A 3D numerical study of a molten solder droplet's wetting and solidifying on a pillar with application to electronic packaging

Abstract

The 3D problem of spreading and solidification of a molten solder droplet (with a melting temperature of Tm and a radius of Rd) on a circular pillar (with a radius Rpillar and a height Hpillar, having a contact angle θpillar at wall temperature Tpillar) above a substrate has important applications in electronic packaging. In this paper, effects of pillar's contact angle and wall temperature on droplet dynamics and solidification of the solder droplet are studied numerically based on a newly developed 3D multi-component, triple- phase-change LB model. For pillar's wall temperature equal to the melting temperature of the molten droplet (Tpillar = Tm), no solidification takes place in the droplet after its contact with the pillar, and droplet's spreading characteristics depend on the pillar's contact angle. If pillar's contact angle (θpillar) is smaller than a critical contact angle (θpillar)cr, i.e., θpillar < (θpillar)cr, the solder droplet spreads toward the edge of the pillar's top, turning around the corner of the pillar and spreading downward along the pillar's side wall. Based on LB simulated results, a map in terms of (θpillar) versus (Rd/Rpillar) is presented, showing regimes of droplet spreading and not spreading around the corner of the pillar. An analytical expression for predicting the critical contact angle of the pillar is derived, which is shown to divide these two regimes in the map. LB simulations are also carried out for the case when pillar's wall temperature is lower than the melting temperature of the molten droplet (i.e., Tpillar < Tm). Under this situation, it is shown that although no solidification takes place during the initial spreading motion, but solder bumps begin to be formed subsequently due to solidification and droplet's spreading motion is arrested as a result. Since formation of solder bumps on pillar's side wall may lead to short circuit of electric connection between solder bumps with other electric sources in the gap between the pillars, it is important to prevent the formation of solder bumps on pillar's side wall. For this purpose, a map of (θpillar) versus (Rd/Rpillar) at different Stefan numbers (denoting the effect of pillar's wall temperature Tpillar) is obtained to define the regime in which no solder bumps are formed on the pillar's side wall.