Transport Phenomena in Picoliter Size Solder Droplet Dispension

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Abstract
This paper presents a study of the fluid dynamics and heat transfer phenomena occurring during the impingement of a picoliter size liquid solder droplet upon a multilayer, composite substrate. The theoretical model, based on the Lagrangian formulation, is solved numerically with the finite element method. A deforming mesh is utilized to accurately simulate the large deformations, as well as the domain nonuniformities characteristic of the spreading process. The occurrences of droplet recoiling and mass accumulation around the deposit periphery are features of the numerical simulations and yield a nonmonotonic dependence of the maximum radius on time. The results also document the transient temperature fields developing in both the solder droplet and the substrate during the impingement process. Convection effects on the temperature field development in a deforming droplet are found to be important for the entire history of spreading. The work is directly applicable to the miniature solder droplet dispension technology for the mounting of microscopic electronic components on various substrates under development at MicroFab Inc. The results of the numerical simulations are used to explain the shape of solidified microscopic solder bumps.