Abstract
The nucleation rate and the transition to step-flow growth are considered in detail in the two limiting cases of surfactant mediated homoepitaxy: (i) reversible exchange of crystal and surfactant atoms (an exchange–de-exchange equilibrium); (ii) irreversible exchange (fast exchange of the atoms upon striking the surface and absence of de-exchange). It is shown that in both cases the critical terrace width above which nucleation takes place displays an Arrhenius behavior as has been experimentally established by Iwanari and Takayanagi [J. Cryst. Growth 119 (1992) 229]. The square of the critical terrace width for step-flow growth scales with the atom arrival rate, the scaling exponents being the same, which determines the scaling behavior of the island densities in the submonolayer regime of growth. It is shown that in the case of Sn mediated growth of Si(111) the surfactant drives the nucleation process closer to the phase equilibrium, the critical nucleus is one order of magnitude larger than in the clean case, and the surfactant stimulates the step-flow growth.
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