Modeling Multi-grain Multi-hole Thin Solid State Films

The modeling of the dynamics of thin solid state films dates back to a series of seminal papers by W.W. Mullins, published in the years 1956–1958. In those years, there was much interest in the stability of bulk bi- and poly-crystalline materials, which can be strongly affected by the dynamics of their exterior surface features. In recent years the focus has been extended to include many new materials, which can enable the manufacture of strong and thin films; however, much of the basic underlying physics remains the same. Thus it is not unreasonable in considering thin film stability, to return and study the implications of the original modeling equations as developed by Mullins, namely surface diffusion and mean curvature motion. We follow this approach, focusing on surface diffusion and mean curvature motions, while neglecting possible anisotropy and elastic effects. We show that even within this somewhat limited framework, it is possible to obtain new criteria for the stability of holes in thin films, based on a new notion of an effective radius. This note summarizes results appearing in [7, 18, 19]. Many open questions remain.