Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ, Delft, The Netherlands.
Department of Precision and Microsystems Engineering, Delft University of Technology, Mekelweg 2, 2628 CD, Delft, The Netherlands.
Nat Commun. 2017 Nov 1;8(1):1253. doi: 10.1038/s41467-017-01351-4.
Owing to their atomic-scale thickness, the resonances of two-dimensional (2D) material membranes show signatures of nonlinearities at forces of only a few picoNewtons. Although the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator's material properties has remained elusive. Here we show a method for determining the Young's modulus of suspended 2D material membranes from their nonlinear dynamic response. To demonstrate the method, we perform measurements on graphene and MoS nanodrums electrostatically driven into the nonlinear regime at multiple driving forces. We show that a set of frequency response curves can be fitted using only the cubic spring constant as a fit parameter, which we then relate to the Young's modulus of the material using membrane theory. The presented method is fast, contactless, and provides a platform for high-frequency characterization of the mechanical properties of 2D materials.
由于其原子级厚度，二维（2D）材料膜的共振在只有几个皮牛顿的力下显示出非线性的特征。尽管膜的线性动力学已经得到很好的理解，但非线性响应与谐振器材料特性之间的确切关系仍然难以捉摸。在这里，我们展示了一种从膜的非线性动力学响应确定悬浮 2D 材料膜的杨氏模量的方法。为了验证该方法，我们在多个驱动力下对静电驱动进入非线性区域的石墨烯和 MoS 纳米鼓进行了测量。我们表明，仅使用三次弹簧常数作为拟合参数就可以拟合一组频率响应曲线，然后我们使用膜理论将其与材料的杨氏模量联系起来。所提出的方法快速、非接触，并为高频表征 2D 材料的机械性能提供了一个平台。
