Epitaxial mounding in limited-mobility models of surface growth

Abstract

We study, through large-scale stochastic simulations using the noise reduction technique, surface growth via vapor deposition, e.g., molecular beam epitaxy (MBE), for simple nonequilibrium limited mobility solid-on-solid growth models, such as the Family model, the Das Sarma--Tamborenea model, the Wolf-Villain (WV) model, the larger-curvature (LC) model, and other related models. We find that $(d=2+1)$-dimensional surface growth in several noise reduced models (most notably the WV and LC models) exhibits spectacular quasiregular mound formation with slope selection in their dynamical surface morphology in contrast to the standard statistically scale-invariant kinetically rough surface growth expected (and earlier reported in the literature) for such growth models. The mounding instability in these epitaxial growth models does not involve the Ehrlich-Schwoebel step-edge diffusion barrier. The mounded morphology in these growth models arises from the interplay between the line tension along step edges in the plane parallel to the average surface and the suppression of noise and island nucleation. The line tension tends to stabilize some of the step orientations that coincide with in-plane high-symmetry crystalline directions, and thus the mounds that are formed assume quasiregular structures. The noise reduction technique developed originally for Eden-type models can be used to control the stochastic noise and enhance diffusion along the step edge, which ultimately leads to the formation of quasiregular mounds during growth. We show that by increasing the diffusion surface length together with supression of nucleation and deposition noise, one can obtain a self-organization of the pyramids in quasiregular patterns. The mounding instability in these simple epitaxial growth models is closely related to the cluster-edge diffusion (as opposed to step-edge barrier) driven mounding in MBE growth, which has been recently discussed in the literature. The epitaxial mound formation studied here is a kinetic-topological instability [which can happen only in $(d=2+1)$-dimensional, or higher dimensional, growth, but not in $(d=1+1)$-dimensional growth because no cluster diffusion around a closed surface loop is possible in ``one-dimensional'' surfaces], which is likely to be quite generic in real MBE-type surface growth. Our extensive numerical simulations produce mounded (and slope-selected) surface growth morphologies which are strikingly visually similar to many recently reported experimental MBE growth morphologies.