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Thin-film growth by random deposition of rod-like particles on a square lattice

Monte Carlo simulations are employed to investigate the surface growth generated by deposition of particles of different sizes on a substrate, in one and two dimensions. The particles have a linear form, and occupy an integer number of cells of the lattice. The results of our simulations have shown that the roughness evolves in time following three different behaviors. The roughness in the initial times behaves as in the random deposition model, with an exponent $β_{1} \approx 1/2$. At intermediate times, the surface roughness depends on the system dimensionality and, finally, at long times, it enters into the saturation regime, which is described by the roughness exponent $α$. The scaling exponents of the model are the same as those predicted by the Villain-Lai-Das Sarma equation for deposition in one dimension. For the deposition in two dimensions, we show that the interface width in the second regime presents an unusual behavior, described by a growing exponent $β_{2}$, which depends on the size of the particles added to the substrate. If the linear size of the particle is two, we found that $β_{2}<β_{1}$, otherwise it is $β_{2}>β_{1}$, for all particles sizes larger than three. While in one dimension the scaling exponents are the same as those predicted by the Villain-Lai-Das Sarma equation, in two dimensions, the growth exponents are nonuniversal.