Investigation of Geometric Correction Factor for Evaluating Elastic Modulus of Flexible Substrates Using Nanoindentation
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With the rapid growth of the flexible electronics industry, evaluating the mechanical reliability of thin films deposited on flexible substrates, such as polyimide (PI), has become a critical challenge. Nanoindentation is the standard method for measuring elastic modulus. However, research on the geometric correction constants required to determine the elastic modulus of flexible substrates remains insufficient. In this study, finite element analysis (FEA) was utilized to calculate the geometric correction factor, β, for PI substrates by varying the indentation depth and indenter contact angle. The results demonstrate that, unlike the constant values assumed in traditional rigid-substrate models, β decreases as both the indentation depth and the indenter cone half-angle increase. Notably, the β values derived for the flexible substrate were approximately twice (1.82–2.03) as large as the standard value (1.034) used for rigid materials. This disparity is attributed to the low elastic modulus and the pronounced elastic recovery characteristic of polymer materials during the unloading.
Abstract
With the rapid growth of the flexible electronics industry, evaluating the mechanical reliability of thin films deposited on flexible substrates, such as polyimide (PI), has become a critical challenge. Nanoindentation is the standard method for measuring elastic modulus. However, research on the geometric correction constants required to determine the elastic modulus of flexible substrates remains insufficient. In this study, finite element analysis (FEA) was utilized to calculate the geometric correction factor, β, for PI substrates by varying the indentation depth and indenter contact angle. The results demonstrate that, unlike the constant values assumed in traditional rigid-substrate models, β decreases as both the indentation depth and the indenter cone half-angle increase. Notably, the β values derived for the flexible substrate were approximately twice (1.82–2.03) as large as the standard value (1.034) used for rigid materials. This disparity is attributed to the low elastic modulus and the pronounced elastic recovery characteristic of polymer materials during the unloading.