A Spectral Stochastic Collocation Method for Capacitance Extraction of Interconnects with Process Variations

In this paper, a spectral stochastic collocation method (SSCM), is proposed for the capacitance extraction of interconnects with either on-chip process variations or off-chip rough surfaces. The proposed method is based on the stochastic spectral method combined with sparse grid technique, and has several advantages over the existing methods. Compared with the perturbation method, the stochastic spectral method based on homogeneous chaos expansion has exponential convergence rate, which makes it very promising for parasitic extraction with process variations. Furthermore, the sparse grid technique significantly reduces the amount of sampling points compared with Monte Carlo method, and greatly saves the computation time for capacitance extraction. Numerical experiments have demonstrated that SSCM can achieve higher accuracy while having the same efficiency compared with the existing methods