5. Dynamic Mesh Adaptation for Simulation of Electromigration

Implementation of copper and low-$\kappa$ materials as major components of interconnect structures have resulted in the necessity to create new design rules to ensure chip immunity to electromigration induced failures. This practical demand causes an enormous interest in understanding the fundamental reliability properties of interconnect copper metalization.

Modeling the micro-mechanics of electromigration-caused void evolution is a long-standing scientific problem. It began with sharp interface models requiring explicit finite element tracking of the void surfaces during the course of evolution. Later, prompted by the complexity of void surfaces, diffuse interface models have been introduced [83]. Diffuse interface models circumvent computationally costly surface tracking by application of a smooth order parameter field for representation of the void structures. We solve the diffuse interface model governing equation with a finite element scheme coupled with a powerful mesh adaptation algorithm [84]. The robustness of the developed finite element approach with respect to the underlying mesh structure enables the efficient simulation of the damage induced by electromigration in complex interconnect geometries.