Multiscale creep modeling of the effect of micro-alloying Manganese into SAC105 solder

Abstract

The current study employs a multiscale mechanistic model to capture the time-dependent viscoplastic response of SAC105-05Mn (Sn1.0Ag0.5Cu doped with 0.05 wt-percent Manganese (Mn)) and SAC105. This study is motivated to explain the improvement in creep resistance (1-2 orders of magnitude) observed in SAC105 due to addition of trace amount of Mn, as reported previously by authors. The effect of the microalloying on the microstructure is characterized using optical image processing techniques by quantifying the size, volume fraction, and inter-particle spacing of both nanoscale Ag <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn intermetallic compounds (IMCs) and micronscale Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> Sn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> IMCs. Addition of Mn as a fourth alloying element is found to promote homogeneous nucleation of micronscale Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> Sn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> IMCs, thereby reducing its size and interparticle spacing compared to that in SAC105. Furthermore, the volume fraction of nanoscale Ag <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn IMCs in eutectic Sn-Ag region is higher in SAC105-05Mn compared to that of SAC105, and the volume fraction of pure Sn dendrites in as-solidified microstructures is found to be lower in SAC105-05Mn compared to that in SAC105. Addition of Mn however does not change the average Sn grain size in SAC105 solder joint, as confirmed by cross-polarized microscopy. The effects of the above microstructural changes (obtained using image processing) on secondary creep constitutive response of SAC105-05Mn solder interconnects are then modeled using a mechanistic multiscale creep model. The mechanistic phenomena modeled include: i] dispersion strengthening and reinforcement strengthening provided by Ag <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn IMCs and Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> Sn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> IMCs respectively; and ii] load sharing between pure Sn dendrites and the surrounding eutectic Sn-Ag structure. The current model is isotropic and is intended for modeling secondary creep behavior, where the anisotropy is found to be weak. The modeling approach therefore uses a directional average of the creep along preferred slip systems and orientations in anisotropic Sn grains present in coarse grained SAC105 solder joints. The above mechanistic model is able to capture the trends in secondary-creep constitutive response of the above alloys fairly accurately and explain the improvement in creep resistance of SAC105 due to the addition of Mn.