Does current crowding induce vacancy concentration singularity in electromigration?

摘要

Mathematical model of electromigration in terms of vacancy concentration is studied analytically and numerically in this paper with the combined effect of vacancy gradient (Fickian term) and electric flow. A 2-D, L-shaped, homogeneous material model with perfect blocking boundary condition (J = 0) is chosen as the problem of interest. Dandu and Fan have shown that current density singularity exists at the tip of the wedges when the angle θ° <90° [13]. This study investigates the effect of current density singularity at the tip of the wedges towards the vacancy concentration at the same location. The results of the study, both analytically and numerically, show that the location of maximum vacancy concentration occurs at cathode side, but not at the location of current density singularity.