Nonmonotonic roughness evolution in unstable growth

The roughness of vapor-deposited thin films can display a nonmonotonic depe ndence 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 fram ework of the continuum theory of unstable homoepitaxy. Using the spherical approximation of phase-ordering kinetics, the effect of nonlinearities and noise can be treated explicitly. The substrate roughness is characterized b y the dimensionless parameter Q=W-0/(k(0)2(a)), where W-0 denotes the rough ness amplitude, k(0) is the small-scale cutoff wave number of the roughness spectrum, and a is the lattice constant. Depending on Q, the diffusion len gth ID and the Ehrlich-Schwoebel length l(Es), five regimes are identified in which the position of the roughness minimum is determined by different p hysical mechanisms. The analytic estimates are compared by numerical simula tions of the full nonlinear evolution equation.