## 4 Discussion  
Cu\({}_{6}\)Sn\({}_{5}\) was not detected in the joints aged at 150-200 \({}^{\circ}\)C for 1000 h except at the chip side interface, as it was fully transformed to Cu\({}_{3}\)Sn. There are two possible reactions for the transformation from Cu\({}_{6}\)Sn\({}_{5}\) to Cu\({}_{3}\)Sn, as shown in Equations (1) and (2):  
\[9\mathrm{Cu}+\mathrm{Cu}_{6}\mathrm{Sn}_{5}\to 5\mathrm{Cu}_{3}\mathrm{Sn}, \tag{1}\]  
\[\mathrm{Cu}_{6}\mathrm{Sn}_{5}\to 2\mathrm{Cu}_{3}\mathrm{Sn}+3\mathrm{Sn}. \tag{2}\]  
The values of the Gibbs free energy changes of the two reactions calculated by [PERSON] et al. [23] are approximately \(-89\) and \(10\) kJ/mol (150-200 \({}^{\circ}\)C), respectively. Thus, the reaction in Equation (1) was the main pathway for the transformation from Cu\({}_{6}\)Sn\({}_{5}\) to Cu\({}_{3}\)Sn under the aging conditions in this study. The transformation from Cu\({}_{6}\)Sn\({}_{5}\) to Cu\({}_{3}\)Sn could affect the joint strengths because of the different mechanical properties of Cu\({}_{6}\)Sn\({}_{5}\) and Cu\({}_{3}\)Sn. For example, numerical studies estimated the  
Figure 12: Fracture surfaces of the joints (**a,b**) as-bonded and aged at (**c,d**) 150, (**e,f**) 175, and (**g.h**) 200 \({}^{\circ}\)C for 1000 h.  
elastic moduli of Cu\({}_{6}\)Sn\({}_{5}\) and Cu\({}_{3}\)Sn [24; 25]. Some experimental studies evaluated [PERSON]'s modulus of Cu\({}_{6}\)Sn\({}_{5}\) at the macro-scale [26; 27] and micro-scale [28; 29; 30; 31]. Furthermore, [PERSON] et al. evaluated the mechanical properties of Cu\({}_{3}\)Sn and Cu\({}_{6}\)Sn\({}_{5}\) through both experimental and modelling techniques of micro-cantilever bending tests of the IMCs [32]. Although there is a wide variability in the values of their mechanical properties, the Cu\({}_{3}\)Sn generally exhibits superior properties--including a high strength, high elongation, and low elastic modulus--compared to those of Cu\({}_{6}\)Sn\({}_{5}\). For instance, [PERSON] et al. reported the tensile strengths of Cu\({}_{3}\)Sn and Cu\({}_{6}\)Sn\({}_{5}\) to be 2.15 and 1.13 GPa and the tensile strains of Cu\({}_{3}\)Sn and Cu\({}_{6}\)Sn\({}_{5}\) to be 0.016 and 0.010, respectively [32]. In addition, [PERSON] et al. reported the bonding strength of TLPS joints composed of Cu\({}_{3}\)Sn to be five times higher than that composed of Cu\({}_{6}\)Sn\({}_{5}\)[10]. Based on these studies, the transformation from Cu\({}_{6}\)Sn\({}_{5}\) to Cu\({}_{3}\)Sn could have a positive effect on improving the joint strengths through thermal aging. Despite the fact that the transformation from Cu\({}_{6}\)Sn\({}_{5}\) to Cu\({}_{3}\)Sn might have improved the mechanical properties of the joints, the shear strengths of the TLPS joints showed little increase (150 and 175 \({}^{\circ}\)C) or a slight decrease (200 \({}^{\circ}\)C) through thermal aging in this study, as shown in Figure 11 in Section 3. The submicron voids observed in the Cu\({}_{3}\)Sn, as shown in the SEM images (i.e., Figures 9 and 10 in Section 3), could adversely affect the TLPS joint strengths. Interestingly, the submicron voids were observed in the Cu\({}_{3}\)Sn layer on the Cu particles, but not on the Cu substrate, as shown in Figures 6, 9 and 10 in Section 3. Some studies demonstrated that submicron voids could be formed because of Kirkendall voids within the TLP layers of Cu-Sn [23; 33; 34], Ni-Sn [35], and Ag-Sn [23] systems. The Kirkendall voids were also observed in joints consisting of Sn-based solders and Cu [15; 36; 37; 38]. [PERSON] et al. reported that the formation of Kirkendall voids as the diffusion rate of Cu atoms is much higher than that of Sn atoms in the Cu\({}_{3}\)Sn layer between the Cu substrate and SAC305 solder [36]. However, previous results on Kirkendall void formation in Cu/Sn systems are not always consistent because of impurity atoms in the joints. [PERSON] et al. [36] demonstrated that S segregation to a Cu/Cu\({}_{3}\)Sn interface localized Kirkendall voids at the interface. [PERSON] et al.