Morphology Evolution of Cobalt Thin Films on Al$_2$O$_3$ (110) Above the Roughening Transition: Formation of Gigantic Multilayered Islands

Co films, 4.0 nm thick, were grown on Al$_2$O$_3$ (110) at 315~$^\circ$C via molecular beam epitaxy. Their surfaces were imaged via atomic force microscopy while annealing at $T\geq 535$~$^\circ$C for several hours. The films exhibited a striking formation of multilayered islands that reach heights more than ten times larger than the initial film thickness. At the early stages of the annealing process ($t< 2 $~hr) the islands' height $h$ grows exponentially with time $t$, which is consistent with height instabilities of the film surface. For $t> 2$~hr, $h$ continues increasing at a slower rate with a power law $h \sim t^\gamma$ with $\gamma = 0.20-0.25$, whereas, interestingly, the base areas of the multilayer islands do not appreciably change with time. This behavior is independent of $T$ in the 535~$^o$C to 590~$^o$C range. These phenomena are discussed within an interface dynamics model incorporating both surface diffusion relaxation and de-wetting forces. The model is used to elucidate the physical origin of the observed island height growth in terms of strong up-hill surface currents caused by long range Casimir-like forces acting across the film.