Step barrier for interlayer diffusion in Fe/Fe(100) epitaxial 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.

Kinetic Roughening of Fe/Fe(100) Epitaxial Thin Films

We model kinetic roughening during Fe(100) homoepitaxy, where the formation of mounds with selected slope has been observed. Our model incorporates irreversible nucleation and growth of two-dimensional square islands in each layer, and a step-edge barrier to diffusive downward transport (which exceeds the barrier, Ed, to terrace diffusion by ESch). We estimate that ESch≈45meV compared with Ed≈450meV. To reproduce observed behavior, it is also essential for the model to incorporate "downward funneling" of depositing atoms to four-fold hollow adsorption sites, as this controls slope selection. Finally, we discuss model predictions for the non-monotonic temperature dependence of kinetic roughening.