Three-dimensional mathematical model of diffusion process during fabrication of isoplanar structure taking into account crystal's anisotropy

Abstract

The paper has been devoted to the development of a three-dimensional mathematical model of a diffusion-based technological process of fabrication of isoplanar semiconductor structure. Such structures with a definite accuracy describe functioning of various devices of micro and optoelectronics. The gradual complication of functions of electron devices by reduction of sizes of their elements requires calculations accuracy increasing and analysis of these elements during designing of devices, which leads to necessity to develop more perfect methods in mathematical modeling.

The calculation of the atoms' concentration of a diffusate in a crystal during fabrication of microelectronics leads to solving classical boundary problems for differential equations of parabolic type with variable coefficients.

In the present paper we consider the particular kinds of boundary problems, which describe the diffusion process during fabrication of isoplanar structure.

For practical solving of these boundary problems we have been using the classical methods of tensor analysis and Riemannian geometry, and the method of Green function (the so called Green's function method modeling) as well. Application of these methods allows us to determine the analytical image of the impurity concentration depending on time and space variables and on other topological, physical and technological parameters of the technological process and the crystal.

The developed method of three-dimensional mathematical modeling has a sufficient importance and is quite promising for the creation of various semiconductor nanostructures.