(53b) Atomistic Modeling of Tin Surface and Grain Boundary Diffusion

As analysis tools in computational materials science develop, transport properties at the atomistic level play an increasingly important role in the study of a material's behavior at large scales. Quantitative transport data explaining diffusion, cracking, or crystal growth, often difficult to study experimentally, can be had with relative ease using a molecular simulation package and a few workstation grade computers. The field of electronics packaging can benefit from this kind of analysis, specifically in the study of electromigration in thin films and SnAgCu (SAC) alloy solder joints. Surface and grain boundaries in these structures provide fast diffusion paths for tin solute atoms, alloyed compounds, and vacancies. In addition, all are given a strong diffusive force from the high electrical current's inherent electron wind. Modeling these specific processes and quantifying the diffusivity of tin atoms and vacancies, both on surfaces and in grain boundaries, will aid in the prediction of failure rates of these types of joints?key parameters for the realization of nano-electronics.

Two methods of molecular simulation are used to compute the diffusivity of tin atoms in our systems. First, common molecular dynamics simulations are used to determine an overall atomic diffusivity in varying angles of symmetric tilt grain boundaries. Second, we use a potential energy surface walker, called the Dimer method, to seek out diffusion mechanism saddle points in a molecular statics style simulation. From the Dimer method results, we use harmonic transition state theory to compute tracer diffusivities of tin on our surface and in grain boundary systems. These methods are compared and quantitative values for activation energies and diffusion coefficients are presented and compared to experiment.