Critical terrace width for step flow growth: Effect of attachment-detachment asymmetry and step permeability

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 Si 111 7 7 surface leads to the conclusion that the nucleation process in the interval 700–850 K takes place in an attachment-detachment limited regime with critical nuclei consisting of one and three atoms below and above 750 K, respectively. The values of 0.525 and 0.535 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 eV for three-atom nucleus has been evaluated.