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In advanced semiconductor devices, most of the reliability issues in interconnect occurs at a very local scale, especially voiding phenomenon in copper lines induced by electromigration. Hence, a better understanding of mechanism governing electromigration is needed for developing more accurate lifetime models. In this paper, finite element simulations are carried out in that frame. Firstly, a model of vacancy migration is proposed. Thermal, stress and concentration gradients, and electrical current driven forces are considered. A realistic configuration of electromigration in a small segment of copper line is studied. The local vacancy accumulation at the cathode is observed. Distinct diffusion paths (lattice, grain boundary and interface) are implemented in a (111) oriented copper grains; it provide more realistic vacancy kinetics and it highlight large heterogeneity of concentration, which is responsible for void nucleation. Secondly, a model of void evolution, coupled with the transport vacancy model is implemented. To distinguish both metal and void phases, an order parameter field is introduced. The motion of the diffuse interface metal/void is solved by mean of the so-called level set method. The normal velocity of the front is directly computed thanks to the local vacancy concentration. Finally, the evolution of the line resistance in function of time and the void shape is output and analyzed. By facing simulation results with measurements and observations, a good agreement is revealed and efficiency of the implemented model is demonstrated.