Boundary Sensitive Mesh Generation using an Offsetting Technique

2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, August 1999

MESHING
RESEARCH
CORNER

Integrated Systems Laboratory, ETH Zurich, CH-8092 Zurich, Switzerland
jens.krause@iis.ee.ethz.ch

Abstract
In the simulation of semiconductor processes and devices it can be necessary to generate surface parallel meshes. One important examples is electron current 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 [1]. If the interface is not axis aligned an quadtree based approach does not generate meshes of this quality, resulting in a larger numerical error.

We present here a modified advancing front 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. Here we follow references [2] and [3], but we use a different point location scheme, in that sense that the opposite face 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.

As it turns out the final mesh quality depends on the initial boundary discretization. Especially at areas of high curvature a fine grid is necessary.

The generation of offsetting layers stops when the front intersects itself and the remaining polygon is triangulated. As a final step the mesh is converted to a Delaunay conforming mesh by swapping edges and inserting points. In this algorithm a set of edges is restricted from being swapped; beside the interface edges these are the parallel edges in the offsetting process.

The implementation in two dimensions has been tested successfully in device simulations.

In order to resolve internally boundary layers, e.g. steep doping gradients in a process simulation we can incorporate an appropriate set of isolines into the initial front.

References:

[1] G. Garreton, 'A Hybrid Approach to 2D and 3D Mesh Generation for Semiconductor Device Simulation', PhD thesis, Integrated Systems Laboratory, ETH Zurich, 1999

[2] B.P. Johnston, J.M. Sullivan, 'Fully Automatic two dimensional mesh generation using normal offsetting', International Journal for Numerical Methods in Engineering, 1992, Vol. 33, 425 - 442

[3] T.D. Blacker, M.B. Stephenson, 'Paving: A New Approach to Automated Quadrilateral Mesh Generation',International Journal for Numerical Methods in Engineering, 1991, Vol. 32, 811 - 847