4.2.1 Layer-Based Method

The layered structure of many devices allows a simplified generation of three-dimensional meshes. Overlaying all layer descriptions into a two-dimensional graph unifies all lateral structural information (Fig. 4.3).

Figure 4.3: Overlaying two layer descriptions and lateral two-dimensional unstructured mesh.

An unstructured triangular mesh is generated for this graph. The resulting triangles are extruded into the third dimension and multiplied for every layer of the device. A following tessellation of the prisms yields the three-dimensional tetrahedral mesh. Local adaptation can be applied to the lateral unstructured mesh, but it will be propagated throughout the third dimension. A detailed description of this method can be found in [13]. Figures 4.4 and 4.5 show an example where a part of the interconnect layout is analyzed for parasitic effects.

Figure 4.4: Layout structure description.

Figure 4.5: Interconnect simulation of a part of the layout using a layer-based product mesh.

Regarding the suitability for anisotropy, lateral planar thin layers can be managed in a trivial way. The orthogonality of the elements resolving such a lateral thin layer is a trivial and welcome by-product of this method. With some limitations thin layers formed by parallel planes which are normal to the lateral expansion -- they lie in the direction of the extrusion -- can be managed as well: If the two-dimensional unstructured method is not capable of producing anisotropic two-dimensional elements for the lateral structure, the resulting lateral mesh will contain a large number of very small triangles. Due to the missing third dimension the number will still be at limits manageable. The following extrusion will introduce a number of needle elements which has the same order of magnitude as the number of small triangles. Hence, the thin layer which is normal to the lateral orientation is not ideally meshed but managed. Arbitrary thin layers (non-planar, non-parallel, non-aligned) cannot be handled with this method.