The Spreading of a Void on a Facet During Electromigration

Abstract

ABSTRACTA void of cross sectional area A may spread perpendicular to the applied electric field Ea during electromigration because its leading surface develops a facet whose advance is limited by the supply of steps. If the facet is immobile (no step source) and the remaining surface is free to move, and if EaA is less than a threshold value, then the void assumes a stationary elongated shape dictated by a balance between capillarity and electric field. If EaA exceeds the threshold value, however, a balance is no longer possible, and the void spreads along the facet without arrest. If the facet has limited mobility, a balance is possible for all values of EaA, resulting in an elongated moving steady-state shape. The treatment simplifies the void shape as rectangular but preserves the essential features of capillarity and surface electromigration. We argue that the motion of a facet on a void along the outward normal requires defects (e.g. intersecting screw dislocations) that act as step sources since homogeneous nucleation of steps on the facet is expected to be negligible. Since voids in fine-line interconnects are often observed to be partially faceted, restricted void motion and resultant spreading which depend sensitively on crystallographic features, such as defect structure and grain orientation, may indeed limit the lifetime of fine-line interconnects in electronic devices.