  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 be treated 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.
