Multistage nucleation of two-dimensional Si islands onSi(111)−7×7during MBE growth: STM experiments and extended rate-equation model

Abstract

The submonolayer density of two-dimensional (2D) islands in $\mathrm{Si}∕\mathrm{Si}(111)\text{\ensuremath{-}}7\ifmmode\times\else\texttimes\fi{}7$ molecular beam epitaxy is measured using scanning tunneling microscopy. At a relatively low deposition temperature of $673\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the density of 2D islands is a power function of the deposition flux ${N}_{2D}\ensuremath{\propto}{F}^{\ensuremath{\chi}}$ with the exponent $\ensuremath{\chi}=0.24$ being smaller than that predicted by the standard nucleation theory. The nonstandard scaling of the 2D island density is explained by the multistage character of the nucleation process on the $\mathrm{Si}(111)\text{\ensuremath{-}}7\ifmmode\times\else\texttimes\fi{}7$ surface which involves consecutive stages of formation of stable Si clusters, formation of pairs of clusters, and transformation of the cluster pairs to 2D islands. Using an extended rate-equation model, we analyze the temperature and growth rate dependencies of the density of single clusters, cluster pairs, and 2D islands and show that an activation barrier of $\ensuremath{\sim}1.26\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ delays the transformation of cluster pairs to 2D islands. The delayed transformation of cluster pairs to 2D islands is the reason for the nonstandard scaling of the 2D island density observed at low deposition temperatures.