Advancing Nanoindentation Analysis for Characterizing the Mechanical, Elastic and Interfacial Properties of Two-Dimensional Materials

2D materials, such as graphene and Molybdenum disulfide (MoS2), offer tremendous potential for future devices due to their atomic-level thinness, intrinsic flexibility, and strain-engineered properties. A thorough understanding of their mechanical, elastic, and interfacial properties is crucial for the successful design of functional 2D devices. However, this task presents challenges, as the ultra-thin nature and relatively large surface areas of 2D materials render them highly sensitive to elasto-capillarity, particularly at small sizes. The nanoindentation technique has demonstrated significant advantages, especially in simultaneously measuring the mechanical, elastic, and interfacial properties of 2D materials, as well as controlling local strain distribution. Nonetheless, the accurate interpretation of the measured indenting-force-to-deflection curves is hindered by the lack of suitable theoretical models. In this study, we have developed a comprehensive model for the nanoindentation of suspended 2D materials, taking into account various factors such as pretension, probe size, probe-suspended-membrane interaction, and interfacial sliding between the 2D materials and substrates in the supported region. Additionally, we have creatively proposed a minimum force method to select the zero points of the indenting-force-to-deflection curves in practical applications. By applying our model to analyze these curves, we have successfully determined the Young’s modulus of the 2D materials, the interfacial shear strength against the supporting substrate, as well as the fracture strength of the 2D materials simultaneously. Our theoretical model for nanoindentation tests has provided accurate insights into the deformation and failure behaviors of 2D materials.