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.