## 4 Results and Discussion
### Impact of the Macro- and Micro-Deformation Behavior on the Thermal Cycling Reliability  
The macroscopic deformation behavior of the model through thermal cycling is shown in Figure 10, where the strain of the TLPS joint is not increased in each subsequent thermal cycle (Figure 10a). This FE simulation result suggests that the TLPS joint deforms macroscopically during the elastic deformation stage. The joint lifetime of elastoplastic materials can be estimated by the following Coffin-Manson equation:  
\[N_{\text{f}}=C\cdot\Delta\varepsilon_{\text{ie}}^{-n}, \tag{4}\]  
where \(N_{\text{f}}\) is the number of cycles till failure, \(\Delta\varepsilon_{\text{ie}}\) is the increase in strain per cycle, and \(C\) and \(n\) are the material-dependent lifetime coefficient and exponent, respectively. The macroscopic strain amplitude of the TLPS joint is shown in Figure 10a, where \(\Delta\varepsilon_{\text{ie}}\sim 0\), which indicates that the thermal-cyclic lifetime might be further improved. Furthermore, thermal stress has to be evaluated against thermal cycling to consider the lifetime of IMC, which is a brittle material. From the macroscopic point of view, the thermal stress of TLPS is much lower than that of the IMC-only joint and SAC305 joint. The thermal stress at the bonding layer between the chip and substrate can be estimated as follows. Assuming the properties of linear elastic materials, the maximum shear stress amplitude \(\Delta\tau\) on the die-attached layer, where the temperature in the chip changes between the minimum temperature \(T_{\text{min}}\) and maximum temperature \(T_{\text{max}}\), is expressed as  
\[\Delta\tau=\frac{E}{1+\
u}\big{(}\alpha_{\text{chip}}-\alpha_{\text{substrate}} \big{)}\cdot(T_{\text{max}}-T_{\text{min}}), \tag{5}\]  
where \(E\) is [PERSON]'s modulus, \(\
u\) is the [PERSON]'s ratio, and \(\alpha_{\text{chip,substrate}}\) is the CTE of the chip and the substrate [43]. Based on this equation, it is clear that the reduction of the modulus of the bonding layer causes a significant reduction of the thermal stress of the TLPS joint as compared to the IMC-only joint. The above observations suggest that the addition of resin causes reduction of stiffness, and the mechanical properties of the IMC-based composite structure are stable against temperature variations, which facilitates the excellent reliability of the Cu-IMC-resin microstructure against thermal cycling. To gain further insights, we now discuss the microscopic deformation characteristics, which include distribution of local stress and strain. Our previous study used die-shear tests to demonstrate the fracture at the Cu-IMC-resin joints within the IMCs or at the interface between the IMCs and Cu particles with brittle surfaces [33]. In addition, [PERSON] et al. [42] demonstrated (both numerically and experimentally) that Cu\({}_{6}\)Sn\({}_{5}\) and Cu\({}_{3}\)Sn fractured in brittle mode using the micro-cantilever bending method. Although, the precise fracture behavior of brittle materials should be discussed by considering fracture toughness based on various influence factors; here, we have simply discussed the behavior in terms of Mises stress at potential crack initiation sites. The microscopic distribution of Mises stress of the TLPS microstructure against macroscopic uniaxial load was numerically evaluated, where the ambient temperature was set as \(-55\)\({}^{\circ}\)C because the maximum macroscopic strain was generated at the minimum temperature stage during the thermal cycling. The results are shown in Figure 11, where it is evident that the stress concentration sites, which are close to the necks between the connected Cu particles, expand with the increase in macroscopic strain (Figure 11b-e).