A phenomenological model for grain-boundary diffusion and electromigration in such barriers was developed. Both diffusional and drift effects were included in the numerical analysis of a multi-dimensional variable mesh structure. Especial attention was paid to the so-called vertical electromigration effect and to a comparison of the 2-dimensional and 3-dimensional simulation results. It was found that 2 fundamental driving forces for impurity grain-boundary diffusion (the concentration gradient across a diffusion barrier, and the current flow perpendicular to the deposited metal film) could reinforce each other. This then led to enhanced impurity diffusion and to a reduced barrier efficiency. Material transport through the diffusion barrier was quantified by using a 2-dimensional model of parallel planar grain boundaries and a 3-dimensional model of rectangular columnar microstructures. Concentration profiles in all of the directions were obtained for cases with and without an electromigration driving force. Average atom penetration as a function of time, and its underestimation by a 2-dimensional model, was revealed.

X.Gui, S.K.Dew, M.J.Brett: Journal of Vacuum Science and Technology B, 1995, 13[5], 2100-4