Atomistic modeling of the microstructure and transport properties of lead-free solder alloys
Sellers, Michael S.
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Damage mechanics models of lead-free solder joints in nanoelectronics continue to improve, and in doing so begin to utilize quantitative values describing processes at the atomic level, governing phenomena like electromigration and thermomigration. In particular, knowledge of the transport properties of specific microstructures helps continuum level models fully describe these larger-scale damage phenomena via multi-scale analysis. For example, diffusivities for different types of grain boundaries (fast diffusion paths for solvent and solute atoms, and vacancies), and a description of the boundary structure as a function of temperature, are critical in modeling solder microstructure evolution and, consequently, joint behavior under extreme temperature and electric current. Moreover, for damage that develops at larger length scales, surface energies and diffusivities play important roles in characterizing void stability and morphology. Unfortunately, experiments that investigate these kind of damage phenomena in the atomistic realm are often inconsistent or unable to directly quantify important parameters. One case is the particular transport and structural properties of grain boundaries in Sn (the main component in lead-free solder alloys) and their behavior in the presence of Ag and Cu impurities. This information is crucial in determining accurate diffusivity values for the common SnAgCu (SAC) type solder. Although an average grain boundary diffusivity has been reported for polycrystalline Sn in several works, the value for grain boundary width is estimated and specific diffusivities for boundaries known to occur in Sn have not been reported, to say nothing of solute effects on Sn diffusivity and grain boundary structure. Similarly, transport properties of Sn surfaces remain relatively uninvestigated as well. These gaps and inconsistencies in atomistic data must be remedied for micro- and macro-scale modeling to improve. As a complement to experimental work and possessing the ability to fill in the gaps, molecular simulation serves to reinforce experimental predictions and provide insight into the atomistic processes that govern studied phenomena. In the present body of work, we employ molecular statics and dynamics simulations in the characterization and computation of βSn surface energies and surface diffusivities, the determination of diffusivities and structural properties of specific βSn grain boundaries, and the investigation of Cu and Ag solute effects on βSn grain boundaries. In our study of βSn surfaces, energies for low number Miller index surfaces are computed and the (100) plane is found to have the lowest un-relaxed energy. We then find that two simple hopping mechanisms dominate adatom diffusion transitions on this surface. For each, we determine hopping rates of the adatom and compute its tracer diffusivity. Our work on grain boundaries investigates the self-diffusion properties and structure of several βSn symmetric tilt grain boundaries using molecular dynamics simulations. We find that larger diffusive widths are exhibited by higher excess potential energy grain boundaries. Diffusivities in the directions parallel to the interface plane are also computed and activation energies are found with the Arrhenius relation. These are shown to agree well with experimental data. Finally, we examine the effect that solute atoms of Ag and Cu have on the microstructure of βSn. Excess energies of the (101) symmetric tilt βSn grain boundary are computed as a function of solute concentration at the interface, and we show that Ag lowers the energy at a greater rate than Cu. We also quantify segregation enthalpies and critical solute concentrations (where the excess energy of the boundary is reduced to zero). The effect of solute type on shear stress is also examined, and we show that solute has a strong effect on the stabilization of higher energy grain boundaries under shear stress. We then look at the self-diffusivity of Sn in the (101) symmetric tilt βSn grain boundary and show that adding both Ag or Cu decrease the grain boundary self-diffusivity of Sn as solute amount in the interface increases. Effects of larger concentrations of Cu in particular are also investigated.