Distribution of “structural” elastic stresses in substrate under a thin epitaxial film

Abstract

A calculation is performed of the “structural” stresses in a substrate that are due to the mismatching of the lattice parameters of the film and the substrate. By assuming the film to be sufficiently small (h ≲ 0.01 p, where p is the distance between the mismatch dislocations), we simplify the initial system of equations for an equilibrium elastic medium, and obtain an exact solution for the parabolic model and an approximate solution for the Peierls-Nabarro model. The analytic and numerical analysis of the solution for the Ge-GaAs system shows that for a depth z ≳ 0.05 p the distribution of stresses is not very sensitive to the choice of model and the size of the shear modulus μ at the separation boundary. Therefore, despite the fact that there are at present no reliable methods for determining μ, the obtained solution allows us to investigate the distribution of stresses in the depth of a substrate by using a small digital computer.