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

TL;DR

This paper introduces a fast, contactless method to determine the Young's modulus of 2D materials by analyzing their nonlinear dynamic response, demonstrated on graphene and MoS2 resonators, enabling high-frequency mechanical characterization.

Contribution

The paper presents a novel approach to extract Young's modulus from nonlinear resonance data using the Duffing equation, applicable to 2D material membranes.

Findings

Young's modulus can be accurately extracted from nonlinear response curves.

The method is validated on graphene and MoS2 resonators.

It offers a rapid, contactless way to characterize 2D materials' mechanical properties.

Abstract

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.