Correction of substrate-induced thin-film modulus deviations in nanoindentation measurements

Abstract

The influence of substrate effects on the accurate measurement of mechanical properties of thin films remains to be clarified. Therefore, in this study, (AlCrNbSiTi)N thin films were deposited on four substrates—Si, SiO2, sapphire (Al2O3), and Ni—with varying thicknesses. Nanoindentation testing was conducted to measure the mechanical properties, revealing variations in the modulus of the thin film depending on the substrate and film thickness. To address these variations, we introduced the concept of two springs connected in series, following Hooke's law, to determine the elastic deformations of the thin film and its underlying substrate. By applying linear regression to four datasets corresponding to equivalent film thicknesses but different substrates, substrate-induced measurement errors were effectively mitigated, and the true modulus of the thin film was determined. Furthermore, we introduced a k value to represent the ratio of the actual force on the substrate to the force exerted by the indenter. Our findings indicate that even when the indenter contact depth is less than 1% of the film thickness, the substrate is still subjected to 7.6% of the applied force. This underscores the non-negligible nature of substrate elastic deformation during the measurement process and importance of correcting for substrate-induced variations in thin-film moduli. The findings can contribute to advancing the understanding of mechanical properties in ceramics and related materials.