Finite-element simulation of a phase-field model for inclusion electromigration in {110}-oriented single crystal metal interconnects due to interface diffusion anisotropy

Microdefects that exist in interconnect lines, such as inclusions, undergo a complex morphological evolution due to electromigration, which poses a challenge to the reliability of the integrated circuit. The investigation of the morphological evolution for inclusions driven by electromigration can be beneficial to improve the performance of the integrated circuit, and the applicability of the nanopattern. In this paper, a phase-field model based on the Cahn–Hilliard equations with anisotropic interface diffusion is established and the corresponding finite-element program is developed to study the evolution of the inclusion in the {110}-oriented single crystal of face-centered-cubic interconnects under electromigration. The bulk free energy density and the degenerate mobility applied in the present model are both constructed by the quartic double-well potential function. The validation of the program is verified by comparing the theoretical solution and the numerical solution. The effects of the misorientation, the anisotropic strength, and the conductivity ratio on the morphological evolution of inclusions are emphasized in detail. The results indicate that the morphological evolution is dependent on the misorientation, the conductivity ratio, and the anisotropic strength. And there are three evolution modes of inclusions: steady-state migration, oscillation, and unstable splitting. Small misorientation or conductivity ratio favors the steady-state migration, while a larger misorientation or conductivity ratio results in the process of merging and splitting. And the frequency of oscillation depends on the misorientation and the conductivity ratio. The migration velocity of the steady state is determined by both the conductivity ratio and the anisotropic strength.