Oxide-growth at a Si surface

Silicon oxidation involves physico-chemical phenomena which may be grouped into three categories: (1) surface effects occurring at the oxide/gas interface (in dry oxygen ambient) and mainly characterized by a sticking coefficient; (2) bulk effects connected to oxygen transport through the more or less stoichiometric oxide which is growing; (3) interface effects at the oxide/Si boundary where a non-stoichiometric sub-oxide reactive layer most probably exists. To describe oxide growth we use Fick's second law, but at the same time we account for the peculiarities of the disordered structure of the growing oxide layer: we allow for inhomogeneities and preferred diffusional pathways as suggested, for example, by Revesz and co-workers, or for a possible ''granular random network''. To do this we introduce a depth-dependent diffusivity as appropriate to fractal dynamics. The oxygen diffusivity at the reactive layer (i.e. at the SiO(x)/Si interface) as well as in the stress-modified region (i.e. at the SiO2/SiO(x) interface) is also modeled to have a general form for the x-dependent diffusion coefficient. The main experimental aspects of the oxide growth can be explained by our model without including empirical forms for D(x) as commonly used in current literature.