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22 SMT007 MAGAZINE I JULY 2019 The only other change in the system pre- dicted by the phase diagram is that as the sys- tem cools the mixed alloy phase will cross the solvus line at about 130°C (Point E), which means that the Bi level has reached its satura- tion limit at that temperature and Bi will start to precipitate out of the Sn-Bi alloy. Effect of Bi Level in Low-Melting-Point Alloy In the example described in the previous sec- tion, the length of the line AD provides an indi- cation of the amount of Sn that will dissolve from the ball alloy before the melting point of the Sn-Bi alloy reaches the reflow temperature and the mixing process stops. If the starting alloy were 60% Bi rather than 50%, then more Sn would have to dissolve from the ball alloy before Sn content of the alloy mixture reaches the solvus limit at that temperature. In reality, for a particular reflow temperature, the loca- tion of the liquidus line on the Bi-rich side of the eutectic sets an upper limit on the Bi con- tent of the solder that is usable at a particular target reflow temperature. Effect of Reflow Temperature As the temperature increases, the amount of Bi that can be held in solid solution decreases. Put another way, as the Bi content of the alloy increases, when the temperature at which the alloy starts to melt, solidus decreases. In the phase diagram, that trend is reflected in the slope of the solidus line that runs from the melting point of Sn to the limit of Bi solubility in Sn at the eutectic temperature. That means that as the reflow temperature increases, the amount of Sn that will dissolve from the solder ball before the solidus line is crossed and the mixed alloy is completely frozen. Calculating Actual Sn Dissolved For a given volume of low-melting-point sol- der, the amount of Sn that will be dissolved from the solder ball at a particular temperature before the composition of the resulting mixed alloy reaches the solvus can be calculated from the slope of the solidus line. In geometric terms, the solidus line on the Sn-rich side of the Sn-Bi equilibrium phase diagram in Figure 5 can be described by Equa- tion 1: Where %Sn S is the minimum Sn content of the Sn-rich Sn-Bi alloy that is solid at the chosen reflow temperature T R . The maximum wt%Sn at the eutectic temperature of 139°C is 79 (Figure 5). When T R is set as the melt- ing point of pure Sn (232°C), the equation cal- culates the wt%Sn at 100% Sn (allowing for rounding errors). For a given quantity of a low-melting-point Sn-Bi alloy with a chosen Sn content and the chosen reflow temperature, this equation can be used to calculate how much Sn will dissolve from the solder ball before the mixing process is brought to a halt by the composition of the resulting alloy crossing the solidus line. If the objective is that a significant proportion of the original solder ball remains at the completion of the reflow profile, then the volume of sol- der paste and its initial Sn content would have to be carefully calculated, accounting for the size of the solder ball and the Sn content of its alloy. Calculating Paste Volume for Reliable BGA Joints For the purpose of demonstrating the appli- cation of this approach to the design of reliable mixed alloy reflow, the reflow of a 500-μm sol- Figure 5: Phase diagram used for expressing the slope of the solidus line as a function of Sn content and temperature.