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 ${\mathrm{\ensuremath{\beta}}}_{\mathrm{eff}}$\ensuremath{\approxeq}0.37 to ${\mathrm{\ensuremath{\beta}}}_{\mathrm{eff}}$\ensuremath{\approxeq}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 dimensions, and also at short time and length scales in 2+1 dimensions. The roughness exponents ${\mathrm{\ensuremath{\zeta}}}_{\mathrm{eff}}^{\mathit{c}}$ obtained from the height-height correlation functions in 1+1 dimensions (\ensuremath{\approxeq}3/4) and 2+1 dimensions (\ensuremath{\approxeq}2/3) cannot be simultaneously explained by any of the continuum equations proposed so far to describe epitaxial growth.