Statistics of adatom diffusion in a model of thin film growth

Scaling of surface roughness in film deposition with height-dependent step edge barriers

We perform kinetic Monte Carlo simulations of film growth in simple cubic lattices with solid-on-solid conditions, Ehrlich-Schwoebel (ES) barriers at step edges, and a kinetic barrier related to the hidden off-plane diffusion at multilayer steps. Broad ranges of the diffusion-to-deposition ratio R, detachment probability per lateral neighbor, ε, and monolayer step crossing probability P=exp[-E_{ES}/(k_{B}T)] are studied. Without the ES barrier, four possible scaling regimes are shown as the coverage θ increases: nearly layer-by-layer growth with damped roughness oscillations; kinetic roughening in the Villain-Lai-Das Sarma (VLDS) universality class when the roughness is W∼1 (in lattice units); unstable roughening with mound nucleation and growth, where slopes of logW×logθ plots reach values larger than 0.5; and asymptotic statistical growth with W=θ^{1/2} solely due to the kinetic barrier at multilayer steps. If the ES barrier is present, the layer-by-layer growth crosses over directly to the unstable regime, with no transient VLDS scaling. However, in simulations up to θ=10^{4} (typical of films with a few micrometers), low temperatures (small R, ε, or P) may suppress the two or three initial regimes, while high temperatures and P∼1 produce smooth surfaces at all thicknesses. These crossovers help to explain proposals of nonuniversal exponents in previous works. We define a smooth film thickness θ_{c} where W=1 and show that VLDS scaling at that point indicates negligible ES barriers, while rapidly increasing roughness indicates a small ES barrier (E_{ES}∼k_{B}T). θ_{c} scales as ∼exp(const×P^{2/3}) if the other parameters are kept fixed, which represents a high sensitivity on the ES barrier. The analysis of recent experimental data in the light of our results distinguishes cases where E_{ES}/(k_{B}T) is negligible, ∼1, or ≪1.

Effects of Adsorbate Diffusion and Edges in a Transition from Particle to Dendritic Morphology during Silver Electrodeposition

During silver electrodeposition on Au nanoparticle (NP)-covered highly oriented pyrolitic graphite, a transition from an initial growth of microsized particles to the growth of dendrites with pine tree shape (nanotrees) is observed, which is an advancement for material growth with hierarchical surface roughness. Using kinetic Monte Carlo simulations of an electrodeposition model, those results are explained by the interplay of diffusive cation flux in the electrolyte and relaxation of adsorbed atoms by diffusion on quenched crystal surfaces. First, simulations on NP-patterned substrates show the initial growth of faceted silver particles, followed by the growth of nanotrees with shapes similar to the experiments. Next, simulations on electrodes with large prebuilt particles explain the preferential nanotree growth at corners and edges as a tip effect. Simulations on wide flat electrodes relate the nanotree width with two model parameters describing surface diffusion of silver atoms: maximal number of random hops (G) and probability of hop per neighbor (P). Finally, simulations with small electrode seeds confirm the transition from initially compact particles to the nucleation of nanotrees and provide estimates of the transition sizes as a function of those parameters. The simulated compact and dendritic deposits show dominant (111) surface orientation, as observed in experiments. Extrapolations of simulation results to match microparticle and nanotree sizes lead to G = 4 × 10¹¹ and P = 0.03, suggesting to interpret those sizes as diffusion lengths on the growing surfaces and giving diffusion coefficients 2 to 3 × 10^-13 m²/s for deposited silver atoms. These results may motivate studies to relate diffusion coefficients with atomic-scale interactions.

Adatom-Driven Oxygen Intermixing during the Deposition of Oxide Thin Films by Molecular Beam Epitaxy

Thin film deposition from the vapor phase is a complex process involving adatom adsorption, movement, and incorporation into the growing film. Here, we present quantitative experimental data that reveals anion intermixing over long length scales during the deposition of epitaxial Fe₂O₃ and Cr₂O₃ films and heterostructures by oxygen-plasma-assisted molecular beam epitaxy. We track this diffusion by incorporating well-defined tracer layers containing ¹⁸O and/or ⁵⁷Fe and measure their redistribution on the nanometer scale with atom probe tomography. Molecular dynamics simulations suggest potential intermixing events, which are then examined via nudged elastic band calculations. We reveal that adatoms on the film surface act to "pull up" subsurface O and Fe. Subsequent ring-like rotation mechanisms involving both adatom and subsurface anions then facilitate their mixing. In addition to film deposition, these intermixing mechanisms may be operant during other surface-mediated processes such as heterogeneous catalysis and corrosion.

Interplay of orientational order and roughness in simulated thin film growth of anisotropically interacting particles

Roughness and orientational order in thin films of anisotropic particles are investigated using kinetic Monte Carlo simulations on a cubic lattice. Anisotropic next-neighbor interactions between the lattice particles were chosen to mimic the effects of shape anisotropy in the interactions of disk- or rodlike molecules with van der Waals attractions. Increasing anisotropy leads first to a preferred orientation in the film (which is close to the corresponding equilibrium transition) while the qualitative mode of roughness evolution (known from isotropic systems) does not change. At strong anisotropies, an effective step-edge (Ehrlich-Schwoebel) barrier appears and a nonequilibrium roughening effect is found, accompanied by reordering in the film which can be interpreted as the nucleation and growth of domains of lying-down disks or rods. The information on order and roughness is combined into a diagram of dynamic growth modes.

Lattice gas study of thin-film growth scenarios and transitions between them: Role of substrate

Thin-film growth is investigated in two types of lattice gas models where substrate and film particles are different, expressed by unequal interaction energy parameters. The first is of solid-on-solid type, whereas the second additionally incorporates desorption, diffusion in the gas phase above the film and readsorption at the film (appropriate for growth in colloidal systems). In both models, the difference between particle-substrate and particle-particle interactions plays a central role for the evolution of the film morphology at intermediate times. The models exhibit a dynamic layering transition which occurs at generally lower substrate attraction strengths than the equilibrium layering transition. A second, flattening transition is found where initial island growth transforms to layer-by-layer growth at intermediate deposition times. Combined with the known roughening behavior in such models for very large deposition times, we present four global growth scenarios, charting out the possible types of roughness evolution.