3.3.3 Final Remarks

Since the box integration method is not limited to orthogonal grids, it has a basic advantage over the finite difference method due to its greater geometrical versatility. However, this greater versatility is payed for by a more difficult grid generation. The vertices connecting two grid points must be chosen in such a way that negative coupling between the grid points is avoided.

One method to obtain a grid of triangles in the simulation domain is to use the DELAUNAY criterion3.3: Given any set of points distributed over a simulation domain, the DELAUNAY criterion requires that the sum of two facing angles obtained from a triangulation is never larger than $ \pi$. However, the plain DELAUNAY algorithm must be supplemented by a number of empirical constraints, which become necessary when dealing with internal interfaces. Moreover, since the algorithm works on a pre-defined set of points, a local grid refinement requires the entire tessellation to be repeated. More details according to DELAUNAY triangulation can be found in [54].

Another method to get a simulation grid is to use a regular mesh structure within the device inner region, such as a rectangular grid. A set of nested rectangles can be used to modulate the mesh point density3.4. Local refinements can be easily performed by splitting any given rectangle into two or four smaller elements. The rectangle set can be easily converted into a set of triangles by diagonalization [11, p.72].

M. Gritsch: Numerical Modeling of Silicon-on-Insulator MOSFETs PDF