Issue link: https://iconnect007.uberflip.com/i/1526114
80 SMT007 MAGAZINE I SEPTEMBER 2024 formed into a more useful form for the pur- poses of electromigration studies as follows: In the above derivation, Z* is the electro- migration effective valence, e is the electron charge, r the electrical conductivity, v is the ion dri velocity, D o is the diffusion pre-exponen- tial constant, R is the solder joint resistance, t is duration of electromigration current stressing, and the other terms have their usual meaning. One advantage of this approach involving the Nernst-Einstein equation is that one solder joint specimen can be stressed at various tempera- tures and current densities to obtain the value of constants C 2 and Q. Using these constants in the last of the above equations, the electro- migration lifetime can be predicted under any current density and temperature condition. An example of the data needed for this approach is shown in Figure 7, in which electromigration data (solder joint resistance versus time) were collected at a constant current at various solder joint temperatures obtained by changing the oven temperature. e test would need to be repeated at various other currents to obtain an Arrhenius plot, an example of which is shown in Figure 8. Joule Heating During Electromigration Testing In electromigration testing, it is important to pay attention to joule heating, especially when the electric currents are high. Given the small size of the solder joints and the lack of line-of-sight optical access, there is no direct way of accurately measuring the solder joint temperature such as by using infrared means or thermocouples. To get accurate tempera- ture measurements, one must resort to indi- rect means such as using the temperature coef- ficient of resistivity of the solder joint. e sol- der joint resistance is measured at a very low current over a range of temperature extend- ing from room temperature to that of the oven during the electromigration test and the resis- tance versus temperature curve plotted. e resistance measurement current should be low enough to cause negligible joule heating. e resistance of the solder joint during the elec- tromigration test is then measured under the electromigration test conditions of high tem- perature and current and graphically obtain- ing the solder joint temperature as illustrated in Figure 9. During the electromigration testing, the rise in the solder joint resistance over time will cause some increase in joule heating. Planar Solder Test Specimens Ball-grid array (BGA), bottom-terminated component (BTC), C4, and other solder joints in actual applications are not convenient for electromigration research though at some point in the design cycle they do need to be Figure 9: Resistance change on the same specimen at a constant current density at various temperatures.