Square lattice gas models for heteroepitaxial growth are studied by means of kinetic Monte Carlo simulations, in order to find a possible origin of anisotropic island shape observed in growth experiments of long organic molecules. When deposited molecules form clusters irreversibly at their encounter during surface diffusion, islands grow in a ramified dendritic shape, similar to DLA. Introduction of molecular detachment from edges makes islands compact with smooth edges. Tilting of adsorbed long molecules or steps in a vicinal substrate may induce orientation-dependence in the detachment rate of edge molecules from an island. In simulations with orientation-dependent detachment rates, a clear anisotropy in an island shape is observed. Shape anisotropy on a vicinal substrate is enhanced as steps get dense, in agreement to the experimental observation.

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