The interstitial supersaturation (
) at
the 
-interface due to oxidation exhibits approximately a
half-power dependence on the oxidation rate, i.e. the velocity of the
interface 
, and therefore is expressed
as (3.2-29).
Here, 
describes the orientation- and temperature dependent
point defect generation, and 
includes the temperature dependence of
the effect of chlorine additions. Chlorine additions (partial pressure
) to the oxidation ambient is known to reduce the excess
interstitials. The increasing interstitial concentration will reduce the
vacancy concentration by recombination such that 
.
The point defects diffuse quite fast, thus the interstitial supersaturation
extends considerably into the bulk. A reasonably conservative assumption for
a vertical decay length is 
. Already Lin
[Lin79] noticed, that the lateral OED effect below a mask extends just
a few microns (
). Assuming that the
supersaturation 
at a lateral position 
at the
-interface causes a two-dimensional Gaussian point response, we
get the two-dimensional analytical approximation of the interstitial
supersaturation, and therefore the interstitial profile, from the
convolution (3.2-30).
The diffusion equations for the dopants are identical to the equations for
the model DIFC (3.2-2) and (3.2-5), the
diffusivities 
are taken from Table 3.2-1, and 
are modeled according (3.2-28) with the local point defect
concentration from (3.2-30).
The boundary conditions for the impurity diffusion at the
-interface is (3.2-31) [Sei83], with 
the equilibrium segregation coefficient and 
the ratio of consumed
silicon to produced oxide. Zero flux boundary conditions are used at the
other (artificial) boundaries for all species.
Parameter values for the analytical point defect model are summarized in Table 3.2-5.
