Linear theory of unstable growth on rough surfaces

Unstable homoepitaxy on rough substrates is treated within a Linear continu um theory. The time dependence of the surface width W(t) is governed by thr ee 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) muc h less than l(D) (weak step edge barriers) and l(0) much less than l(m) sim ilar to l(D) root l(D)/l(ES), then W(t) displays a minimum at a coverage th eta(min) similar to (l(D)/l(ES))(2), where the initial surface width is red uced by a factor l(0)/l(m). The role of deposition and diffusion noise is a nalyzed. The results are applied to recent experiments on the growth of InA s buffer layers [M.F. Gyure et al, Phys. Rev. Lett. 81, 4931 (1998)]. The o verall features of the observed roughness evolution are captured by the lin ear theory, but the detailed time dependence shows distinct deviations whic h suggest a significant influence of nonlinearities. [S0163-1829(99)50748-0 ].