A theoretical analysis of the electromigration-induced void morphological evolution under high current density

In this work, analysis of electromigration-induced void morphological evolution in solder interconnects is performed based on mass diffusion theory. The analysis is conducted for three typical experimentally observed void shapes: circular, ellipse, and cardioid. Void morphological evolution is governed by the competition between the electric field and surface capillary force. In the developed model, both the electric field and capillary force on the void's surface are solved analytically. Based on the mass conversation principle, the normal velocity on the void surface during diffusion is obtained. The void morphological evolution behavior is investigated, and a physical model is developed to predict void collapse to a crack or to split into sub-voids under electric current. It is noted that when the electric current is being applied from the horizontal direction, a circular void may either move stably along the electric current direction or collapse to a finger shape, depending on the relative magnitude of the electric current and surface capillary force. However, the elliptical-shaped void will elongate along the electric current direction and finally collapse to the finger shape. On the other hand, the cardioid-shaped void could bifurcate into two sub-voids when the electric current reaches a critical value. The theoretical predictions agree well with the experimental observations.