Hexahedral Mesh Generation of Layered Solids with Sloped Laterals

We present an algorithm for fully-automated all-hexahedral mesh generation for 3D models of Very Large Scale Integration (VLSI) geometries, based on layered 2D polygonal mask layouts as input. Specifically, we propose a mapping procedure in three stages, based on integrating topology of 2D polygon sets from different layers, which define the architecture of a 3D VLSI geometry model. Three successive steps ensure that all geometric levels share the same topological structure, enabling extruded 3D meshing. In the first stage, the intersections between each pair of polygon sets are collected from top to bottom. The polygon sets which are absent on lower geometric levels are mapped downward. In the second stage, the polygon sets which are absent on upper geometric levels are mapped upward. In the third stage, we integrate the topology of each geometric level and construct a mapping through the levels. Finally, we generate a quadrilateral mesh on the bottom level and extrude the mesh to a hexahedral mesh through the mapping generated by the third stage. In the examples, we present the full hexahedral meshing result of various 3D models representing various sections of typical VLSI geometries. Moreover, we applied a quadrilateral and a hexahedral mesh optimization to ensure the validity of the meshes.