Growth instability due to lattice-induced topological currents in limited-mobility epitaxial growth models

Abstract

The energetically driven Ehrlich-Schwoebel barrier had been generally accepted as the primary cause of the growth instability in the form of quasiregular moundlike structures observed on the surface of thin film grown via molecular-beam epitaxy (MBE) technique. Recently the second mechanism of mound formation was proposed in terms of a topologically induced flux of particles originating from the line tension of the step edges which form the contour lines around a mound. Through large-scale simulations of MBE growth on a variety of crystalline lattice planes using limited-mobility, solid-on-solid models introduced by Wolf-Villain and Das Sarma-Tamborenea in 2+1 dimensions, we show that there exists a topological uphill particle current with strong dependence on specific lattice crystalline structure. Without any energetically induced barriers, our simulations produce spectacular mounds very similar, in some cases, to what have been observed in many recent MBE experiments. On a lattice where these currents cease to exist, the surface appears to be scale invariant, statistically rough as predicted by the conventional continuum growth equation.

Modeling of nonequilibrium surface growth by a limited-mobility model with distributed diffusion length

“…Growth instabilities can induce the formation of mound-like patterns and it is well accepted that the original DT model displays quasiregular mound formation [62][63][64][65][66][67]84]. To investigate how diffusional fluctuations alter this characteristic feature, we show exemplary interface profiles for two diffusion lengths l and different values of σ 2 in Fig.…”

Effects of a kinetic barrier on limited-mobility interface growth models

“…Such a growth instability has been mainly attributed to the presence of Ehrlich-Schwoebel (ES) step barriers [12,13] that reduce the rate with which atoms move downwardly on the edges of terraces leading to net uphill flows. Growth instabilities can also emerge from topologically induced uphill currents which depend on the crystalline structure [14] or from fast diffusion on terrace edges [15,16] among other mechanisms [1,2]. The existence of ES barriers is supported by molecular dynamic simulations [17].…”

“…Effects of a step barrier were investigated in both WV [36] and DT [37] models introducing two additional probabilities for downward and upward interlayer diffusion with the former larger than the latter, and mound formation was observed in both models. WV and DT models without step barrier were investigated in several lattices [14,38] and it was found that the WV model can present topologically induced mound morphologies on some lattices but not in others while no clear evidence for three-dimensional structures was observed for DT. In one-dimension, it is widely accepted that both DT and WV models asymptotically produce self-affine surfaces belonging to nonlinear MBE [32] and Edwards-Wilkinson [39] universality classes, respectively.…”

Transitions between epitaxial growth regimes: A (1+1)-dimensional kinetic Monte Carlo study

“…There has been a substantial amount of effort focused on the study of submonolayer deposition, island formation and growth, and island-island coalescence [5,18,19,20,21,22], while for multilayer growth several questions remain open [23,24,25,26,27]. Typically, either a detailed approach is considered, which attempts to make no assumptions, or as few as possible [9,28,29,30,31,32,33], or simple models are developed, where mechanisms are restricted to the most relevant ones [34,35,36,37,38,39,40,41]. In this work, we adopt the latter approach, which allows us to better understand the relevance of each process.…”