This paper presents a mathematical analysis to predict the solder fillet shape for ceramic ball grid array joints. Unlike the past analyses, the solder fillet is not assumed to be linear. The solder fillets on both the module and the card side are represented as arcs, and the solder shape is calculated from an analysis that incorporates the major factors affecting the solder fillet, including the solder volume, the pad size, the solder ball size, the wetting angle between the solder and the solder ball, and the gap between the solder ball and the pad. Three of these parameters (the card pad size, the solder ball size and the card-side eutectic solder volume) were selected for investigation of their effect on the reliability of solder joints. To this end, a central composite design of experiment was set up, and the mathematical analysis and finite element methods were used to predict the fatigue life corresponding to each of the design settings in the design array. The results of analyzing the data reveal that the solder volume, the solder ball size and their interaction are statistically significant; the interaction between the pad size and the solder volume is also significant but to a less degree; the pad size and the interaction between the pad size and the solder ball size are not significant. In addition, a response surface model was built to find the optimum settings for maximum reliability. Finally, inaccuracy due to the linear solder fillet assumption is assessed in light of the present analysis.

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