Crossover effects in the Wolf-Villain model of epitaxial growth in 1+1 and 2+1 dimensions

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 ${\beta }_{\mathrm{eff}}\approx 0.37$ to ${\beta }_{\mathrm{eff}}\approx 0.33$ 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 ${\zeta }_{\mathrm{eff}}^{\mathrm{c}}$ obtained from the height--height correlation functions in 1+1~D ($\approx 3/4$) and 2+1~D ($\approx 2/3$) cannot be simultaneously explained by any of the continuum equations proposed so far to describe epitaxial growth.

arXiv comment11 pages, REVTeX 3.0, IC-DDV-93-006

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