Reactive wetting behaviors of Sn/Cu systems: A molecular dynamics study

1Department of Mechanical Engineering, Ming Hsin University of Science and Technology, Hsinchu 30401, Taiwan 2Institute of Precision Mechatronic Engineering, Ming Hsin University of Science and Technology, Hsinchu 30401, Taiwan 3Department of Mechanical Engineering, WuFeng Institute of Technology, Chiayi 621, Taiwan 4Department of Information Management, Meiho Institute of Technology, Pingtung 912, Taiwan 5Department of Engineering Science, National Cheng Kung University, Tainan 70101, Taiwan *Corresponding author. Email: chchwang@mail.ncku.edu.tw Reactive wetting behaviors of Sn/Cu systems: A molecular dynamics study J. Y. Hsieh1,2, J. L. Chen3, C. Chen4, H. C. Lin5, S. S. Yang5 and C. C. Hwang5,*

In recent years, lead free solders have been extensively proposed in utility of connecting devices to printed-circuit boards in microelectronic manufacturing because of legal, environmental and technological considerations [1]. In the soldering process, a metallurgical bond is formed between a molten solder and a metal surface. Therefore, the molten solder is required to properly spread, or wet, on the metal substrate for the formation of a proper metallic bond. The tendency for a metal to spread on a solid surface has been defined as the wettability [2]. In the case of inert liquid/solid combinations, the wettability can be evaluated by calculating the contact angle between the solder and the substrate via Young's equation, which gives the balance of the solid surface/gas, solid/liquid, and gas/liquid interfacial tensions at equilibrium. Nevertheless, Young's equation is less useful for the realistic soldering process, where the mechanical strength of a material joint depends significantly on the degree of reaction between the spreading solder and the solid substrate.
Even so, a lower contact angle between the solder and the substrate in general corresponds to a lower surface interfacial energy and indicates a higher wettability. Particularly, surface alloying, which is resulted from the reaction between the solid surface and the liquid spreading on it, has been observed to improve wettability [3]. Therefore, reactive wettings are of particular interest in studies relevant to lead free soldering.
They found the Sn-3.5Ag-4.8Bi alloy exhibited the lowest contact angles indicating improved wettability with addition of bismuth and the contact angle decreased with increasing temperature, depending on the type of flux used in the sessile-droplet method. Amore et al. [6] have experimentally studied the surface tension and wetting behavior of molten Cu-Sn alloys on Ni substrate. They found their results of the surface tension of the Cu-Sn system are in good agreement with DOI: 10.5101/nml.v2i2.p60-67 http://www.nmletters.org the works of Drath et al. [7] and Lee et al. [8] and concluded that the contact angle decreases with the increase of Sn-content for the Sn-rich Cu-Sn alloys. Other experimental studies on the wetting behavior of Sn-based lead free solders on metal substrate can also be found in refs [9][10][11][12][13][14][15][16][17].
Besides experimental methods, theoretical continuum models have also been proposed in studying the reactive wetting of solid surfaces [18][19][20]. However, continuum models inevitably make significant approximations because of lacking  [21]. They also demonstrated that as liquid Ag spreads on Cu surface, wetting kinetics is enhanced by dissolution reactions [22].
In particular, knowledge of the reactive wetting of Sn/Cu systems is important for a lead free soldering process since Sn-Cu binary alloys can represent a basic subsystem of some  [23]. All MEAM parameters used in the present calculations are from the report of Aguilar et al. [24]. In each of the present simulations, the spreading was considered as an isothermal process that both the droplet and the substrate were controlled at a common temperature that is higher than the solidifying point of the droplet. Figure 1 shows the configuration of the droplet wetting system considered in this work. Four droplets of pure Sn and Sn-Cu alloys, namely,  The spreading stage lasted for 300 ps, which is long enough for the spreading process to become steady. In all the present MD simulations, the temperatures of the whole spreading system were held at a desired value using the rescaling method [26,27].
The leap-frog algorithm was implemented to derive new position and velocity vectors of the droplet and the substrate atoms from the corresponding data obtained in the previous step.
The motion of each atom in the system was governed by Newton's law of motion in which the resulting force acting on the atom was deduced from energy potential relevant to the interactions with the neighboring atoms within a cut-off radius.
In the studies of dissolutive wettings of Cu substrates by liquid Pb and Ag, Webb III et al. [21,22] 100)) plane, however, gives rise to a lesser (denser) density of Cu in the alloy film, so Cu atoms from deeper (shallower) planes of the Cu crystal will melt into the droplet to complete the spreading at the specific temperature. As a result, the wettings on these planes tend to become steady at equal times. The R(t) curves in Fig. 4 also indicate that in the early stage of the reactive wetting, all the film radii grow with t 1/2 and they have become steady quite early before 300 ps. Furthermore, the R(t) curves in Fig. 4   Further increase of Cu content will cause the Sn-Cu binary composition to reach another limit, so the specific system temperature will become the solidus temperature of the alloy at which the Sn-Cu alloy will be solidified to its crystalline structure. The descending density peaks for Cu along z axis in  Table 2   between the planes z 1 and z 2 . Under the interface, the core zone of plane z 1 is in solid phase and above it, the core zone of plane z 2 is still in liquid phase. Obviously, the melting of Cu into the liquid stops when the core zone of the theoretical interface is saturated with the solidus weight fraction W S Cu . Figure 8 shows the influence of droplet composition on the radial extension R(t); a richer Cu content in the alloy droplet results in a slower wetting kinetics, the same trend as in the case of wetting by Cu-Ag alloys [22]. However, radial extensions in the wettings by the alloys in different compositions require approximately equal time to become steady. This is simply due to that, during the reactive wetting by a richer (diluter) Cu content droplet, fewer (more) Cu atoms are required to melt into the droplet to cause its saturation with Cu. Similar to the wettings by Sn, the time required for the radius growth in the Sn-Cu wettings to become steady is almost independent of the crystalline direction of the substrate surface. The final contact angles of the wettings of the various Sn-Cu droplets performed at the various temperatures considered in this work are also listed in Table 1. This table depicts that the contact angle decreases with the decrease of Cu content for the Sn-rich Cu-Sn alloys, qualitatively consistent with the macroscopic observations of Amore et al. [6]. The hypothesis and theory described above can also be applied to the wettings by Sn-Cu alloy droplets. In the cases of the Sn-Cu droplet wettings, the final positions of the liquid/solid interface z int,f and the corresponding values of W Cu (z int,f ) were obtained following the same procedure mentioned above. The results are listed in Table 2. Again, the hypothesis presented in this work is verified by the fact that, at a common temperature T, the weight fractions of Cu at the liquid/ solid interfaces W Cu (z int,f ) have approximately the same value of W S Cu (T) for the wettings of the various alloy droplets. However, a richer Cu content in the binary alloy droplet results in an upper position of the liquid/solid interface.
In this work, a total of 36 MD calculations for simulating  (111) substrates by pure Sn and Sn-10Cu, Sn-20Cu, and Sn-30Cu(wt%) alloy droplets at the temperatures of 800K, 900K, and 1000K were considered, respectively. The simulation results show that the spreading of Cu(110)(Cu(100)) substrate has the fastest (slowest) wetting kinetics and the highest (lowest) final position of the theoretical liquid/solid interface separating the liquidus and solidus Sn-Cu alloys in the surface alloy film. Wettings performed at a higher temperature also have faster kinetics but require longer times to become steady. A higher temperature will lower the position of the liquid/solid interface in the surface alloy. Meanwhile, the influence of the droplet's alloy composition is that a richer Cu content causes the alloy droplet to wet the substrates with a slower kinetics and a higher position of the liquid/solid interface. This work considered the regime where the dissolution of the substrate Cu into the liquid dominates the reactive wetting. A hypothesis that the reactive wetting will come to the end as the theoretical liquid/solid interface saturates with the temperature-dependent solidus weight fraction of Cu and stops moving into the droplet has been confirmed through a theory successfully developed in this work for positioning the liquid/solid interface in the spreading film. However, the realistic distribution of the weight fraction of Cu in the surface alloy is axially symmetric. In the region farther from z axis richer contents of Cu are observed both in the alloys above and under the substrate surface, reflecting less amount of Cu in the crystal have melted into the liquid droplet and the Cu atom that have melted into the droplet tend to diffuse to the edge of the liquid film. In the zone of coexisting liquid and solid alloys, the liquid alloy is surrounded by the solid alloy. Summarized, this work has presented detail knowledge of the reactive wetting of Sn/Cu systems, which is necessarily required in relevant lead free soldering processes.