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Scaling and Dynamic Stability of Model Vicinal Surfaces
journal contribution
posted on 2018-12-12, 00:00 authored by Filip Krzyżewski, Magdalena Załuska-Kotur, Anna Krasteva, Hristina Popova, Vesselin TonchevWe
propose an integrated modeling approach to the fundamental problem
of vicinal crystal surfaces destabilized by step-down (SD) and step-up
(SU) currents with focus on both the initial and the intermediate
stages of the process. We reproduce and analyze quantitatively the
step bunching (SB) instability, caused by the two opposite drift directions
in the two situations of step motion mediating sublimation and growth.
For this reason we develop further our atomistic scale model (vicCA)
of vicinal crystal growth (Gr) destabilized by SD drift of the adatoms
in order to account for also the vicinal crystal sublimation (Sbl)
and the SU drift of the adatoms as an alternative mode of destabilization.
For each of the four possible casesGr + SD, Gr + SU, Sbl +
SD, Sbl + SU, we find a self-similar solutionthe time-scaling
of the number of steps in the bunch N, N=2T/3, where T is the time,
rescaled with a combination of model parameters. In order to study
systematically the emergence of the instability, we use N further as a measure and probe the model’s stability against
SB on a dense grid of points in the parameter space. Stability diagrams
are obtained, based on simulations running to fixed moderate rescaled
times and with small-size systems. We confirm the value of the numerical
prefactor in the time scaling of N, 2/3 by results obtained
from systems of ordinary
differential equations for the step velocity that contain, in contrast
to vicCA, step–step repulsions. This last part of our study
provides also the possibility to distinguish between diffusion-limited
and kinetic-limited versions of the step bunching phenomenon.
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Keywords
bunch NSD driftModel Vicinal SurfacesSU driftsmall-size systemsDynamic StabilitySblkinetic-limited versionsstep velocitySBmodel parametersuse Ndrift directionsvicinal crystal sublimationStability diagramsalternative modestep motionvicinal crystal growthrescaled timesvicinal crystal surfaces destabilizedatomistic scale modelmodeling approachparameter space