Effect of Non-Uniform Moisture Distribution on the Hygroscopic Swelling Coefficient

The coefficient of hygroscopic swelling is a material property used to measure the volumetric change with moisture absorption under given humidity and temperature conditions. Current hygroscopic swelling characterization techniques use an averaged approach based on the averaged moisture content. However, the moisture distribution is not uniform across the test specimen during measurement. This introduces analysis errors in determining the material property. In this paper, an exact analytical solution was derived to obtain the accurate coefficient of hygroscopic swelling, with the consideration of 3-D moisture diffusion across the specimen. The correlation between the locally defined and the averaged coefficient of hygroscopic swelling was obtained analytically. The results showed that the coefficient of hygroscopic swelling obtained based on the previous method using the averaged approach may overestimate the property up to 250%. The methodology and formulation developed in this paper was then applied to analyze a set of existing experimental data, and results were compared to the current approach. This paper also investigated the reliability of a flip chip ball grid array package under high accelerated stress test condition (120degC/100%RH). Finite element analysis simulation results revealed the significance of contribution of hygroscopic swelling induced tensile stresses under bump region. The finite element results gave an insight of the failure mechanism associated with moisture absorption.