Multiscale modeling of oxygen diffusion through the oxide during silicon oxidation
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 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 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 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 O-2 diffusion directly at the Si-SiO2 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 O-2 diffusion for this model and obtain the dependence of the diffusion rate on oxide thickness. For oxide thicknesses down to about 2 nm, we find that the presence of an oxide layer of higher density at the Si-SiO2 interface causes a drop of the O-2 diffusion rate with respect to its value in bulk SiO2, in qualitative agreement with the observed oxidation kinetics.