We address the rate of O-2 diffusion through the oxide layer at Si-SiO2 interfaces using an atomic-scale approach. In particular, we investigate the combined effect of a percolative diffusion mechanism and of a dense oxide layer located close to the silicon substrate. We first extend our atomic-scale description of O-2 diffusion in amorphous SiO2 to the case of a densified oxide. This yields an activation energy which compares well with the experimental result. Next, we investigate the dependence of the O-2 diffusion rate on oxide thickness at Si-SiO2 interfaces using Monte Carlo simulations. We consider both homogeneous and nonhomogeneous oxide layers. The nonhomogeneous oxide is composed of two layers, a normal and a densified one. The thickness and the mass density of the densified layer are taken from experiment. In the case of a normal oxide, we find that the O-2 diffusion rate increases with decreasing thickness, as a result of the percolative nature of the diffusion mechanism. When a densified layer is inserted, the diffusion coefficient drops below its value for bulk amorphous SiO2, for oxide thicknesses larger than 2 nm. This result is consistent with the experimental behaviour of the oxidation kinetics.