Modeling of nonequilibrium surface growth by a limited-mobility model with distributed diffusion length

Abstract

Kinetic Monte-Carlo (KMC) simulations are a well-established numerical tool to investigate the time-dependent surface morphology in molecular beam epitaxy (MBE) experiments. In parallel, simplified approaches such as limited mobility (LM) models characterized by a fixed diffusion length have been studied. Here, we investigate an extended LM model to gain deeper insight into the role of diffusional processes concerning the growth morphology. Our model is based on the stochastic transition rules of the Das Sarma-Tamborena (DT) model, but differs from the latter via a variable diffusion length. A first guess for this length can be extracted from the saturation value of the meansquared displacement calculated from short KMC simulations. Comparing the resulting surface morphologies in the sub-and multilayer growth regime to those obtained from KMC simulations, we find deviations which can be cured by adding fluctuations to the diffusion length. This mimics the stochastic nature of particle diffusion on a substrate, an aspect which is usually neglected in LM models. We propose to add fluctuations to the diffusion length by choosing this quantity for each adsorbed particle from a Gaussian distribution, where the variance of the distribution serves as a fitting parameter. We show that the diffusional fluctuations have a huge impact on cluster properties during submonolayer growth as well as on the surface profile in the high coverage regime. The analysis of the surface morphologies on one-and two-dimensional substrates during sub-and multilayer growth shows that the LM model can produce structures that are indistinguishable to the ones from KMC simulations at arbitrary growth conditions.

An electrodeposition model with surface relaxation predicts temperature and current effects in compact and dendritic film morphologies

“…Note that, in recent simulations of submonolayer growth, the Gaussian hop number distributions were shown to provide better results than a delta distribution ( σ = 0). 37 We confirm the advantage of the Gaussian distribution over other simple forms (delta and exponentially decreasing distributions) in the ESI †…”

Height fluctuations in homoepitaxial thin film growth: A numerical study

“…As pointed out above and stressed recently in Refs. [53,58], the existence of this kind of simplified model reproducing the surface features of a more realistic and complex one (the IACV model here) is very important since this allows us to investigate regimes of the latter model, which would not be computationally accessible in a feasible amount of time, through simulations of the former one.…”

“…This corresponds to strong intraterrace adatom-adatom interactions (E NN k B T ), where effectively only free adatoms can move and there is only a single parameter, R, to be considered. Although this seems an oversimplification, we notice that this "irreversible aggregation CV" (IACV) model has already been investigated for multilayer growth [24,53]. Moreover, it is a very common practice to assume that aggregation is irreversible in studies of island nucleation and growth during the submonolayer regime, where the model considered here is a kind of multilayer version of the situation with "critical nucleus" i * = 1 [3,4,[54][55][56][57].…”

Height fluctuations in homoepitaxial thin film growth: A numerical study

“…This corresponds to strong intra-terrace adatom-adatom interactions (E N N k B T ), where effectively only free adatoms can move and there is only a single parameter, R, to be considered. Although this seems an oversimplification, we notice that this "irreversible aggregation CV" (IACV) model has already been investigated for multilayer growth [24,53]. Moreover, it is a very common practice to assume that aggregation is irreversible in studies of island nucleation and growth during the submonolayer regime, where the model considered here is a kind of multilayer version of the situation with "critical nucleus" i * = 1 [3,4,[54][55][56][57].…”