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

TL;DR

This study uses Monte Carlo simulations to analyze how rod-like particles of various sizes deposit on a lattice, revealing different roughness growth behaviors over time and highlighting universal and non-universal scaling exponents in one and two dimensions.

Contribution

It demonstrates the impact of particle size and system dimensionality on surface roughness evolution during thin-film deposition, with new insights into nonuniversal growth exponents in two dimensions.

Findings

Initial roughness follows a /2 exponent consistent with random deposition.

In 2D, the growth exponent  varies with particle size, showing nonuniversality.

In 1D, the exponents match the Villain-Lai-Das Sarma equation predictions.

Abstract

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 $\beta_{1} \approx 1/2$. 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 $\alpha$. 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 $\beta_{2}$, which depends on the size of the particles added to the substrate. If the linear size of the particle is two, we found that $\beta_{2}<\beta_{1}$, otherwise it is $\beta_{2}>\beta_{1}$, 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.