A Spectral Stochastic Collocation Method for Variation-Aware Capacitance Extraction of Interconnects under Nanometer Process Technology

In this paper, a Spectral Stochastic Collocation Method (SSCM) is proposed for variation-aware capacitance extraction of interconnects for nanometer process technology. The proposed SSCM has several advantages over the existing methods. Firstly, compared with the PFA (Principal Factor Analysis) modeling of geometric variations, the K-L (KarhunenLoeve) expansion involved in SSCM can be independent of the discretization of conductors, thus significantly reduces the computation cost. Secondly, compared with the perturbation method, the stochastic spectral method based on Homogeneous Chaos expansion has optimal (exponential) convergence rate, which makes SSCM applicable for most geometric variation cases. Furthermore, Sparse Grid combined with a MST (Minimum Spanning Tree) representation is proposed to reduce the number of sampling points and the computation time for capacitance extraction at each sampling point. Numerical experiments have demonstrated that SSCM can achieve higher accuracy and faster convergence rate compared with the perturbation method.