Modeling reaction front propagation of intermetallic compounds by using isogeometric analysis

This paper is concerned with the modeling of InterMetallic Compound (IMC) formation in tin (Sn) based solders on copper (Cu) interconnects. IMC formation is the result of diffusion and chemical reaction processes. There is a change in shape and volume between the products and reactants, and, consequently, in addition to temperature it is driven and impeded by the resulting residual stresses and strains. Strictly speaking IMC formation is based on multi-component diffusion in solids, including vacancies as a migrating species leading to Kirkendall voiding, and in addition to mechanical stress it can be enhanced by electric currents. In order to get a first cut at the problem we developed a general numerical procedure, based on isogeometric analysis in combination with FE-modeling, for solving boundary value problems for elastic solids undergoing chemical transformations and specialized it to IMC formation. The kinetic equation for the reaction front propagation is based on an expression for the chemical affinity tensor, which allows us to study the influence of stresses and strains on the chemical reaction rate and the normal component of the reaction front velocity. Isogeometric analysis is highly accurate when finding the normal to the reaction front, and it is applied by using the commercial FE code Abaqus for a numerical simulation of the front propagation. In order to test and demonstrate the capabilities of the developed procedures an idealized problem is considered: The propagation along a straight front is examined and compared to analytical results.