Université Joseph Fourier ( Grenoble 1 )

In this Thesis, we study three problems related to the modeling of interconnects in Integrated Circuits. The common denominator among them is the use of physical arguments in order to produce efficient models that simplify the mathematical complexity of each problem. The first problem deals with a fast and accurate calculation of mutual inductance. We adopt a loop inductance formalism, wherein the circuit elements represent current loops. Within this formalism, we develop the dipole approximation, which keeps the leading-order terms for the inverse separations, and leads to significant reductions in the cost of computing mutual inductance. We show representative examples for parasitics extraction, as well as for the estimation of noise figures between intentional inductors. Ranges of validity are for separations larger than a threshold comparable the typical sizes of loops. The second problem is related to the modeling of non-uniform currents, along the conductors’ cross-sectional dimensions, due to skin and proximity effects. We represent this nonuniformity by expanding the current distribution with a reduced set of basis functions, called conduction modes, which are eigenfunctions to the differential equation satisfied by the current density inside the conductors. Our contributions fall in two main categories: on one side, we have expanded the existing one-dimensional current formulation into a three dimensional one, including currents and charges; on the other, we have systematically optimized the computation of non-trivial integrals appearing in the conduction modes formulation, translating the previously reported gains in size into savings in runtimes, of two orders of magnitude compared to the standard references. The third problem concerns the representation of the frequency behavior of loop impedance using simple circuits. In order to capture the expected transitions, we use Foster pairs. These circuits are particularly useful in conjunction with realizable circuit approaches to model order reduction. We reproduce the salient features related to proximity effects and skin effects in IC’s, and suggest enhancements to represent the frequency variation of mutual inductance between circuit elements. iii te l-0 01 65 96 9, v er si on 2 19 F eb 2 00 8