Improved polynomial chaos discretization schemes to integrate interconnects into design environments

Recently, an efficient stochastic modeling method for interconnects with inherent variability in their physical parameters was proposed, based on applying the so-called polynomial chaos (PC) approach in conjunction with a Stochastic Galerkin Method (SGM) onto telegrapher´s equations. Although this approach was already very successful from a numerical point of view, the novel technique could not be conveniently integrated into SPICE-like solvers, limiting the applicability of the method. In this letter, the PC-SGM scheme for telegrapher´s equations is revisited, pinpointing the origin of this inconvenience and immediately allowing to mitigate the issue. By adapting the traditional discretization of the stochastic telegrapher´s equations approach, an augmented, yet deterministic, set of ordinary differential equations is obtained that turns out to be of the same type as the telegrapher´s equations, and hence, the physical property of reciprocity is preserved. Consequently, it can be directly and more efficiently handled using SPICE-like solvers, which usually assume matrix symmetries. As an application example, the variability analysis of a state-of-the-art on-chip line for millimeter-wave applications is performed in a SPICE solver.