Thermal oxidation of silicon is one of the most important steps in the fabrication of highly integrated electronic circuits, and is mainly used for efficient isolation of adjacent devices from each other.

If a surface of silicon has contact with an oxidizing atmosphere, the chemical reaction of the oxidant (oxygen or steam) with silicon results in silicon dioxide. This reaction consumes silicon, and the newly formed silicon dioxide has more than twice the volume of the original silicon. If a silicon dioxide domain is already existing, the oxidants diffuse through the oxide domain and react at the interface of oxide and silicon to form new oxide so that the dioxide domain is penetrated.

Thermal oxidation is a complex process where the three subprocesses oxidant diffusion, chemical reaction, and volume increase occur simultaneously. The volume increase is the main source of mechanical stress and strain, and these cause displacement.
From the mathematical point of view, the problem can be described by a coupled system of partial differential equations, one for the diffusion of the oxidant through the oxide, the second for the conversion of silicon into silicon dioxide at the interface, and a third for the mechanical problem of the silicon-silicon dioxide-body, which can be modeled as an elastic, viscoelastic, or viscous body.

For a realistic and accurate oxidation simulation, the three subproblems should be coupled. However, most oxidation models decouple them into a sequence of quasi-stationary steps. Our model takes into account that the diffusion of oxidants, the chemical reaction, and the volume increase occur simultaneously in a so-called reactive layer. This reactive layer has a spatial finite width, in contrast to the sharp interface between silicon and silicon dioxide in the conventional formulation. The oxidation process is numerically described by a coupled system of equations for reaction, diffusion, and displacement. In order to solve the numerical formulation of the oxidation process, the finite element scheme is applied.

During the last year a viscoelastic mechanical model has been designed and implemented which is more realistic than the elastic one, because both silicon oxide and silicon nitride have a viscoelastic behavior. The current work deals with the so-called stress-dependent oxidation, because the oxidant diffusivity and the intensity of the chemical reaction are significantly influenced by the local stress values in the material. Because of this fact the resulting geometry of the silicon dioxide strongly depends on the stress distribution.