Exploration of the Origin of Substrate Effects and Elastic Strain Properties during Thin Film Nanoindentation

Abstract

In this study, the main goal was to investigate the true origin of an influence of substrate effects during nanoindentation of thin films. The work examined the proper relation between the elastic strain intensities in the film and substrate, and modified the Doerner & Nix function used to first describe this situation. A universal mathematical model/formula was developed to better describe the nanoindentation Modulus–Displacement curve. Furthermore, a physical explanation was suggested for the new function. In this project, 15 specimens (including 14 amorphous thin films and 1 nanocrystalline film deposited on Si substrates) were tested using a MTS nanoindentation XP system. The films were tested with a continuous stiffness measurement (CSM), where flat regions were found in the early stage of the E-h curves that reflected the true film modulus. The flat region (the region without substrate effects) and critical indentation depth (hcr) was determined for each material. A unique non-linear trend was found between the critical indentation depth/film thickness ratio (hcr/t) and film/substrate modulus ratio (Ef/Es). It was found parameter α in Doerner & Nix function was not a constant as originally suggested. Instead, it changed with the indentation depth. To improve Doerner & Nix function, two parameters α1 and α2 were suggested in the equation instead of one, as the elastic strain growth is not continuous in the film and substrate. Based on the experimental investigation and analytical modeling, the two parameters were determined as the Poisson’s ratios of the film and substrate. The new function was found to be adept at closely matching all experimental data collected, which spanned both soft films on hard substrates and hard films on soft substrates.