A new analytical approach to the geometry of a compressed liquid bump

The shape of a compressed solder bump under mechanical load stemming from the weight of an IC or IC package has an important influence on the contact angles and the stresses that results from thermal cycling. In this work an expression is derived that provides a more accurate description of this shape. The shape of the small solder bump is dominated by surface tension and the shape of the unloaded solder bump is given by a truncated sphere. In the new approach, a correction function in the form of a series expansion is applied to incorporate the flattening due to the loading of the bump. The terms of the series are evaluated through the expression for force equilibrium found in earlier work. The results are compared with the results for an elliptical model and with a “hypothetical” ideal solution and the new approach is demonstrated for two representative cases.