Linear theory of unstable growth on rough surfaces

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 of the substrate roughness, the terrace size l and the Ehrlich-Schwoebel length lES. If l≪l (weak step edge barriers) and l≪lml√l/l, then W(t) displays a minimum at a coverage θ(l/l), where the initial surface width is reduced by a factor l/lm. The role of deposition and diffusion noise is analyzed. The results are applied to recent experiments on the growth of InAs buffer layers [M.F. Gyure et al., Phys. Rev. Lett. 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. © 1999 American Physical Society.