Epitaxial Ge islands less than 7 nm in base diameter and 2.5 nm in height, and with a number density of about $2\times {10}^{12}{\mathrm{cm}}^{\mathrm{-}2}$ were created on Si(111) surfaces covered with 0.3-nm-thick ${\mathrm{SiO}}_2$ films. The low- and high-temperature limits for the epitaxy were found to be dependent on the Ge deposition flux. The experimental results suggest that the island nuclei and the conditions for epitaxial growth appear through a reaction between individual Ge adatoms and ${\mathrm{SiO}}_2,$ and the mechanism of island formation corresponds to a growth model with the critical island size $i^{*}=0.\mathrm{}$ The relationship between the rate of the nucleation reaction and the diffusion coefficient of Ge adatoms was used to estimate the island density.