Direct Concentration Approach of Moisture Diffusion and Whole-Field Vapor Pressure Modeling for Reflow Process—Part I: Theory and Numerical Implementation

Moisture concentration is discontinuous at interfaces when two material, which have different saturated moisture concentrations, are joined together. In order to perform moisture diffusion modeling in a multimaterial system such as electronic packages, normalization methods have been commonly used to remove the discontinuity of moisture concentration at interfaces. However, such treatments cannot be extended to a reflow process, in which ambient temperature and/or humidity vary with time. This paper develops a direct concentration approach, with which the moisture concentration is used as afield variable directly. Constraint equations are applied to meet the interface continuity requirements. Further in this paper a simplified vapor pressure model based on a multiscale analysis is developed. The model considers the phase change in moisture, and links the macroscopic moisture concentration to the moisture state at a microscopic level. This model yields the exact same results with the original vapor pressure model (Fan, et al., 2005, "A Micromechanics Based Vapor Pressure Model in Electronic Packages, " ASME J. Electron. Packag., 127(3), pp. 262-267). The new model does not need to relate to a reference temperature state. Numerical implementation procedures,for calculating moisture concentration and ensuing vapor pressure, which are coupled with temperature analysis, are presented in this paper.