A Viscous Compressible Model for Stress Generation/Relaxation in SiO2

In this work, a model has been developed and characterized to account for the mechanical behavior of silicon dioxide and its effect on oxidation kinetics. Conservation of mass, momentum balance, and the transport equation along with appropriate boundary conditions have been formulated. The material law used for the oxide is that of compressible viscous material applied via mass and momentum balance (Navier‐Stokes equation). The oxidation is modeled by a steady‐state diffusion oxidants, with reaction at the interface. Due to an increase in volume, the newly created oxide is assumed to be highly compressed, relaxing as oxidation (or annealing) proceeds. Thus, thermal history effects which occur even in planar oxides can be accounted for. Mechanical behavior of the oxide is characterized based on stress relaxation data. The model is then matched to both two‐step and single‐step oxidation kinetics, extracting stress‐dependent diffusivity and solubility parameters.