Coupling model of electromigration and experimental verification – Part I: Effect of atomic concentration gradient

This paper presented integrated electromigration (EM) studies through experiment, theory, and simulation. First, extensive EM tests were performed using Blech and standard wafer-level electromigration acceleration test (SWEAT)-like structures, which were fabricated on four-inch wafers. Second, a molecular dynamics (MD) simulation-based diffusion-induced strain was incorporated into the existing coupled theory. Third, one-dimensional (1D) governing equations in terms of atomic concentration for un-passivated and passivated configurations were derived for void formation and growth, using a modified Eshelby's solution to consider the effect of passivation. Fourth, a systematic approach was established, including theoretical formulations and experimental methods, to obtain key material properties, i.e., critical atomic concentration and diffusivity. We then determined the material's properties from a specific set of experimental data, using aluminium (Al) as a carrier for demonstration. These properties were then used to predict the time to failure and void growth under various conditions. The theoretical results agreed well with the experimental data. Moreover, we theoretically determined the critical threshold products of current density and conductor length for the un-passivated and passivated configurations, respectively. Both experiment and theory showed that, in the absence of mechanical stress in un-passivated configurations, the atomic self-diffusion, which was opposite to electron wind, was significant in resisting EM development. However, when mechanical stress was present, such as in passivated configurations, stress migration played a dominant role in resisting EM development. Our numerical results showed that the current density exponent n in Black's law remained as 2 in the range of the current density greater than 0.2 MA/cm² and rapidly approached infinity at a low level of current density.