Due to the progressive miniaturization of integrated circuits the exact and fast simulation of physical processes becomes more and more important. On the one hand, due to the miniaturization, parasitic effects begin to influence the device characteristics. Therefore, existing models must be extended. On the other hand, due to the reduction of the device dimension, a limited spatial expansion in the third dimension cannot be neglected any longer. At geometry corners, parasitic effects can occur and may even dominate the device behavior severely. Since these effects are not describable in two dimensions, the models must be extended to three dimensions and the development and simulation tools have to be adapted to three-dimensional requirements. The extension of the simulation tools involves the extension of the simulators, which contains the adaption for three-dimensional structure descriptions and the embedding of the new and extended models. Additionally, the mesh generators must be extended for three dimensions. Since the necessary amount of data and computing time that is needed for the simulation increases enormously, it is inevitable to adapt the simulation meshes to the given requirements in order to obtain accurate simulation results even with limited resources. As will be shown this task is far from trivial.

In the context of this work the issue of three-dimensional mesh generation for specific simulation problems in microelectronics is outlined. Chapter 4 describes the development of a method for the fast computation of diffusion processes in simple semiconductor structures. Since diffusion processes are transient procedures, an exact three-dimensional simulation needs a set of simulations on partially very dense meshes. Therefore the required computing time can increase enormously. With the developed method, a Green's Function approach of the diffusion equation can be used if complicated nonlinear models can be neglected, which offers the advantage to supply the final diffusion profile after only one simulation step. It can be performed without the frequent computation of only temporarily used distributions. Moreover, with this method the result is independent of the simulation mesh. Since the meshes, holding the initial and the final distribution, are independent, both of them can be adapted to their respective requirements.

An adapted Delaunay mesh generation approach for the electrical simulation of semiconductor devices is described in the following chapter. Since particularly with the simulation of MOS transistors a very high resolution of the mesh is necessary below the gate oxide, global mesh refinement methods are impracticable due to high resource consumption. The frequently used ortho grids, where an anisotropic grid density can be relatively easily obtained, cannot be used with non-axes-parallel and non-planar geometries. With the developed method, the grid points are placed along computed equipotential surfaces. Since the positive characteristics of the ortho grids are preserved, the mesh lines near the surface match the contours of the geometry edges and no restriction on planar structures exists. Along these equipotential faces a high point density can be selected within desired regions. A further advantage of this method is that the point density can be tuned in relation to the direction, along three almost orthogonal axial directions, which results in controllable anisotropy. Similar procedures are well-known as elliptical grid generation.

Finally, the relevance of each topic is clarified by accomplished applications. The boundary region of a power field-effect transistor is optimized concerning its electrical characteristics with the help of the diffusion simulation. The developed potential method is used for the development of a simulation mesh of a FinFET structure. A final example shows a complete process simulation of an EEPROM memory cell, whereby also the potential method is used in a somewhat modified operational area.

J. Cervenka: Three-Dimensional Mesh Generation for Device and Process Simulation