Anisotropic Multi-scale Modeling for Steady-state Creep Behavior of Oligocrystalline SnAgCu (SAC) Solder Joints

Abstract

Heterogeneous integration is leading to unprecedented miniaturization of solder joints. The overall size of solder interconnections in current-generation microelectronics assemblies has length-scales that are comparable to that of the intrinsic heterogeneities of the solder microstructure. In particular, there are only a few highly anisotropic grains in each joint. This makes the mechanical response of each joint quite unique. Rigorous mechanistic approaches are needed for quantitative understanding of the response of such joints, based on the variability of the microstructural morphology. The discrete grain morphology of as-solidified oligocrystalline SAC (SnAgCu) solder joints is explicitly modeled in terms of multiple length scales (four tiers of length scales are used in the description here). At the highest length-scale in the joint (Tier 3), there are few highly anisotropic viscoplastic grains in each functional solder joint, connected by visoplastic grain boundaries. At the next lower tier (Tier 2), the primary heterogeneity within each grain is due to individual dendrites of pro-eutectic β-Sn. Additional microscale intermetallic compounds of Cu6Sn5 rods are located inside individual grains. Packed between the dendrite lobes is a eutectic Ag-Sn alloy, The next lower length-scale (Tier 1), deals with the microstructure of the Ag-Sn eutectic phase, consisting of nanoscale Ag3Sn IMC particles dispersed in a β-Sn matrix. The characteristic length scale and spacing of the IMC particles in this eutectic mix are important features of Tier 1. Tier 0 refers to the body-centered tetragonal (BCT) anisotropic β-Sn crystal structure, including the dominant slip systems for this crystal system. The objective of this work is to provide the mechanistic framework to quantify the mechanical viscoplastic response of such solder joints. The anisotropic mechanical behavior of each solder grain is modeled with a multiscale crystal viscoplasticity (CV) approach, based on anisotropic dislocation mechanics and typical microstructural features of SAC crystals. Model constants are calibrated with single crystal data from the literature and from experiments. This calibrated CV model is used as single-crystal digital twin, for virtual tests to determine the model constants for a continuum-scale compact anisotropic creep model for SAC single crystals, based on Hill’s anisotropic potential and an associated creep flow-rule. The additional contribution from grain boundary sliding, for polycrystalline structures, is investigated by the use of a grain-boundary phase, and the properties of the grain boundary phase are parametrically calibrated by comparing the model results with creep test results of joint-scale few-grained solder specimens. This methodology enables user-friendly computationally efficient finite element simulations of multi-grain solder joints in microelectronic assemblies and facilitates parametric sensitivity studies of different grain configurations. This proposed grain-scale modeling approach is explicitly sensitive to microstructural features such as the morphology of: (i) the IMC reinforcements in the eutectic phase; (ii) dendrites; and (iii) grains. Thus, this model is suited for studying the effect of microstructural tailoring and microstructural evolution. The developed multiscale modeling methodology will also empower designers to numerically explore the worst-case and best-case microstructural configurations (and corresponding stochastic variabilities in solder joint performance and in design margins) for creep deformation under monotonic loading, for creep-fatigue under thermal cycling as well as for creep properties under isothermal aging conditions.