Vapor condensation on weakly interacting substrates leads to the formation of three-dimensional (3D) nanoscale islands (i.e., nanostructures). While it is widely accepted that this process is driven by minimization of the total film/substrate surface and interface energy, current film-growth theory cannot fully explain the atomic-scale mechanisms and pathways by which 3D island formation and morphological evolution occurs. Here, we use kinetic Monte Carlo simulations to describe the dynamic evolution of single-island shapes during deposition of Ag on weakly interacting substrates. The results show that 3D island shapes evolve in a self-similar manner, exhibiting a constant height-to-radius aspect ratio, which is a function of the growth temperature. Furthermore, our results reveal the following chain of atomic-scale events that lead to compact 3D island shapes: 3D nuclei are first formed due to facile adatom ascent at single-layer island steps, followed by the development of sidewall facets bounding the islands, which in turn facilitates upward diffusion from the base to the top of the islands. The limiting atomic process which determines the island height, for a given number of deposited atoms, is the temperature-dependent rate at which adatoms cross from sidewall facets to the island top. The overall findings of this study provide insights into the directed growth of metal nanostructures with controlled shapes on weakly interacting substrates, including two-dimensional crystals, for use in catalytic and nanoelectronic applications.

The growth dynamics of faceted three-dimensional (3D) Ag islands on weakly-interacting substrates are investigated-using kinetic Monte Carlo (kMC) simulations and analytical modelling-with the objective of determining the critical top-layer radius R-c required to nucleate a new island layer as a function of temperature T, at a constant deposition rate. kMC shows that R-c decreases from 17.3 to 6.0 angstrom as T is increased at 25 K intervals, from 300 to 500 K. That is, a higher T promotes top-layer nucleation resulting in an increase in island height-to-radius aspect ratios. This explains experimental observations for film growth on weakly-interacting substrates, which are not consistent with classical homoepitaxial growth theory. In the latter case, higher temperatures yield lower top-layer nucleation rates and lead to a decrease in island aspect ratios. The kMC simulation results are corroborated by an analytical mean field model, in which R-c is estimated by calculating the steady-state adatom density on the island side facets and top layer as a function of T. The overall findings of this study constitute a first step toward developing rigorous theoretical models, which can be used to guide synthesis of metal nanostructures, and layers with controlled shape and morphology, on technologically important substrates, including two-dimensional crystals, for nanoelectronic and catalytic applications.

We use kinetic Monte Carlo simulations and analytical modelling to study coalescence of three-dimensional (3D) nanoscale faceted silver island pairs on weakly-interacting fcc(111) substrates, with and without concurrent supply of mobile adatoms from the vapor phase. Our simulations show that for vapor flux arrival rates F < 1 monolayer/second (ML/s) coalescence manifests itself by one of the islands absorbing the other via sidewall facet migration. This process is mediated by nucleation and growth of two-dimensional (2D) layers on the island facets, while the supply of mobile atoms increases the nucleation probability and shortens the time required for coalescence completion. When F is increased above 1 ML/s, coalescence is predominantly governed by deposition from the vapor phase and the island pair reaches a compact shape via agglomeration. The crucial role of facets for the coalescence dynamics is further supported by a mean-field thermodynamic description of the nucleation energetics and kinetics. Our findings explain experimental results which show that two-dimensional film growth morphology on weakly-interacting substrates is promoted when the rate of island coalescence is suppressed. The present study also highlights that deviations of experimentally reported film morphological evolutions in weakly-interacting film/substrate systems from predictions based on the sintering and particle growth theories may be understood in light of the effect of deposition flux atoms on the energetics and kinetics of facet-layer nucleation during coalescence.

Fabrication of high-performance heterostructure devices requires fundamental understanding of the diffusion dynamics of metal species on 2D materials. Here, we investigate the room-temperature diffusion of Ag, Au, Cu, Pd, Pt, and Ru adatoms on graphene using ab initio and classical molecular dynamics simulations. We find that Ag, Au, Cu, and Pd follow Lévy walks, in which adatoms move continuously within ∼1–4 nm2 domains during ∼0.04 ns timeframes, and they occasionally perform ∼2–4 nm flights across multiple surface adsorption sites. This anomalous diffusion pattern is associated with a flat (<50 meV) potential energy landscape (PEL), which renders surface vibrations important for adatom migration. The latter is not the case for Pt and Ru, which encounter a significantly rougher PEL (>100 meV) and, hence, migrate via conventional random walks. Thus, adatom anomalous diffusion is a potentially important aspect for modeling growth of metal films and nanostructures on 2D materials.