Quantitative Structural Hierarchy of Phase Separation Dynamics in Miniaturized Solder Joints

The microstructural hierarchy descriptor $(\mu \text{SHD})$ is used to investigate the effects of geometry and shear stress on the kinetics of phase separation in miniaturized solder joints. All joints are ${3.5}\ {\mu} \mathrm{m}$ in height and subjected to aging at 125 °C. From a scale perspective, the results reveal a negative linear correlation between the logarithm of the $\mu \text{SHD}$ value $(\log_{10}S_{J}^{1})$ and the logarithm of aging time $({\log}_{10}t)$ on smaller scales ${J} \leq {4}$, but turns out to be positive on a larger scale ${J}={6}$. Compared to an hourglass joint, smaller-scale features decrease faster, but larger-scale features increase slower in a barrel joint. Shear stress has been found to decrease kinetics on smaller scales $J\leq 4$, but increase it on a larger scale $J=6$. For barrel joints, the top region exhibits faster kinetics on smaller scales $J \leq 4$ compared to other regions, while for hourglass joints, the top region exhibits slower kinetics. Shear stress leads to a horizontal and a vertical orientation in the top region of the barrel and hourglass joints, respectively.