Germanium/silicon systems are among the most promising
materials
for development of current semiconductor electronics and photonics.
Structures with germanium quantum dots on silicon are very interesting
from the point of view of the creation of fast-speed transistors,
photodetectors, and solar cells. The basic method of the synthesis
of nanoislands is their self-organization in the process of molecular
beam epitaxy. It was experimentally shown that ultrahigh surface densities
(up to 1012–1013 cm–2) of nanometer-sized clusters may be achieved by deposition of germanium
on oxidized rather than bare silicon surfaces. Nevertheless, this
system with a thin layer of silicon oxide is poorly investigated.
In this work, fundamental peculiarities of epitaxial formation and
growth of quantum dots by the Volmer–Weber growth mechanism
are considered. A kinetic model of nucleation and growth of three-dimensional
islands by the Volmer–Weber mechanism based on the general
nucleation theory is proposed for the first time. The developed model
allows one to evaluate not only equilibrium values of a system with
quantum dots (their average size and surface density), but also principally
nonequilibrium parameters such as islands nucleation rate, size distribution
function, and its time evolution. Dependencies of mean lateral size
and surface density of Volmer–Weber quantum dots on the conditions
of their synthesis (growth temperature and deposition rate) are obtained.
The results of numerical simulations of Volmer–Weber growth
for the Ge/SiO2/Si system show very good agreement with
experimental data. The proposed theoretical model may be easily applied
for other material systems where growth of islands by the Volmer–Weber
mechanism is realized.