Assessment of current density singularity in electromigration of solder bumps

This paper investigates the current density singularity in electromigration of solder bumps. A theoretical analysis is performed on a homogenous wedge with arbitrary apex angle, 2(π-θ₀), when the current flow passes through. A potential difference is applied at a distance far away from the tip of the wedge. It is found that current density singularity exists at the tip of the wedges when the angles θ₀ <; 90°. The acute angles represent the corner configuration of the actual solder bump and the interconnect. The current crowding in bumps is a result of singularity exhibited at such corners. Finite element results confirm that the maximum current density has strong dependence on mesh size. To eliminate the singularity effect, a volume-averaged current density approach, over a crescent shape where the maximum current density occurs, is suggested. Such an averaged value represents the concentration of current flow in the region, and is also insensitive to mesh sizes over a large range of crescent thickness.