Phase field modelling combined with data-driven approach to unravel the orientation influenced growth of interfacial Cu6Sn5 intermetallics under electric current stressing

Microstructure of interfacial intermetallics plays an important role in determining the service performance and reliability of interconnects especially due to the anisotropic properties of intermetallic grains, preferential growth of intermetallics induced by the electric current is observed in experiments, but the exact mechanisms for this have not been understood completely. For this endeavor, a phase field model considering the free energy arisen from the applied electric current is developed to tackle the intermetallic grain growth behavior in Sn/Cu interconnects, the focus falls on the influence of anisotropic electric conductivity. Simulation results show that electric current stressing preferentially accelerates the intermetallic growth, and the orientation effects are more pronounced with higher value of electric current density. Due to the competitive growth of multiple Cu6Sn5 grains in the presence of electric current, most region of the intermetallic layer is occupied by the grains whose caxis is along the direction of the electric current. The intermetallic grain with higher electric conductivity along the electron flow holds smaller current field, while the phase boundaries own higher electric field. It is found that the higher local electric field concentrating at phase boundary drives faster phase boundary migration. The data generated from physics-based phase field simulations are utilized to train a neural network model that functionally maps the area of a particular grain with the applied current density, simulation time, grain identification, orientation of the grain and its neighboring grains. The prediction model reveals that that electric current stressing preferentially accelerates the intermetallic growth, and the orientation effects are more pronounced with higher value of electric current density. The results from phase field simulation and physically informed machine learning model further deepen understandings of the microstructure evolution and selective intermetallic growth in the context of electric current, and shed light on the in-silico studies and design route of interconnects under other types of loadings.