Nucleation on a stepped surface with an Ehrlich–Schwöbel barrier

Abstract

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 ( 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.