| A limiting factor for the signal integrity and reliable operation of tightly integrated analog/mixed-signal circuits is the parasitic interaction among circuit components on-chip through the semiconductor substrate, commonly referred to as substrate coupling. In this thesis a method is described for electrically characterizing the parasitics between a number of contacts representing the noise interaction ports in the substrate coupling problem. It is based on an integral equation formulation of the problem that makes use of the electroquasistatic Green's function for arbitrary, planar, layered media. This function is given in terms of an integral function over a semi-infinite interval, with no analytical solution. To impove the efficiency of the method, a numerical function-fitting method is introduced that results in closed-form formulas for the fast and accurate calculation of the impedance matrix elements.;For a full-wave modeling of the substrate coupling problem the thesis elaborates on a number of features for the time domain finite integration technique (FIT), a volumetric discretization scheme, aimed at improving its computational performance for the type of geometrical characteristics encountered in substrate coupling problems on-chip. Along these lines, the implicit Newmark-beta scheme is proposed as the time-marching scheme to overcome the severe restrictions on the maximum stable time step imposed by stability constraints to the more frequently used explicit leapfrog scheme. Furthermore, a previously proposed FDTD subgridding scheme, based on a finite element method (FEM) formalism, has been reformulated and adapted to work within the FIT framework. One important element of the presented subgridding scheme is that it maintains the transpose property between the discrete curl operators for electric and magnetic fields. This is a key ingredient for the implementation of a global discrete system that is energy conserving, consistent with the modeled continuous problem; hence any subgridding induced, late time instabilities are avoided. |
