Elastic Behavior of Coarse-Grained SnAgCu (SAC) Solder Joints Based on an Anisotropic Multi-scale Predictive Modeling Approach

Lead-free electronic interconnections made of Sn-rich solder alloys usually contain only a few highly anisotropic grains, rendering their overall thermo-mechanical behavior highly dependent on each crystal's morphology and orientation. Miniaturization and heterogeneous integration will further reduce the length-scale of interconnections and exacerbate this piece-to-piece variation among different solder joints. The objective of this paper is to predict the elastic response and intergranular stresses in coarse-grained SAC (SnAgCu) solder joints, starting with orientation sensitive anisotropic predictive models of the elastic behavior of single crystals. The properties of the single crystal are, in turn, predicted by a multi-scale method, where each grain is modeled as a collection of Sn dendrites embedded in a eutectic Sn-Ag matrix. The eutectic phase, in turn, is modeled as an effective homogenized composite material consisting of nano-scale Ag3Sn particles embedded in a highly anisotropic tin matrix. All homogenization for prediction of single-crystal elastic properties is based on composite micromechanics, using Eshelby's method and Mori-Tanaka homogenization. Elastic response of a few-grained solder joints is then numerically predicted from the anisotropic behavior of the single crystal, by explicitly modeling the grain morphology in finite element analysis (FEA). Stress distributions along grain boundaries are simulated and analyzed in terms of the misorientation angle between neighboring grains. The mismatch in von Mises stress along the boundaries varies up to 55% for grain structures considered here. This multi-scale predictive modeling approach is explicitly sensitive to microstructural features such as the morphology of: (1) the intermetallic compound (IMC) reinforcements in the eutectic phase; (2) dendrites; and (3) grains. Thus, this modeling approach is ideally suited for: (1) parametric studies of the effect of microstructural tailoring on solder joint thermo-mechanical behavior and (2) examining the effects of microstructural evolution caused by static and cyclic thermo-mechanical aging. This work forms the starting point for future development of microstructurally based anisotropic models of crystal-scale inelastic behavior.