Submonolayer epitaxial growth with long-range (Levy) diffusion

The effects of long-range (Levy) diffusion in submonolayer epitaxial growth are studied via kinetic Monte Carlo simulations and rate equations. Such l ong-range diffusion may be relevant in the case of liquid-phase epitaxy and electrochemical deposition. Results for the scaling of the submonolayer is land density and size distribution are presented as a function of the Levy distribution exponent beta and the ratio D/F of the diffusion rate to the d eposition rate. Both one- and two-dimensional Levy flights (corresponding t o infinitely fast hops) and one- and two-dimensional Levy walks (correspond ing to finite hopping velocity) are examined. Good agreement is found betwe en theoretical predictions and simulations for the dependence of the island -density scaling exponent chi on the Levy exponent beta in both one and two dimensions. [S1063-651X(98)12012-3].