On modelling thermal oxidation of Silicon II: numerical aspects

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 finite 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 finite element containing multiple materials is described. A discontinuously varying oxidant density field 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.