Solder bump size and shape modeling and experimental validation

Capillary physics was used to predict the size of solder bumps processed through a heated reflow cycle. Based on the density, surface tension, and volume of the solder material the effects of body forces are negligible compared to surface tension effects. For this case the predicted equilibrium shape of the molten solder is a truncated sphere, where the base of the sphere is defined by the bump input/output (I/O) pad on the integrated circuit (IC). Experiments using different size bumps on Si wafers were conducted to test the validity of the truncated sphere model. The experimental results matched the model to within 11% for the predicted height and 8% for the predicted radius. Using dimensionless variables for the solder volume, bump height, and bump radius allows these results for reflowed height and radius to each be plotted on a single curve and fitted with a single equation. These results can be used to design ICs, solder bumps, and solder bump assemblies in order to ensure that the attached IC can be underfilled reliably, and to ensure reliable products.