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5.4.1 First approach of Local Oxidation
The first problem that has been successfully solved had a comparable
simple geometry. Nevertheless it was a big progress in the
development, since it was not sure if the developed model will lead to
acceptable results because of the numerical conditions:
- Instead of decoupling the diffusion and displacement calculation a coupled system has to be solved:
- The characteristics of the quantities differ in magnitudes of order.
- The immediate jump of the material (silicon and silicon dioxide interface) within the transition zone may cause problems concerning convergence.
- High reactive terms (5.19) at the interface are reducing the convergence behavior of the total system.
- The implicitly solved boundary movement, that requires a Lagrange formulation, where even the shape functions
itself have to be considered to calculate the Jacobian matrix.
As first example two typical three-dimensional effects occurring in the
corners of the nitride mask have been calculated
(Fig. 5.7 and Fig. 5.8). Starting
from a pure silicon block the results show, that the introduced model
can even handle structures without pad oxide below the nitride mask.
This leads to the effect that the interface meets the nitride layer
vertically that can hardly be solved by algorithms based on a sharp
interface formulation. Nevertheless, the interface conditions are too
smooth for a physical interpretation of the material interface and an
improvement must be made using grid adaptation to accurately resolve
the interface layer.
Figure 5.7:
Oxide growth around a nitride mask covering one quarter of the geometry
|
Figure 5.8:
Oxide growth around a nitride mask covering
three quarters of the geometry
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Next: 5.4.2 Local oxidation with
Up: 5.4 Three-Dimensional Simulation Results
Previous: 5.4 Three-Dimensional Simulation Results
Mustafa Radi
1998-12-11