Mapping the elastic properties of two-dimensional MoS2 via bimodal atomic force microscopy and finite element simulation

Elasticity is a fundamental mechanical property of two-dimensional (2D) materials, and is critical for their application as well as for strain engineering. However, accurate measurement of the elastic modulus of 2D materials remains a challenge, and the conventional suspension method suffers from a number of drawbacks. In this work, we demonstrate a method to map the in-plane Young’s modulus of mono- and bi-layer MoS 2 on a substrate with high spatial resolution. Bimodal atomic force microscopy is used to accurately map the effective spring constant between the microscope tip and sample, and a finite element method is developed to quantitatively account for the effect of substrate stiffness on deformation. Using these methods, the in-plane Young’s modulus of monolayer MoS 2 can be decoupled from the substrate and determined as 265 ± 13 GPa, broadly consistent with previous reports though with substantially smaller uncertainty. It is also found that the elasticity of mono- and bi-layer MoS 2 cannot be differentiated, which is confirmed by the first principles calculations. This method provides a convenient, robust and accurate means to map the in-plane Young’s modulus of 2D materials on a substrate. Elastic properties: quantitative mapping of MoS 2 Young’s modulus A robust and accurate determination of the in-plane Young’s modulus of 2D materials can be accomplished directly on the supporting substrate. A team led by Jiangyu Li at the Shenzhen Institutes of Advanced Technology and University of Washington developed a method to map the in-plane Young’s modulus of 2D materials supported on a substrate with high spatial resolution. Considering the case of mono- and by-layered MoS 2 , bimodal atomic force microscopy (AFM) was used in combination to the finite element method to map the effective spring constant between the AFM tip and the sample, whist also accounting for the effect of the substrate. The in-plane Young’s modulus of monolayer MoS 2 was found to be 265 ± 13 GPa, with less than 5% uncertainty, whereas that of bilayer MoS 2 is indistinguishable from the monolayer counterpart.