Stochastic Model for Surface Erosion Via
Ion-Sputtering
Surfaces eroded by ion-sputtering are sometimes observed to develop
morphologies which are either ripple (periodic), or rough
(non-periodic). We introduce a discrete stochastic model that allows us
to interpret these experimental observations within a unified
framework. We find that a periodic ripple morphology characterizes the
initial stages of the evolution, whereas the surface displays
self-affine scaling in the later time regime. Further, we argue that
the stochastic continuum equation describing the surface height is a
noisy version of the Kuramoto-Sivashinsky equation
[R. Cuerno, H. A. Makse, S. Tomassone, S. Harrington,
and H. E. Stanley,
Stochastic Model for Surface Erosion via
Ion-Sputtering: Dynamical Evolution from Ripple Morphology to
Rough Morphology,
Phys. Rev. Lett. 75, 4464-4476
(1995);
K. L. Lauritsen, R. Cuerno, and H. A. Makse,
Noisy
Kuramoto-Sivashinsky Equation for an Erosion Model,
Phys. Rev. E 54, 3577-3580 (1996)].
From initial ripples morphology to a rough morphology
The experimental development of a ripple structure
is well understood in terms of the unstable linear theory
of ion-sputtering describing the early stages of the time evolution of
the model presented here. Moreover, the model predicts that in the late
regime the large slopes generated by the unstable growth trigger the
action of nonlinearities which stabilize the surface. The nonlinearity
we find is of the KPZ type, consistent with the experimental observation
of KPZ scaling reported by Eklund et al.
To confirm the above picture, it would be of interest to
study experimentally if both regimes do effectively take place in the
time evolution of the same physical system.
Collaborators
R. Cuerno (Carlos III, Madrid),
K. Lauritsen (NBI),
S. Tomassone (Northeastern University) and
H. E. Stanley (BU).
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