A geometric model for coarsening during spiral-mode growth of thin films

We study the coarsening observed in spiral-mode growth of thin films. The high-temperature superconductor YBa2Cu3O7−δ provides a suitable model system. The density of spirals at the surface decreases as the film gets thicker. In other words, the grain size coarsens with distance from the substrate. We propose a simple mechanism for this coarsening, based on geometrical competition of spirals with different vertical growth rates. The consequences of this mechanism are developed both analytically and numerically in the limit where adatom attachment is controlled by surface diffusion. In particular, we show how the time-evolution of spiral density, film thickness, and surface roughness depend on the spiral growth rate statistics.