A general expression for the critical terrace width for step flow growth accounting for both the step permeability and the asymmetric incorporation of atoms to ascending and descending steps is derived. It covers both cases of diffusion and attachment-detachment limited regimes of growth at high and low temperatures. It is found that when at least one of the excess step-edge barriers is equal to zero, only diffusion-limited behavior regime is allowed. The step permeability does not affect both limiting cases at high and low temperatures. Comparing the theory with experimental data for the $\mathrm{Si}\left(111\right)(7\times 7)$ surface leads to the conclusion that the nucleation process in the interval $700–850\mathrm{K}$ takes place in an attachment-detachment limited regime with critical nuclei consisting of one and three atoms below and above $750\mathrm{K}$, respectively. The values of 0.525 and $0.535\mathrm{eV}$ have been estimated for the energy barriers for incorporation of adatoms into descending and ascending steps, respectively, thus demonstrating an inverse Ehrlich-Schwoebel effect [J. Chem. Phys. 44, 1039 (1966)]. A binding energy of $1.65\mathrm{eV}$ for three-atom nucleus has been evaluated.

The critical terrace width $$\lambda${}$ for 2D island nucleation and growth (2DNG) on large-scale atomically flat terraces of a step-bunched Si(111)-($7\ifmmode\times\else\texttimes\fi{}7$) surface has been studied by in situ ultrahigh vacuum reflection electron microscopy as a function of the substrate temperature $T$ and Si deposition rate $R$. The dependence of ${$\lambda${}}^{2}(R)$ is characterized by a power law with scaling exponent $$\chi${}=1.36\char21{}1.46$, validating an attachment limited (AL) growth kinetics up to $720\text{ }\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$. At this temperature, the Arrhenius dependencies $\mathrm{ln}{}{$\lambda${}}^{2}(1/T)$ change their slope, so that the effective 2DNG activation energy ${E}_{2\mathrm{D}}$ drops from 2.4 eV down to 0.5 eV at $T>720\text{ }\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$. We first show that the ${E}_{2\mathrm{D}}$ change is caused by a transition between AL and DL (diffusion limited) growth kinetics accompanied by a step shape transformation. The AL growth mode is characterized by kinetic length ${d}_{-}$\sim${}{10}^{5}a$ and the preferential step-down attachment of atoms to steps limited by an energy barrier ${E}_{\mathrm{ES}}^{-}$\approx${}0.9\text{ }\text{ }\mathrm{eV}$.