Theoretical modeling developed to evaluate the hardness and reduced modulus for the C/a-Si composite film using nanoindentation tests

A general mechanical model, which is composed of the mechanical models employed to describe the contact behaviors and deformations arising in all layers (including the substrate), is successfully developed in the present study for multilayer specimens in order to evaluate the contact projected area by a theoretical model, and thus the hardness and reduced modulus, using nanoindentation tests. The governing differential equations for the depth solutions of the indenter tip formed at all layers of the specimen under their contact load are developed individually. The influence of the material properties of the substrate on a multilayer specimen's hardness and reduced modulus at various indentation depths can thus be evaluated. Transition and pop-in occurred at depths near, but still before, the C (top layer)/a-Si (buffer layer) interface and the a-Si/Si (substrate) interface, respectively. Using the present analysis, the depths corresponding to the transition and pop-in behaviors can be predicted effectively