Recent Advances in Models for Thermal Oxidation of Silicon

Recent advances are presented in the models for thermal oxidation that have been been introduced by Rao and co-workers. The level-set formulation for movement of the Si–SiO2 interface has been improved by the application of an efficient velocity–projection scheme for noninterface points. A penalty formulation has been introduced to enforce positive concentrations in the presence of discontinuities. The annealing-induced expansion of SiO2 has been established as an important effect and a phenomenological relation has been identified for it. Inelastic volumetric strains have been proposed, evolution equations have been specified, and the underlying thermodynamics has been elucidated. The enhanced strain finite-element method has been applied to the inhomogeneous expansion of interface elements that have silicon and SiO2 parts to them.