Multiscale Modeling of the Anisotropic Creep Response of SnAgCu Single Crystal
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The lack of statistical homogeneity in functional SnAgCu (SAC) solder joints due to their coarse grained microstructure, in conjunction with the severe anisotropy exhibited by single crystal Sn, renders each joint unique in terms of mechanical behavior. An anisotropic multiscale modeling framework is proposed in this dissertation to capture the influence of the inherent elastic anisotropy and grain orientation in single crystal Sn on the primary and secondary creep response of single crystal SnAgCu (SAC) solder. Modeling of microstructural deformation mechanisms in SnAgCu (SAC) solder interconnects requires a multiscale approach because of tiered microstructural heterogeneities. The smallest length scale (Tier 0) refers to the Body Centered Tetragonal (BCT) structure of the Sn matrix itself because it governs: (1) the associated dislocation slip systems, (2) dislocation line tension (3) dislocation mobility and (4) intrinsic orthotropy of mechanical properties in the crystal principal axis system. The next higher length scale, (Tier 1), consists of nanoscale Ag3Sn intermetallic compounds (IMCs) surrounded by Body Centered Tetragonal (BCT) Sn to form the eutectic Sn-Ag phase. The next higher length scale (Tier 2) consists of micron scale lobes of pro-eutectic Sn dendrites surrounded by eutectic Sn-Ag regions and reinforced with micron scale Cu6Sn5 IMCs. Unified modeling of above two length scales provides constitutive properties for SAC single crystal. Tier 3 in coarse-grained solder joints consists of multiple SAC crystals along with grain boundaries. Finally, Tier 4 consists of the structural length scale of the solder joint. Line tension and mobility of dislocations (Tier 0) in dominant slip systems of single crystal Sn are captured for the elastic crystal anisotropy of body centered tetragonal (BCT) Sn by using Stroh's matrix formalism. The anisotropic creep rate of the eutectic Sn-Ag phase of Tier I is then modeled using above inputs and the evolving dislocation density calculated for the dominant glide systems. The evolving dislocation density history is estimated by modeling the equilibrium between three competing processes: (1) dislocation generation; (2) dislocation impediment (due to backstress from forest dislocations in the Sn dendrites and from the Ag3Sn IMC particles in the eutectic phase); and (3) dislocation recovery (by climb/diffusion from forest dislocations in the Sn dendrites and by climb/detachment from the Ag3Sn IMC particles in the eutectic phase). The creep response of the eutectic phase (from Tier 1) is combined with creep of ellipsoidal Sn lobes at Tier 2 using the anisotropic Mori-Tanaka homogenization theory, to obtain the creep response of SAC305 single crystal along global specimen directions and is calibrated to experimentally obtained creep response of a SAC305 single crystal specimen. The Eshelby strain concentration tensors required for this homogenization process are calculated numerically for ellipsoidal Sn inclusions embedded in anisotropic eutectic Sn-Ag matrix. The orientations of SAC single crystal specimens with respect to loading direction are identified using orientation image mapping (OIM) using Electron Backscatter Diffraction (EBSD) and then utilized in the model to estimate the resolved shear stress along the dominant slip directions. The proposed model is then used for investigating the variability of the transient and secondary creep response of Sn3.0Ag0.5Cu (SAC305) solder, which forms the first objective of the dissertation. The transient creep strain rate along the  direction of SAC305 single crystal #1 is predicted to be 1-2 orders of magnitude higher than that along the / direction. Parametric studies have also been conducted to predict the effect of changing orientation, aspect ratio and volume fraction of Sn inclusions on the anisotropic creep response of SAC single crystals. The predicted creep shear strain along the global specimen direction is found to vary by a factor of (1-3) orders of magnitude due to change in one of the Euler angles (j1) in SAC305 single crystal #1, which is in agreement with the variability observed in experiments. The second objective of this dissertation focuses on using this proposed modeling framework to characterize and model the creep constitutive response of new low-silver, lead-free interconnects made of Sn1.0Ag0.5Cu (SAC105) doped with trace elements, viz., Manganese (Mn) and Antimony (Sb). The proposed multiscale model is used to mechanistically model the improvement in experimentally observed steady state creep resistance of above SAC105X solders due to the microalloying with the trace elements. The third and final objective of this dissertation is to use the above multiscale microstructural model to mechanistically predict the effect of extended isothermal aging on experimentally observed steady state creep response of SAC305 solders. In summary, the proposed mechanistic predictive model is demonstrated to successfully capture the dominant load paths and deformation mechanisms at each length scale and is also shown to be responsive to the microstructural tailoring done by microalloying and the continuous microstructural evolution because of thermomechanical life-cycle aging mechanisms in solders.