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

Abstract

Moisture concentration is discontinuous at interfaces when two materials, 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 a field 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.