THE FINITE THICKNESS MODEL CALIBRATES THE BIMODAL-AFM YOUNG'S MODULUS MEASUREMENTS OF THE TWO-DIMENSIONAL MoS₂

Because the two-dimensional (2D) materials possesses unique crystal structures, novel physical properties and excellent mechanical properties, the 2D materials is of broad application prospects in many fields including micro- and nano-electromechanical systems and flexible electronic devices, etc. The elastic modulus is one of the basic mechanical parameters for 2D materials, which is of an important influence on its device application and strain regulation. However, restricted by the characteristics of two-dimensional structure and atomic thickness, it is difficult to measure the accurate elasticity modulus of 2D materials. Amplitude modulation and frequency modulation within the bimodal atomic force microscopy is an efficient method for measuring Young's modulus of 2D materials, but the influence of rigid substrates cannot be ignored for the measurement results. In this work, the Young's modulus distribution of the substrate and 2D molybdenum sulfide were directly measured by the bimodal atomic force microscopy. Based on the finite thickness model, the intrinsic Young's modulus value of the sample was obtained after corrected the substrate effect. The elastic coefficient and Young's modulus of 2D molybdenum disulfide were calculated by the first principles calculation. The experimental results are consisted with the calculation results. That’s to say, the bimodal atomic force microscopy is a reliable direct characterization method for Young's modulus of 2D materials. This method does not require tedious steps like preparing suspended 2D materials, and can avoid shortcomings of conventional characterization methods. For thin films of large area two-dimensional materials, this work provides a reliable experimental basis for the programmed characterization analysis of their mechanical properties. Meanwhile, it provides firm experimental basis for future mechanistic statistical analysis of high throughput experimental data.