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JULY 2019 I SMT007 MAGAZINE 25 To interpret the volume of Sn that dissolves in the low-melting-point paste in terms of the extent to which the mixed alloy penetrates into the ball, the volume of a slice of a sphere is used as an approximation (Figure 6). Because of the difficulty of solving the equa- tion in Figure 6 to calculate h when V is known, a graphical solution is used (Figure 7). In the example illustrated in Figure 7, a 100- μm thickness, 500-μm print of Sn-50wt%Bi solder paste reflowed at 165°C would result in the formation of a zone of mixed solder that would penetrate about 220 μm into a 500-m pure Sn solder ball. Conclusions In practice, as indicated in Figure 2, the interface between the mixed alloy and the remaining solder ball is not planar, but since it is determined by tempera- ture, follow the thermal gra- dients. However, the point of this exercise is not to make an accurate prediction but to demonstrate the underly- ing principle that the extent of penetration of the mixed alloy phase into solder can be calculated on the basis of the following: • The location of the solvus line in the relevant equilibrium phase diagram • The composition of the low-melting-point solder • The volume of low-melting-point solder in the solder paste deposit • The peak reflow temperature How far the mixed alloy penetrates into the solder ball will depend on the volume of the solder ball. If a limit is to be set on the amount of origi- nal ball alloy that has to be retained to ensure the reliability of the joint than the paste alloy, Figure 6: Equation from which the distance h of penetration of the mixed alloy into a solder ball can be estimated. Figure 7: The plot on the right is the volume of Sn dissolved in the low-melting-point solder as a function of the thick- ness of a 500-μm diameter paste deposit, and the plot on the left is the height of a slice of a 500-μm diameter solder ball as a function of the volume of the slice.

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