Effects of the Ehrlich–Schwoebel potential barrier on the Wolf–Villain model simulations for thin film growth

Abstract

Wolf-Villain (WV) model is a simple model used to study ideal molecular beam epitaxy (MBE) growth by using computer simulations. In this model, an adatom diffuses instantaneously within a finite diffusion length to maximize its coordination number. We study statistical properties of thin films grown by this model. The morphology of the WV model is found to be kinetically rough with a downhill particle diffusion current. In real MBE growth, however, there are additional factors such as the existence of a potential barrier that is known as the Ehrlich-Schwoebel (ES) barrier. The ES barrier is an additional barrier for an adatom that diffuses over a step edge from the upper to a lower terrace which is known to induce an uphill particle current. We found that with the addition of the ES barrier, the WV-ES model morphology is rough with mound formation on the surface when the barrier is strong enough. To confirm these results, the correlation function is also studied. We find no oscillation in the correlation function in the WV model. For the WV-ES model, the correlation function oscillates. These results confirm that a strong enough ES barrier can cause mound formation on the WV surface in our study.

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

“…A central contribution of this work is to show that a very simple mechanism neglected in previous analysis, in which particles also diffuse in the direction perpendicular to the substrate, is able to change markedly the surface morphology of basic growth models with limited mobility. Our results are qualitatively very similar to those obtained when an explicit step barrier, with a smaller probability to move downward, is considered [36]. Particularly, asymptotic mound morphology has been reported for limited mobility models in d = 2 without barriers with the application of the noise reduction method [38].…”

“…A variation of the CV model with limited mobility has been considered [33,34] and many features of the original model have been reproduced with this simplified version [35]. 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.…”

Kinetic modelling of epitaxial film growth with up- and downward step barriers

“…For the symmetric barrier model, the origin of the kinetic roughening is similar but the imbalance between downward and upward currents is additionally because of particles in ascending steps (bonded by definition) are, in an average, less diffusing than those in descending ones. Notice that symmetric barriers hinder mound formation in the WV model in d = 1 + 1 dimensions [27]. Mound formation was observed in the WV model in d = 2 + 1 without step-barrier, but the artefact of noise reduction was necessary to overcome the very slow crossover to the asymptotic limit [22].…”

“…However, the barrier in monolayers was implemented as usual and the model is not fully symmetric in to relation down-and upward step diffusion. Barriers in ascending steps were also considered in the limited mobility model of Wolf-Villain [27], where probabilities of moving to lower or upper terraces after a deposition step were introduced. Mound formation is obtained when the probability of upward diffusion is larger than downward diffusion.…”

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

“…The mounding instability through SED current did not emerge spontaneously, and was observed only after the use of the so-called "noise reduction technique" to suppress the deposition and nucleation noise. [24][25][26] It is unclear that SED mechanism, initially studied in a simple cubic system, always occurs, and always leads to mounding structure in all crystalline lattice structures. Do other topological currents exist in other structurally different crystalline lattices?…”