Spreading and solidification of a molten microdrop in the solder jet bumping process

This work develops a model to predict the spreading and solidification of solder droplets deposited on a solid pad in the solder jet bumping process. The variational principle is employed to solve the fluid flow and the semi-solid phase is modeled as a non-Newtonian slurry. This modeling greatly saves the computational expenses of conventional numerical procedures. The simulations reveal that the substrate temperature is the single dominant controlling parameter that determines the final bump diameter (or height) when the substrate possesses a high effusivity. When the effusivity of a substrate is relatively low, both the substrate temperature and the droplet temperature at impact play important roles in determining the final bump diameter. Our model can be used in designing the experimental conditions to find the optimal process conditions for a desired bump geometry.