CROSSOVER EFFECTS IN THE WOLF-VILLAIN MODEL OF EPITAXIAL-GROWTH IN 1+1 AND 2+1 DIMENSIONS

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(eff) almost-equal-to 0.37 to beta(eff) almost-equal-to 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 zeta(eff)c obtained from the height-height correlation functions in 1+1 dimensions (almost-equal-to 3/4) and 2+1 dimensions (almost-equal-to 2/3) cannot be simultaneously explained by any of the continuum equations proposed so far to describe epitaxial growth.