Pattern formation and localized structures in monoatomic layer deposition

Statistical properties of nanosized clusters on a surface in overdamped stochastic reaction-Cattaneo systems

“…[26,28,44,45]. It was shown that in such systems nano-localized patterns representing islands of adsorbate or vacancy islands can be controlled by adsorption and desorption rates.…”

Nanosize pattern formation in overdamped stochastic reaction-diffusion systems with interacting adsorbate

“…[42,43] one can estimate R 0 considering deposition of Al on TiN(100): at room temperature one has the lattice constant a Al = 4.05 × 10 −10 m, and the pair interaction energy 2 = −0.22eV with the coordination number Z = 4 gives r 0 = Za Al 1.6 × 10 −9 m and the diffusion constant D = 10 −10 cm 2 s −1 . Hence the patterns have the size R 0 ∼ (10-60) × 10 −9 m. One can say that condensation processes with formation of metallic islands can be described in the limit τ J /ω −1 D 10 −3 (here ω D is the Debye frequency), whereas nanoislands' formation with τ J /ω −1 D ∼ 10 −1 -10 −2 is possible for soft matter condensation (semiconductors, polymers, etc.…”

A mesoscopic model of nanoclusters self-assembly on a graphene Moiré

“…For the adatoms undergoing diffusion on graphene in a Moiré energy landscape m (x, y), the dimensionless aerial density, or coverage ρ(x, y, t) evolves according to the mass conservation [22,23,25]:…”

“…In this notice we propose a continuum model for computational studies of adsorbate self-assembly by diffusion on the graphene Moiré. Our model is rooted in the established "mesoscopic" continuum model framework for adsorbate transport [19][20][21][22][23][24][25]. Although understandably not as detailed as the atomistic studies, this model operates on a diffusion time scale and allows for uninterrupted tracking of the process of cluster self-assembly from the random initial coverage to dense clusters.…”