An efficient 3D Green´s function approach for fast impedance extraction of interconnects and spiral inductors in CMOS RF/Millimeter-wavelength circuits

Compact modeling and design of spiral inductors and interconnects in RF/mm-wave circuits require accurate yet efficient computation of their impedances. Till date, this task relies on electromagnetic (EM) field solvers with computational expense that does not scale beyond a few individual circuit components. This paper introduces an approach to compute impedances of interconnects and multiple inductors over a typical multi-layered substrate, as well as the electromagnetic couplings between them. The proposed methodology is based on a three-dimensional (3D) loop formalism that uses discrete complex images approximations applied to a quasi-magnetostatic treatment of the vector potential. The accuracy and performance - errors less than 3% and 5% with respect to quasi-static and full-wave field solvers, respectively, with an order of magnitude lower computation cost - make it possible, for the first time, to overcome the scalability limitations of traditional EM field solvers in handling multiple interacting on-chip inductors up to 100 GHz.