Known mechanisms of relaxation of tension in the film at small misfit deformation: the formation of waviness on the initially flat free surface of the film (the instability of the Asaro-tiller-Grinfeld); nucleation of misfit dislocations at the interface film-substrate; a redistribution of atoms near the wavy surface of the film due to the reduction of elastic energy in napylenie on a substrate a semiconductor film; reducing surface energy of the film by increasing its thickness; formation of nanoscale isolated Islands on the surface of the film (Stransky-Krastanov growth); due to the formation of misfit twinning. This paper presents the results of calculations taking into account these factors for different values of the parameters of the film and Islands.The equilibrium conditions of a two-component elastic layer containing mismatch dislocations are investigated. A nanometer-thick SiGe film on a Si substrate and nanometer-sized SiGe Islands on a wetting layer are considered. The uneven distribution of Ge in the sample volume is taken into account. Three-dimensional models of a flat film with dislocation and Islands are constructed. The calculation of elastic deformations is performed using the finite element method. Approximating formulas and iterative algorithm are used to calculate the Ge distribution in the film. According to the results obtained, the uneven distribution of Ge provides relaxation of elastic energy in the alloy, and Ge atoms are concentrated on the protrusions of the disturbed surface of the film and in the vertices of the Islands. Taking into account the heterogeneity of the Ge distribution in the samples has a significant impact on the growth of islets (stable growth occurs with smaller islets) and undulation on the free surface.

Keywords: thin film, heteroepitaxy, Ge, SiGe, misfit dislocations, elastic energy density, finite element method

Solved calculation of equilibrium distribution of Ge and the density of elastic energy in semiconductor film SiGe/Si. Built the 3D model of flat film with pyramid islands and dislocations. Calculation of elastic deformation is made using the finite element method. In this model takes into account the uneven distribution of Si and Ge due to threading dislocations, misfit stress and dislocation loops. The results showed that in the two-part elastic layer SiGe provision balance dislocation is located in the depth of the inconsistencies of the film and not on the boundary of film-substrate. This conclusion applies to the penetrating dislocation, while changing the orientation of dislocation much changes box elastic stresses and distribution component of Si and Ge in the film. The results of the calculation model of the sample, including prismatic dislocation loop, shown a significant impact on the value of the elastic energy of the film. While accounting for the effects of non-uniform distribution of SiGe alloy component does not result in a significant change in the magnitude of elastic energy model and critical values of height. According to calculations, taking into account the heterogeneity of the distribution component of the alloy transition to the formation of Epitaxial islets on the film surface occurs at lower values of their critical size, especially when small concentrations of Ge in the alloy. The results of calculation of the elastic energy of the film received at work, can be applied to calculate the conditions of occurrence of defects in nanometer dimension on the original flat free surface of semiconductor films.

Keywords: germanium, thin film, heteroepitaxy, SiGe, misfit dislocations, threading dislocation, elastic energy density, dislocation loop