Effect of diffusivity variation on capillarity and electromigration-induced surface and grain boundary diffusion

Abstract

The authors present a detailed analysis of capillarity effect in the presence of surface diffusivity variation and use this as a basis to describe evolution of the surface profiles generated by the electromigration-induced surface and grain boundary (GB) diffusion in a bicrystal film. Thermal GB grooving is asymmetric in the presence of diffusivity variation across the GB, but the extent of asymmetry is rather significant, less than 0.14% from the symmetric case, but up to 60% in diffusivity variation considered. Surface profiles of the electromigration-induced surface and GB diffusion for the samples with and without prior heat treatments have been carefully analysed and compared. The surface morphological changes can be understood in terms of the combined action of the following effects: (i) Dynamic balance between the surface tension and the GB tension incorporation with surface diffusivity variation across the GB generates further disparity in the profile changes. The effect lasts as long as the sample is under power stressing. (ii) The non-vanishing surface flux divergence with the GB acting either as a sink or source of the flux contributes dominantly to the GB disfiguration. (iii) Four additional transient terms originating from the capillarity effect aggravate the surface profile changes in the early stage of electromigration, causing surface undulation and so on, but gradually, the effect is overshadowed. Electromigration damages are mainly dictated by a quantity M which in turn is determined by the interplay between the GB flux and the surface diffusivity variation. With a negative M the profile starts with a sharp cusp which in time turns obtuse, then the minimum moves downstream into the grain. When M is positive, the GB profiles change rapidly with a small increase in M and in power stressing time. The profiles contract and protrude like a mound, and quickly rise above the x axis. Beyond this point, the shape of the surface morphology becomes relatively unchanged. Furthermore, when two or more GB diffusions are activated simultaneously, the superpositional effect of the GB fluxes may lead to trapezoidal growth and/or faceted voids, among other types of profiles. Finally, the problems with respect to further quantification of the quantity M are briefly discussed.