Kinetic roughening of the Kossel (100) surface: comparison of classical criteria with Monte Carlo results
vanVeenendaal-E; vanHoof-PJCM; vanSuchtelen-J; vanEnckevort-WJP; Bennema-P
SURFACE-SCIENCE. NOV 8 1998; 417 (1) : 121-138.
Abstract:
Kinetic roughening is not a phase transition and, as such, it lacks an exact definition. Many criteria are used to mark the onset of kinetic
roughening. Criteria stemming from the classical two-dimensional nucleation theory are widely used. On the other hand, experimentalists observe a
transition from flat to rounded crystal facets at certain driving forces. And measuring the growth rate as a function of driving force, a change from
exponential to linear growth kinetics is frequently found. It is assumed that these experimental phenomena coincide with the onset of kinetic
roughening. These experimental criteria, three classical criteria for kinetic roughening and statistical mechanical criteria based on the interface width
and the surface roughness, are compared with each other by means of Monte Carlo simulations on a Kossel (100) SOS model. Surface diffusion is
neglected, and only attachment/detachment kinetics is considered. The change from flat to rounded facets with increasing driving force turns out to
be quite gradual. Nevertheless, this experimental criterion is made explicit by defining a critical driving force for which the curvature of a facet
becomes visible by optical microscopy. The conditions for an experiment to detect kinetic roughening using this criterion are described. The different
criteria for kinetic roughening yield different values for the critical driving force, although most of the criteria studied show a similar, almost linear,
dependence of the critical driving force on the nearest neighbor bond strength. This again indicates that kinetic roughening is diffuse in nature, and
shows that in discussions on kinetic roughening it is imperative to mention the criterion used. Some attention is also paid to the two-dimensional
anisotropy of step motion on a Kossel (100) surface. An anisotropic step velocity is found far below thermal roughening. The anisotropy is reduced
by increasing the driving force. (C) 1998 Elsevier Science B.V. All rights reserved.