Impact of anisotropic interactions on non-equilibrium cluster growth at surfaces

Abstract

Using event-driven kinetic Monte-Carlo simulations we investigate the early stage of non-equilibrium surface growth in a generic model with anisotropic interactions among the adsorbed particles. Specifically, we consider a two-dimensional lattice model of spherical particles where the interaction anisotropy is characterized by a control parameter $\eta$ measuring the ratio of interaction energy along the two lattice directions. The simplicity of the model allows us to study systematically the effect and interplay between $\eta$, the nearest-neighbor interaction energy $E_n$, and the flux rate $F$, on the shapes and the fractal dimension $D_f$ of clusters before coalescence. At finite particle flux $F$ we observe the emergence of rod-like and needle-shaped clusters whose aspect ratio $R$ depends on $\eta$, $E_n$ and $F$. In the regime of strong interaction anisotropy, the cluster aspect ratio shows power-law scaling as function of particle flux, $R\sim F^{-\alpha }$. Furthermore, the evolution of the cluster length and width also exhibit power-law scaling with universal growth exponents for all considered values of $F$. We identify a critical cluster length $L_c$ that marks a transition from one-dimensional to self-similar two-dimensional cluster growth. Moreover, we find that the cluster properties depend markedly on the critical cluster size $i^{\ast }$ of the isotropically interacting reference system ($\eta =1$).

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• Analytic self-similar solutions of the Kardar-Parisi-Zhang interface growing equation with various noise term