## 4 Results and Discussion
### Thermal Annealing with Constant Electric Currentand Current Density (Uniform Cross-Sectional Areas)
Based on the results, the IMC formation was thicker in the samples heated at 180 \({}^{\circ}\)C than those heated at 130 \({}^{\circ}\)C. This is because the diffusion energy was greater in the former than the latter (see Tables 5 and 6). Moreover, similar with the second experiment, it was found that the IMC layer formed was thicker at the anode end than at the cathode end. The reason for this is that the temperature of the anode end was higher resulting in a higher thermal energy than that of the cathode end (see Figure 15) [4]. In terms of current density, it was found that the IMC layer formed in the sample heated at 180 \({}^{\circ}\)C was considerably greater than those in the sample heated at 130 \({}^{\circ}\)C. Further, regardless of the temperature, the growth of the IMC layer at the cathode end was not as obvious as that at the anode end. This is consistent with the result in experiment 2, wherein the IMC growth was more obvious at the anode end. As observed in Figures 11 and 12 (samples heated at 130 \({}^{\circ}\)C) and Figures 13 and 14 (samples heated at 180 \({}^{\circ}\)C), there were more holes and cracks at the cathode ends than at the anode ends. It appears that at the high electric current density, the direction of electron flow is from the cathode end towards the anode end; while electromigration enhances atomic flux to move towards the anode to thicken the IMC thickness and causes holes and cracks at the cathode end [20]. Consequently, it was found that the current densities on the anode ends of the 1 mm end of the 1:9 sample and the 3 mm end of the 3:7 sample were relatively higher than that of the 7 mm end of the 3:7 sample and the 9 mm end of the 1:9 sample. This resulted in the former having a thicker IMC formation than the latter. There were also fewer defects at the 7 mm end of the 3:7 sample and the 9 mm end of the 1:9 sample at the anode ends. Figure 16c, d shows the degree of IMC growth in the samples. Figure 14: SEM images of various samples heated at 180 \({}^{\circ}\)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. Figure 16: Analysis of the degree of IMC growth in the samples with different cross-sectional areas. (**a**) Anode end; (**b**) cathode end; (**c**) samples heated at 130 \({}^{\circ}\)C; (**d**) samples heated at 180 \({}^{\circ}\)C.  
Figure 15: The temperature read-out of the sample located at the (**a**) anode heated at 130 \({}^{\circ}\)C with input current; (**b**) cathode heated at 130 \({}^{\circ}\)C with input current; (**c**) anode heated at 180 \({}^{\circ}\)C with input current; (**d**) cathode heated at 180 \({}^{\circ}\)C with input current. [PERSON] [9; 10], [PERSON] [13], and [PERSON] [21] illustrated that the electromigration mechanism is the massive atomic diffusion driven by a high electric current density in the direction of electron flow. While electromigration drives atomic flux to the anode side, an equal flux of vacancies diffuses to the cathode side. This study considers both atomic flow and electric carrier flow as well as their interaction of thermal energy. We found that as the cross-section decreased on the sample anode ends from 9 mm and 7 mm down to 3 mm and 1 mm, the density of the electrons increased. This would increase the driving force in Equation (1) and the atom diffusion flux in Equation (3); the increase in the driving force indicates that the atomic diffusion capacity J would also increase. Therefore, because the atomic diffusion capacity increases, the atoms move from the cathode to the anode and finally cause voids and cracks at the cathode end and a stacking phenomenon at the anode end.