An example using the analytical model for oxide growth has been shown in Section 3.7.3.
In the example to be discussed, we evaluate the grid generation strategies
implemented in PROMIS (cf. Section 3.3.3). A structure
with 
etched recess, 
Å native oxide and a 
nitride mask is oxidized for 
at 
in wet ambient. This
oxidation process was simulated using a provisional implementation of the
equations (4.1-1) - (4.1-3).
With the oxide growing process calculated in advance, we solved the oxidation enhanced diffusion problem in the beneath silicon segment using model OED (cf. Section 3.2.3). We applied different grid generation methods and judged the quality of the generated grids upon the CPU-time required for solving the diffusion problem in the silicon segment. The time for the grid generation is negligible in all cases.
Figure 4.2-1 shows the initial structure and the final silicon
shape with an algebraically generated grid. The same structure with a grid
generated by an elliptic method is shown in Figure 4.2-2. Another
grid for this structure, generated with a variational method
(
, 
,
) has already been shown in Section 3.3.1
(Figure 3.3-4).
In Figure 4.2-3 the relative computation time for the solution
with respect to the algebraic case is shown. The elliptic grid saves about
of CPU-time, if at least 5 boundary orthogonality iterations are
used. With suitable parameters 
, 
and 
a
variational grid saves up to 
of CPU-time.
From Figure 4.2-3 we clearly see that orthogonality at the boundary and area control are most important, followed by some smoothness control, and then orthogonality in general. Note that, historically, orthogonality has received the most attention.
