An examination on the direct concentration approach to simulating moisture diffusion in a multi-material system

In 2009, Xie et al. proposed a diffusion simulation method called direct concentration approach (DCA), which aimed at solving moisture diffusion problems in electronic packages under a transient temperature environment such as reflow process (“Direct Concentration Approach of Moisture Diffusion and Whole Field Vapor Pressure Modeling for Reflow Process: Part I — Theory and Numerical Implementation,” ASME J. Electron. Packag., 131, p. 031,010). However, our study shows that although the DCA may give reasonably accurate concentration results under several circumstances, its relative error in concentration result can be as high as 10% in one of our test cases. More importantly, the DCA generally leads to the discontinuity of diffusion flux at the bi-material interface, which means that the result may violate the law of mass conservation. A theoretical derivation based on a one-dimensional (1-D) diffusion case is presented to demonstrate the flaw of the DCA using the finite element formulation.