## 3 Results and Discussion
### Growth Mechanism of Interfacial IMCs  
Figure 6 shows the thickness of total IMC layer at the lead side and (Ni, Cu)\({}_{3}\)Sn\({}_{4}\) IMC layer at the Ni-P layer side during extreme temperature thermal shock. It is obvious that the IMC layers both at the lead side and at the Ni-P layer side represented a parabolic growth law, implying the growth of IMC layers followed the diffusion-controlled mechanism. The interfacial IMC growth both at the lead side and at the Ni-P layer side became slower with the increase of thermal shock cycles. During extreme temperature thermal shock, Cu, Ni and Sn atoms diffused across the interfacial IMC layer to form IMCs. The IMC layer thickness increased during extreme temperature thermal shock, which obstructed the diffusion of Sn, Cu and Ni atoms and thus suppressed the growth of interfacial IMCs [16; 17]. The interfacial IMC growth at the Cu lead side was found to be much faster than that at the Ni-P layer side during extreme temperature thermal shock.  
To further study the growth mechanism of interfacial IMCs, an empirical power-law relationship was adopted as follows [17; 18]:  
\[x=x_{0}+A\ t_{\mathit{off}}n, \tag{2}\]  
where \(x\) is the IMC thickness at equivalent time \(t_{\mathit{eff}}\), i.e., the total time at the extreme high temperature; \(x_{0}\) is the initial IMC thickness; and \(A\) is a constant, and \(n\) is the time exponent. Equation (1) is converted into the following logarithmic expression:  
\[\ln\left(x-x_{0}\right)=\ln A+n\ln t, \tag{3}\]  
The value of the time exponent \(n\) was obtained from the slop of the plot of \(\ln\left(x-x_{0}\right)\) versus \(\ln t\). Figure 7 presents the \(\ln\) plot of the growth of interfacial IMCs both at the lead side and at the Ni-P layer side during extreme temperature thermal shock. Table 1 lists the values of the time exponent \(n\) and the correlation factor \(R^{2}\) for the interfacial IMCs. The \(n\) value is considered to be a pointer to the growth mechanism of interfacial IMCs [18; 19]. If the \(n\) value is closer to 0.33, the IMC growth is dominated by grain-boundary diffusion. If the \(n\) value is on the order of 0.5, the IMC growth is dominated by bulk diffusion [18; 19]. The values of the time exponent \(n\) implied that the growth of the interfacial IMCs at the lead side was dominated by bulk diffusion, and the growth of the interfacial IMCs at the Ni-P layer side was dominated by grain-boundary diffusion under extreme temperature thermal shock. The diffusion mechanism for interfacial IMC growth at the lead side was quite different from that of interfacial IMC growth at the Ni-P layer side. It is presumably due to the differences in initial  
Figure 6: The thickness of interfacial Cu-Sn IMCs and Ni-Cu-Sn IMCs during extreme temperature thermal shock.  
morphologies, phase constitutions and thicknesses of the interfacial IMCs, which affected the diffusion of atoms across the interfacial IMCs, and thus resulted in various IMC growth mechanisms [20].  
In this study, the \(n\) value for the interfacial IMC growth at the lead side was higher than 0.5. This can be attributed to the thermal stress generated from the coefficient of thermal expansion (CTE) mismatch between the Cu lead (17 ppm/\({}^{\circ}\)C) [17] and the Sn-37 Pb solder (24.5 ppm/\({}^{\circ}\)C) [21], and the large temperature variation (\(\Delta T\) = 346 \({}^{\circ}\)C). The thermal stress near the solder/Cu lead interface contributed to atom diffusion, and thus accelerated the IMC growth process [22].