Growth Kinetics of Intermetallic Compounds between Sn and Fe Liquid-Solid Reaction Couples

Growth behavior of the intermetallic compound (IMC), FeSn 2 , was investigated in the liquid Sn/solid Fe reaction couple over the annealing temperatures from 250°C to 400°C. Low carbon steel AISI 1018 was chosen to make Fe samples. The morphology and thickness of the IMC formed between Sn and Fe were examined using scanning electron microscopy (SEM). In addition, energy-dispersive X-ray spectroscopy (EDX) and X-ray diffraction (XRD) were used to confirm that the IMC is FeSn 2 . The growth kinetics of FeSn 2 was modeled by parabolic law and empirical power law. Based on the models, the growth constants, activation energy and time exponents were established at different annealing temperatures. It was found that the time exponent values obtained by fitting with empirical power law deviate from 0.5, meaning that volume (bulk) diffusion is not the only rate-controlling process in the liquid Sn/solid Fe reaction couple. Also, a variation in the time exponent values is indicative that the growth behavior is correlated with grain size growth and irregular grain morphology at different annealing stages. The results of this research show that AISI 1018 steel can readily react with Sn to form IMC on the interface. This is an essential requirement of soldering action using Sn-rich solders.


Introduction
Ferrous metals have had various applications in automotive and electronic industries. Ultra low carbon, low carbon, and micro-alloyed steels have been widely used as auto body material [1][2][3]. Invar (Fe-36Ni) is known for its uniquely low coefficient of thermal expansion (CTE) around 0.8 to 1.6 ppm/°C (measured between 30-100°C). It has been utilized in manufacturing precision instruments where high dimensional stability is required. Alloy 42 (Fe-42Ni) and Kovar (Fe-29Ni-17Co) are controlled expansion alloys with CTE of 4.0 to 4.7 ppm/°C (measured at 30-300°C) and 5.1 to 5.5 ppm/°C (measured at 30-450°C), respectively [4][5][6]. In electronics, these alloys have been used to make lead-frames of plastic packages and headers of transistor packages because their CTE is close to that of silicon (3 ppm/°C) and lead-sealing glass. They have also been chosen for manufacturing headers of laser diodes because their CTE matches well with that of gallium arsenide (GaAs) semiconductor (7 ppm/°C). One downside of these alloys is the relatively low thermal conductivity (10-17 W/m-K) [7]. We thus looked into ferrous metals that have higher thermal conductivity and reasonably low CTE for electronic packaging applications. After a thorough search, AISI 1018 low carbon steel was selected for this study. It has thermal conductivity of 51.9 W/m-K and CTE of 11.5 ppm/°C [8].
During the process of producing the metallic bonding between solder and metal, molten phase solder wets metal surface and reacts with metal to form an intermetallic compound (IMC) layer between solder and metal. However, the brittle nature of IMC could make it possible to be the most vulnerable point in the solder joint. Last but not least, the formation of IMC occurs not only by liquid (molten solder)-solid (metal) reaction during reflow process but by the solid-solid reaction during storage and service life. It is therefore essential to study the mechanism and kinetics of the formation of IMC at the lead-free solders/metal substrate interface. The aim of this work is to explore the growth behavior of intermetallic compound between electroplated tin (Sn) and iron (Fe) at the temperatures above the melting point of Sn (231.93°C). Although the IMC formation could be more complicated in soldering process since sometimes other metals also involve in the IMC composition, the impact from other metals is not considered in this research. In what follow, experimental design is first presented. Experimental results are reported and discussed. A brief summary is then given.

Experimental design
Substrates of 15 mm×13 mm×3.3 mm (width×length×thickness) were cut from AISI 1018 low carbon steel (Fe) sheet. They were ground using 800 and 1200 grit SiC-coated papers to smoothen out the surface. They were cleaned with acetone and deionized water before electroplating. Sn of 85 μm thick was electroplated over the Fe substrate in a stannous methanesulfonate bath under the condition of 43°C and pH of 1 with current density of 30 mA/cm 2 . Matte Sn electroplating solution was chosen instead of bright Sn because matte is less prone to whisker formation [9]. The Sn-coated Fe substrates were then treated isothermally at 250°C, 335°C and 400°C for different durations of time in a convection furnace that had been preheated to the desired temperature. After the reactions, the Sn-coated Fe substrates were cooled in air and then mounted in epoxy resin. The samples were then cross-sectioned into halves.
Microstructure observation and composition analysis were studied using scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX). The composition of the IMC was also studied by X-ray diffraction (XRD) after etching the reacted Sn-coated Fe substrate with diluted HCl. Figure 1 exhibits the cross-section SEM images of the interfacial layer between Sn and Fe reacted at 250°C for 2, 12, 50, and 200 hours, respectively. It was seen that molten Sn reacted readily with Fe to form IMC, an essential requirement of soldering action. This indicates that Fe is easily solderable without using flux, provided that the soldering interface is free of oxides. To estimate the average thickness of the IMC layer, the region of IMC layer was first evaluated using image processing software. The average thickness was then determined by dividing the area of the IMC layer by the total length of the interface from the cross-section SEM micrographs. The average IMC thickness obtained is 5.8 μm after isothermal annealing at 250°C for 2 hours as shown in Figure 1(a). A thin layer of IMC about 1 μm was formed adjacent to Fe, which is composed of many IMC granules. IMC also grew vertically toward Sn matrix to form columnar crystals of different lengths, ranging from submicron to 5 μm. It was observed that some IMC columnar crystals detached from the continuous IMC layer and drifted into to the Sn solder bulk.

Microstructural evolution of the intermetallic compound layer
This "spalling behavior" is similar to the literature data reported by Lin et al. and Teo et al [10][11]. EDX analysis confirmed the IMC composition to be FeSn2, as shown in Table 1. As annealing time increased to 12 hours, it was seen that the columnar IMC crystals grew in both longitudinal and lateral direction as displayed in Figure 1 Presented in Figure 2 are the cross-section SEM images of the interfacial layer between Sn and Fe reacted at 335°C for 2, 12, 50 and 100 hours. Compared to the samples annealed at 250°C, the columnar IMC crystals in the samples annealed at 355°C exhibit more rounded edges. With longer annealing time up to 50 hours, the spalling behavior became obvious. It was also observed that, when the annealing was extended to 100 hours, a large amount of the IMC spalled off and sporadically distributed in Sn matrix.
Similar to the samples annealed at 250°C, the only IMC found is FeSn2 as examined by EDX analysis.
The chemical composition is shown in Table 1. The average IMC thicknesses of the samples annealed at hours is shown in Figure 4. Only Sn and FeSn2 were identified in the XRD pattern. This is in agreement with the results obtained from EDX analysis ( Table 1) that only FeSn2 was found at the interface, so were observed in the samples after annealing at 250°C and 335°C. Although FeSn is also shown as a stable IMC in the Fe-Sn binary phase diagram, FeSn IMC was not identified [12]. This result is consistent with the observations in other Sn-containing solder/ferrous metal reaction systems [13][14][15].

Growth kinetics of the intermetallic compound layer
The data of the average FeSn2 IMC thickness with respect to annealing time for each annealing temperature are plotted in Figure 5(a). It is evident that the average IMC thickness increases as the annealing time and annealing temperature increases. Assuming that IMC formation is diffusioncontrolled, the parabolic law holds.
where k0 is the pre-exponential factor, Q is the activation energy, R is the gas constant and T is the absolute temperature. Therefore, as shown in Figure 7, the activation energy obtained from the plot of ln(k) versus 1/T is 50 KJ/mol (0.52 eV). This value is smaller than those reported previously [18][19][20], where different annealing time, temperature and environment were conducted and diffusion couples were made with different process.
Analyzing the data shows the growth kinetics may also be modeled with an empirical power law: Equation 3 is analogous to equation 1, except that the time exponent, n, is adopted as a variable . Figure   5(b) presents the regression curves. The values of time exponent, n, obtained by regression analysis, are 0.298, 0.466 and 0.509 at 250°C, 335°C and 400°C, respectively. The growth exponent, n, at 250°C takes a value of 0.298. The value deviates from the value (0.5) in parabolic law, indicating that the layer growth mechanism is not a simple Fickian diffusion process whereby volume (bulk) diffusion is assumed as the predominant diffusion path. In fact, it is possible that not only volume (bulk) diffusion but other diffusion paths contribute to the rate-controlling process as well. For instance, grain boundaries, dislocations and free surfaces are high-diffusivity paths or diffusion short circuits [21] in metals. Here, grain boundary diffusion could account for this deviation from parabolic law. As can be seen in Figure 1, at early stage (annealed for 12 hours) of the annealing process, the grain sizes of the IMC near the interface close to Fe is small, suggesting that there are still enough fast paths (grain boundaries) for the interdiffusion of Sn and Fe atoms at the interface. In the course of time, the IMC grain size grows larger and the density of grain boundary is reduced. At some point the grain become large enough and connect together to form a continuous layer of IMC, as displayed in Figure 1(d), the slow path (volume diffusion) turns out to take over the major diffusion transport mechanism. This is manifested by the observation of flatten-out of the growth curve at prolonged annealing time for annealing at 250°C. Similar studies in the literature have reported that the growth exponents range from 0.25 to 0.32 for similar solid-liquid reactive diffusion couples [22][23][24]. On the other hand, the obtained growth exponents are close to 0.5 for the annealing experiments conducted at higher temperatures: 0.466 at 335°C and 0.509 at 400°C. This means that the growth kinetics at 335°C and 400°C is diffusion-controlled. The spalling-out of large amount of IMC occurred at higher annealing temperature explains that the growth kinetics complies with parabolic law.
At higher annealing temperature, the diffusing components have higher mobility so as to the rate of formation IMC is faster. The IMC grows quickly but some of them float towards to Sn molten phase. The IMC grains do not have chance to undergo grain growth or Ostwald ripening. As shown in Figure 2(d) and Figure 3(d), the IMC does not form a continuous layer but sporadically distributes in the Sn matrix.
The channels between IMC grains provide enough interdiffussion paths of reaction components. It is also worth mentioning that the irregular morphology of the IMC could cause the disparity of growth exponent values as well. The parabolic model derived from Fick's first law is based on assumptions as mentioned previously. It is assumed that the change in concentration of diffusing components with distance within the IMC layer is linear. This reminds us of the fact that this is not the situation in the real case though. The shape of IMC varies from spherical to ellipsoidal or elongated columnar. At higher annealing temperature, the IMC even disintegrates into fragments. Here, the concentration of diffusing components, Sn and Fe atoms, cannot be linear with the FeSn2 IMC layer. This makes the assumption inadequate in real case.

Summary
The