Transitions between epitaxial growth regimes: A (1+1)-dimensional kinetic Monte Carlo study

To study epitaxial thin-film growth, a new model is introduced and extensive kinetic Monte Carlo simulations performed for a wide range of fluxes and temperatures. Varying the deposition conditions, a rich growth diagram is found. The model also reproduces several known regimes and in the limit of low particle mobility a new regime is defined. Finally, a relation is postulated between the temperatures of the kinetic and thermal roughening transitions.

💡 Research Summary

The authors present a minimalist (1+1)-dimensional kinetic Monte Carlo (KMC) model for homo‑epitaxial thin‑film growth that captures a broad spectrum of growth regimes by varying only three control parameters: the deposition flux F, the temperature‑dependent mobility ratio φ = J_pp/(k_B T), and the diffusion‑barrier ratio R_E = E_m/J_pp. Particles are deposited randomly on a lattice and may hop to neighboring sites with rates given by an Arrhenius law r_i = ν exp(−E_i/k_B T), where the activation energy E_i is defined as E_i = E_m − (n_f − n_0) J_pp, i.e., it depends linearly on the change in coordination number between the initial and final positions. All processes share a common attempt frequency ν, which greatly simplifies the parameter space while retaining essential physical ingredients such as corner rounding, coordination‑driven hopping, and a rule that forbids detachment of clusters from the substrate (implemented via the Hoshen‑Kopelman algorithm).

Simulations are performed on a lattice of 10³ sites, averaged over 10³ independent runs. Time increments follow the standard KMC prescription Δt = −ln ξ/∑_i r_i. The primary observables are the surface roughness W(t) = ⟨