**2. Microstructural changes of Sn-rich solder interconnections**

The microstructure of a solder alloy has a very significant effect on its material properties. A brief introduction of the microstructural changes of tin (Sn) rich solder interconnections is addressed in this section. With the implementation of lead (Pb) free technology in microelec‐ tronics [27], tin based lead-free solder alloys have replaced the traditional SnPb alloys. Cur‐ rently, the three-component tin-silver-copper (SnAgCu) alloy with near-eutectic composition is the most widely used solder alloy. For simplicity, the following microstruc‐ tural study focuses on one solder alloy with the composition Sn3.0Ag0.5Cu.

## **2.1. As-solidified microstructures of Sn-rich solder interconnections**

After reflow the solder interconnections normally consist of relatively few solidification col‐ onies (less than five) [28]. Micrographs of a typical as-solidified SnAgCu solder interconnec‐ tion are presented in Fig. 2. The boundaries between the contrasting areas, as seen in polarized light image in Fig. 2b are high-angle boundaries (larger than 15°) between matrix‐ es of solidification colonies composed of Sn cells and Cu6Sn5 and Ag3Sn particles. Within the colony boundaries, a uniformly oriented cellular solidification structure of tin is enclosed [29-33]. The cellular structure of tin is clearly distinguishable as cells are surrounded by eu‐ tectic regions. Besides the cellular structure, there are also some large Cu6Sn5 and Ag3Sn bulk intermetallic compound (IMC) precipitates.

Simulation of Dynamic Recrystallization in Solder Interconnections during Thermal Cycling http://dx.doi.org/10.5772/53820 93

**Figure 2.** The as-solidified microstructure of a SnAgCu solder interconnection; (a) optical bright field image, (b) crosspolarized light image.

#### **2.2. Recovery and recrystallization of Sn-rich solder interconnections**

Since failure of solder interconnections is a typical failure mode in many electronic devices, the reliability and life time prediction of solder interconnections become crucial. Various re‐ liability test and computer-aided simulations have been carried out to study the solder inter‐ connection reliability [8-17]. With the experimental and simulation results, a number of lifetime prediction models have been established and they can be classified into two main categories: strain-based and energy-based. For instance, the Engelmaier model is based on the total shear strain range, the Coffin-Manson model on the plastic strain, and the Dar‐ veaux model on the energy density [18-20]. However, microstructural changes in the bulk solder have not yet been included in any of the popular prediction models. Especially the microstructural changes associated with recrystallization and grain growth are of impor‐ tance because they can significantly affect the mechanical properties and can cause recrystal‐ lization induced failure of solder interconnections [21-26]. A new approach for lifetime prediction needs to be developed that takes into account the microstructural changes. In or‐ der to achieve this, the first step is to quantitatively study the recrystallization and grain

In this chapter, the current understanding of the microstructural changes in solder intercon‐ nections is introduced, followed by a brief review of the Monte Carlo simulations of grain growth and recrystallization. Then, a new algorithm for predicting dynamic recrystallization

The microstructure of a solder alloy has a very significant effect on its material properties. A brief introduction of the microstructural changes of tin (Sn) rich solder interconnections is addressed in this section. With the implementation of lead (Pb) free technology in microelec‐ tronics [27], tin based lead-free solder alloys have replaced the traditional SnPb alloys. Cur‐ rently, the three-component tin-silver-copper (SnAgCu) alloy with near-eutectic composition is the most widely used solder alloy. For simplicity, the following microstruc‐

After reflow the solder interconnections normally consist of relatively few solidification col‐ onies (less than five) [28]. Micrographs of a typical as-solidified SnAgCu solder interconnec‐ tion are presented in Fig. 2. The boundaries between the contrasting areas, as seen in polarized light image in Fig. 2b are high-angle boundaries (larger than 15°) between matrix‐ es of solidification colonies composed of Sn cells and Cu6Sn5 and Ag3Sn particles. Within the colony boundaries, a uniformly oriented cellular solidification structure of tin is enclosed [29-33]. The cellular structure of tin is clearly distinguishable as cells are surrounded by eu‐ tectic regions. Besides the cellular structure, there are also some large Cu6Sn5 and Ag3Sn

in solder interconnections during thermal cycling tests is presented.

**2. Microstructural changes of Sn-rich solder interconnections**

tural study focuses on one solder alloy with the composition Sn3.0Ag0.5Cu.

**2.1. As-solidified microstructures of Sn-rich solder interconnections**

bulk intermetallic compound (IMC) precipitates.

growth occurring in solder interconnections.

92 Recent Developments in the Study of Recrystallization

For decades, the industry has used recrystallization to control microstructures, and static re‐ crystallization of structural metals after deformation is probably the best understood recrys‐ tallization process [22]. On the other hand, dynamic recrystallization during cyclic deformation, which occurs in solder interconnections, has received much less attention and is still poorly understood. This is because the related microstructural events are highly com‐ plex from the microstructural point of view. The major understanding of this subject is brief‐ ly summarized as follows.

Thermal cycling tests with extreme temperatures in the range of about -40 °C to +125 °C are usually carried out to assess the reliability of electronic devices [35, 36]. During thermal cy‐ cling, the solder interconnections are under cyclic loading conditions. The induced thermo‐ mechanical stresses are often higher than the yield strength of the material, which leads to plastic deformation. A fraction of the energy associated with the plastic deformation of sol‐ der interconnections is stored in the metal, mainly in the form of dislocations. The stored en‐ ergy is subsequently released during restoration, which can be divided into three main processes: recovery, primary recrystallization and grain growth. Recovery and recrystalliza‐ tion are two competing processes, which are driven by the increased internal energy of the deformed solder. Recovery decreases the driving force for recrystallization and thus hinders the initiation of recrystallization. In high stacking fault energy metals such as Sn, the release of stored energy takes place so effectively by recovery that recrystallization will not practi‐ cally take place [22, 23]. Studies have shown that after a single deformation static recrystalli‐ zation rarely occurs in Sn-rich solders [37]. However, under dynamic loading conditions such as in thermal cycling tests, recrystallization often takes place in the high stress concen‐ tration regions of solder interconnections [28, 38, 39].

Experimental observations indicate that the microstructure of solder interconnections may change significantly during thermal cycling tests. The as-solidified microstructure can trans‐ form locally into a more or less equiaxed grain structure by recrystallization. An example is presented in Fig. 3 where the cross-section images of a solder interconnection after 6000 thermal cycles are shown. Part of the solder interconnection was recrystallized near the component side after 6000 thermal cycles (see Fig. 3b). It is noteworthy that optical micro‐ scopy with polarized light shows the areas of different orientations with different colors and it is an excellent tool for observing the recrystallized region. In the recrystallized region a continuous network of high angle grain boundaries provides favorable sites for cracks to nucleate and to propagate intergranularly, which can lead to an early failure of the compo‐ nent. This kind of failure mode is regarded as the recrystallization-assisted cracking. More details can be found in the references [14, 26, 28].

**3. Monte Carlo simulations**

other applications, e.g. [38, 39, 43-45].

ture evolution, e.g. [47-49].

lattice, an integer number *Si*

key steps [51-53].

orientation

**a.** Choose a lattice site *i* in random

**3.1. Monte Carlo simulation of grain growth**

dary energy contributions throughout all the sites.

neighbor sites of the site *i*, and *δij* is the Kronecker delta.

Many models have been developed to simulate microstructural evolution, such as vertex model, Monte Carlo (MC) Potts model, phase field model, and cellular automata (CA) mod‐ el [22, 23, 41, 42]. For modeling recrystallization, the MC Potts model and CA model are per‐ haps the two most popular candidates. In general, the MC Potts model and CA model are similar to each other since both models include a lattice, use discrete orientations and de‐ scribe stored energy in terms of a scalar stored energy term. The MC Potts model provides a convenient way to simulate the changes in microstructures and it has been successfully ap‐ plied to simulate the recrystallization process in solder interconnections as well as in many

Simulation of Dynamic Recrystallization in Solder Interconnections during Thermal Cycling

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

95

The MC grain growth simulation originates from Ising and Potts models for magnetic do‐ main evolution [46]. The Ising model consists of two spin states, namely up and down, and the Potts model allows multiple states (*Q* states) for each particle in the system. The Potts model has been widely used for modeling material behaviors, such as grain growth and tex‐

During the MC grain growth simulation, a continuum microstructure is mapped onto a 2D MC lattice, which can be either triangular or rectangular lattice [50]. In order to initialize the

resents the total number of orientations in the system. Two adjacent sites with different grain orientation numbers are regarded as being separated by a grain boundary and each pair of unlike neighboring sites contributes a unit of grain boundary energy, *J*, to the system. A group of sites having the same orientation number and surrounded by grain boundaries are considered as a grain. The total energy of the system, *E*, is calculated by the grain boun‐

where the sum of *i* is over all *N*MC sites in the system, the sum of *j* is over all the nearest-

The Monte Carlo method iteratively simulates the grain growth process by the following

**b.** If the selected site is an interior site, no reorientation will be tried. Go back to 'step a'

**c.** If the selected site is at the grain boundary, its neighboring sites are checked. Assign a new orientation number to the site. The new orientation is limited to those orientations of the neighboring grains, and is weighted by the number of neighbors with the same

*E* = *J* ∑ <*ij*> (1 - *δSi S j*

(between 1 and *Q*) is assigned to each lattice site, where Q rep‐

) (1)

**Figure 3.** Micrographs of the solder interconnection after 6000 thermal cycles; (a) optical bright field image, (b) crosspolarized light image.

#### **2.3. Effect of intermetallic compound precipitates**

In the near-eutectic SnAgCu alloys, mainly two kinds of IMC precipitates, Cu6Sn5 and Ag3Sn, can form upon solidification. The size of intermetallic particles (IMPs) varies a lot: the small and finely distributed IMPs are located at the boundaries of tin cells (eutectic structure) while the relatively large IMPs are randomly distributed in the bulk solder. Fine particles usually prevent the motion of grain boundaries by exerting a pinning force, and therefore, suppress the progress of recrystallization. The influence of fine particles on recrys‐ tallization has been studied in earlier work, e.g. [40]. It is believed that fine particles do not remarkably affect the distribution of stored energy within the grains. However, coarse parti‐ cles exert localized stress and strain concentrations due to the mismatch of mechanical prop‐ erties and thermal expansion coefficients during thermal cycling. Dislocation density is increased in the particle-affected deformation regions, which provide favorable sites for nu‐ cleation of recrystallization.
