The problem of coefficients identification in the mathematical model of the ion implantation diffusion process

摘要

A mathematical model of diffusion attendant on the ion implantation process is considered. An ion flow is assumed to be a sum of diffusive and convective components. The inverse problem to determine the model coefficients is described and analyzed throughout this article. An idea of integral representation derived from the integral transformations is used for solving this problem. The lack of space and time partial derivatives of the concentration function in the obtained expressions is the advantage of this approach. Moreover, the integral representation allows one to produce the formulae for identification of model coefficients in a simple and explicit form. The integral representations of diffusivity and coefficient of driftviatime and volume-time integral characteristics are derived. As an example, we refer to the diffusion process attendant on the nitrogen ions implantation in a titanium alloy VT18U. The numerical values of model factors are calculated by the obtained expressions and the associated nitrogen concentration in the alloy is found by the numerical solution of direct diffusion problem. From these results as well as from their comparison with the corresponding experimental data it is concluded that the method of integral representation is appropriate for model coefficients identification.