Effects of interlayer interactions on the nanoindentation response of freely suspended multilayer gallium telluride

Freestanding indentation is a widely used method to characterise the elastic properties of two-dimensional (2D) materials. However, many controversies and confusion remain in this field due to the lack of appropriate theoretical models in describing the indentation responses of 2D materials. Taking the multilayer gallium telluride (GaTe) as an example, in this paper we conduct a series of experiments and simulations to achieve a comprehensive understanding of its freestanding indentation behaviours. Specifically, the freestanding indentation experiments show that the elastic properties of the present multilayer GaTe with a relatively large thickness can only be extracted from the bending stage in the indentation process rather than the stretching stage widely utilised in the previous studies on thin 2D materials, since the stretching stage of thick 2D materials is inevitably accompanied with severe plastic deformations. In combination with existing continuum mechanical models and finite element simulations, an extremely small Young's modulus of multilayer GaTe is obtained from the nanoindentation experiments, which is two orders of magnitude smaller than the value obtained from first principles calculations. Our molecular dynamics (MD) simulations reveal that this small Young's modulus can be attributed to the significant elastic softening in the multilayer GaTe with increasing thickness and decreasing length. It is further revealed in MD simulations that this size-induced elastic softening originates from the synergistic effects of interlayer compression and interlayer shearing in the multilayer GaTe, both of which, however, are ignored in the existing indentation models. To consider these effects of interlayer interactions in the theoretical modelling of the freestanding indentation of multilayer GaTe, we propose here novel multiple-beam and multiple-plate models, which are found to agree well with MD results without any additional parameters fitting and thus can be treated as more precise theoretical models in characterising the freestanding indentation behaviours of 2D materials.