Numerical Analysis of Coalescence Characteristics of Low Melting Point Alloy Fillers Using a Non-Equilibrium Phase Field Model

A non-equilibrium phase field model (NPFM) is proposed to examine the three-dimensional coalescence characteristics of low melting point alloy (LMPA) fillers, widely used for self-organized interconnection applications. This model sufficiently considers the non-equilibrium process during phase transitions, resulting in accurate prediction of interfaces between two different phases with a high density ratio. The preliminary simulation is carried out for validation of the present model and numerical predictions are in good agreement with analytical solutions for a one-dimensional solidification problem. The proposed NPFM successfully predicts the phase transition, the heat transfer from solid to liquid, and the coalescence behaviors of LMPA fillers, whereas the conventional enthalpy method fails to describe the non-equilibrium phase transition. Moreover, the results show that there exists grid dependency in the mush zone, suggesting that special care should be taken of the mush zone for better prediction of interfaces between different phases.