Crossover effects in the Wolf-Villain model of epitaxial growth in 1+1
and 2+1 dimensions
release_7at6e33gbjb6xli3kqhygzt4wa
by
Pavel Šmilauer,
Miroslav Kotrla
1994
Abstract
A simple model of epitaxial growth proposed by Wolf and Villain is
investigated using extensive computer simulations. We find an unexpectedly
complex crossover behavior of the original model in both 1+1 and 2+1
dimensions. A crossover from the effective growth exponent β_
eff≈0.37 to β_ eff≈0.33 is observed in 1+1
dimensions, whereas additional crossovers, which we believe are to the scaling
behavior of an Edwards--Wilkinson type, are observed in both 1+1 and 2+1
dimensions. Anomalous scaling due to power--law growth of the average step
height is found in 1+1 D, and also at short time and length scales in 2+1 D.
The roughness exponents ζ_ eff^ c obtained from the
height--height correlation functions in 1+1 D (≈3/4) and 2+1 D
(≈2/3) cannot be simultaneously explained by any of the continuum
equations proposed so far to describe epitaxial growth.
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