A Model for Assessing the Shape of Solder Joints in the Presence of PCB and Package Warpage

Our goals in this paper are to develop and demonstrate a computationally efficient methodology for assessing the effect of circuit board warpage, component warpage, and solder volume variation on the shape of the solder joints in area array packages. The effect of warpage is analyzed using a two-step procedure in the present paper. In the first step, the restoring forces and moments (in the molten state of solder droplet) that result from a given solder joint height, solder material volume, pad diameter, and pad inclination are predicted using the surface tension theory. In the second step of the analysis, the forces and moments at individual solder joints caused by varying solder heights and pad tilts are combined to predict the equilibrium configuration of the package. A program written in the MATHEMATICA® environment was developed to implement the above-described methodology. The developed procedure was validated on an experimental test vehicle with nine solder joints. The heights of solder joints computed by the program matched the experimentally measured heights to within $±5%$ error. Further, the general capabilities of the modeling procedure are demonstrated by assuming complex combinations of package and PCB warpage.