An Investigation of the Indentation Elastic Modulus for Metal Films on Flexible Substrates Considering the Substrate Effect.

The accurate measurement of the elastic modulus of thin metal films on flexible substrates is critical for understanding the mechanical reliability of flexible electronics. However, conventional methods, such as the Oliver-Pharr model, often underestimate the modulus due to substrate effects, particularly with low-modulus substrates like polyimide (PI). In this study, we propose an improved weighting model that replaces the empirical weighting factor with a variable X to better account for substrate contributions. Nanoindentation experiments were performed on Cu and Al films with thicknesses of 0.5, 1, and 1.5 μm, deposited on PI and silicon substrates. The results show a significant underestimation of the elastic modulus when traditional methods were applied, especially on PI substrates, where values decreased by up to 95%. Using the proposed X-based model, the corrected elastic modulus aligned with the inherent properties of the films, with errors reduced to within 2%. A finite element analysis (FEA) validated the stress and displacement distributions, demonstrating the substrate's influence on indentation behavior. This study provides a robust framework for accurately measuring the elastic modulus of thin films on flexible substrates, paving the way for a more reliable mechanical characterization in flexible electronics.