Critical thickness of 2D to 3D transition in GexSi1−x/Si(001) system

Abstract

In this paper, Stranski–Krastanov growth of GexSi1−x epitaxial layers on the Si(001) surface is considered. Experimental investigations show that the moment of transition from 2D to 3D growth and the critical thickness of 2D layer at which this transition occurs play a key role during the synthesis of such materials. Among the most important parameters determining the peculiarities of the growth process and characteristics of emerging island ensembles are growth temperature and surface conditions (for example, the presence of surfactants). But existing theoretical models are not able to predict the values of the critical thickness in the whole range of growth temperatures and compositions x of solution for these systems. For the calculations of the critical thickness of transition from 2D to 3D growth, in this paper, a theoretical model based on general nucleation theory is proposed. This model is specified by taking into account dependencies of elastic modulus, lattices mismatch, and surface energy of the side facet on the composition x. As a result, dependencies of the critical thickness of Stranski–Krastanov transition on composition x and temperature are obtained. This allows one to determine conditions of transition from 2D to 3D growth mode in these systems. The simulated results explain experimentally observed results on temperature dependencies of the critical thickness for different germanium contents.