Analytical Solution for Moisture Diffusion with Initial Non-Uniform Moisture Concentration used in Bake Time Study in Electronics Packaging

Insufficient dry baking is a potential concern for both suppliers and users in semiconductor packaging. The purpose of the bake by suppliers is to remove most residual moisture prior to sealing the devices in dry bags and avoid device damage during subsequent board-level solder reflow. Dry baking by the user, however, is required whenever the recommended floor-life limits are exceeded at the user's site. Excessive bake times are a manufacturing cycle time concern for both suppliers and users. IPC/JEDEC J-STD-033 provides the conditions for bake prior to dry pack for various moisture sensitivity levels and various configurations of packages. The recommended bake time was based on a one-dimensional moisture diffusion analysis. However, the equation used in the calculations of the bake time tables was not given. In this paper, we derived the analytical solution for one-dimensional moisture diffusion with non-uniform initial moisture concentration. We applied this equation in various scenarios and provided the numerical results for both bake times in both bake time tables for suppliers and users, respectively. It was shown that for most of the package thickness, the moisture absorption is often far from saturated after typical accelerated moisture-soak conditions defined in IPC/JEDEC J-STD-020. As a result, the moisture diffusion state is not in equilibrium. Consequently, baking will initially force moisture to diffuse inwards toward critical interfaces before the total gradient can begin to decrease. This means that the moisture-sensitive package may be potentially at risk if baking time is too short, even if the overall moisture weight loss appears significant. In this paper, a detailed parametric study will be conducted for a multi-step analysis, including moisture diffusion during absorption and desorption during oven baking.