On stress-affected kinetics of intermetallic compound growth in the presence of electromigration

This paper is concerned with the analytical modeling of an intermetallic compound formation in a eutectic tin solder joint on copper interconnects subjected to an electrical current. We propose a model that couples mechanical stresses, chemical reaction, diffusion, temperature, and electromigration. The kinetics of the chemical reaction fronts of the intermetallic phase formation is investigated based on the notion of the chemical affinity tensor within the small strain approximation. It allows incorporating the influence of stresses and strains on the chemical reaction rate and the normal component of the reaction front velocity in a rational manner. Electromigration is introduced into the model as an additional summand in the total flux of the diffusive constituents, which, in turn, also affects the reaction front velocity. In the considered model, the mechanical stresses arise due to the internal strains produced by the chemical transformation and by the thermal expansion. We formulate a model problem for planar reaction fronts. Within this model, the influence of stresses and electromigration on the reaction front kinetics is studied analytically. Based on the Mean-Time-To-Failure (MTTF) criteria, we calculate the critical thickness of the solder joint and estimate the amount of the accumulated vacancies. We introduce a dimensionless parameter, which characterizes the accumulation of vacancies due to electromigration enhanced diffusion. Finally, we discuss the coupling between the accumulated vacancies and Kirkendall void nucleation.