This paper presents an effective formulation tailored for electromagnetic-technology computer-aided design coupled simulations for extremely-high-frequency ranges and beyond (>;50 GHz). A transformation of variables is exploited from the starting A-V formulation to the E-V formulation, combined with adopting the gauge condition as the equation for scalar potential. The transformation significantly reduces the cross-coupling between electric and magnetic systems at high frequencies, providing therefore much better convergence for iterative solution. The validation of such transformations is ensured through a careful analysis of redundancy in the coupled system and material properties. Employment of the advanced matrix permutation technique further alleviates the extra computational cost introduced by the variable transformation. Numerical experiments confirm the accuracy and efficiency of the proposed E-V formulation.

This is the second paper in a series on the simulation of on-chip high-frequency effects. A computer-aided approach in three dimensions is advocated, describing high-frequency effects such as current redistribution due to the skin-effect or eddy currents and the occurrence of slow-wave modes. The electromagnetic environment is described by an electric scalar potential and a magnetic vector potential as well as a ghost field. The latter one guarantees a stable numerical implementation. This paper deals with the software implementation, the treatment of interfaces and domain boundaries, scaling considerations, numbering schemes, and solver requirements. Some illustrative examples are shown.

This paper presents a new method to discretize the equations for the physical modeling of semiconductor devices and back-end patterns. The method assembles planes in two dimensions and cubes in three dimensions and allows for adaptive meshing without the occurrence of spurious nodes due to mesh smoothing. Whereas the applications that are discussed focus on the design of microelectronic devices, the method is generally applicable to all fields of engineering where ab initio physical modeling is required.

In order to design on-chip interconnect structures in a flexible way, a computer-aided design approach is advocated in three dimensions, describing high-frequency effects such as current redistribution due to the skin effect or eddy currents and the occurrence of slow-wave modes. The electromagnetic environment is described by a scalar electric potential and a magnetic vector potential. These potentials are not uniquely defined and in order to obtain a consistent discretization scheme, a gauge transformation field is introduced. The displacement current is taken into account to describe current redistribution and a small-signal analysis solution scheme is proposed based upon existing techniques for fields in semiconductors.