Vapor pressure prediction for stacked-chip packages in reflow by convection-diffusion model

Moisture plays a critical role in the reliability of electronic devices, especially in the desorption process at reflow temperatures (around 270° C) when severe damages may occur due to high-pressure vapor concerted from condensed moisture. Such pressure-driven vapor flow, however, could not be described by conventional Fick´s Law. Furthermore, using conventional Fick´s Law for multi-materials always encounters interface discontinuity issues. Therefore, this paper adopts a Convection-Diffusion Model that is able to describe complex desorption behavior in a multi-material media without the discontinuity issue. Both pressure gradient-driven (convection) and concentration-gradient driven (diffusion) moisture transports are considered in the model. To achieve this, absorbed moisture is partitioned into vapor phase and liquid phase (condensed water), with the vapor flux governed by Darcy´s Law and the water flux by Fick´s Law. Henry´s Law is also implemented so that the Fickian term is converted to pressure, resulting in a unified vapor pressure model. The model is applied to analyze a stacked-chip package by two numerical cases: desorption under 2 typical reflow temperature profiles. Numerical validations are also performed to show that the Convection-Diffusion Model can be reduced to traditional Fickian Model and Convection-Only Model as special cases. The numerical results show that the concentration desorption rate is much faster than that of the traditional Fickian diffusion, and somewhat faster than the Convection Model, this results in a much lower pressure in the material. However, the desorption profile with time and the pressures at low temperatures of the different models- the Convection-Only, Diffusion-only and the Convection-Diffusion Model are indistinguishable which can be seen in both reflow profiles. The sensitivity of the CD Model to the gas permeability k and the reflow temperature profiles governs the maximum pressure that is predicted a- well as the concentration content.