The goals of the present paper are to demonstrate a methodology for studying the effect of printed circuit board (PCB) warpage and volume variation on the final equilibrium configuration of area-array packages. Although the eventual goal is the development of a predictive methodology for the reliability impact of circuit board and component warpage, the present study is limited to an assessment of solder joint shape in the presence of PCB warpage and volume variation. 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 tilt 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, pad tilts, and solder volume are combined using an optimization procedure to predict the equilibrium configuration of the package. The developed procedure is demonstrated on a hypothetical area-array package with nine solder joints. Through an analysis of two scenarios, (1) constant solder volume with symmetric and non-symmetric package warpage, and (2) linearly distributed solder volume without warpage, it is shown that printed circuit board warpage can cause electronic packages to tilt during solder reflow resulting in variations in solder joint heights and pad tilts.
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