A simulation system based on mixed-hybrid finite elements for thermal oxidation in semiconductor technology

摘要

In this work we deal with the numerical simulation of thermal oxidation in silicon device technology. This application involves the coupled solution of a diffusion-reaction problem and of a mechanical problem. These two problems are mutually dependent through the exchange of stresses and fluxes that are typically post-processed fields in standard finite element approaches, and as such they may suffer from a lack of accuracy and from physical inconsistencies. In this paper, we propose a novel numerical approach to the simulation of the thermal oxidation process, that is characterized by the use of mixed and hybrid finite elements. The main advantage of such formulations is that stresses and fluxes are directly computed quantities, rather than obtained from post-processing techniques. We also address the procedures and the techniques that must be devised for handling the coupled interaction problem and the presence of a computational grid moving in time. The numerical approach we propose is eventually validated on a realistic example of the thermal oxidation process in a local oxidation structure (LOCOS).