The Nature of Centroidal Locus in Misaligned Flip-Chip Solder Joints

The self-alignment mechanism of molten flip-chip solder joints is being increasingly used in passive alignment of optoelectronic devices. For these applications, three-dimensional models of misaligned solder joints are necessary to understand the effect of solder joint design parameters on self alignment. To reduce the complexity of fully three-dimensional models, intuitively reasonable assumptions are often made in their theoretical development. Two such assumptions for misaligned flip-chip solder joints with circular pads are that the locus of centroids is a straight line and that the cross sections are circular in shape. In the present paper, the limits of validity of these two assumptions are explored. In general, if either the top and bottom pad radii are identical, or if there is no misalignment between the pads, then the centroidal locus is a straight line and the cross sections are circular. The extent of deviation from straight line centroidal locus or circular cross section depends on the ratio of the top and bottom pad radii and on the extent of misalignment between the pads. For a misalignment equal to 20 percent of the solder joint height and a joint with 90 percent pad diameter ratio, the deviation from straight line locus is 7 percent and the deviation from circularity is less than 1 percent. However, as the pad ratio is decreased to 50 percent, and as the misalignment is increased to 100 percent, the deviation in centroidal locus increases to 43 percent and the deviation from circularity increases to 33 percent. Thus, straight line locus and circular cross sections are reasonable assumptions for flip-chip solder joints provided the pad diameter ratio and misalignment are small.