnest elastic material and displays exceptional mechanical(1,2) and electronic properties(3-5). Ripples are an intrinsic feature of graphene sheets(6) and are expected to strongly influence electronic properties by inducing effective magnetic fields and changing local potentials(7-12). The ability to control ripple structure in graphene could allow device design based on local strain(13) and selective bandgap engineering(14). Here, we report the first direct observation and controlled creation of one- and two-dimensional periodic ripples in suspended graphene sheets, using both spontaneously and thermally generated strains. We are able to control ripple orientation, wavelength and amplitude by controlling boundary conditions, and making use of graphene's negative thermal expansion coefficient (TEC), which we measure to be much larger than that of graphite. These results elucidate the ripple formation process, which can be understood in terms of classical thin-film elasticity theory. This should lead to an improved understanding of suspended graphene devices(15,16), a controlled engineering of thermal stress in large-scale graphene electronics, and a systematic investigation of the effect of ripples on the electronic properties of graphene.