A phenomenological model of grain‐boundary diffusion and electromigration in thin‐film diffusion barriers for microelectronic device metallizations is developed by using the transmission line matrix method. Both diffusion and drift effects are included in the numerical analysis with a multidimensional variable mesh structure. Special attention is paid to the ‘‘vertical’’ electromigration effect and a comparison of the two‐dimensional (2D) and three‐dimensional (3D) simulation results. Two fundamental driving forces for impurity grain‐boundary diffusion, the concentration gradient across a diffusion barrier, and the current flow perpendicular to the deposited metal films can reinforce each other, leading to an enhanced impurity diffusion and a reduced barrier efficiency. Such material transport through the diffusion barrier is quantified with a 2D model of parallel planar grain boundaries and a 3D model of rectangular columnar microstructures. Concentration profiles along all directions are visualized in graphs for the cases with and without the electromigration driving force. Average atom penetration as a function of time and the underestimation by the 2D model are also illustrated.