Force and collapsed shape of a liquid solder bump under load

It is shown that a collapsed solder bump carries load through a bump force that depends on the collapsed shape in a way that closely resembles the Young-Laplace (YLP) equation. The relation between force and shape allows deriving the force constant of the bump, which is important in solder bump reliability. For the commonly used ellipsoid shape model, the new force method gives similar results as the results derived conventionally from the increase in free surface energy but in a mathematically simpler way, omitting the difficult surface integral. The results confirm that the ellipsoid shape model is not a true solution for the collapsed shape. The new force based approach enables developing an improved shape model and it is shown that this satisfies both the YLP equation and minimum increase in surface energy better.