Submonolayer epitaxial growth with long-range (Lévy) diffusion

Abstract

The effects of long-range (L\'evy) diffusion in submonolayer epitaxial growth are studied via kinetic Monte Carlo simulations and rate equations. Such long-range diffusion may be relevant in the case of liquid-phase epitaxy and electrochemical deposition. Results for the scaling of the submonolayer island density and size distribution are presented as a function of the L\'evy distribution exponent $\ensuremath{\beta}$ and the ratio $D/F$ of the diffusion rate to the deposition rate. Both one- and two-dimensional L\'evy flights (corresponding to infinitely fast hops) and one- and two-dimensional L\'evy walks (corresponding to finite hopping velocity) are examined. Good agreement is found between theoretical predictions and simulations for the dependence of the island-density scaling exponent $\ensuremath{\chi}$ on the L\'evy exponent $\ensuremath{\beta}$ in both one and two dimensions.