Thin film growth models with long surface diffusion lengths

In limited mobility (LM) models of thin film deposition, the final position of each atom or molecule is chosen according to a set of stochastic rules before the incidence of another atom or molecule. Here we investigate the possibility of a LM model to reproduce features of a more realistic approach that represents the interplay of collective adatom diffusion and the external flux. In the LM model introduced here, each adatom may execute G hops to neighboring columns of the deposit, but a hop attempt from a site with n lateral neighbors has probability Pn, with P<1. These rules resemble those of the Clarke–Vvedensky (CV) model without energy barriers at step edges, whose main parameters are the diffusion-to-deposition ratio R on terraces and the detachment probability ϵ per lateral neighbor. At short times, the roughness of the LM model can be written in terms of a scaling function of G and P and the growth exponent is consistent with the Villain-Lai-Das Sarma universality class. The evolution of the surface roughness and of the autocorrelation function of the CV model is reproduced with reasonable accuracy by the LM model with suitable choices of parameters. The increase of the parameters G and R of those models produces smoother film surfaces, while the increase of P and ϵ smoothen the terrace boundaries at short lengthscales. However, the detachment probabilities of the two models have very different effects on the surface roughness: in the LM model, for fixed G, the surface roughness increases as P increases; in the CV model, the surface smoothens as ϵ increases, for fixed R. This result is related to the non-Markovian nature of the LM model, since the diffusivity of an adatom depends on its history at the film surface and may be severely reduced after a detachment from a terrace step; instead, in a collective diffusion model, the detached adatom has the same mobility as a freshly deposited adatom in the same environment. This interpretation is supported by the correlation between the surface roughness and the average number of hops after the last detachment from lateral neighbors in the LM model. We conclude that, although a limited mobility model can reproduce morphological properties of a collective diffusion model, the role of apparently equivalent parameters may be very different, which have consequences for their physical interpretation.