Atomistic modeling to predict and improve the strength of doped Sn-Cu solder interfaces
Authors: Woodcox Michael , Smeu Manuel 
Published: February 2022

Abstract
The reliability of solder joints depends upon the strength of the interface where two materials are joined. The strengthening of solder joints has been routinely achieved via doping with other elements, though this is not yet well understood at a fundamental level, and typically accomplished by trial and error. In the present work, we have used atomistic modeling based on density functional theory (DFT) and ab initio molecular dynamics (AIMD) to study the mechanical strength of the Sn-Cu interface under various conditions. We have investigated the cleavage energy (CE) of the Sn-Cu interface, and how it changes with various dopants (Ag, Au, Bi, Cu, Ni, Zn) to determine the benefit (or detriment) to the strength of this simulated solder joint. We have also tested multiple faces of Sn ([001], [100] and [110]) as potential interfaces with Cu. Our simulations show that each of the dopants considered, except for Bi, increases the strength of the interface. In all our constructed Sn-Bi interfaces, a single atomic layer of Sn atoms deposits on the Cu and binds strongly to it. The weakest point of the interface is located between the deposited Sn layer and the remaining bulk Sn. For the undoped [001] Sn-Cu system, the cleavage energy between the Sn and Cu layers is 1.63 J/m2, whereas the cleavage energy between the deposited layer of Sn and the remaining Sn bulk is considerably lower: 0.54 J/m2; this is likely the location of joint failure, and the focus of our investigation. We observed this trend in each interface that we studied. As expected, the strength of the Sn-Cu interface can be modified with dopants; the CE of the weakest point can be increased (strengthening it) by 0.1–0.2 J/m2 when doping it with Ag, Au, Cu, Ni and Zn, though Bi results in a decrease (weakening it) by 0.15 J/m2. As a complementary method for investigating this interface, we have used AIMD to simulate a mechanically controlled break junction (MCBJ) of the solder interface by gradually increasing the separation between the two ends of the simulated junction. The process is continued until the junction completely breaks, yielding an energy vs. distance curve, which provides information about the strength of the solder joint that is similar to a stress-strain curve. We observe that, as the Sn is moved away from the Cu, there is a relatively steady increase in energy until the system begins to separate. From this separation point, the energy curve plateaus as the interaction between the two halves of the system vanishes. The location of the breaking point is in excellent accordance with our CE calculations; there is also a correlation between the CE and the amount of distance that the system must be stretched before reaching the breaking point. Furthermore, we have adapted the MCBJ method in AIMD to simulate shearing of the Sn-Cu interface. In these simulations, as opposed to moving Sn atoms away from the Cu atoms perpendicularly to the interface, we are sliding the Sn atoms laterally across the interface relative to the Cu atoms. The deposited Sn layer remains strongly bonded to the Cu surface, with most of the shearing occurring inside the bulk Sn region. The first principles nature of the methods employed makes them highly transferable and applicable to any chemical composition. These atomistic simulations provide valuable insights that can be used to design stronger solder joints based on physical understanding.