Abstract
We report on the investigation of height distributions (HDs) and spatial covariances of two-dimensional surfaces obtained from extensive numerical simulations of the celebrated Clarke-Vvedensky (CV) model for homoepitaxial thin film growth. In this model, the effect of temperature, deposition flux, and strengths of atom-atom interactions are encoded in two parameters: the diffusion to deposition ratio $R=D/F$ and $\varepsilon$, which is related to the probability of an adatom "breaking" a lateral bond. We demonstrate that the HDs present a strong dependence on both $R$ and $\varepsilon$, and even after the deposition of $10^5$ monolayers (MLs) they are still far from the asymptotics in some cases. For instance, the temporal evolution of the HDs' skewness (kurtosis) displays a pronounced minimum (maximum), for small $R$ and $\varepsilon$, and only at long times it passes to increase (decrease) toward its asymptotic value. However, it is hard to determine whether they converge to a single value or different nonuniversal ones. For large $R$ and/or $\varepsilon$, on the other hand, these quantities clearly converge to the values expected for the Villain-Lai-Das Sarma (VLDS) universality class. A similar behavior is observed in the spatial covariances, but with weaker finite-time effects, so that rescaled curves of them collapse quite well with the one for the VLDS class at long times. Simulations of a model with limited mobility of particles, which captures some essential features of the CV model in the limit of irreversible aggregation ($\varepsilon=0$), reveal a similar scenario. Overall, these results point out that the study of fluctuations in homoepitaxial thin films' surfaces can be a very difficult task and shall be performed very carefully, once typical experimental films have $\lesssim 10^4$ MLs, so that their HDs and covariances can be in the realm of transient regimes.
Highlights
The list of applications of thin film deposition is very vast, underlying a number of recent important technological advances [1–3]
We focus on the behavior of the height distributions (HDs) during the transient growth regime
The case of irreversible aggregation is discussed, which is followed by an analysis of the full CV model
Summary
The list of applications of thin film deposition is very vast, underlying a number of recent important technological advances [1–3]. In most of the techniques and relevant conditions for thin film production, molecules coming from a vapor or a liquid phase adsorb onto the substrate or film surface (with a flux F per adsorption site) and pass to diffuse at the surface. This thermally activated diffusion process may depend on the local environment of the adatoms, on the diffusion mechanism (e.g, by hopping or by exchange), on how adatoms interact at the surface, and so on [2,3].
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