First stages of epitaxial growth in the presence of an extended defect: Kinetic Monte Carlo simulations versus rate equation study on a vicinal surface

Abstract

We study the influence of atom confinement during the growth process on vicinal surfaces with different terrace widths. The behavior of the mean island density $n$ and size $s$ is analyzed in a general way as a function of the flux $F$ over diffusion ${D}_{1}$ ratio and terrace width using kinetic Monte Carlo simulations. We show that the exponent in the scaling law $n\ensuremath{\propto}{(F∕{D}_{1})}^{\ensuremath{\alpha}}$ changes from $\ensuremath{\alpha}=1∕3$ for infinite terrace to $\ensuremath{\alpha}=1$ in the case of finite terrace when the flux is lowered. In the same condition, the island size is limited by confinement, leading to a critical value which depends on the terrace width, only. Very simple rate equations are shown to be able to quantitatively explain, through three parameters determined independently, the simulation results at small deposition flux, whatever the description of the islands (point, compact, or fractal). Application of these results to a physical case $\mathrm{Ag}∕\mathrm{Pt}$ leads to an excellent agreement with more complete simulations based on an atomic description of the growth mechanisms.