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

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 $i^{*}$ of the isotropically interacting reference system ($\eta = 1$).