## 4 Results and Discussion
### Thermal Annealing with Constant Electric Currentand Current Density (Uniform Cross-Sectional Areas)
The results showed that after being heated at 130 \({}^{\circ}\)C, the current density at the 1 mm end of the 1:9 sample was \(1.1\times 10^{6}\) A/cm\({}^{2}\), at the 3 mm end of the 3:7 sample it was \(1.0\times 10^{6}\) A/cm\({}^{2}\), at the 7 mm  
The resulting IMC formations in the anode end of the samples with different cross-sectional areas heated at 180 \({}^{\circ}\)C after 3 days and 4 days are shown in Table 7 and Figure 13, and those in the cathode end are shown in Table 8 and Figure 14. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**IMC**} & \multicolumn{8}{c}{**Cathode End (130 \({}^{\circ}\)C)**} \\ \cline{2-9}  & \multicolumn{4}{c}{**3 Days**} & \multicolumn{4}{c}{**4 Days**} \\ \hline
**Position** & **1 mm** & **3 mm** & **7 mm** & **9 mm** & **1 mm** & **3 mm** & **7 mm** & **9 mm** \\ \hline Cu\({}_{6}\)Sn\({}_{5}\) & 1.84 & 1.59 & 1.24 & 1.39 & 1.84 & 1.32 & 1.48 & 1.21 \\ \hline Cu\({}_{3}\)Sn & 2.04 & 1.98 & 2.03 & 1.74 & 1.86 & 1.74 & 1.64 & 1.70 \\ \hline Total & 3.88 & 3.57 & 3.27 & 3.14 & 3.7 & 3.06 & 3.12 & 2.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The IMC formation and their corresponding thickness in the cathode end of the sample heated at 130 \({}^{\circ}\)C and subjected to a current of 0.8 A.  
Figure 12: SEM images of various samples heated at 130 \({}^{\circ}\)C and subjected to a current of 0.8 A after 4 days. (**a**) Cathode ends (indicated on red circle) on the 1 mm side of 1:9 sample; (**b**) Cathode ends (indicated on red circle) on the 3 mm side of 3:7 sample; (**c**) Cathode ends (indicated on red circle) on the 7 mm side of 3:7 sample; (**d**) Cathode ends (indicated on red circle) on the 9 mm side of 1:9 sample. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**IMC**} & \multicolumn{8}{c}{**Anode End (180 \({}^{\circ}\)C)**} \\ \cline{2-9}  & \multicolumn{8}{c}{**3 Days**} & \multicolumn{8}{c}{**4 Days**} \\ \hline
**Position** & **1 mm** & **3 mm** & **7 mm** & **9 mm** & **1 mm** & **3 mm** & **7 mm** & **9 mm** \\ \hline Cu\({}_{6}\)Sn\({}_{5}\) & 9.18 & 6.98 & 7.16 & 9.98 & 9.51 & 8.17 & 9.02 & 8.38 \\ \hline Cu\({}_{3}\)Sn & 3.92 & 3.38 & 3.06 & 3.17 & 3.99 & 4.63 & 4.16 & 3.7 \\ \hline Total & \multirow{2}{*}{13.11} & \multirow{2}{*}{10.99} & \multirow{2}{*}{10.22} & \multirow{2}{*}{9.98} & \multirow{2}{*}{13.51} & \multirow{2}{*}{12.8} & \multirow{2}{*}{12.19} & \multirow{2}{*}{12.08} \\ IMC & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The IMC formation and their corresponding thickness in the anode end of the sample heated at 180 \({}^{\circ}\)C and subjected to a current of 0.8 A. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**IMC**} & \multicolumn{8}{c}{**Cathode End (180 \({}^{\circ}\)C)**} \\ \cline{2-9}  & \multicolumn{8}{c}{**3 Days**} & \multicolumn{8}{c}{**4 Days**} \\ \hline
**Position** & **1 mm** & **3 mm** & **7 mm** & **9 mm** & **1 mm** & **3 mm** & **7 mm** & **9 mm** \\ \hline Cu\({}_{6}\)Sn\({}_{5}\) & 5.56 & 5.34 & 5.3 & 3.38 & 6.14 & 6.24 & 5.36 & 5.03 \\ \hline Cu\({}_{3}\)Sn & 3.27 & 2.99 & 1.84 & 2.83 & 3.44 & 3.37 & 4.05 & 3.66 \\ \hline Total & \multirow{2}{*}{8.83} & \multirow{2}{*}{8.34} & \multirow{2}{*}{7.13} & \multirow{2}{*}{6.21} & \multirow{2}{*}{9.58} & \multirow{2}{*}{9.61} & \multirow{2}{*}{9.41} & \multirow{2}{*}{8.69} \\ IMC & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The IMC formation and their corresponding thickness in the cathode end of the sample heated at 180 \({}^{\circ}\)C and subjected to a current of 0.8 A.  
Figure 13: SEM images of various samples heated at 180 \({}^{\circ}\)C and subjected to a current of 0.8 A after 4 days. (**a**) Anode ends (indicated on red circle) on the 1 mm side of 1:9 sample; (**b**) Anode ends (indicated on red circle) on the 3 mm side of 3:7 sample; (**c**) Anode ends (indicated on red circle) on the 7 mm side of 3:7 sample; (**d**) Anode ends (indicated on red circle) on the 9 mm side of 1:9 sample.