Underfill flow simulation based on lattice Boltzmann method

• A generalized interparticle-potential model is proposed to model capillary flow.
• A mesoscale underfill simulation method is established based on 3D LBM.
• The proposed model can well characterize capillary action.
• LBM is competitive in underfill simulation for effective interface dynamics manner.
• The result-based model has poor estimate of capillary force in underfill simulation.

Underfill process is carried out mainly to prevent interconnection failures caused by the mismatch of CTE between the die and the substrate in flip chip encapsulation. Owing to troubles in calculating the capillary force, i.e., result-based and interface reconstruction, the underfill flow cannot be well characterized by current simulation methods. In this paper, we present a mesoscale underfill simulation method based on three-dimensional LBM (lattice Boltzmann method) with D3Q19 velocity set and LBGK (lattice-Bhatnagar–Gross–Krook) evolution model. In this method, the GIPM (generalized interparticle-potential model) is first proposed to model the capillary flow, which can solve the fluid–fluid interaction and the solid–fluid interaction in a unified manner. A geometric model for underfill simulation is then developed. The solid wall is divided into three parts, i.e., the substrate, the die and the solder bump, and each part is allowed to have a different wettability by assigning a mesoscale interaction parameter. For verification purpose, three underfill cases, which are different in wall wettability, are examined. In each case, besides the experimental results, we also present numerical results predicted by a VOF multiphase method with CSF capillary model. The results show that the proposed method has a good performance in the underfill simulation.

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