Claudio Castellano
Universita' di Roma I
Nonmonotonic roughness evolution in unstable growth
Autori: Claudio Castellano and Joachim Krug
The roughness of vapor-deposited thin films can display a nonmonotonic
dependence on film thickness, if the smoothening of the small-scale features
of the substrate dominates over growth-induced roughening in the early
stage of evolution. We present a detailed analysis of this phenomenon in
the framework of the continuum theory of unstable homoepitaxy. Using the
spherical approximation of phase ordering kinetics, the effect of nonlinearities
and noise can betreated explicitly. The substrate roughness is characterized
by the dimensionless parameter $Q = W_0/(k_0 a^2)$, where $W_0$ denotes
the roughness amplitude, $k_0$ is the small scale cutoff wavenumber of
the roughness spectrum, and $a$ is the lattice constant. Depending on $Q$,
the diffusion length $l_D$ and the Ehrlich-Schwoebel length $l_{ES}$, five
regimes are identified in which the position of the roughness minimum is
determined by different physical mechanisms. The analytic estimates are
compared by numerical simulations of the full nonlinear evolution equation.