Combining multi-phase field simulation with neural network analysis to unravel thermomigration accelerated growth behavior of Cu6Sn5 IMC at cold side Cu–Sn interface

Abstract

In Pb-free solder alloys used in solder balls of diameter of 50 µm or smaller, larger proportion of Cu6Sn5 intermetallics formation is a major reliability concern, and this is aggravated in presence of external thermal gradient. A complete understanding of the mechanism for intermetallics compound (IMC) growth under thermomigration is essential for devising solder materials resistant to degradation under thermal gradient. This work integrates neural network analysis with multi-phase field method to quantify the mechanism of thermomigration at the cold side of a solder-substrate system. At hot side temperature of 523.15 K, 1D multi-phase field model is built for a combined driving force of bulk diffusion and thermomigration, and is solved using finite element method (FEM). The free energy density function for the thermomigration driving force is introduced, and coupled with the functions for bulk and interfacial free energy density of each phase. Data of heats of transport, temperature difference and growth rate constant of IMC are obtained from multiple FEM simulations, and the FEM-generated dataset is employed in the neural network. The machine learning predicted growth rate constant is tallied with experimental value, and heat of transport of Cu in IMC phase (QCuimc) is determined from the inverse method. The obtained value of optimized QCuimc is +35.10 kJ/mol. 2D IMC grain growth simulations are performed with hot-side at 523.15 K and the cold side lowered to 523.0817 K and 522.0 K respectively, thereby revealing that the accelerated grain growth for larger temperature difference is noticed within the first 20 s of the simulations.