The need for interpolation of attributes arises for two different reasons. Firstly, input attributes may be given on entirely different, but spatially overlapping grids which have been merged and re-triangulated to form a single grid for the overlap region. Secondly, additional grid points may have been created as a result of the boundary refinement step, which do hence not carry attribute information.
In any case, one ends up with a single Delaunay grid for a given region, where attribute values are defined for certain points and are not defined for all others. The percentage of undefined values can be rather large (90% are no exception), depending on the spatial density and number of different grids that have been merged.
A practical example of this situation is shown in Figures 6.25 - 6.28. The device geometry consists of multiple segments, some are planar and some are non-planar. Attributes are defined both on a non-geometry-conform tensor product grid (Figure 6.25) which is used by the Monte Carlo simulation module (of PROMIS) for the ion implantation and on a triangular grid (Figure 6.26) that was generated by the well-known Trigen [113] grid generator. The second grid also covers the whole device geometry.
Figure 6.25: Non-geometry-conform tensor product grid defined on
a non-planar geometry
Figure 6.26: Multi-segment triangular grid
generated with Trigen
According to Algorithm 6.4 the points of these two grids have been merged to form a single point cloud which has then be triangulated after a boundary refinement step. This intermediate grid has then been split into segment-specific grids. Figure 6.27 shows the grid for the Silicon segment and Figure 6.28 shows the grid for the Oxide segment. If an input attribute is given on the triangular source grid in Figure 6.26, and an output attribute is required on the dense target grid in Figure 6.27, the majority of attribute values on the target grid have to be interpolated.
Figure: Merged triangulated grid created by
VORONOI for the Silicon segment
Figure: Merged triangulated grid created by
VORONOI for the oxide segment