Coalescence and percolation in thin metal films

Abstract

Metals thermally evaporated onto warm insulating substrates evolve to the thin-film state via the morphological sequence: compact islands, elongated islands, percolation, hole filling, and finally the thin-film state. The coverage at which the metal percolates (${\mathit{p}}_{\mathit{c}}$) is often considerably higher than that predicted by percolation models, such as inverse swiss cheese or lattice percolation. Using a simple continuum model, we show that high-${\mathit{p}}_{\mathit{c}}$’s arise naturally in thin films that exhibit a crossover from full coalescence of islands at early stages of growth to partial coalescence at later stages. In this interrupted-coalescence model, full coalescence of islands occurs up to a critical island radius ${\mathit{R}}_{\mathit{c}}$, after which islands overlap, but do not fully coalesce. We present the morphology of films and the critical area coverages generated by this model.