Unstable homoepitaxy on rough substrates is treated within a linear continuum theory. The time dependence of the surface width $W(t)$ is governed by three length scales: The characteristic scale $l_0$ of the substrate roughness, the terrace size $l_D$ and the Ehrlich-Schwoebel length $l_{ ES}$. If $l_{ ES} \ll l_D$ (weak step edge barriers) and $l_0 \ll l_m \sim l_D \sqrt{ l_D/l_{ ES}}$, then $W(t)$ displays a minimum at a coverage $\theta_{ \rm min} \sim (l_D/l_{ ES})^2$, where the initial surface width is reduced by a factor $l_0/l_m$. The r\^{ o}le of deposition and diffusion noise is analyzed. The results are applied to recent experiments on the growth of InAs buffer layers [M.F. Gyure { \em et al.}, Phys. Rev. Lett. { \bf 81}, 4931 (1998)]. The overall features of the observed roughness evolution are captured by the linear theory, but the detailed time dependence shows distinct deviations which suggest a significant influence of nonlinearities.
Categories: cond-mat.stat-mech cond-mat.mtrl-sci