We investigate a solid-on-solid model on two-dimensional substrates as a natural extension of the Wolf-Villain model for molecular-beam epitaxial growth [D. E. Wolf and J. Villain, Europhys. Lett. 13, 389 (1990)]. In this extended Wolf-Villain model, freshly landed atoms relax into the local energy minima calculated within a next-nearest-neighbor approximation. We calculate the surface width, the correlation function, and the averaged step height and show the surface morphologies. In the transient regime, the model can be described by the nonlinear continuum equation proposed by Lai and Das Sarma [Z. W. Lai and S. Das Sarma, Phys. Rev. Lett. 66, 2348 (1991)]. At relatively smaller lateral size ${\mathit{L}}_{\mathit{c}}$∼35 and earlier growth time ${\mathit{t}}_{\mathit{c}}$∼1800 than in the original model, it shows a crossover behavior to the Edwards-Wilkinson class, i.e., logarithmic kinetic roughening.

• Received 16 March 1995

DOI:https://doi.org/10.1103/PhysRevE.52.2424