Young's modulus of 2D materials extracted from their nonlinear dynamic response

Due to their atomic-scale thickness, the resonances of 2D material membranes show signatures of nonlinearities at amplitudes of only a few nanometers. While the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator's material properties has remained elusive. In this work, we propose a method to determine the Young's modulus of suspended 2D material membranes from their nonlinear dynamic response. The method is demonstrated by interferometric measurements on graphene and MoS2 resonators, which are electrostatically driven into the nonlinear regime at multiple driving forces. It is shown that a set of response curves can be fitted by the solutions of the Duffing equation using only one fit parameter, from which the Young's modulus is extracted using membrane theory. Our method is fast, contactless, and provides a platform for high-frequency characterization of the mechanical properties of 2D materials.