Synergistic crystal plasticity and machine learning unraveling TSV-Cu fatigue

Thermally induced copper (Cu) protrusion in through-silicon vias (TSVs) represents a critical thermo-mechanical reliability challenge in three-dimensional integrated systems. To resolve the roles of crystallographic anisotropy and microstructural geometry, an integrated framework combining physics-based crystal plasticity finite element modeling and data-driven machine learning was developed in this study. Ex-situ electron backscatter diffraction measurements demonstrated that the macroscopic grain network remained statistically invariant during low-ΔT thermal cycling. This observation justified the assumption of a non-evolving microstructure in the simulations. The crystal plasticity results indicated that non-uniform protrusion originated from strain incompatibility driven by Schmid-factor mismatch between neighboring grains. Due to idealized boundary conditions, the model underestimated the absolute stress level. However, it accurately reproduced the normalized protrusion kinetics and predicted the onset of interfacial cracking near the sidewall at approximately 20 cycles. Machine-learning analysis further identified grain size as the most influential statistical descriptor among the considered single-grain features. From a mechanistic perspective, grain size did not replace crystallographic effects but served as a geometric proxy reflecting boundary density and local mechanical constraints. Together, these results established a hierarchical failure mechanism in TSV-Cu, where crystallographic anisotropy governed the initiation of strain incompatibility, while the geometric microstructural network controlled the intensity and spatial localization of damage.