Abstract

This thesis deals with different methods for the numerical calculation of
inductances in interconnect structures. Two of these methods are based on the
numerical integration of the Neumann formula, the third on an approach via the magnetic vector potential. All of them use the finite element
method for the precalculation of the current density in the interconnects. The
geometrical modeling is done with an unstructured tetrahedral mesh to gain
high flexibility and to ensure a latter integration of the process flow. Hence,
some simplifications compared to the real geometry, as other published approaches do implicitly, are obsolete. For example, other approaches are
not able to handle more general structures, only geometries can be treated,
which are build by prisms elements.

The first implemented method utilizes a scheme of different integration formulae based on triangles and tetrahedrons. The second evaluates the Neumann formula with the Monte Carlo method. This is performed by efficient localization of the elements for the random point coordinates to compute this integral. Classical implementation of the Monte Carlo method, where the whole geometry has to be hunted for the associated element loses efficiency. The third method is based on a rigorous approach using the magnetic vector potential to take a steady state electromagnetic analysis that can be extended for time dependent problems.

C. Harlander: Numerische Berechnung von Induktivitäten in dreidimensionalen Verdrahtungsstrukturen