Folks,

The temperature for electronics in a modern automobile can be **higher than 125°C**. These high temperatures raise the concern of copper-tin intermetallic growth in solder joints.

Often, we don’t think about the fact that even room temperature is a considerable fraction of the melting temperature of tin, e.g., 293K/505K = 0.5802. A reminder that we have to use the **Kelvin scale** when making these calculations. However, 125°C is 0.788 of the way to tin’s melting point. This temperature is the equivalent of a blacksmith’s wrought iron being at 895°C. Figure 1 shows a **blacksmith’s forge temperature** chart. Note that 895°C is beyond red hot.

Figure 1. A Blacksmith’s forge temperature chart

So, what is SAC solder’s copper-tin intermetallic growth at 125°C as a function of time? **Fick’s law of diffusion** tells us that the growth of the intermetallic, D, is given by:

D = (k(T)t)^0.5 Eq 1.

Where k(T) is a temperature dependent growth rate constant and t is time. Siewert etal**[i]** performed experiments in which D was measured for various temperatures and times for SAC solders. Following Siewert’s lead I will use time in hours. By using their data in their Figures 2a through 2c for SAC solder, I was able to plot k in an **Arrhenius graph**, see Figure 2.

Figure 2. An Arrhenius Plot of Siebert’s Data

From Figure 2, we see that Ln k = -6784.7/T + 14.81 or k = exp (14.81)*exp-(6784.7/T). So, at 125°C or 398°K, k = 0.1068. Using this value of k, we can plot D as a function of time. The results are in Figure 3. Note that both scales are logarithmic. In 1,000 hr. (42 days) the intermetallic has grown 10 microns. In three years, it hits 53 microns. We should be cautious, as Siewet’s data has error bars. But, my sense is that these projections are within a factor of two.

Figure 3. Intermetallic Growth as a Function of Time at 125°C in SAC Solder.

What is the effect of these thick intermetallics in a harsh auto environments? No one knows, but I would encourage someone to perform some experiments to find out.

Cheers,

Dr. Ron

**[i]** Siewert, T. A. etal, *Formation and Growth of Intermetallics at the Interface between Lead-Free Solders and Copper Substrates*, IPC Apex, 1994.