Abstract
Mathematical model of technological process of manufacturing thin films taking into account their anisotropy and heterogeneity. / V. Gogichaishvili. – 2021–2022. – # 21/22. – pp. 277-286. – eng. The problem of diffusion in the fabrication process of thin-film structures with crystal anisotropy and heterogeneity is considered. Two boundary value problems A and B are posed with respect to impurity atoms in the crystal bulk. Boundary value problem A describes the process of diffusion with an open window for atoms in the gas phase (to penetrate through it into the crystal), and boundary value problem B is a diffusion process with a closed window (diffusant atoms are redistributed in the crystal during high-temperature oxidation). These boundary value problems are solved by the Green’s function method. Using the methods of tensor analysis and Riemannian geometry, the modified Green’s functions for boundary value problems A and B are determined in the form of finite analytic functions. Solutions are found as finite integral expressions, with the help of which the diffusant concentrations are calculated at an arbitrary point for various moments of time. The cases of thick (when the crystal thickness exceeds the diffusion length) and thin (when it is less than the diffusion length) crystals are considered. The Green’s function for thin crystals is plotted as infinite coinciding lines. Fig. 1, Ref. 4.