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 βeff~=0.37 to βeff~=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 ζceff obtained from the height-height correlation functions in 1+1 dimensions (~=3/4) and 2+1 dimensions (~=2/3) cannot be simultaneously explained by any of the continuum equations proposed so far to describe epitaxial growth.
- Publication:
-
Physical Review B
- Pub Date:
- February 1994
- DOI:
- 10.1103/PhysRevB.49.5769
- arXiv:
- arXiv:cond-mat/9401075
- Bibcode:
- 1994PhRvB..49.5769S
- Keywords:
-
- 68.55.-a;
- 68.35.Fx;
- 61.50.Cj;
- 64.60.Ht;
- Thin film structure and morphology;
- Diffusion;
- interface formation;
- Dynamic critical phenomena;
- Condensed Matter
- E-Print:
- 11 pages, REVTeX 3.0, IC-DDV-93-006