Substrate coupling modeling in integrated circuits using analytical Green´s function

The aim of this paper is the development of two different analytical Green´s functions for the modeling of the substrate electrical coupling in integrated circuits. The first procedure solves directly the Poisson´s equation of the substrate as a two-layer problem using the adequate boundary conditions. An accurate and stable expression is obtained which is compared to other numerical methods. The second one is an heuristic approach that divides the actual substrate in two single one-layer substrates; although the accuracy is reduced, the computation of the coupling is faster. Both models are applied to the computation of the capacitance between two contact patches.