We investigate at the atomic scale the oxygen diffusion process occurring during silicon oxidation. First, we address the energetics of several oxygen species in the oxide using density-functional calculations. Our results support the interstitial ${\mathrm{O}}_2$ molecule as the most stable oxygen species. We then adopt a classical scheme for describing the energetical and topological properties of the percolative diffusion of the ${\mathrm{O}}_2$ molecule through the interstitial network of the oxide. By studying a large set of disordered oxide structures, we derive distributions of energy minima, transition barriers, and the number of connections between nearest-neighbor minima. These distributions are then mapped onto a lattice model to study the long-range ${\mathrm{O}}_2$ diffusion process by Monte-Carlo simulations. The resulting activation energy for diffusion is found to be in agreement with experimental values. We also extend our atomic-scale approach to an oxide of higher density, finding a significant decrease of the diffusivity. To address the ${\mathrm{O}}_2$ diffusion directly at the $\mathrm{Si}-\mathrm{Si}{\mathrm{O}}_2$ interface, we construct a lattice model of the interface which incorporates the appropriate energetic and connectivity properties in a statistical way. In particular, this lattice model shows a thin oxide layer of higher density at the interface, in accord with x-ray reflectivity data. We carry out Monte-Carlo simulations of the ${\mathrm{O}}_2$ diffusion for this model and obtain the dependence of the diffusion rate on oxide thickness. For oxide thicknesses down to about $2\mathrm{nm}$, we find that the presence of an oxide layer of higher density at the $\mathrm{Si}-\mathrm{Si}{\mathrm{O}}_2$ interface causes a drop of the ${\mathrm{O}}_2$ diffusion rate with respect to its value in bulk $\mathrm{Si}{\mathrm{O}}_2$, in qualitative agreement with the observed oxidation kinetics.

• Received 16 March 2004

DOI:https://doi.org/10.1103/PhysRevB.70.195312