**5. Simulation results and experimental verifications**

#### **5.1. Simulation with no presence of IMPs**

A solder interconnection was selected to verify the performance of the presented algo‐ rithm. The interconnection was the second diagonal solder interconnection from the right end as shown in Fig. 7. The heterogeneous deformation of the interconnection after 1000 thermal cycles is shown in Fig. 11 (a). The image was taken with bright light before re‐ polishing. The persistent slip bands are visible in the image, which show the severe plas‐ tic deformation near the interface on the component side. The distribution of the heavily deformed regions agrees well with the calculated inelastic strain energy density distribu‐ tion (see Fig. 11 (b)). This agreement verifies that the energy input for the microstructur‐ al simulation is valid. The dashed rectangle in Fig. 11 (b) shows the domain of the following microstructural simulation.

Different from the experimental observations, the Monte Carlo simulation results offer a continuing process of the microstructural evolution. Three snapshots from the MC simula‐ tion with a time interval, 500 thermal cycles (TCs), are shown in Fig. 12. On the left side of the simulated microstructures, the related micrographs are presented. According to the sim‐ ulation results, the incubation time for the recrystallization is about 400 TCs. During the in‐ cubation period, the stored energy is accumulated, but the magnitude remains below the critical value. As a result, no new grains are formed before 400 TCs. The upper right corner of the solder interconnection is the location where the highest inelastic strain energy is con‐ centrated (see Fig. 11 (b)). It is this very same location where the magnitude of the stored energy first exceeds the critical value and recrystallization is initiated (see Fig. 12 (a) and Fig. 12 (d)). Then, as shown in Fig. 12 (e), the recrystallized region expands towards the lower left of the interconnection, which is in good agreement with the experimental finding (see Fig. 12 (b)). By comparing Fig. 12 (e) and 12 (*f*), it is found that the migration rate of the re‐ crystallization front slows down during the period from 1000 TCs to 1500 TCs due to the decreasing driving force in the lattice. In the micrograph, Fig. 12 (c), cracks and voids are obvious, meaning that the continuity assumption of the finite element model is no longer valid. Therefore, the difference between the experimental finding and the simulated micro‐ structure, Fig. 12 (f), is understandable. A possible solution is to simulate the behaviors of cracks and voids in the Monte Carlo model, output the microstructures to the finite element model, and then, use the calculated results as the inputs for the next round Monte Carlo simulation.

**Figure 11.** *a*) Plastic deformation of the solder interconnection after 1000 thermal cycles, (*b*) FEM-calculated inelastic strain energy density distribution, dashed rectangle shows the domain of the microstructural simulation [39].

#### **5.2. Simulation with presence of IMPs**

updated during the recrystallization simulation, the energy increment is multiplied by the associated EAF before being added to the site. By introducing the EAF, stored energy densi‐ ty close to IMPs is higher than usual, leading to a higher driving force for nucleation and growth of recrystallized grains. Thus, the particle stimulated nucleation is well taken into

consideration in the MC simulation.

106 Recent Developments in the Study of Recrystallization

**Figure 10.** von Mises stress contour and 'EAF vs. distance' curve [39].

**5.1. Simulation with no presence of IMPs**

following microstructural simulation.

**5. Simulation results and experimental verifications**

A solder interconnection was selected to verify the performance of the presented algo‐ rithm. The interconnection was the second diagonal solder interconnection from the right end as shown in Fig. 7. The heterogeneous deformation of the interconnection after 1000 thermal cycles is shown in Fig. 11 (a). The image was taken with bright light before re‐ polishing. The persistent slip bands are visible in the image, which show the severe plas‐ tic deformation near the interface on the component side. The distribution of the heavily deformed regions agrees well with the calculated inelastic strain energy density distribu‐ tion (see Fig. 11 (b)). This agreement verifies that the energy input for the microstructur‐ al simulation is valid. The dashed rectangle in Fig. 11 (b) shows the domain of the

Different from the experimental observations, the Monte Carlo simulation results offer a continuing process of the microstructural evolution. Three snapshots from the MC simula‐ tion with a time interval, 500 thermal cycles (TCs), are shown in Fig. 12. On the left side of

There was no obvious IMP-affected recrystallization in any of the in situ samples. Most of the observed recrystallized microstructures were located close to the interface region where the stored energy density was the highest. In order to focus on the influence of the IMPs and exclude the effects of the heterogeneous energy distribution, a uniform stored energy densi‐ ty distribution was assumed during the simulation. The assumption is valid when the calcu‐ lation domain is located in the center part of the solder interconnection, where the energy magnitude is relatively low and energy distribution is quite uniform. Furthermore, the ener‐ gy amplification factors introduced in Section 4.5.3 were used to increase the energy around the IMPs.

grains and most of the stored energy is released, there is practically no difference between Fig. 14 (c) and Fig. 14 (d). Furthermore, it is found that the IMPs tend to located at the grain boundaries or triple junctions of the new grains as a result of the energy minimization calcu‐

Simulation of Dynamic Recrystallization in Solder Interconnections during Thermal Cycling

http://dx.doi.org/10.5772/53820

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**Figure 13.** *a*) Micrograph shows IMP-affected recrystallization, (*b*) initial microstructure for the Monte Carlo simula‐

**Figure 14.** Simulated microstructural evolution with the present of IMPs, (*a*) after 1500 TCs, (*b*) after 3000 TCs, (*c*) after

In this chapter, the current understanding of the microstructural changes in solder intercon‐ nections was introduced, followed by a brief review of the Monte Carlo simulations of grain

lation, which is consistent with the experimental results (see Fig. 13 (a)).

tion [39].

4000 TCs, (*d*) after 5000 TCs [39].

**6. Conclusions**

**Figure 12.** *a*), (*b*), and (*c*) are experimentally observed microstructures of the same location; (*d*), (*e*), and (*f*) are simulat‐ ed microstructures after 500, 1000, and 1500 thermal cycles respectively [39].

A micrograph from a normal thermal cycling test was used to verify the simulation results (see Fig. 13 (a)). The sample was examined after 5000 TCs and the micrograph was taken from the center of the cross section. The major IMPs were highlighted in Fig. 13 (a) for easy recognition and Fig. 13 (b) was used as the initial microstructure for the microstructural sim‐ ulation. As compared with in situ samples, solder interconnections in normal thermal cy‐ cling tests experience moderate plastic deformation, and thereby, require long incubation time for recrystallization.

Four snapshots (after 1500, 3000, 4000, and 5000 TCs respectively) of the simulated micro‐ structural evolution are presented in Fig. 14. Since there are no interfaces and pre-existing grain boundaries in the calculation domain, the intermetallic particles are the most favorable sites for nucleation in this case. The particle stimulated nucleation is shown in the simula‐ tion results and the initiation of recrystallization near the IMPs is clearly visible in Fig. 14 (a). The growth of the new grains at the expense of the strain-hardened matrix is presented in Fig. 14 (b)-(*d*). After 4000 TCs, since the whole matrix is consumed by the recrystallized grains and most of the stored energy is released, there is practically no difference between Fig. 14 (c) and Fig. 14 (d). Furthermore, it is found that the IMPs tend to located at the grain boundaries or triple junctions of the new grains as a result of the energy minimization calcu‐ lation, which is consistent with the experimental results (see Fig. 13 (a)).

**Figure 13.** *a*) Micrograph shows IMP-affected recrystallization, (*b*) initial microstructure for the Monte Carlo simula‐ tion [39].

**Figure 14.** Simulated microstructural evolution with the present of IMPs, (*a*) after 1500 TCs, (*b*) after 3000 TCs, (*c*) after 4000 TCs, (*d*) after 5000 TCs [39].
