# An investigation of interconnect geometry and fatigue life of ball-grid array electronic packages

A model for the shapes and residual forces for an individual, axisymmetric BGA solder interconnect is developed from the basic assumption that the surface bounding the solder possesses constant mean curvature. The inputs for the model include: pad radius, stand-off height, and the volume of the solder. The model is contrasted with simpler ones to identify the combinations of parameters for which more relaxed assumptions regarding the shape of the interconnect (e.g., a cylinder, truncated sphere, or circular arc meridian) may lead to unacceptable errors when designing for the demanding requirements of aerospace applications. The parameter combinations include situations when there exists a large stand-off height in conjunction with residual tension in the interconnect and when there is considerable tension or compression in the interconnect. The errors can be especially significant if one is designing around presumed surface contact angles at the solder/pad/PCB junction The results of this model are incorporated into a fatigue life analysis for BGA packages. In the aerospace industry the fatigue loading on the individual interconnects is Mode II shearing due to cyclic temperatures. A fracture mechanics approach is taken which accounts for this Mode II fatigue loading as well as a constant Mode I loading that is due to the residual forces arising from the surface tension within the molten interconnect. This model, which is referred to as the relative life model, is capable of demonstrating how the relative fatigue life of an interconnect can be altered as a result of a change in the residual force (and, therefore, the shape) of the interconnect. The model is capable of capturing this relationship for variable joint dimensions (i.e., volumes, stand-off heights, radii), service loading, and material constituents (i.e., solder alloys, PCBs, and IC carriers). For an array of pads of known radii, a procedure is presented for determining the optimal volumes of each solder joint so as to optimize the relative life of the entire package