FEDOS stands for Finite Element Diffusion and Oxidation Simulator and is in principle a framework for three-dimensional process simulation, which is based on the finite element method. The name has more traditional character and does not enumerate all its abilities, because, when FEDOS was launched, it was only planned to simulate different forms of diffusion and thermal oxidation processes. Since the concept of FEDOS allows to simulate all process phenomena, if the problem can be formulated with the finite element method, it is also used for the investigation of other process topics like electromigration or stress analysis. In the course of this doctoral work FEDOS was extended and modified for the simulation of oxidation and various kinds of stress analysis.
The finite element method offers some benefits in process simulation compared with other numerical techniques. At first it enables to discretize all kinds of (partial differential) equations in a similar way and with good mathematical stability. Because FEM was developed for mechanical simulation, it is also most suitable for displacement problems as occur during thermal oxidation. Another advantage is that after the discretization of the equations which describe the respective physical phenomenon analytically, FEM only needs standardized routines to built up the global equation system. This means that in FEDOS the same assembling procedure can be used for all different process models.
The FEM formulation goes hand in hand with the used elements. In the current version FEDOS is designed for simulation regions which are exclusively discretized with tetrahedrons and linear shape functions. Since the accuracy can be increased with a finer mesh, which means more elements, the linear FEM approach meets all requirements and has the advantage that it is the most simple FEM formulation (see Section 5.2). Furthermore, tetrahedrons are qualified for fitting non-planar surfaces with coarse elements in acceptable quality.
Regarding the implementation aspect an advantage of FEDOS is that a new model can be included in a straightforward procedure. It is only necessary that the new model is implemented in C++ with a defined interface in a separate file. For including a model in FEDOS only a knowledge about the program interface is demanded, but not about the complex internal FEDOS routines or even other models. The new model must only supply the finite element formulation of the discretized equations which describe the phenomena on a single element.