3.4.1 Moving Boundaries

Element deformation, moving mesh points, and changing structure boundaries occur for instance during the oxidation step in semiconductor process simulation. The situation is often referred to as a local adaptation problem, because portions of the mesh remain unchanged and should be reused. It is not feasible to repeatedly mesh the entire domain with every slight change of the structure boundary and to transfer the data to the completely new set of mesh points. However, difficulties arise when the device structure changes qualitatively. The existing surface mesh topology may not be suitable to represent the new boundaries and interfaces correctly. More global techniques might be necessary to extract a new surface mesh in such cases (see Section 3.5). In this sense moving boundaries during oxidation are related to moving surfaces during topography simulation of etching and deposition steps. Although in the latter case no internal mesh points are moving and the translation velocities are only applied to points of the surface, techniques from etching and deposition tools might successfully be applied to oxidation.

When the mesh is only distorted the following local adaptation steps suffice to maintain mesh quality and consistency.

1. The mesh points are moved and the elements are deformed. Ideally this happens only inasmuch as certain constraints are fulfilled. An effective and simple to implement constraint is to check the sign of the volume of the mesh element to avoid folding and overlapping elements. A mesh point can then only be moved as far as none of the volumes of the incident elements reaches a too small value. It might be necessary to cover the exterior of the structure with an outside mesh to fully detect all possible areas of collision.
2. Through a linear scan too small, too large, badly shaped, or extremely distorted elements are tagged. If no constraints enforcing consistency were applied in the previous stage, the detection of overlapping elements would be much more costly at this stage. If the mesh is ``folded'', elements with a negative volume could be detected easily, but their removal does not restore the consistency. A large number of positive elements would have to be checked as well for possible overlappings.
3. Tagged elements are removed with the usual techniques of refinement and local transformation (see following paragraphs). This changes the internal mesh topology (not the topology of the surface) so that a further translation of the mesh points including previously constrained points becomes possible. It is returned to step one and the process is repeated as long as changes are significant or the end time of the simulation is not reached.