On modelling thermal oxidation of Silicon II: numerical aspects

Abstract

The implementation of a new model to simulate the oxidation of silicon see Part I is presented in this paper. The implementation is done within a nite element framework. The work involves representation of the silicon silicon dioxide interface in a mesh independent manner. The interface description and evolution is accomplished using the level-set method. Formulation of a single nite element containing multiple materials is described. A discontinuously varying oxidant density eld is modelled along with its reaction with silicon. Large expansion of silicon dioxide is incorporated into the constitutive equations. A staggered scheme to obtain the solution to the coupled set of equations is given.

Doubling of conductance steps in Si∕SiO2 quantum point contact

“…Although we used in the current model ϳ10 5 elements, the numerical accuracy had to be improved by a thorough smoothening procedure of the simulated strain data. With further computational efforts the oxidation model could be formulated within the mean-field-like theory [12][13][14] to account for the time dependence of true oxidation process. Even within the mean field theory, all calculations rely upon poorly known process parameters and constants, such as a stress-dependent viscosity and anisotropic reaction rates.…”