Anticoarsening and complex dynamics of step bunches on vicinal surfaces during sublimation

Abstract

A sublimating vicinal crystal surface can undergo a step bunching instability when the attachment-detachment kinetics is asymmetric, in the sense of a normal Ehrlich-Schwoebel effect. Here we investigate this instability in a model that takes into account the subtle interplay between sublimation and step-step interactions, which breaks the volume-conserving character of the dynamics assumed in previous work. On the basis of a systematically derived continuum equation for the surface profile, we argue that the non-conservative terms pose a limitation on the size of emerging step bunches. This conclusion is supported by extensive simulations of the discrete step dynamics, which show breakup of large bunches into smaller ones as well as arrested coarsening and periodic oscillations between states with different numbers of bunches.

Step bunching process induced by the flow of steps at the sublimated crystal surface

“…In most analytical models step movement factor is neglected 8,10-15 . However as it was discussed lately particle advection is in fact comparable with electromigration or Schwoebel barrier asymmetry 10,[34][35][36] . Results of our Monte Carlo (MC) simulations show that the step bunching happens at the ideal stepped surface with Schwoebel barrier assumed to be zero and no external particle driving present.…”

Non-conserved dynamics of steps on vicinal surfaces during electromigration-induced step bunching

“…where R = n 0 eq ΩD s , s i = sinh(l i /l D ), c i = cosh(l i /l D ) and To simplify these expressions we use the approximation of attachment-detachment limited kinetics, l D ≫ l ± ≫ l [32,33]. After some calculations along the lines of [14] we arrive at…”

“…(11) and (12), respectively, on the continuum level. Following the procedure outlined in [14] for both models, we find that the continuum evolution equation takes the general form…”

“…In earlier work based on the continuum approach [9, 10] the non-conservative contributions were generally neglected because of the smallness of g [14], and it was therefore concluded that step bunching phenomena induced by electromigration and by the ES-effect belong to the same universality class [9,36]. However, it has subsequently be-come clear that small non-conservative terms may qualitatively change the nonlinear dynamics of surface steps [14], and the fact that these terms are of different form for the two instability mechanisms implies that their equivalence needs to be reexamined. In the following we therefore explore the nonlinear behavior of the electromigration model (11) using numerical simulations.…”

“…fined to belong to a bunch, if its distance to the next closest step of the bunch is smaller than l = 1. where an initial large step bunch splits into smaller bunches [14]. In fig.…”