Step Bunches, Nanowires and Other Vicinal “Creatures”—Ehrlich–Schwoebel Effect by Cellular Automata

Abstract

Different patterns can be created on the surface of growing crystals, among which the step bunches and/or step meanders are two of the most studied. The Ehrlich–Schwoebel effect at the surface steps is considered one of the “usual suspects” of such patterning. A direct step barrier is when it is easier to attach a particle to the step from the lower terrace than from the upper terrace. Thus, during the process of crystal growth leads to the formation of meanders, while an inverse barrier leads to step bunching. Based on our vicinal Cellular Automaton model, but this time in (2 + 1)D, we show that the combination of a direct and inverse step barrier and the proper selection of the potential of the well between them leads to the formation of bunched step structures. Following this is the formation of anti-bands. In addition, changing the height of the direct step barrier leads to the growth of nanocolumns, nanowires, and nanopyramids or meanders, in the same system.

Modelling Crystallization: When the Normal Growth Velocity Depends on the Supersaturation

“…. We use this to exclude the crystal size from (10): (11) and, performing the differentiation in the numerator of the left hand side of (11), to arrive at:…”

“…The process of kink generation could be rather complex one, especially during the growth of three-dimensional crystals since the attachment of a single crystallizing unit to a smooth on the atomic scale crystal plane does not result in kink. This is why the various realizations of the so called epitaxy employ as substrates ordered arrays of steps (and kinks on them) -the vicinal crystal surfaces, see for further discussion [9,10] and the references therein.…”

Theoretical aspects of the growth of a non-Kossel crystal from vapours: the role of advacancies

“…[34][35][36] Modelling soware has also seen development in recent years. Crystal growth, considering surface phenomena, such as surface diffusion, reactions, and defects (dislocations), is easy to model using molecular dynamics, 37 Monte Carlo, 38 cellular automata 23 and other methods, even on a personal computer, though with…”

“…During the synthesis of the latter, the same problems arise as are observed in the heteroepitaxy of classical semiconductors, which are already solved for single-component systems. Many of these problems are well-described and analysed, including spiral growth, 21,22 step-bunching, 23 nucleation, 24 growth of nanowires, 25 step–step interaction, 26 impact of stress 27–29 and impurities. 30 However, although the single-component analytical models describe multicomponent systems well in certain cases, 31 it is obvious that the latter demonstrate some peculiarities and effects caused by the presence of several components.…”

“…34–36 Modelling software has also seen development in recent years. Crystal growth, considering surface phenomena, such as surface diffusion, reactions, and defects (dislocations), is easy to model using molecular dynamics, 37 Monte Carlo, 38 cellular automata 23 and other methods, even on a personal computer, though with some limitations. 39 Thus, we are gradually obtaining new instruments to analyse atomistic and kinetic phenomena in multicomponent systems and compare them with the theory.…”