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 ͑MBE͒, for simple nonequilibrium limited mobility solid-onsolid growth models, such as the Family model, the Das Sarma-Tamborenea model, the Wolf-Villain ͑WV͒ model, the larger-curvature ͑LC͒ model, and other related models. We find that (dϭ2ϩ1)-dimensional surface growth in several noise reduced models ͑most notably the WV and LC models͒ 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 literature͒ 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 barrier͒ 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 (dϭ2ϩ1)-dimensional, or higher dimensional, growth, but not in (dϭ1 ϩ1)-dimensional growth because no cluster diffusion around a closed surface loop is possible in ''onedimensional'' surfaces͔, which is likely to be quite generic in real MBE-type surface growth. Our extensive numerical simulations produce mounded ͑and slope-selected͒ surface growth morphologies which are strikingly visually similar to many recently reported experimental MBE growth morphologies.

Mound morphology of the 2+1 -dimensional Wolf–Villain model caused by the step-edge diffusion effect

“…Mound morphologies are also found [18][19][20][21][22][23][24][25] in several local (no non-local effects exist) non-equilibrium growth models that incorporate no ES barrier. In these models, such as the well-known Wolf-Villain (WV) model [26] (in 2 + 1-dimensions)…”

“…In many common modern deposition techniques, however, many mechanisms can play an important role in defining the surface morphology during growth. Some mechanisms give rise to a mound structure [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] that cannot be described within the context of self-affinity. The origin of this phenomenon is ascribed to a growth instability caused by these mechanisms.…”

“…This mechanism is called step-edge diffusion (SED) in Ref. [18]. The SED generates a local uphill surface diffusion current during the deposition process, leading to a morphological instability, i.e., the starting substrate is no longer stable after growth.…”

“…In Ref. [18], the mound surface is studied using noise reduction factor m = 5, and n = 0.24 is obtained for the 2 + 1-dimensional WV model. What is the situation when different values of m are used, or what is the situation when we change the strength of SED?…”

Self-assembly of InAs quantum dots on GaAs(001) by molecular beam epitaxy

“…The layer-by-layer growth mode can usually be achieved by controlling the experimental parameters such as the temperature T and incident flux F . If some intrinsic physical mechanism becomes dominant over the effect of T and F so that the layer-by-layer growth mode becomes out of control, a growth instability is said to occur; this generally results in 3D growth features or morphologies at the nanoscale [178]. This subsection focuses on the growth instability induced by the additional energy barrier an adatom meets when it steps down a step edge on the growth surface.…”