Application of water activity-based theory for moisture diffusion in electronic packages using ANSYS

Polymeric materials used in electronic packages can absorb moisture from ambient environment, causing moisture-related reliability issues. To model moisture diffusion, concentration-based theory has been widely used, assuming the driving force as the gradient of moisture concentration. However, moisture concentration becomes discontinuous at material interface, which creates great numerical difficulty in multi-material systems. While several normalization schemes were developed to mitigate the issue, much confusion still exists regarding the principle of moisture diffusion. Meanwhile, an activity-based theory was recently developed according to the fundamental moisture diffusion mechanism: water transports from a high water activity region to a low one. Unlike moisture concentration, water activity is a state variable and is always continuous at material interface. These concepts of water activity-based theory, however, have not been well recognized in electronic packaging industry. In this paper, a unified activity-based diffusion theory was implemented in commercial finite element software (ANSYS) to study moisture diffusion in electronic packages. We showed that the original theory can be simplified by using temperature-dependent generalized solubility (which corresponds to a temperature-dependent Henry's law). The new theory has no issue of interface discontinuity since water activity is always continuous. We also showed that the activity-based model can be used to unify the existing normalized concentration-based theories. The activity-based theory was then implemented using concentration-activity analogy within ANSYS computational framework. The coupled field elements, however, must be adopted as diffusion-only element in ANSYS cannot consider temperature-dependent material property. As a validation, numerical study was conducted to model moisture diffusion through a bi-material interface under dynamic temperature and humidity conditions. Great agreement was obtained between the ANSYS results and the literature data. We concluded that the unified activity-based diffusion theory is effective for modeling moisture diffusion in electronic packages.