THERMAL oxidation of silicon is described by the diffusion of
oxidant species through an existing oxide layer and chemical reaction at the
-interface. The chemical reaction is accompanied by a 225%
volume expansion compared to the consumed silicon so that the existing oxide
is forced away by the newly formed oxide layer. Historically, modeling of
thermal oxidation has been based upon the well-known linear-parabolic growth
model due to Deal and Grove [Dea65]. This model is inaccurate for oxide
thicknesses less than about 20
. This `very thin' oxide regime has
become very important in present technologies, and many models have been
proposed to account for the growth of thin oxides, e.g. [Ghe72],
[Ire78], [Hu84], [Sch85], [Wol89].
For two-dimensional modeling of oxidation the mechanical behaviour of the growing oxide can no longer be ignored. Specifically, oxide is known to exhibit fluid flow at process temperatures, but there is no concensus as to whether it is viscous, viscoelastic, or even plastic flow [Chi83], [Kao88], [Pen90].
In this chapter we describe the model which we have implemented for calculation of the oxide growth. For standard LOCOS applications an analytical model is supplied in PROMIS' model library. This model has been used in Section 3.7.3 for simulating a field oxide isolation. For more general surface structures we have solved the equations for steady state oxidant diffusion and creeping flow of oxide with the transformation method explained in Section 3.3. However, this attempt is not rigorous enough for state-of-the-art device structures.
We applied this method for a recessed local oxidation in Section 4.2. Using the beforehand calculated oxide growing process we simulated the oxidation enhanced diffusion in the underneath silicon segment. The influence of different grid generation methods is reflected in a distinct change in CPU-time required for the solution of the equations for the coupled dopant defect system.