Nanocomposites and nanomaterials

Interactions between islands in thermodynamic and kinetic models of epitaxial quantum dot growth
Izhnin I.I.1, Fitsych O.I.1,Voitsekhovskii A.V.2, Kokhanenko A.P.2, Lozovoy K.A.2
1 Scientific Research Company “Electron-Carat”, Stryjska St., 202, Lviv 79031, Ukraine.
E-mail: i.izhnin@carat.electron.ua
2 National Research Tomsk State University, Lenina Av., 36, Tomsk 634050, Russia.

Today there is no theoretical model capable to precisely predict characteristics of the ensemble of quantum dots self-organized in the method of molecular beam epitaxy at various growth conditions. These characteristics are the shape, surface density and average size of an island. And growth conditions are defined by substrate temperature, growth rate and thickness of the deposited material.
Existing growth models consider the expression for the change in free energy during transition of atoms from growing 2D layer to an emerging 3D island. This change is due to increase in surface area, lessening of atoms attraction to the substrate and relaxation of elastic strains in an island. However, the influence of interactions between growing islands has never been taken into account, as it was considered that contribution of these interactions is negligible compared to other energy factors.
In this work influence of interactions between 3D islands on the change in free energy during formation of nanoclusters is assessed. Ensemble of quantum dots of germanium on silicon surface with crystallographic orientation (100) is chosen as a model system for numerical estimations. Critical thickness of transition from 2D to 3D growth, surface density and size distribution function of quantum dots in this system are calculated. It is supposed that the energy of interactions between two islands is directly proportional to a product of islands volumes and inversely proportional to a distance between them.
The results of the work show that taking into account energy of interactions between islands is essential for obtaining more realistic estimations of dependencies of characteristics of islands array on growth conditions in the method of molecular beam epitaxy. Moreover, the higher is surface density of islands, the stronger are interactions between them (as the mean distance between clusters decreases). It is also shown, that neglecting this contribution leads to the predictions of higher surface densities and smaller sizes of quantum dots, which is a traditional problem of all theoretical models.