Lee Jong-Hyup, Ham Ju-Been, Kim Young-Cheon
Materials Research Centre for Energy and Clean Technology, School of Materials Science and Engineering, Andong National University, Andong 36729, Republic of Korea.
Materials (Basel). 2025 Jan 2;18(1):154. doi: 10.3390/ma18010154.
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.
准确测量柔性基板上薄金属膜的弹性模量对于理解柔性电子产品的机械可靠性至关重要。然而，传统方法，如奥利弗 - 法尔模型，由于基板效应往往会低估模量，特别是对于像聚酰亚胺（PI）这样的低模量基板。在本研究中，我们提出了一种改进的加权模型，用变量X取代经验加权因子，以更好地考虑基板的贡献。对沉积在PI和硅基板上的厚度为0.5、1和1.5μm的铜和铝膜进行了纳米压痕实验。结果表明，应用传统方法时弹性模量被显著低估，特别是在PI基板上，其值下降高达95%。使用所提出的基于X的模型，校正后的弹性模量与薄膜的固有特性一致，误差降低到2%以内。有限元分析（FEA）验证了应力和位移分布，证明了基板对压痕行为的影响。本研究为准确测量柔性基板上薄膜的弹性模量提供了一个强大的框架，为柔性电子产品中更可靠的机械表征铺平了道路。
