Bulk model of rapid thermal oxidation of silicon

A model of rapid thermal oxidation of silicon in dry oxygen based on the reaction of volume oxidation is constructed. It is assumed that the coefficient of oxygen diffusion for silicon dioxide decreases because of internal compressive stress, which is at a maximum near the SiO₂-Si interface; as the distance from the interface increases, this stress decreases according to the time-dependent exponential law because of viscoelastic relaxation from the value of the diffusion coefficient for strained oxide to that for fused quartz. The characteristic relaxation time of the coefficient of oxygen diffusion in silicon dioxide correlates with the relaxation time of internal stress in silicon dioxide films on silicon and with the relaxation time of the refraction index. Because the refraction index is related to the density of silicon dioxide, we arrive at the conclusion that the relaxation of the diffusion coefficient is related not only to the relaxation of internal mechanical stress, but also to the relaxation of the density of silicon dioxide.