Investigation of the effect of current singularity on vacancy concentration in 2D coupled electromigration

In this thesis, electromigration driven vacancy transport equation is taken into consideration. Vacancy transport equation is formed by the divergence of the fluxes generated by two driving forces; electromigration and self-diffusion. First an asymptotic analysis of the electromigration problem in polar coordinates is done to address singularity issues and to examine the effect of current singularities on vacancy concentration. William's method for the analysis of singular stress fields is used for the asymptotic analysis. It is shown with the asymptotic analysis that current singularity has no effect in vacancy concentration in the electromigration-induced vacancy transport problem where perfect blocking boundary conditions are employed. Dirichlet boundary conditions on anode and cathode side boundaries, and Neumann boundary conditions on remaining boundaries are imposed.;Electromigration-induced vacancy transport equation is also analyzed numerically by using a coupled finite element model. Electromigration driving force is computed with information gathered from the solution of Laplacian electric conduction equation. Coupled equation system for electromigration problem is modeled by implementing weak form equations in Comsol Multiphysics software. Two electromigration problems are numerically investigated by using the same FE model; first one being rectangular shaped line, and the second one being L-shaped line. First problem is beneficial to test the accuracy of the implementation of the coupled vacancy transport equations into the software. The problem is 1D in nature due to the electric insulation and the constant cross sectional area property that its geometry possesses. Second problem shows current singularity due to the change in the cross sectional area, and this problem is also the main focus. The purpose of this problem is to assess whether the vacancy concentration singularity is induced by current singularity.;Both analytical and numerical solutions conclude that, current singularity with the consideration of perfect blocking boundary conditions and where vacancy transport is considered with only self-diffusion and electromigration driving forces does not induce vacancy singularity.;In conclusion, results are discussed and compared with experimental data in literature. According to the numerical and analytical solutions and the experimental data for the electromigration of metallic conductor lines under the effect of strong passivation layer, perfect blocking boundary condition, current singularities seen in the conductor does not induce vacancy singularity.