While moisture diffusion in microelectronic device and packaging has been studied for decades, the problems involving complex nonlinear moisture diffusion in multi-material assembly have not been fully studied. This paper has developed a general nonlinear diffusion model by adopting water activity, a continuous state variable, as the field variable. The generalized solubility is introduced, which is temperature- and water activity-dependent. The effective diffusivity is defined and derived in terms of generalized solubility and water activity. By comparing the water activity-based model with the existing various normalized models, the present theory can unify and generalize the current approaches. More importantly, the present model can solve both linear and nonlinear moisture diffusion in inhomogeneous material system without normalization. The commercial finite element software has been applied to solve the nonlinear generalized moisture diffusion problem using the analogy of water activity and temperature. A source code of user-defined subroutines in ABAQUS has been provided in the Appendix of the paper. The mathematical formulation and the numerical implementation method presented in this paper can be applied to any nonlinear sorption or diffusion problems in inhomogeneous material system.@en

This paper presents a comprehensive review and comparison of different theories and models for water vapor pressure under rapid heating in moisture permeable materials, such as polymers or polymer composites. Numerous studies have been conducted, predominately in microelectronics packaging community, to obtain the understanding of vapor pressure evolution during soldering reflow for encapsulated moisture. Henry's law-based models are introduced first. We have shown that various models can be unified to a general form of solution. Two key parameters are identified for determining vapor pressure: the initial relative humidity and the net heat of solution. For materials with nonlinear sorption isotherm, the analytical solutions for maximum vapor pressure are presented. The predicted vapor pressure, using either linear sorption isotherm (Henry's law) or nonlinear sorption isotherm, can be greater than the saturated water vapor pressure. Such an "unphysical" pressure solution needs to be further studied. The predicted maximum vapor pressure is proportional to the initial relative humidity, implying the history dependence. Furthermore, a micromechanics-based vapor pressure model is introduced, in which the vapor pressure depends on the state of moisture in voids. It is found that the maximum vapor pressure stays at the saturated vapor pressure provided that the moisture is in the mixed liquid/vapor phase in voids. And, the vapor pressure depends only on the current state of moisture condition. These results are contradictory to the model predictions with sorption isotherm theories. The capillary effects are taken into consideration for the vapor pressure model using micromechanics approach.@en