A Direct Multi-Field Coupling Methodology for Modeling Moisture-Induced Stresses and Delamination in Electronic Packages

Abstract

A direct multi-field coupling method is proposed to integrate hygroscopic swelling and vapor pressure effects with thermos-mechanical stress. Moisture diffusion is modeled using water activity theory that is a unified and versatile approach for multi-materials systems. Water activity theory can be simply understood as an alternative normalization approach with normalized concentration defined as ${\overline C _k} = {a_w} = C/K$, where K is the generalized solubility. Vapor pressure pw is calculated as pw = psat • aw according to water activity definition (i.e., water activity is the ratio between the vapor pressure and saturated vapor pressure psat). The integration of water vapor pressure is achieved by the effective stress theory assuming polymeric materials as porous medium with vapor pressure acting on the skeletal portion. An equivalent coefficient of diffusion expansion (CDE) is derived as a new material property to consider both the hygroscopic swelling and vapor pressure effects. For isotropic materials, CDE can be expressed as CDE=CHS+pSat(/(3B • K), where CHS is the coefficient of hygroscopic swelling and B is bulk modulus. It can be seen from the equation that vapor pressure effects can be significant at high temperatures when the saturated vapor pressure is high but material modulus is low. The equivalent CDE method is applied to study the delamination of solder mask in a low-profiled ball grid array (LPBGA) package subjected to moisture preconditioning and reflow process. The direct coupling of thermal stresses and moisture-induced stresses is performed in ANSYS using its coupled-field elements. The results of the simulation match well with the experimental observations. The design of experiments shows that increasing the solder mask thickness could reduce solder mask tensile stress/strain and thus provides a viable solution to reduce the delamination issues.