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 criterion^3.3: 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 density^3.4. 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