Fractal aspects related to the Si oxidation process

Abstract

We propose a model for the silicon oxidation process in dry atmosphere, where the growing oxide is seen not as a continuous random lattice but instead as a granular random lattice through which oxygen diffusion occurs. A reactive layer connects the oxide with the Si bulk at the ${\mathrm{SiO}}_{2}$/Si interface. The model is applied to a representative set of experimental results, obtained at different temperatures and oxygen pressures, leading to a consistent picture of the oxidation process in terms of a fractal geometry with a definite correlation length \ensuremath{\xi}\ensuremath{\simeq}4 nm, and random-walk dimension ${\mathit{d}}_{\mathit{w}}$\ensuremath{\simeq}3.25.