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-SiO
2
interface 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-SiO
2
interface 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-SiO
2
interface is found to be about 0.4-1.0/µm within the oxidation temperature range between 900° and 1100°C.