Fast and efficient modeling methods for substrate coupling in VLSI circuits

Crosstalk due to substrate coupling is a severe prohibitive problem in today's submicron mixed-signal and system-on-a-chip designs. This thesis addresses the phenomenon of substrate coupling and presents closed-form formulas, efficient numerical techniques, and an analytical solution to the modeling of behaviour and effects of substrate coupling. It also applies the developed methods to a number of examples and reports the results.; The closed-form formulas characterize the behaviour of contact-to-substrate coupling. These formulas are obtained in two ways through exhaustive simulations and the application of the microstrip lines theory. A good agreement between the results obtained from the two approaches verifies the accuracy of the formulas. Also, the efficiency of the proposed models, their applicability to two-layer substrates, and the accurate modeling of spiral inductors using these formulas are demonstrated.; The numerical analyses are based on boundary-element methods. We derive several fast-convergent Green's functions, in general and simplified forms, for various substrate types and various levels of application. Part of this work is devoted to developing accurate models for substrate parasitic elements and two modeling techniques for large circuits, where the Green's functions are effectively involved. The accuracy and efficiency of the proposed models are demonstrated through some examples. In addition, they are applied to a mixed-signal RF IC for substrate crosstalk analyses.; The fully analytical approach to modeling substrate coupling consists of solving a fourfold integration of the proposed Green's functions. Compared to the numerical techniques, the analytical solution improves accuracy and lowers computation time.; The thesis concludes by presenting a methodology for modeling substrate coupling in VLSI circuits. The mutual shielding effects of the contacts on substrate coupling are analyzed in detail. We show that the total coupling of each component in a complex substrate structure can be computed from the corresponding decomposed problem set.