Study of Flexoelectricity in Graphene Composite Structures

This paper introduces the theoretical and experimental investigation of flexoelectric behavior in a graphene composite structure consisting of multilayer CVD-graphene deposited on an ALD-platinum catalyst layer deposited on top of n-silicon substrate. The polarization induced by varying the radius of curvature from 200-1500 mm by applying bending stresses was investigated experimentally. Meanwhile, due to the cluster-growth nature of the ALD-platinum catalyst layer, a strong correlation was observed between the resulting number of graphene layers and the Pt catalyst layer thickness, which subsequently had a strong impact on the induced polarization. A polarization current of up to 7.4 mA was detected when the composite structure was bent through a 600-mm radius of curvature. Residual stresses at the interface of the different layers were estimated experimentally in the order of 85-217 MPa. The effect of thermally-induced stresses, residual stresses at the interface layers, thickness of graphene layers, and radius of curvature were investigated theoretically using the finite element method (FEM) and first-principle analyses. Theoretically, it was confirmed that non-uniform strain results in an appreciable non-uniform graphene band gap opening, in addition to non-uniform change of the band structure across the surface and thickness which results in increasing the potential energy difference between the graphene layers. FEM confirmed that thermally induced strains could further enhance the power output of the device by inducing a flexoelectric current combined with the thermionic response. This is verified by estimating a lattice displacement up to 0.31 angstrom in response to 2-mW heat flux, which corresponds to an appreciable graphene band opening and a potential energy difference across the graphene layers in the order of 1.23 eV, as estimated by the tight binding model.