Recent interest in functionalised graphene has been motivated by the prospect of creating a two-dimensional semiconductor with a tuneable band gap. Various approaches to band gap engineering have been made over the last decade, one of which is chemical functionalisation. However, the patterning of molecular adsorption onto graphene has proved to be difficult, as grown structures tend to be stochastic in nature.
In the first part of this work, a predictive physical model of the self-assembly of halogenated carbene layers on graphene is suggested. Self-assembly of the adsorbed layer is found to be governed by a combination of the curvature of the graphene sheet, local distortions, as introduced by molecular adsorption, and short-range intermolecular repulsion. The thermodynamics of bidental covalent molecular adsorption and the resultant electronic structure are computed using Density Functional Theory. It is predicted that a direct band gap is opened that is tuneable by varying coverages and is dependent on the ripple ampli- tude. This provides a mechanism for the controlled engineering of graphene’s electronic structure and thus its use in semiconductor technologies.
In the second part of this work, the formation of intrinsic ripples in graphene sheets under isotropic compression is examined. An isotropic compression of graphene is shown to induce a structural deformation on the basis of Density Functional Perturbation Theory. Static instabilities, indicated by imaginary fre- quency phonon modes, are induced in the high symmetry Γ – K (zigzag) and Γ – M (armchair) directions by an isotropic compressive strain of the graphene sheet. The wavelength of the unstable modes (ripples) is directly related to the
magnitude of the strain and remarkably insensitive to the direction of propagation in the 2D lattice. These calculations further suggest that the formation energy of the ripple is isotropic for lower strains and becomes anisotropic for larger strains. This is a result of graphene’s elastic property, which is depen- dent on direction and strain. Within the quasi harmonic approximation this is combined with the observation that molecular adsorption energies depend strongly on curvature to suggest a strategy for generating ordered overlayers in order to tune the functional properties of graphene.
Based on the results of this work, we can conclude that (pre-)rippled graphene sheets can be used to direct molecular adsorption in order to form specific patterns by tuning the thermodynamic equilibrium of the addition reaction of small (organic) molecules.