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During deposition on a stepped surface the growth mode depends on the conditions such as temperature T, deposition rate F and width of the terraces w. In this work we studied the influence of all the above mentioned characteristics using the kinetic Monte Carlo (kMC) technique. We concentrated on the conditions on the terrace at the moment of the first nucleation. The critical density of monomers for nucleation ηm decreases with the width of the terrace and the nucleation starts at surprisingly low densities of monomers. We tested several definitions of the critical width for nucleation wc used in various articles in the past and we compared our results with results of the analytical steady-state mean-field model (Ranguelov and Altman 2007 Phys. Rev. B 75 245419). To check how the simplified assumption about the steady-state regime during deposition influences the resulting dependence of wc =/~ (D/F)(κ), we set and also solved a time-dependent analytical model. This analytical model as well as kMC predict that wc =/~ (D/F)(1/5). kMC simulation also shows that the Ehrlich-Schwöbel barrier has only limited influence on the nucleation on the stepped surface at conditions close to the nucleation regime. For all widths of terraces there is a critical value of the Ehrlich-Schwöbel barrier ΔE(c)(ES)/k(B)T ~ 7.3 (ΔE(c)(ES) ~0.11 eV at T = 175 K), and only below this critical value does the Ehrlich-Schwöbel barrier affect the final value of the density of nuclei. The results of the kMC are summarized in a semi-empirical analytical formula which describes the dependence of the step-flow growth and nucleation on the terrace width w, diffusion coefficient D and deposition rate F. In our simulations we tested two models of the stepped surface with different thicknesses of the step, both with an Ehrlich-Schwöbel barrier on the edge of the terrace.

We present a theoretical investigation of the influence of domain boundaries on the Ge/Si(111)-5 × 5 phase using both large-scale DFT simulations and an analytical model. It is shown that different boundary types modify the atomic and electronic structure of the adjoining 5 × 5 domains in very different ways. A simple theoretical model, that describes the energy interaction J between the boundaries and the 5 × 5 phase, is presented and the interaction energy decay J(x) ≈ x(-n) for different domain boundaries is estimated. Additionally, the influence of the boundaries on the atomic and electronic structure of adatoms in the parental 5 × 5 phase is analyzed and it is argued that the presence of domain boundaries may strongly affect not only the physical but also the chemical properties of the Ge/Si(111)-5 × 5 phase.

Recent experiments on epitaxial growth of metals on graphene have shown a strong dependence of island densities on coverage. These investigations cannot be explained by the standard mean-field nucleation theories. To understand them, we extend to higher coverage the former theory of rate equations developed for the initial state of nucleation, in a system where adsorbate interaction is included. We account for that, in the case of high coverage, the repulsive interaction influences both the attachment of monomers to clusters and the mobility of atoms. In our work we analyze the modification of the dependence of the island density on coverage, temperature and F/D ratio. In some regimes our theory results in the experimentally observed substantial growth of island density with coverage for a high deposited amount and a weak dependence on deposition rate F. We also find out the local maxima in temperature dependence of island density, as a consequence of long-range repulsive interactions., (© 2012 IOP Publishing Ltd)

We extend a standard theory of second-layer nucleation in the regime of low temperature, where the diffusion is the limiting process. The theory takes into consideration the fluctuations of the adatoms and the distribution of stable clusters on a surface, and yields an expression for the nucleation rate and time evolution of the density of stable clusters. When diffusion is slow, the fluctuations of the monomer distribution play an important role and results differ qualitatively and quantitatively from those obtained using the standard rate-equation approach to nucleation. We argue that in this case the standard theory fails because slow diffusion delays nucleation and the nucleation rate depends on the fluctuations of interatomic distances. It is shown that the final density of stable clusters depends on the fluctuations of the monomer and stable clusters distribution and can be even independent of the deposition rate, as was experimentally observed at low temperatures.

We have extended a recently proposed correlated cluster mean-field (CCMF) theory to two-dimensional binary alloys with interactions up to the next-nearest neighbors and investigated their critical behavior. A very good agreement with results from the renormalization group theory was obtained for the critical temperatures of a simple model. We finally successfully compared our results obtained using the CCMF with the results of Monte Carlo simulations for the case of ordering in a random Fe(0.5)Co(0.5) overlayer on the Cu(001) substrate. The proposed theory represents a numerically efficient alternative to existing approaches like the cluster variation method and Monte Carlo simulations.