Self-organizing growth of Ge quantum dots (QDs) on Si carried out using molecular-beam epitaxy is characterized by the random process of Ge nanoisland nucleation that leads to disordered positions of QDs in plane of growth and QDs size dispersion. In this work the experimental and theoretical studies of the growth of dense space-ordered arrays of Ge QDs on prepatterned Si substrates, obtained by ion irradiation/plasma etching through specially prepared masks on Si surface are carried out. The formation of heterostructures with regular surface relief method is developed which is based on the ion irradiation of surface through masks formed by lithography to produce sites for favorable nucleation of nanocrystals during heteroepitaxy. The technology of pre-patterned substrate creation is based on the effect of Si etching sensitive to disordered structure in comparison with crystalline Si. It is developed with using nanoimprint/electron-beam lithography. The optimal conditions of ion irradiation are determined. Two regimes of Ge island growth on pre-patterned Si surface are observed: the growth nearby and inside the nucleation sites. Method of multilayer nanocluster structures  growth on pre-patterned substrates is developed. It provides the formation of three-dimensional (3D) crystals of quantum dots in a crystalline matrix. By Raman scattering, high resolution electron microscopy and photoluminescense (PL) the chemical content, structure and electronic properties of the grown structures are studied. Intensity of PL of structures with space-arranged islands is found to be three times greater than that in case of randomly located islands.

The experimental results observed have been studied by molecular dynamics (MD) and Monte-Carlo simulation (MC). Microscopic mechanism of atom diffusion on pre-patterned surface is studied by MD (for the cases of pits and grooves). Energy surface of Ge/Si on pre-patterned Si substrate is mapped out. The activation energy and the main paths of surface diffusion of Ge on the pits walls are determined. It is shown that formation of 3D islands on defect-free prepatterned surface at the conditions close to experimental ones must occur mainly on the bottoms of the pits and inside the grooves.

The way of taking an account of strain effects in Monte Carlo simulation of epitaxial growth is suggested. Simulation of growth of multilayered Ge/Si structures is carried out. It is shown that areas of local surface extension above the ion-irradiation-induced clusters of interstitials become favourable sites for nucleation of Ge 3D islands. It is shown theoretically and experimentally, that in order to obtain high density of Ge islands in each next Ge layer of multilayered structures formed under ion-beam irradiation it is necessary to introduce interstitials, which play the main role in nucleation of 3D islands. The MC modeling reproduces the stacking effect in multilayered structures with Ge quantum dots.

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