Computational evaluation of optimal reservoir and sink lengths for threshold current density of electromigration damage considering void and hillock formation

Abstract

Reservoirs, extensions at the cathode-end, are constructed to extend the lifetime of integrated circuit (IC) lines in terms of electromigration (EM) damage. The threshold current density jth is the maximum current density that can be supported without causing EM damage due to the matching of the EM driving force and the back flow force, which is related to the atomic density gradient. In a previous study, we reported that reservoirs can affect jth. In this present study, the jth of straight Al polycrystalline lines covered with passivation was evaluated using a numerical simulation technique focusing not only on the formation of voids but also hillocks. The optimum reservoir/sink length based on ease of formation of voids and hillocks was discussed. The reservoir suppressed void formation but promoted hillock formation. Conversely, the sink suppressed hillock formation but promoted void formation. Therefore, when void and hillock formation occurred with equal case, it was considered that either no extension, or reservoir and sink of identical length were preferable for optimal threshold current density jth. Additionally, when considering the diffusivity of atoms depending on grain boundary direction, the absence of the extension represented the optimum condition because longer reservoirs/sinks produced smaller jth. When the ease of void and hillock formation changed, the critical atomic density of void and hillock formation shifted in response, causing the optimal extension length to change. It was found that the optimum extension length changed almost linearly based on the ease of void and hillock formation.