Mapping the elastic properties of two-dimensional MoS_(2) 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.