Mathematical Analysis of Surface Diffusivity Variation on Surface Morphology and Electromigration

楊志信(Jyh-Shinn Yang) ； 黃暉理(Huei-Li Huang)

《Chinese Journal of Physics》 24卷3期 (1986/10) Pp. 166-182

並列摘要

We present a thorough mathematical analysis of capillarity effect in the presence of surface diffusivity variation and using this as a starting basis to describe time evolution of the surface profile generated by 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. Electromigration-induced surface morphological changes can be understood in terms of combined action of the following effects: (1) The dominant contribution engendering GB disfiguration is the nonvanishing surface flux divergence with the GB acting either as a source or sink of the fluxes. (2) Dynamic balance between surface tension and GB tension incorporation with the surface diffusivity variation across the GB generates further disparity in the GB profile changes. (3) Four additional terms originate from interplay between capillarity effect and electromigration-induced surface diffusion act to further aggravate the surface profile changes, causing surface undulation and so on, if the sample received heat treatment prior to power stressing.