A Unified and Versatile Model Study for Moisture Diffusion

All electronic packages involve with a multi-material system, in which many of the materials or films are susceptible to moisture absorption. Despite dissimilar material properties, moisture transports in a multi-material system from a high "water activity" region to a low one, where water activity is a measure of water energy in a specific substance. This, however, has not been well recognized in electronic packaging industry. Furthermore, moisture concentration gradient is often deemed as the driving force for moisture transport, which inevitably poses a challenging discontinuity issue at interface for moisture diffusion in multi-material systems. Even though several normalization schemes have been developed in the literature, much confusion has existed on the fundamental principle of moisture diffusion. This paper derived an activity-based diffusion model using the concepts of chemical potential and water activity. We showed that the continuity of water activity at interface in dissimilar materials is warranted, and furthermore, many nonlinear water sorption isotherms can be applied in the activity-based model by using a new property called "generalized solubility". The activity-based model thus is capable to study complex moisture diffusion in multi-material system. Moreover, in this paper, the activity-based model was used to unify the different normalization theories, such as solubility-based and the so-called wetness normalization approaches. We also discussed how water sorption isotherm would affect the conventional moisture diffusivity, finding that only for some limiting cases (e.g., Henry sorption isotherm), the "effective moisture diffusivity" becomes independent of moisture concentration. We pointed out that the generalized solubility that are needed to solve the diffusion can be obtained using conventional terms such as saturated moisture concentration and solubility. As demonstration, a numerical example was performed in commercial finite element software to study the moisture diffusion through a bi-material interface under dynamic temperature and humidity conditions. The results from different nonlinear sorption isotherms were compared to demonstrate the capability and versatility of the model. We concluded that the activity-based moisture diffusion model is a unified and versatile approach to study and understand the moisture diffusion mechanism in IC packages.