# Thermal and compositional fields to maneuver Cu6Sn5 intermetallic growth on (111) nanotwinned copper substrate

Zhijie Zhang, Hong Wei, Xing Gao, Anil Kunwar

► To cite this version:

Zhijie Zhang, Hong Wei, Xing Gao, Anil Kunwar. Thermal and compositional fields to maneuver Cu6Sn5 intermetallic growth on (111) nanotwinned copper substrate. Journal of Alloys and Compounds, 2024, 998, pp.174876. 10.1016/j.jallcom.2024.174876. hal-04981125

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Graphical Abstract

# Thermal and Compositional Fields to Maneuver Cu₆Sn₅ Intermetallic for (111) Nanotwinned Copper Substrate

Zhijie Zhang, Hong Wei, Xing Gao, Anil Kunwar

<figure><img src="image_2.png" /></figure>
Highlights

**Thermal and Compositional Fields to Maneuver Cu₆Sn₅ Intermetallic for (111) Nanotwinned Copper Substrate**

Zhijie Zhang, Hong Wei, Xing Gao, Anil Kunwar

* Scallop-type IMC are with {2\bar{1}\bar{1}3} texture.

* Rooftop-type IMC have {2\bar{1}\bar{1}0} orientation.

* At 533 K, solder composition has no role on morphology transition.

* At T = 573 K, low Cu wt. % in solder guarantees rooftop-type morphology.

* Effects of interface energy on grain evolution pattern is modeled.
Thermal and Compositional Fields to Maneuver Cu₆Sn₅ Intermetallic
for (111) Nanotwinned Copper Substrate

Zhijie Zhang<sup>a</sup>, Hong Wei<sup>a</sup>, Xing Gao<sup>a</sup> and Anil Kunwar<sup>b,*</sup>

<sup>a</sup>Key Laboratory of Advanced Welding Technology of Jiangsu Province, Jiangsu University of Science and Technology, Zhenjiang 212003, China

<sup>b</sup>Faculty of Mechanical Engineering, Silesian University of Technology, Konarskiego 18A, 44-100 Gliwice, Poland

ARTICLE INFO

Keywords:

Nanotwinned substrate

Temperature

Solder composition

Preferred texture

Rooftop-type IMC

Coherent interface

ABSTRACT

The microstructure of Cu₆Sn₅ phase plays a pivotal role in the functionality of microbumps utilized in 3D packaging. In this study, we present an experimental methodology aimed at maneuvering the orientation and morphology of Cu₆Sn₅ grains formed on (111) nanotwinned Cu substrate, achieved through variations in reflow temperatures (260°C and 300°C) and initial Cu proportion in solder (ranging from 0 to 3.0 wt. %). At 300°C and lower initial Cu concentrations (0 and 0.7 wt. %), irregularly arranged roof-type Cu₆Sn₅ grains exhibiting a pronounced {2\bar{1}\bar{1}0} texture were observed. Conversely, typical scallop-type Cu₆Sn₅ grains displaying a specific preferential {2\bar{1}\bar{3}} texture were identified at this temperature for Cu concentrations of 1.5 and 3.0 wt. %. At 260°C, the scallop-type morphology was solely present at all Cu composition variants. The differing rates of solute controlled intermetallic phase clustering mechanism at altered solubility limits and magnitudes of thermodynamic driving force for different temperatures, can decide the relative loss of interface coherency and subsequently change the preferred orientation direction of evolving interfacial structures. Our findings demonstrate that the precise control over soldering temperature, solder Cu composition, and the microstructure of Cu UBM can enable the attainment of Cu₆Sn₅ microstructure with a designated orientation and morphology.

**1. Introduction**

Three-dimensional integrated circuits (3D IC) based on chips vertical stacking using through-Si via (TSV) and microbump are a current trend in the microelectronics industry [1–5]. In order to enhance performance by increasing input/output density and shortening interconnect distance on a chip surface, the diameter of a microbump is currently about 100 µm, and efforts are being made to reduce this to 20 µm [6, 7]. This enhancement will increase the proportion of intermetallic compounds (IMCs) in the area between the solder and under bump metallization (UBM), potentially leading to a complete conversion into an IMCs joint after further assembly or operation processes. Therefore, the IMCs will dominate the properties of microbumps and become potential candidates of structural materials. Cu₆Sn₅ is the most important IMC among all the IMCs encountered in solder joints, due to the widespread use of Sn-based solder and Cu UBM. However, the electrical, thermal and mechanical properties of Cu₆Sn₅ grains exhibit strong anisotropy [8–10], which may in turn lead to early failure and low reliability [11, 12]. Because there are a large number of microbumps on a stack of chips in a 3D IC, achieving a uniform microstructure of interfacial Cu₆Sn₅ grains is a critical issue.

The preferred orientation relationship between the inter-
metallic compound Cu₆Sn₅ and copper (Cu) is significant
or crucial in actual packaging solder joints. This preferred
relationship might affect the properties or behavior of the

solder joints, influencing their performance in practical ap-
plications. Maintaining control over the uniform microstruc-
ture of the interfacial Cu₆Sn₅ IMC can be achieved via con-
trolling the grain microstructure of the Cu UBM [8–10, 13–
16]. At the interface of Sn-based solder and Cu-substrate,
interfacial Cu₆Sn₅ IMCs attain basically two categories of
morphologies - (i) scallop-type, and (ii) prismatic type.
Arranged as a series of small, rounded, and usually convex
indentations or protrusions, the scalloped IMC morpholo-
gies are quantitatively understood as of having a Jackson
parameter (α<sub>J</sub>) less than two [17–23]. On the other hand,
the prismatic morphology refers to IMCs with elongated or
columnar shapes resembling prisms. The Jackson parameter
for prismatic IMCs is usually greater than two [17–23]. Re-
sembling the shape of the slanted rooftops, the morphology
of prismatic IMCs is also commonly reffered to as rooftop-
type morphology. The growth mechanisms for these two
morphology variants are different. It is also to attain mixed-
mode of morphologies in the interface of a single experi-
mental specimen. Suh et al. [14] observed a rooftop-type
Cu₆Sn₅ grains elongated along two low misfit directions
preferred orientation grew on (001) single-crystal Cu. Zou
et al. [15] found strong texture of prism-type and scallop-
type Cu₆Sn₅ grains on (001),(111), and (123) single-crystal
Cu, respectively . Zhang et al. [16] reported that the shear
strength of solder bump with (111) Cu UBM was higher than
that with (001) Cu UBM . Further, it has been identified that
the solder joints containing prism-type Cu₆Sn₅ would have
better mechanical property and lower electrical resistance
comparing with those containing scallop-type Cu₆Sn₅ [8–
10]. However, in electronic packaging process, Cu UBM is
generally produced via electroplating process, and achieving

<figure><img src="image_3.png" /></figure>

<footnote>*Corresponding author</footnote>

<footnote>zjzhang@just.edu.cn (Z. Zhang); 1417502362@qq.com (H. Wei);
410819934@qq.com (X. Gao); anil.kunwar@pols1.pl (A. Kunwar)
ORCID(s): 0000-0001-7008-2142 (Z. Zhang); 0000-0003-4295-5772 (A.</footnote>

<footnote>Kunwar)</footnote>
the Cu phase with a single, continuous crystal throughout its
entire volume is not so easy with this method.

One of the practical materials is the nanotwinned (nt) metals with face-centered cubic (FCC) crystal structure. The nanoscale growth twins are usually formed in FCC metals (e.g. Ag, Au, Cu, stainless steel) having a very low intrinsic stacking fault energy [24, 25]. In context of its enormous use in electronic packaging devices as a substrate, FCC Cu metal will be considered hereafter for the description of nanotwins. The numerous twin boundaries present within the crystal structure of nanotwinned face-centered cubic (nt-FCC) Cu metals are associated with abrupt change in the crystal orientation. Therefore it is quite common for nanotwinned Cu (nt-Cu) to contain zones of highly ordered atomic arrangements separated by these boundaries. Due to its high mechanical strength, high electrical conductivity, low oxidation rate, high electromigration resistance, and resistance of the interfacial IMCs growth, the nt-Cu with (111) preferred orientation is regarded as the ideal UBM for 3D IC packaging technology [25–34]. Upon finetuning of the microstructure dimensions, such as twin boundary spacings and average grain size, the nt-FCC Cu metals with nanoscale coherent twin boundaries inside ultrafine grains exhibit a blend of excellent strength and ductility compared to their twin-free polycrystalline counterparts [35]. The nt-Cu features a distinct structure characterized by a dense array of twin boundaries within the grain, facilitating lower temperatures for Cu-Cu direct bonding through its (111) plane-dominated texture with increased atomic diffusivity [33]. Utilizing nanotwinned Cu enables a manufacturing route for Cu-Cu bonding with reduced thermal budget requirements, thereby facilitating the realization of more efficient and cost-effective manufacturing processes. Moreover, (111) nt-Cu can be obtained by electroplating. Lin et al. [36] reported scallop-type Cu₆Sn₅ formed on (111) nt-Cu showing a highly preferential growth along the <0001> direction after reflow, but the preferred texture of Cu₆Sn₅ changed to {211̄3} with extending the reflow time. Huang et al. [37] and Wu et al. [38] found the (112̄0) preferred orientation roof-type Cu₆Sn₅ formed on (111) nt-Cu at 300 °C, while random orientation scallop-type Cu₆Sn₅ formed at 250 °C. The reflow conditions significantly affect the nucleation and growth of interfacial Cu₆Sn₅ IMC on (111) nt-Cu UBM. Therefore, it is important to properly understand the conditions and mechanisms governing the formation as well as growth of specifically shaped and preferentially oriented Cu₆Sn₅ compound on (111) nt-Cu UBM. Besides the experimental observations, theoretical and computational models can provide an in-depth knowledge about the mechanistic aspects of interfacial IMC growth in multiphase material systems. Phase field model (PFM) is one of the most popular computational tools that can be utilized for description of spatio-temporal evolution of micro- or nano-structures at material interfaces [39].

In this study, by electroplating (111) nt-Cu pads and by
immersing in the Sn, Sn-0.7Cu (wt.%), Sn-1.5Cu (wt.%) and
Sn-3.0Cu (wt.%) solders at 260 °C (≈ 533.0 K) and 300 °C

(≈ 573.0 K) for 30 s, respectively, we form Cu₆Sn₅ with a highly preferential growth. The morphology and orientation of Cu₆Sn₅ grains and the (111) nt-Cu UBMs were studied experimentally, and the PFM has been developed to simulate the growth mechanisms of interfacial grains. In context of the present study, both the acronyms nt-Cu and nt-FCC will mean the same nanotwinned substrate that has FCC crystal structure, and is rich in Cu element. While nt-Cu will be used to emphasize the composition aspect, nt-FCC will be used when the emphasis is laid on the crystal structure of the phase.

## 2. Experimental

The (111) nt-Cu film was electroplated at anode using a
CuSO4 -based plating solution with appropriate additives on
the 2 mm thick polycrystalline copper substrate (cathode).
Thus, a 2 mm thick polycrystalline copper substrate and
a phosphorus-containing copper plates serve as cathodes
and anodes respectively. As shown in Fig. 1(i), the con-
tainer or tank holding the electrodes and electrolytes is also
equipped with a magnetic stirrer. The plating solution inside
the container consists of 1.38M Cu2+, 30ppm Cl-, 0.48M
H2SO4 and organic additives which can largely assist in the
nanotwin formation. Before starting the electrodeposition
process, the two electrodes are placed in citric acid and
acetone in turn to remove surface oxides, contaminants
and organic molecules. The electrodeposition parameters
(current density = 40 A/dm², duration = 20 min.) were set,
and the two electrodes were inserted into the plating tank.
Subsequently, the DC power was turned on to initiate the
process. A 20 µm thick (111)-oriented nt-Cu coating was
prepared at the anode side electrode.

The as-prepared (111) nt-Cu pads were dipped into Sn, Sn-0.7Cu, Sn-1.5Cu, and Sn-3.0Cu solders bath at 260 °C and 300 °C for 30 s to grow Cu₆Sn₅, respectively, and then the as-soldered (111) nt-Cu pads quenched to 25 °C in the distilled water. It is to be noted that the choice of the soldering process parameters (reflow temperature and time) are well within the acceptable range from the practical point of view for Pb-free solders [40–44].

The texture structure of (111) nt-Cu film was examined by scanning electron microscopy (SEM), X-ray diffraction (XRD), electron back-scatter diffraction (EBSD), and focused ion beam (FIB) techniques. To study the cross-section and top-view structure of IMC, the as welded (111) nt-Cu pads were ground, polished, and etched in 5% HNO 3 + 2% HCl (wt.%) ethanol solution to remove the solder and expose interface IMC grains. Then SEM and EBSD were employed to examine the structure and orientation of Cu₆Sn₅ grains. The Merlin Compact Field Emission Scanning Electron Microscope (Carl Zeiss Microscopy GmbH, Oberkochen, Germany) was utilized for performing microstructural characterization (SEM + EBSD tests) in both of the nt-Cu Substrate and the intermetallic compounds samples.
<figure><img src="image_4.png" /><figcaption>**Figure 1:** Schematic sketch of the electroplating experimental process is presented in (i). The microstructural characterization of the electroplated nt-Cu is illustrated in (ii). The (a) top-view micrograph, (b) XRD image, (c) cross-sectional FIB micrograph, (d) EBSD map, (e) the 111 pole figure and (f) the reference figure (color coding) in (ii) describe the structural features of the nanotwinned Cu material.</figcaption></figure>

**3. Results from the experiments**

The experimental methods (Sec. 2) in this study are aimed at fabricating the nanotwinned Cu structure and utilizing it as a substrate of Pb-free solders to grow Cu₆Sn₅ IMC at their interface. In accordance to these experimental designs, there are two types of results presented in this section. The primary result, related to the characterization of nanotwinned substrate, is provided in Sec. 3.1. The morphological characterization of the interfacial intermetallic compounds, termed as the secondary experimental results, is presented in Sec. 3.2.

**3.1. Characterization of (111) nt-FCC Copper UB**

It is very important to experimentally quantify the microstructure of nt-Cu. The structural characteristics of the electroplated Cu film is graphically presented through Fig. 1(ii). We notice that there are many cone-shaped grains on the surface of the film with a diameter ranging from 1 to 5 µm (Fig. 1(ii)-(a)). The presence of these conical-profiles [45] validates the robustness of the experimental characterization procedure. XRD indicates that these Cu grains possess a strong texture of [111] preferred orientation (Fig. 1(ii)-(b)). Furthermore, the cross-sectional FIB image

shows each Cu grain comprises a robust lamellar stacked structure, i.e., twins, and which are aligned parallel to the film growth direction (Fig. 1(ii)-((c)). And the spacing of the twins ranges from 10 to 100 nm, i.e., nanotwins. EBSD shows that the colors of Cu surface grains were all blue in the orientation image map, indicating that they all have approximately the same orientations (Fig. 1(ii)-((d)). The inverse pole figure also shows the grain boundaries including twin boundaries on the top surface of the Cu film (Fig. 1(ii)-((e)). Referring to Fig. 1(ii)-((f) showing the orientation of Cu, the orientation of all the Cu surface grains on the film and which was again confirmed to be either <111> or very close to it. Since the twinning plane is also the {111} plane of face-centered cubic Cu, we have obtained oriented and nanotwinned Cu.

**3.2. Morphology and orientation of interfacial Cu₆Sn₅ grains formed on (111) nt-FCC Cu UBM**

The morphological and orientation-based features of interfacial IMCs can provide useful information regarding the mechanical performance of the joint formed by these structures. And, it will be now known that such features are dictated by not only the processing temperature but also the
<figure><img src="image_5.png" /><figcaption>**Figure 2:** Microstructure and the orientation image maps of Sn-xCu (x=0, 0.7, 1.5, 3.0)/(111) nt-Cu solder joints soldered at 260 °C for 30s: (a1)-(a4) cross-sectional SEM images, (b1)-(b4) top view SEM images, (c1)-(c4) EBSD orientation maps, and (d1)-(d4) inverse pole figures of the Cu₆Sn₅ grains.</figcaption></figure>

initial Cu concentration in the solder alloy. Figs. 2 (a1-a4) illustrate the cross-sectional microstructure of Sn-xCu/(111) nt-Cu (x=0, 0.7, 1.5, 3.0) joints after soldering at 260 °C for 30 s, respectively. The layer thickness of Cu₆Sn₅ was increased with increasing Cu concentrations. At x = 0 and 0.7 wt. %, the IMC layer thickness attained after 30 s were 0.69 µm and 0.94 µm respectively. For larger concentrations of Cu, the layer thickness was larger than 1 µm (1.78 µm for Sn-1.5Cu sample and 1.92 µm for Sn-3.0Cu sample). Figs. 2 (b1-b4) show the morphology of Cu₆Sn₅ grains, which were typically scallop-type regardless of the intensity of initial Cu concentration in the solder samples. However, it is noteworthy to mention from the figure that the average grain diameter ($\bar{d}_g$) of scalloped IMC grains corresponding to Sn-1.5Cu and Sn-3.0Cu solders is very large ($\bar{d}_g > 4$ µm) whereas that for Sn and Sn-0.7Cu solders is too small ($\bar{d}_g < 2$ µm). This observation about the absolute magnitude of $\bar{d}_g$ is consistent with the experimental results reported by Huang et al. [46] where the Sn, Sn-0.7Cu and Sn-2.0Cu solders had been reflowed at T = 523 K for 60 s to form joint with polycrystalline Cu substrate. At 523 K, it had been discovered that the Sn and Sn-0.7Cu solders are unsaturated with Cu whereas the solder Sn-2.0Cu is supersaturated with Cu [46]. Since the diffusion rate of Cu from substrate to solder is faster at substrate/unsaturated solder and slower at substrate saturated solder, the availability of Cu atoms

at the grain boundary of evolving interfacial IMC grains is different for the two contexts. For saturated solder samples, the relatively slower diffusion rate of Cu causes the local accumulation of Cu atoms at the interface thereby rendering it a more Cu-rich region. Thus, the ripening kinetics is more pronounced in context of interfacial reaction of the substrate and saturated solders. As the saturated solubility($S_{sat}^{523K}$) is attained in the solder for a weight percentage of Cu located somewhere between 0.7 and 2.0 i.e. $0.7 < x < 2.0$, the $\bar{d}_g$ in Sn-2.0Cu/Cu sample is significantly larger than that of Sn/Cu and Sn-0.7Cu samples [46]. The present works includes four initial solder compositions (Sn, Sn-0.7Cu, Sn-1.5Cu and Sn-3.0Cu) and thus helps in narrowing down the estimation of the range of Cu weight percentage that includes saturated solubility value ($S_{sat}^{533K}$). As the $\bar{d}_g$ of interfacial IMC grains for Sn-1.5Cu and Sn-3.0Cu solder samples at 533 K are significantly larger than the $\bar{d}_g$ of Sn and Sn-0.7Cu, it can be inferred that $S_{sat}^{533K}$ is attained in solder for Cu concentration located somewhere between 0.7 and 1.5 wt. % i.e. $0.7 < x < 1.5$.

Figs. 2 (c1-c4) show the cross-sectional EBSD orientation maps of as soldered joints. Each scallop type Cu₆Sn₅ grain has a uniform but different color with red, purple, and orange, indicating that the Cu₆Sn₅ grains have a certain preferred orientation on the (111) nt-Cu UBM. Corresponding to the inverse pole figures in Figs. 2 (d1-d4), the texture
<figure><img src="image_6.png" /><figcaption>**Figure 3:** Microstructure and the orientation image maps of Sn-xCu (x=0, 0.7, 1.5, 3.0)/(111) nt-Cu solder joints soldered at 300 °C for 30 s: (a1)-(a4) cross-sectional SEM images, (b1)-(b4) top view SEM images, (c1)-(c4) EBSD orientation maps, and (d1)-(d4) inverse pole figures of the Cu₆Sn₅ grains.</figcaption></figure>

of lie between {0001} and {2\bar{1}\bar{1}0}, which was defined as {2\bar{1}\bar{1}3} using the software of the analysis system, which is consistent with the previous results [36]. Figs. 3 (a1-a4) illustrate the cross-sectional microstructure of (111) nt-Cu/Sn-xCu (x=0, 0.7, 1.5, 3.0) joints after soldering at 300 °C for 30 s, respectively. The measured thickness values of Cu₆Sn₅ IMC layer at t=30 s for Sn, Sn-0.7Cu, Sn-1.5Cu and Sn-3.0Cu samples were 0.64, 0.75, 1.86 and 1.96 µm respectively. A similar Cu₆Sn₅ growth trend was observed as that in the cases at 260 °C, but the IMC layers were more flat and thinner with 0 and 0.7 Cu concentrations. Furthermore, irregularly arranged prism-type Cu₆Sn₅ grains were formed on (111) nt-Cu with the Cu concentrations were 0 and 0.7, and typical scallop-type Cu₆Sn₅ grains were observed with 1.5 and 3.0 Cu concentrations, as shown in Figs. 3 (b1-b4). Figs. 3 (c1-d4) illustrate the cross-sectional EBSD orientation maps and corresponding inverse pole figures of as soldered joints. Each prism-type Cu₆Sn₅ grain has a uniform green color, meaning that the Cu₆Sn₅ grains had a strong preferred texture, and the inverse pole figure shows that the new texture as {2\bar{1}\bar{1}0}. The scallop-type Cu₆Sn₅ grains appeared in red, purple and yellow, which also had a major texture {2\bar{1}\bar{1}3}.

## 4. Discussions

An intriguing finding indicates that the morphology and preferred orientation of the Cu₆Sn₅ IMC grains formed on (111) nt-Cu UBM have correlation with both reflow temperature and Cu concentration within the solder alloy at a higher temperature of 300 °C or 573.0 K. For this temperarure, an experiment for a relatively lower Cu weight fraction (x=0, 0.7) inside the solder, would result in the formation of irregularly arranged roof-type Cu₆Sn₅ grains which exhibit a strong 2\bar{1}\bar{1}0 texture. When the weight fraction of Cu is increased to higher values (x=1.5, 3.0) at this temperature ( 573.0 K), Cu₆Sn₅ grains transit to scalloped morphology with the preferred orientation of 2\bar{1}\bar{1}3. At a lower temperature of 260 °C or 533.0 K; the composition of Cu had little to no influence on morphology of the IMC. This is evidenced by the fact that the IMC grains exhibit the scalloped morphology with the texture of 2\bar{1}\bar{1}3 for all weight fractions of Cu (x=0, 0.7, 1.5, 3.0) in the solder samples.

### 4.1. Interface coherence between {2\bar{1}\bar{1}0} roof-type Cu₆Sn₅ grains and {111} nt-Cu

Because the soldering temperature exceeded 260°C and subsequently cooled to room temperature, the stable phase of intermetallic compound (IMC) was conclusively identified as η-Cu₆Sn₅ rather than η'-Cu₆Sn₅ [47, 48]. The focus of
<figure><img src="image_7.png" /><figcaption>Figure 4: The pole figures and the 2D atomic site correspondence of (a) and (d) (111) nt-Cu of {111} plane, (b) and (e) roof-type η-Cu₆Sn₅ of {2110} plane, (c) and (f) scallop-type η-Cu₆Sn₅ of {2113} plane. The mutually coplanar poles in each of the pole figures (a)-(c) are marked with the help of red colored dashed triangles. The direction of {111} plane within the geometry of the cubic FCC structure of nt-Cu is illustrated in (d) whereas the orientation of {2110} and {2113} planes within HCP structure of IMC grains are shown in (e) and (f) respectively.</figcaption></figure>

this study is on the preferred growth relationship between η-Cu₆Sn₅ grains and Cu-rich (111) nt-FCC substrate. The crystal structure of η-Cu₆Sn₅ is hexagonal (P63/mmc, a = 4.2032 Å, c = 5.1107 Å), and that of nanotwinned pure Cu (nt-Cu) is a face-centered cubic crystal system (a = b = c = 3.615 Å). Figures 4(a) and 4(b) present respectively the pole figures of (111) nt-FCC and roof-type Cu₆Sn₅ with the latter constructed by merging the roof-type Cu₆Sn₅ grains' EBSD orientation data from Figs. 3(c1) and 3(c2). In these pole figures, the mutually coplanar poles are highlighted within triangular boundary with sides of red colored dashed lines. Specific two groups of {2110} η and {111} Cu, {0001} η and {110} Cu are parallel. However, the {111} Cu planes are uniquely parallel to the {2110} η planes (red dashed triangles in Figs. 4(a) and 4(b)), and the habit planes of these two phases should be {2110} η || {111} nt-Cu. While three groups of orthogonal directions exist on the (111) FCC Cu plane ([110] Cu ⊥ [112] Cu, [101] Cu ⊥ [121] Cu, and [011] Cu ⊥ [211] Cu), only one group of orthogonal direction exists on the {2110} η IMC plane ([0001] η ⊥ [0110] η). After superimposing the Cu atoms of these two planes, we found two directions that are of lower lattice mismatch and are able to form semicommon-lattice structure. As shown in Fig. 5, the lattice mismatch degree of Cu atoms between the < 110 > orientation of {111} Cu plane and < 0001 > orientation of {2110} η plane (only 1.46%) is lower than that in other orientation, meaning that the < 110 > orientation of {111} Cu plane is parallel to the < 0001 > orientation

of {2110} η plane. Therefore, the orientation relationships between Cu₆Sn₅ grains and (111) nt-Cu UBM are as follows:

$$ \text{OR1: } \{2\bar{1}\bar{1}0\}\eta \parallel \{111\} \text{ nt-Cu,} \\ \text{and } <0001> \eta \parallel <110> \text{ nt-Cu} \quad (1) $$

$$ \text{OR2: } \{2\bar{1}\bar{1}0\}\eta \parallel \{111\} \text{ nt-Cu,} \\ \text{and } <1010> \eta \parallel <112> \text{ nt-Cu} \quad (2) $$

Furthermore, the irregularly arranged roof-type Cu₆Sn₅ grains are attributed to the (111) nt-Cu UBM retaining a polycrystalline textured surface [16, 49, 50]. This is supported by the (111) nt-Cu films in the current study exhibiting a strong (111) preferred orientation in the normal direction (ND), while their grain orientation is random in the rolling direction (RD) and transverse direction (TD), as illustrated in Figs. 1-3. That is, (111) nt-Cu shows strong polycrystalline character in RD and TD. Due to the different rotation angles of the grains on the (111) nt-Cu surface, the prismatic η-Cu₆Sn₅ grains formed on the (111) nt-Cu surface are not aligned at a certain angle. So prismatic Cu₆Sn₅ grains with random distribution but {2110} preferred textures are formed on (111) nt-Cu UBM.

## 4.2. Limited coherence between {2113} scallop-type Cu₆Sn₅ grains and {111} nt-Cu

The pole figures of (111) nt-Cu of {111} plane and scallop-type Cu₆Sn₅ of {2113} plane are shown in Figs. 4 (a) and 4(c) respectively. By integrating the scallop-type
<figure><img src="image_8.png" /><figcaption>**Figure 5:** 2D atomic site correspondence of (a) (111) nt-Cu of {111} plane, (b) roof-type η-Cu₆Sn₅ of {2110} plane, and (c) the merging image of (a) and (b).</figcaption></figure>

Cu₆Sn₅ grains EBSD orientation data of Fig. 2 (c1)-(c4) and Fig. 3 (c3)-(c4), the pole figure of Fig. 4(c) has been constructed. After locating the mutually coplanar regimes in these pole figures (marked with red colored dashed triangles), it can be inferred that the {2113} plane of the scallop-type Cu₆Sn₅ was nearly parallel to the {111} plane of the (111) nt-Cu, thus the habit surfaces of these two crystals should be {2113} η {111} nt-Cu.

However, in the aftermath of superimposing the Cu
atoms of these two planes through the entire interface, we
could hardly find two directions that have a lower lattice
mismatch. Therefore, it is difficult to explain this coherent
relationship in terms of Cu atom lattice mismatch degree.
Furthermore, at the interface the bonding energy between
Cu and Sn atoms must be lower than between the Cu and
Cu atoms due to the inclined tendency of Cu atoms for
interaction with Sn atoms to form Cu₆Sn₅ during the in-
terfacial reaction [51]. However, the interaction between
Sn in {2113} plane of the scallop-type Cu₆Sn₅ and the Cu
in {111} plane of the (111) nt-Cu is such that it makes
it difficult for achievement of interface coherence between
IMC and substrate. Fig. 4(f) that a large number of Sn
atoms are located mainly along the {2113} plane in Cu₆Sn₅
grains, implying that this position is more favorable than
other locations inside the hexagonal lattice. Besides, the net
diffusion rate of Sn atoms within the lattice is higher than
that of Cu atoms [52]. Therefore, it can be inferred for a
system with hexagonal IMC and nt-FCC substrate, the Sn
atoms being located in large numbers near the {2113} plane
and being deficit elsewhere in context of Cu₆Sn₅ lattice,
undergo a faster diffusion, thereby allowing them to bond

with Cu atoms of (111) nt-Cu and achieve a stable state via
reduction of interfacial energy. As the coherence of interface
between the scalloped IMC and nt-FCC is more imperfect
as compared to that between roof-type IMC and nt-FCC ,
the interface energy for the former interface will be larger as
compared to that of latter .

4.3. Reflow temperature and initial solder
composition dictate IMC growth behavior

It is difficult to explain the nucleation principle of the
two preferred orientation interfacial Cu₆Sn₅ grains simulta-
neously using a low lattice mismatch degree. Hence, in this
section, we propose the concept of liquid metal clusters of
Cu₆Sn₅ to further explain the nucleation and growth mech-
anism of the preferred roof-type and scallop-type Cu₆Sn₅
grains uniformly. Based on Sn-based lead-free solders liquid
structure analysis, Cu atoms tend to interact with Sn rather
than Cu with increasing Cu concentration, due to the bond
energy between Cu and Sn being lower than that between
Cu and Cu [53]. In contexts of Sn-xCu(x=1.5, 3.0) solders
with larger initial weight percentage of Cu element , the
net diffusion of Cu into the liquid solder during causes the
solder to attain a saturation solubility quite early in the stage
of interfacial reaction [54]. When the saturation solubility
is reached, then Cu species within the bulk solder start to
precipitate as clusters. Mechanistically, the enhanced rate of
interaction between Sn and Cu atoms in solders with large
amount of Cu, leads to the formation of Cu₆Sn₅ short-range
order (SRO) and even medium-range order (MRO) clusters
[55], which nucleate and then rapidly expand to critical
size through structural and energy fluctuation. In general,
the number density and size of the clusters decrease with
increasing soldering temperature due to the broken clusters,
and then the liquid solder becomes more uniform and dis-
orderly. The saturation solubility of Cu in Sn-rich liquid
solder is 1.89×10⁻³ mol/cm³ at 533 K whereas it is 3.15
×10⁻³ mol/cm³ for T = 573 K [56]. At lower temperature,
saturation will be attained earlier to enable more pronounced
occurrence of the clustering mechanism. The larger presence
of clustering mechanism is also associated with the lowered
value of interface structure constant ξ in the expression of
Jackson parameter (α<sub>J</sub> = ξ ΔH<sub>f</sub>/RT) for intermetallic grain
[18, 21]. Therefore, the clustering mechanism greatly inter-
feres with the coherence of the interface between nt-FCC
substrate and adjacent IMC grain. It will be shown later in
Sec. 4.4, the degree of interference will be reduced when
the temperature is larger.

At a lower reflow soldering temperature (260 °C), it
is now clear that the size and number density of Cu₆Sn₅
clusters in the liquid solder is large. And, at this constant
reflow temperature; Fig. 6 schematically illustrates that the
clustering is more pronounced with increase in the initial
weight percentage of Cu in Sn-xCu solder. These influential
clusters directly emerge as the crystalline nucleus in the
solder, then land incoherently onto (111) nt-Cu UBM, and
continue to grow. Consequently, the scallop-type Cu₆Sn₅
grains are formed on the Sn-xCu/(111) nt-Cu interface. The
<figure><img src="image_9.png" /><figcaption>**Figure 6:** A schematic sketch on how the morphology of interfacial Cu₆Sn₅ grains nucleated and grown at the Sn-xCu/(111) nt-Cu UBM is influenced by temperature (T) and composition (x) values. T is the reflow temperature and x is the wt. % of Cu initially in the Sn-xCu solders prior to reflow procedure. For the current work, T is either 260 °C or 300 °C, and x takes one of the values among 0, 0.7, 1.5 and 3.0. The roof-type IMC gets formed only for condition (a) characterized with (T, x) as either (300 °C, 0) or (300 °C, 0.7). On the other hand, scalloped morphology is formed for all of the cases (b)-(d) described by the remaining (T,x) coordinates.</figcaption></figure>

abundant Sn atoms within the hexagonal Cu₆Sn₅ lying on the plane close to {2\bar{1}\bar{1}3} will interact with the Cu atoms of the nanotwinned FCC substrate to enable further growth of intermetallic grains. The fact that scallop-type interfacial IMC morphology is formed at this temperature even in context of Sn solder initially without Cu (refer Fig. 2(b1)), reveals that there is no any of workable solder composition for binary Sn-Cu system that allows prismatic IMC to be formed at the interface between (111) nt-FCC substrate and solder. The notable distinctions between the scalloped grains of Fig. 2(b1,b2) and Fig. 2(b3,b4) is that the individual grains of the latter are wider (characterized with larger horizontal grain diameter). This means that solder alloy with initial Cu concentration larger than 1.5 wt. %, will have few but very wide IMC grains at the interface. Such an observation at a single reflow temperature (T = 533 K) highlights the dominant effect of solder's initial composition on the intensity of clustering mechanism that interferes the events happening on {2\bar{1}\bar{1}3} plane (Fig. 2(d1-d4)) to subsequently dictate the IMC growth behavior.

In context of solders with a lower initial Cu weight percentage (x = 0, 0.7) reflowed at higher soldering temperature (300 °C), the elevated value of saturation solubility for them limits the availability of excess Cu species required for formation of Cu₆Sn₅ clusters within the bulk solder. As sketched in Fig. 6, a very small numbers IMC clusters of small size are formed, and which gradually exhibit a short-range disordered state. Thus, they are not so significant to

interfere the events occurring at the interface. Eventually, the roof-type Cu₆Sn₅ IMC grains are possibly nucleating directly on top of (111) nt-Cu substrate, with {2\bar{1}\bar{1}0} plane of the former (Fig. 3(d1,d2)) being the preferred direction. This allows the events to unfold via the rule of low lattice mismatch between Cu₆Sn₅ and (111) nt-Cu and let the system obtain the minimum Gibbs free energy [38]. Such an unperturbed event ensures the IMC grain growth at a relatively more coherent interface, enabling them bear the prismatic morphologies (αᵢ > 2) of Fig. 3(b1,b2). On the other hand, for solder alloys with larger initial Cu concentration (x = 1.5, 3.0) reflowed at T=300 °C, the size and number density of Cu₆Sn₅ MRO clusters will increase as depicted schematically in Fig. 6. These large sized abundant clusters are prone to an ordered state induced nucleation at the interface. The chaotic clusters will inhibit the unperturbed crystal growth mechanism that was supposed to unfold mainly via {2\bar{1}\bar{1}0} orientation, and subsequently enforce clustering mechanism based perturbed crystal growth to happen thereby making the resulting grains attain {2\bar{1}\bar{1}3} texture. Furthermore, the Cu₆Sn₅ grain size in these samples (refer Fig. 3(b3,b4)) is relatively larger than the layered columnar crystal of (111) nt-Cu, meaning that a single IMC grain must grow on the multiple grains of substrate. Compared to sample using Sn-1.5Cu alloy, the Sn-3.0Cu solder based sample has wider Cu₆Sn₅ IMC grains. This corresponds obviously to high lattice mismatch degree and incoherent interfaces. Hence, scallop-type Cu₆Sn₅ grains are predominantly observed in
<figure><img src="image_10.png" /><figcaption>**Figure 7:** The images show the initial conditions and bulk free energy curves for phase field simulation at (a) 533.0 K and (b) 573.0 K respectively. The CU6SN5 IMC grains-G1, G2, G3, G4 and G5 are located at the interface of Sn-rich LIQUID phase and Cu-rich (111)nt-FCC phase. The IMC grains in model of (a) are assumed to have a semicircular shape initially whereas those for model of (b) present a non-circular shape. This assumption is based upon experimental observations of IMC morphologies. While the free energy($F_{bulk}$) curves of (111)nt-FCC, CU6SN5 IMC and LIQ (acronym for LIQUID) phases at (a) 533.0 K are shown as solid lines, the corresponding curves for the three phases of interest are shown as dotted lines for temperature of (b) 573.0 K.</figcaption></figure>

the Sn-3.0Cu/(111) nt-Cu interface with an obvious {2\bar{1}\bar{1}3} texture (Fig. 3(d4)). As shown in Fig. 3(d3), the IMC grains of Sn-1.5Cu/(111) nt-Cu also reveal the {2\bar{1}\bar{1}3} orientation, and so they can be also categorized as scallop-type ($\alpha_J < 2$).

It is noteworthy to mention that Fig. 6 summarizes the two categories of morphologies for Cu<sub>6</sub>Sn<sub>5</sub> grains formed at Sn-xCu/(111) nt-FCC substrate decided by the temperature field and the initial composition of the solder alloy. The first category includes the prismatic Cu<sub>6</sub>Sn<sub>5</sub> grains ($\alpha_J > 2$) of a strong {2\bar{1}\bar{1}0} texture, which historically nucleate and grow directly on UBM to possess irregularly arranged roof-type morphology. These IMC grains correspond to a higher reflow temperature (300 °C) and lower Cu initial concentration ($x = 0, 0.7$) in solder, and are characterized with low lattice mismatch. The second category consists of scalloped Cu<sub>6</sub>Sn<sub>5</sub> grains ($\alpha_J < 2$) with a certain preferred {2\bar{1}\bar{1}3} texture. Their growth at solder/nt-FCC interface is interfered heavily by self-nucleating clusters and eventually they are associated with the high degree of lattice mismatch. They correspond to zero, low and large Cu initial concentration of solder at a lower soldering temperature (260 °C) implying that clustering mechanism at this temperature is present even from the Cu supplied via the substrate to the solder. At a higher soldering temperature (300 °C), this type of IMC

morphology is evident for samples characterized with higher Cu initial concentration ($x = 1.5, 3.0$) in the solder.

## 4.4. Modeling the effects of temperature and interfacial energy

The mechanistic aspects of growth behavior of η-Cu<sub>6</sub>Sn<sub>5</sub> at the interface of Sn-rich liquid solder and Cu-rich nt-FCC substrate can be studied using multi-phase field model. The main aspects that will be investigated in this section are the role of reflow temperature and the interfacial energy on the growth of the IMC grains. As shown in Fig. 7(a)-(b), the computational domain is a square of length 500 nm, initially consisting of 5 grains (G1, G2, G3, G4 and G5) of CU6SN5 IMC phase interfaced between (111) nt-FCC and LIQUID phases (The thermodynamic phases - CU6SN5 IMC, FCC and LIQUID are denoted using block letters. So, CU6SN5 is used to denote its phase name whereas Cu<sub>6</sub>Sn<sub>5</sub> represents its molecular formula.). Denoting phase as $\psi$ and order parameter as $\phi$, the model is based upon 3 $\psi$-7 $\phi$ system. Each of the scalloped grains with {2\bar{1}\bar{1}3} texture can be approximated to be of nearly semicircular morphology in 2D view. As all cases of experimental results at 533 K provide scalloped IMCs, this choice of grain's initial shape is relevant. Thus, the initial condition (IC) geometry with semicircular 5 IMC grains interfaced between LIQUID and
nt-FCC phases corresponds to T = 533 K. On the other hand, a different initial shape has been provided to the 5 IMC grains in context of simulation set up at 573 K. Each grain in Fig. 7(b) has been assigned a geometrical shape of a stepped rectangle. The choice for non-circular IMC grains for IC design is inspired from the experimental observation that the grain growth with {2110} texture which is initially not influenced by the clustering mechanism has a rooftoptype-morphology. The model consists of binary Cu-Sn system, with its global composition (c) described solely by the mole fraction of Sn i.e. c = c<sub>Sn</sub>. The global mole fraction of Cu (c<sub>Cu</sub>) is 1-c. For the simplification of the phase field model, the composition of the liquid solder will be assigned the value which corresponds to the thermodynamic equilibrium of LIQUID phase with IMC phase at a given temperature. This implies that the design consideration of different composition sets of the solder alloy is beyond the scope of the present model. This will limit the investigation associated with the roles of Cu clustering mechanism on overall growth kinetics of IMC phase. The nt-FCC solid phase consists of a single grain with an initial area (=1.25×10<sup>5</sup> nm<sup>2</sup>) quite larger than that of individual IMC grains. So the model does not take into account the grain boundary phenomena within nt-FCC phase.

The composition evolution in the binary Cu-Sn system is in accordance to the following partial differential equation (PDE):

$$ \frac{\partial c}{\partial t} = \nabla \cdot \sum (h_i M^i) \nabla \left( \frac{\partial f_{\text{bulk}}}{\partial c^i} \right) \quad (3) $$

In Eq. 3, the mobility M<sup>i</sup> for phase i at a given temperature is quantified in Table 1. From the table, it is obvious that the model assumes that the diffusivity of Cu and Sn within a phase to be the same. The grain boundary mobility between IMC grains is taken as 5 times larger than its phase mobility. It is to be noted that the mobility for a given phase is larger at 573 K as compared to the one at 533 K. In the table, the numerical values for diffused interface width (δ) and the interface energy (σ) are also provided. In a given model, both δ and σ are assumed constant at all the interfaces. The value of interface energy is designed upon the interface between IMC and nt-FCC phases, and this constant value is then assigned to other remaining interfaces as well. The parameters m and κ are the mathematical functions of interface width and interface energy:

$$ m = 6 \times \frac{\sigma}{\delta} \quad (4) $$

$$ \kappa = \frac{3}{4} \times \delta\sigma \quad (5) $$

For understanding the role of interface energy in the IMC grain evolution, two separate models will be developed for the initial condition of Fig. 7(b) by considering two different constant values of σ. As shown in Table 1, both of the values i.e. 0.96 and 0.74 J/m<sup>2</sup> are between 0.5-1.0 J/m<sup>2</sup>, implying

that the IMC and nt-FCC interfaces are considered to have incoherent interfaces. Corresponding to the two different interface energy, the table also lists two different values for m and κ. The evolution of non-conserved order parameter in context of this 3 phase-7 order parameter system is described by the following PDE:

$$ \frac{\partial \phi_i}{\partial t} = -L(\phi_1, \dots, \phi_N) \left( \frac{\partial f_{\text{bulk}}}{\partial \phi_i} + \frac{\partial f_o}{\partial \phi_i} - \nabla \cdot \frac{\partial f_{\text{grad}}}{\partial (\nabla \phi_i)} \right) \quad (6) $$

The quantity f<sub>bulk</sub> in Eqs. 3 and 6 is the bulk free energy density. The bulk chemical free energy of a phase i is obtained by multiplying f<sub>bulk</sub> with molar volume of the phase i.e. F<sup>i</sup><sub>bulk</sub> = V<sub>m</sub> × f<sup>i</sup><sub>bulk</sub>. Fig. 7 presents the parabolic composition dependence of bulk free energy of nt-FCC, CU6SN5 IMC (HCP) and LIQUID phases at 533 K and 573 K. The CALPHAD thermodynamic data for binary Cu-Sn system are obtained from reported works [57–60]. The necessary thermodynamic computations related to the quantification of the bulk free energy data of three phases were performed using pycalphad software [61]. Besides bulk-free energy density, Eq. 6 consists of the barrier energy density (f<sub>barrier</sub>) and gradient energy density (f<sub>grad</sub>) which together constitute the interfacial free energy density.

$$ f_{\text{barrier}} = m \left( \sum_{i} \left( \frac{(\phi_i)^4}{4} - \frac{(\phi_i)^2}{2} \right) + \gamma \sum_{i} \sum_{j \neq i} \phi_i^2 \phi_j^2 + \frac{1}{4} \right) \quad (7) $$

$$ f_{\text{grad}} = \frac{\kappa}{2} \sum_{i} (\nabla \phi_{i})^{2} \quad (8) $$

The physical quantity L<sup>k</sup> = L(φ<sub>1</sub>, ..., φ<sub>N</sub>) appearing in Eq. 6, is mathematically defined using the following expression.

$$ L^k = \frac{\sum_{i=1}^{N} \sum_{j>1}^{N} (L_{ij} \times \phi_i^2 \phi_j^2)}{\sum_{i=1}^{N} \sum_{j>1}^{N} \phi_i^2 \phi_j^2} \quad (9) $$

The interfacial mobility L<sub>ij</sub> for the interface between phase i and j is then defined as follows:

$$ L_{ij} = \frac{4m}{3\kappa} \times \frac{M_i + M_j}{2 \times (c_{i,eq,j}^i - c_{j,eq,i}^j)(c_{i,eq,k}^i - c_{k,eq,i}^k)} \quad (10) $$

The term (c<sup>i</sup><sub>i,eq,j</sub> - c<sup>j</sup><sub>j,eq,i</sub>)(c<sup>i</sup><sub>i,eq,k</sub> - c<sup>k</sup><sub>k,eq,i</sub>) is quantified using the free energy curves of Fig. 7(a)-(b). On projecting the common tangent not only between nt-FCC and IMC phases but also between the IMC and LIQUID phases on the composition axis, and multiplying the length of these projected composition values, the value has been determined to be around 0.16.

In a system comprising multiple phases, the material properties within the interface regime are determined in a thermodynamically consistent manner through interpolation using the function (h<sub>i</sub>(φ)) as proposed by Moelans [62]. The
definition of the interpolation function depends on the quantity of grains within a specific phase, and so the following two cases are relevant in our work:

$$h_i = \begin{cases} \frac{\sum_{j=1}^{5} \phi_{i,j}^2}{\sum_{k=1}^{7} \phi_k^2} & ; \text{IMC} \\ \frac{\phi_i^2}{\sum_{k=1}^{7} \phi_k^2} & ; \text{FCC, LIQUID} \end{cases} \quad (11)$$

The set of PDEs (Eqs. 3 and 6) are solved using finite element method in Multiphysics Object Oriented Simulation Environment (MOOSE) Framework software [63]. The results of the simulation are presented in Figs. 8 and 9. The influence of temperature on the phase and grain evolutions (at constant $\sigma$=0.96 J/m²) has been investigated in Fig. 8. The model of Fig. 8(i)(a) and Fig. 8(ii)(a) corresponds to T = 533. Initially semi-circular IMC grains of Fig. 7(a) evolve spatio-temporally into scalloped-type structure. On the other hand, Fig. 8(i)(b) and Fig. 8(ii)(b) corresponds to results for T = 573 K. The IMC grains initially with stepped rectangular morphology (Fig. 7(a)) gradually evolve into scallop-type morphology. In this higher temperature model, the assumption of incoherent interface ($\sigma$=0.96 J/m²) between the phases and between the grains; and the presence of considerable amount of Cu in LIQUID solder ($c_{Sn}^{LIQ} < 0.97$ and so $c_{Cu}^{LIQ} > 0.03$), are the major reasons that finally cause these grains to have $\alpha_J < 2$. Modeling the prismatic growth at 573 K (with very low mole fraction of Cu in the solder ($c_{Cu}^{LIQ} \approx 0.005$) and highly coherent interface between FCC and IMC, the evolving grains retain prismatic structure $\alpha_J > 2$.) is considered the work of future. At both temperatures, the trend is that IMC grains grow at the expense of LIQUID and nt-FCC phases. However owing to the larger magnitudes of the driving force $F_{bulk}$ (refer Fig. 7) and mobilities (refer Table 1) at larger temperature, the growth of $\eta$-Cu$_6$Sn$_5$ grains is more pronounced at 573 K. While at 533 K the IMC phase attains an overall area (sum of individual areas of grains) of $6.26 \times 10^4$ nm² for a time duration of 1.4 ms, it obtains the total area of $5.51 \times 10^4$ nm² just within 13.3 $\mu$s at 573 K. The growth rate kinetics of IMC layer follows $t^{1/4}$ dependence on time for reflow soldering based interfacial reaction [64]. The growth rate constants obtained from the phase field model at 533 K and 573 K are $0.782 \ \mu m/s^{0.25}$ and $1.29 \ \mu m/s^{0.25}$ respectively. The experimentally estimated values [56] are $0.92 \ \mu m/s^{0.25}$ (T = 533 K) and $1.36 \ \mu m/s^{0.25}$ (T = 573 K). As the computational model follows the same trend with that of experiment, it can be inferred that the computational model has reasonable accuracy in terms of relaying the information related to thermal field effects. By further finetuning the model parameters, increasing the length scale and time scale, results more comparable to the experiments can be achieved, and this again is the topic of future study.

This study also aims to investigate the role of interface energy on the evolution mechanism of intermetallic grains. For that two models with $\sigma$=0.96 J/m² and $\sigma$=0.74 J/m² corresponding to constant T=573 K are compared as shown

in Fig. 9. As revealed in Fig. 9(a), the grain G3 is the largest one while G4 is the smallest one, and regardless of the value of interface energy, all of the IMC grains grow larger with time. The largest grain G3 grows the fastest and the smallest grain grows the slowest at a given value of $\sigma$ as shown in Fig. 9. From the figure, it can also be inferred that the dotted curves ($\sigma$=0.74 J/m²) correspond to a slightly smaller area than the solid lines ($\sigma$=0.74 J/m²). The gap starts to become pronounced only after 4 $\mu$s from the simulation start time, implying that the role of $\sigma$ comes into play more significantly when two IMC grains interact with each other. For time duration 5-10 $\mu$s, it is observable that the larger the initial grain size is the more difference is its area for two models. The area difference measurement accounts the differential growth pattern driven by change of grain shape or morphology. Compared to the grain morphologies of model with $\sigma$=0.74 J/m², the morphologies of the model with larger $\sigma$ bear abit round profile. Such profile difference is noted when observing along the boundaries between the corresponding two grains of each model. As both values of $\sigma$ represent incoherent interfaces, both models represent scallop-type morphology. Future work will be aimed at lowering $\sigma$ to values less than 0.1 J/m² so as to simulate growth of roof-type IMC. The free energy curve for LIQUID phase needs to be designed such that its equilibrium composition matches that with the experimental Sn-0.7Cu alloy. Combining the experimental observation, and inferences from computational study; it can be been understood that the presence of Cu solute in liquid solder alloy in larger amount may increase the grain boundary energy between IMC grains, and also between the IMC phase and substrate.

<table><caption>**Table 1:** The numerical values of input properties and parameters of the phase field model are provided along with their units. (*)The current mathematical formulation requires the molar volume of all the three phases to have a single value.</caption><thead><tr><th>Properties</th><th>Values</th></tr></thead><tbody><tr><td>M<sup>fcc</sup> (T=533 K)</td><td>1.03 &times; 10<sup>-23</sup> m<sup>5</sup>/Js</td></tr><tr><td>M<sup>imc</sup> (T=533 K)</td><td>1.03 &times; 10<sup>-22</sup> m<sup>5</sup>/Js</td></tr><tr><td>M<sup>liq</sup> (T=533 K)</td><td>1.03 &times; 10<sup>-21</sup> m<sup>5</sup>/Js</td></tr><tr><td>M<sup>fcc</sup> (T=573 K)</td><td>2.5 &times; 10<sup>-22</sup> m<sup>5</sup>/Js</td></tr><tr><td>M<sup>imc</sup> (T=573 K)</td><td>2.5 &times; 10<sup>-21</sup> m<sup>5</sup>/Js</td></tr><tr><td>M<sup>liq</sup> (T=573 K)</td><td>2.5 &times; 10<sup>-20</sup> m<sup>5</sup>/Js</td></tr><tr><td>V<sub>m</sub> (*)</td><td>1.629 &times; 10<sup>-5</sup> m<sup>3</sup>/mol</td></tr><tr><td>grid space</td><td>3.57 &times; 10<sup>-9</sup> m</td></tr><tr><td>&delta;</td><td>3.50 &times; 10<sup>-8</sup> m</td></tr><tr><td>&sigma;</td><td>0.96 J/m<sup>2</sup><br>0.74 J/m<sup>2</sup></td></tr><tr><td>&kappa;</td><td>3.36 &times; 10<sup>-9</sup> J/m</td></tr><tr><td>m</td><td>2.59 &times; 10<sup>-9</sup> J/m</td></tr><tr><td>&gamma;</td><td>2.7 &times; 10<sup>7</sup> J/m<sup>3</sup><br>2.1 &times; 10<sup>7</sup> J/m<sup>3</sup></td></tr><tr><td></td><td>1.5</td></tr></tbody></table>
<figure><img src="image_11.png" /><figcaption>**Figure 8:** Investigation of the effect of temperature on phase and grain evolutions at constant $\sigma$=0.96 J/m$^2$. Scalloped IMC growth at liquid/nt-Cu interface at i(a) $T$ = 533.0 K. Even though the initially prismatic IMCs for i(b) $T$ = 573.0 K had been represented via a stepped rectangular (non-circular) profile at initial condition (Fig. 7(b)), they gradually evolve to attain scallop-type morphology with tapered top. From (i) and (ii), it is understandable that IMC phase grows at the expense of LIQUID and nt-FCC phases. It is to be noted from (ii) that the IMCs of (b) grow faster than those of (a). The unit of time is ms for (a) and $\mu$s for (b).</figcaption></figure>

In summary, the phase field model has been successfully utilized to explain the role of temperature and interface energy on guiding the growth behavior of intermetallic grains at solder/substrate interface. The integrated computational and experimental insights have allowed us to establish the tentative range of interfacial energy in context of experimental samples. As shown in Table 2, it is proposed that the interface energy for phase/grain interfaces in all types of experimental samples at 533 K must be equal to or larger than 0.5 J/m$^2$ to produce scallop-type IMC grains with

$\{2\bar{1}\bar{1}3\}$ texture. For Sn/(111) nt-Cu and Sn-0.7Cu/(111) nt-Cu samples reflow soldered at 573 K and characterized with roof-type IMC grains of $\{2\bar{1}\bar{1}0\}$ texture, $\sigma < 0.5$ J/m$^2$. On the other hand, $\sigma \ge 0.5$ J/m$^2$ for Sn-1.5Cu/(111) nt-Cu and Sn-3.0Cu/(111) nt-Cu as these samples are associated with scalloped IMC grains of $\{2\bar{1}\bar{1}3\}$ texture.

**5. Conclusions**

The orientation and morphology of Cu$_6$Sn$_5$ grains on (111) nt-Cu UBM at different reflow soldering temperatures
<figure><img src="image_12.png" /><figcaption>**Figure 9:** A numerical illustration on how the interfacial energy can impact the evolution profile of the interfacial Cu₆Sn₅ grains Gᵢ, (i=1,2,...,5). For a given initial geometry of Fig. 7(b), the two models (one with σ=2.5 J/m² and another with σ=1.87 J/m²) in (a) reveal the phase/grain boundary morphologies of interfacal grains corresponding t=0.48 µs. The temporal evolution of individual grain areas for the two models is presented in (b).</figcaption></figure>

(260 °C and 300 °C) and Cu concentrations (0, 0.7, 1.5, and 3.0 wt.%) were investigated. At the larger temperature of 300 °C and for lower initial concentration of Cu in solder (0 and 0.7 wt.%), the interfacial Cu₆Sn₅ intermetallics bore the roof-type morphology with a strong {2\bar{1}\bar{1}0} texture. At the temperature unchanged but concentration of Cu increased to 1.5, and 3.0 wt.%, the interfacial IMC revealed the scallop-type morphology with a {2\bar{1}13} orientation. Finally, when the temperature was lowered to 260 °C, the {2\bar{1}13} oriented scalloped interfacial IMC was the single morphology type present for all the four solder compositions. Based on liquid structure analysis of Sn-based lead-free solders, the Cu₆Sn₅ clusters within the solder undergo a transition towards short-range disorder as soldering temperature increases beyond 573 K and Cu concentration decreases. Consequently, Cu₆Sn₅ IMC nucleate directly on (111) nt-Cu with proper adherence to the principle of minimizing

lattice mismatch. The abundance of both short-range ordered (SRO) and medium-range ordered (MRO) Cu₆Sn₅ clusters rises with decreasing soldering temperature, independent of Cu concentration, or with increasing soldering temperature and higher Cu concentration. As a result, these Cu₆Sn₅ clusters first self-nucleate and subsequently adhere to (111) nt-Cu under bump metallization (UBM), facilitating their continued growth in the scallop morphology. While temperature has a significant effect on the magnitude of driving force, and the saturation solubility of solder, the interface energy between substrate and IMC grains can largely manipulate the morphology of the latter during evolution. The roles of temperature and interfacial energy on the growth of interfacial scallop-type IMC have been mechanistically investigated using phase field model. By exerting control over the microstructure of the Cu under bump metallization (UBM), adjusting the Cu concentration within the solder,
**Table 2**

Sample and temperature dependence of interface energy of IMC/FCC interface. The table provides σ estimates which are based on IMC morphology study.

<table><thead><tr><th>Reflow Sample</th><th>Condition</th></tr></thead><tbody><tr><td>Sn/(111) nt-Cu</td><td>σ ≥ 0.5 J/m² (533 K)<br>σ &lt; 0.5 J/m² (573 K)</td></tr><tr><td>Sn-0.7Cu/(111) nt-Cu</td><td>σ ≥ 0.5 J/m² (533 K)<br>σ &lt; 0.5 J/m² (573 K)</td></tr><tr><td>Sn-1.5Cu/(111) nt-Cu</td><td>σ ≥ 0.5 J/m² (533 K)<br>σ ≥ 0.5 J/m² (573 K)</td></tr><tr><td>Sn-3.0Cu/(111) nt-Cu</td><td>σ ≥ 0.5 J/m² (533 K)<br>σ ≥ 0.5 J/m² (573 K)</td></tr></tbody></table>

and regulating the soldering temperature, it is possible to maneuver the specific orientation and morphology of Cu₆Sn₅ within the microbump.

**CRediT author statement**

**Zhijie Zhang:** Writing – original draft, Validation, Methodology, Formal analysis, Data curation, Conceptualization. **Anil Kunwar:** Writing – review & editing, Validation, Software, Methodology, Data curation, Conceptualization. **Xing Gao:** Writing – review & editing, Visualization, Validation, Investigation. **Hong Wei:** Writing – review & editing, Validation, Methodology, Investigation.

**Acknowledgements**

This work was supported by the National Natural Science Foundation of China (Grant Number: 51801079), the Natural Science Foundation for Young Scientists of Jiangsu Province, China (Grant Number: BK20180987), and the National Science Centre, Poland (UMO-2021/42/E/ST5/00339).

**Declaration of Competing Interests**

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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