Graphene membranes with a great potential to be used in precise measuring apparatuses like pressure or motion sensors must themselves first be characterized — at least as precisely. A method reported in the Journal of Applied Physics provides an alternative approach to atomic force microscopy measurements currently ubiquitous to characterization of graphene. Analogous to altering a drumhead’s tension and measuring its dynamic responses to various tapping frequencies, this method avoids the structural damage risks that come from scanning a relatively sharp tip near the surface for similar information.

By tuning the DC electrostatic load, the suspended graphene membrane deforms, and because this deformation is a function of the Young’s modulus, the stiffness changes. This leads to a measurable shift in the resonance frequency of the membrane, and tracking this frequency change provides accurate values for the graphene’s Young’s modulus.

This dynamic characterization approach makes two regimes of operation available: nonlinear, large-amplitude oscillations; and linear, low-amplitude modes. The current method only measures the latter procedure, i.e., the linear responses, though the model can provide accurate modeling of nonlinear dynamic behavior as well. The former, low DC high AC-actuation results in large amplitude oscillations with a nonlinear Duffing response that gives a more direct assessment of nonlinear dynamics.

Both regimes offer accurate characterization of the Young’s modulus of a graphene membrane without a spatially scanning probe that risks causing damage during scanning. However, the linearity of measurements in the newly proposed method, while still able to provide insight to the nonlinear phenomena, poses even less direct risk of membrane damage.

Source: “Experimental characterization of graphene by electrostatic resonance frequency tuning,” by Banafsheh Sajadi, Farbod Alijani, Dejan Davidovikj, Johannes (Hans) Goosen, Peter G. Steeneken, and Fred van Keulen, Journal of Applied Physics (2017). The article can be accessed at