A phase field computational procedure for electromigration with specified contact angle and diffusional anisotropy

Abstract

Electromigration in electrical interconnects with high current density causes voids to form and grow near the cathode. These voids can possibly grow large enough to cause open circuit failure. The simulation of electromigration void nucleation and growth is challenging because of the complex interaction of electrical, thermal and mechanical fields that lead to the observed voids. In this paper, a phase-field approach is developed to study void growth due to electromigration taking into account diffusional anisotropy and specified contact angle. Consideration of anisotropy and contact angle is critical in applications including electronic assemblies that most commonly use Sn-based solder interconnects. In such systems, Sn exhibits significant anisotropy in its self-diffusivity, which assumes importance in small solder joints that are known to contain only a few grains. Furthermore, the contact angle at the void-bonding pad-solder triple junction is known to influence the void size and shape. To the best of the authors’ knowledge, only anisotropy in surface diffusivity has been considered in phase-field electromigration literature, whereas the contact angle at a triple junction has not been considered. The developed phase-field model incorporates effects of both contact angle and anisotropy in self-diffusivity. The model is used to simulate systems with different contact angles and dominant directions of diffusion. It is observed that diffusional anisotropy plays a more dominant role in failure, while the contact angle dictates evolution of the shape of voids.