This thesis elaborates electromagnetic numerical simulations in microelectronics for field calculations and parameter extraction in interconnect structures based on the finite element analysis with the special usage of edge elements. The method is demonstrated by the quasi-magnetostatic case, which is well suited for the small simulation domains typical for the interconnects in modern integrated circuits even at very high frequencies. In a similar way the proposed approach can be applied to the wave equation for the electric field or to the equations for the electrodynamic potentials in the frequency domain. It is not difficult to see, that the assembling formulas for the element matrices proposed can be used without any modifications, just the notation of the field variables and the constitutive parameters taking part are different. Of coarse, the way how to apply the boundary conditions and how to extract the corresponding parameters must be reconsidered.
The assembling of the approximation of the Neumann boundary conditions is given in the appendix for further implementation. This will allow inhomogeneous Neumann boundary conditions to be taken into account. It can be also used as a foundation for future integration of a combination of the finite element method with a boundary integral method for the analysis of open domains.
Another interesting area for further development and implementation represents the treatment of higher order vector finite elements to achieve efficiently better accuracy of the simulation results. In this case the efficiency bears on the computation, the research and adaptation of the method is much more difficult.
In spite of the fact that the simulation in the frequency domain meets the requirements for a large amount of applications, it is not sufficient, if nonlinear (field dependent) parameters are used. In such a case time domain edge finite element techniques must be addressed and the parameters have to be updated with each computational time step.