A two-dimensional model for the excess interstitial distribution in silicon during thermal oxidation

A steady-state solution for the partial differential equation governing the two-dimensional distribution of the excess interstitials during thermal oxidation of silicon was obtained using a finite difference method. It is assumed that the excess interstitials at the unoxidizing Si-SiO2interface are annihilated at a rate proportional to the excess interstitial concentration at the interface and the surface recombination velocity of the excess interstitials. Lin et al.´s experimental observation that the lateral diffusion length of the excess interstitials under the unoxidizing Si-SiO2interface is much shorter than the vertical diffusion length in the bulk can be explained by this interface annihilation model. Surface recombination velocity divided by the bulk diffusivity of self-interstitials in silicon at the Si-SiO2interface is found to be about 0.4-1.0/µm within the oxidation temperature range between 900° and 1100°C.