Boundary-sensitive mesh generation using an offsetting technique

Abstract

In the simulation of semiconductor processes and devices it may be necessary to generate surface parallel meshes. One important example occurs in MOS transistors where the electrons flow along the silicon surface underneath a gate. It is desired beneficial in terms of accuracy to have rather long mesh edges parallel and rather small edges orthogonal to those currents. For most of the devices quadtree techniques have been used with big success (Garretón G. A hybrid approach to 2D and 3D mesh generation for semiconductor device simulation. PhD Thesis, Integrated Systems Laboratory, ETH Zurich, 1999. Garretón G, Villablanca L, Strecker N, Fichtner W. Unified grid generation and adaptation for device simulation. Proceedings of SISDEP'95, Erlangen, Germany, 6–8 September 1995; 6:468–471.) If the interface is not axis aligned, however, a quadtree-based approach does not generate meshes of this quality, resulting in a larger numerical error or in convergence problems during equation solution. We present here a modified advancing front grid generator that inserts surface parallel mesh lines; the interior of the region is filled with layers of nearly rectangular quadrilaterals, and not triangles as in conventional advancing front generators (see George PL, Sveno E. The advancing front mesh generation method revisited. International Journal for Numerical Methods in Engineering 1994; 37: 3605–3619 and Schöberl. Computing and Visualization in Science 1997; 1:41–52). Here we follow references of Johnston BP, Sullivan JM. Fully automatic two dimensional mesh generation using normal offsetting. International Journal for Numerical Methods in Engineering 1992; 33:425–1pt442; Blacker TD, Stephenson MB. Paving: a new approach to automated quadrilateral mesh generation. International Journal for Numerical Methods in Engineering 1991; 32:811; Rees M. Combining quadrilateral and triangular meshing using the advancing front approach. Proceedings of the 6th International Meshing Roundtable 1997; 337–348; White DR, Kinney P. Redisign of the paving algorithm: robustness enhancements through element by element meshing. Proceedings of the 6th International Meshing Roundtable 1997; 323–335, but we use a different point location scheme, in the sense that the opposite edge of the quadrilateral is kept parallel if possible. At each layer the marching distance is increased by a coarsening factor; refinement is therefore controlled by the initial marching distance and the coarsening factor. A maximum edge length is guaranteed. The generation of offsetting layers stops when the front intersects itself. The remaining polygon is triangulated. As a final step the mesh is converted to a Delaunay conforming mesh by swapping edges and inserting points. The implementation in two dimensions has been tested successfully using realistic examples from device simulations. Copyright © 2000 John Wiley & Sons, Ltd.