Mesh generation is the partitioning of a domain into a large number of simple pieces called elements. The domain is usually defined through the boundary of a geometrical structure or given by a Computer Aided Design (CAD) model. The elements must be well connected, neither gaps nor overlapping elements are permitted. A numerical analysis or computer simulation involves the formulation of i.e. non-linear coupled partial differential equations which describe the physical problem on a physical domain, in terms of algebraic equations on the discrete domain. The large system of linear algebraic equations which is assembled after discretization can be solved using direct or iterative solvers.

Among the various approaches [156,193,154]
the *finite element
method* and the *finite volume method* or *control volume
method* are the most established discretization schemes.
All methods imply specific qualities of the generated mesh to ensure
convergence of the iterative solution process and to yield correct
simulation results.
With the growing importance of three-dimensional simulation mesh
generation has become a critical factor. Surprisingly the generation
of a suitable mesh often becomes the bottle neck and poses more
difficulties than the subsequent simulation.
The amount of data in three
dimensions requires efficient and more sophisticated algorithms and
data structures. Meshing algorithms which have worked well for
two-dimensional problems are often not feasible for higher dimensions.
Manual partitioning techniques are not desirable and cannot be
efficiently applied to model descriptions which contain several
thousand or more vertices.
At the same time automatic meshing schemes are challenged by the
increasing topographical complexity of the CAD model.

This situation is also experienced in semiconductor device and process simulation. The complexity of a modern semiconductor device often makes a three-dimensional analysis necessary to capture important physical effects which would not be exhibited by idealization to fewer dimensions. With the upcoming of three-dimensional device and process simulation the importance of three-dimensional mesh generation for Technology CAD (TCAD) has significantly increased. The stiff and highly non-linear equations governing the behavior of a semiconductor device [156] and the moving boundary situation during oxidation in process simulation require a powerful and efficient meshing tool. The need for a better fitted mesh with regard to certain quality or error measures necessitates fast global and local mesh adaptation techniques. Local remeshing also becomes important to repair mesh deformations resulting from moving boundaries and interfaces of the semiconductor device.

2000-01-20