Finite element simulation of the evolution process of inclusions in interconnects due to stress-induced interface migration

Based on the weak statement of microstructure evolution, we develop a finite-element method to simulate the evolution behavior of solid-solid interface due to stress-induced interface migration. The numerical calculation process is introduced in detail. The agreement between the numerical solution of the undulating surface and the analytical solutions verifies the effectiveness of the numerical method. The results indicate that the inclusion evolution in interconnects is sensitive not only to the ratio of the Young's modulus between the inclusion and the matrix, alpha, but also to its initial aspect ratio, beta, the applied stress, (sigma) over tilde, and the line width, (h) over tilde, and these parameters have corresponding critical values. When (sigma) over tilde > (sigma) over tilde (c),beta > beta(c) or (h) over tilde < <(h)over tilde>(c) the inclusion grows along the long axis, while when (sigma) over tilde < <(sigma)over tilde>(c), beta < beta(c) or <(h)over tilde> > (h) over tilde (c) the inclusion shrinks and tends to be round. The increase of the aspect ratio or the applied stress accelerates the inclusion growth but hinders the inclusion shrinkage. The increase of the line width can hinder the inclusion growth and accelerate the inclusion shrinkage. When (h) over tilde > 50, the effect of line width on beta(c) and (sigma) over tilde (c) can be ignored.