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 MoS2 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 MoS2 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 MoS2 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.

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The mechanical properties of two-dimensional (2D) materials are critical for their applications in functional devices as well as for strain engineering. Here, we report the Young's modulus and breaking strength of multilayered InSe, an emerging 2D semiconductor of the layered group III chalcogenide. Few-layer InSe flaks were exfoliated from bulk InSe crystal onto Si/SiO 2 substrate with microfabricated holes, and indentation tests were carried out using an atomic force microscopy probe. In combination with both continuum analysis and finite element simulation, we measured the Young's modulus of multilayer 2D InSe (>5 L) to be 101.37±17.93 GPa, much higher than its bulk counterpart, while its breaking strength is determined to be 8.68 GPa, approaching the theoretical limit of 10.1 GPa. Density functional theory calculations were also carried out to explain the insensitivity of Young's modulus to the layer count. It is found that 2D InSe is softer than most 2D materials, and exhibits breaking strength higher than that of carbon fiber, yet remaining more compliant, making it ideal for flexible electronics applications. The reliability of our method is also validated by measurement of graphene.

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