Cui et al. propose a novel statistical capacitance-extraction method, StatCap, for three-dimensional (3D) interconnects considering process variations. The new method is based on the spectral stochastic method, where orthogonal polynomials are used to represent the variational geometrical parameters in a deterministic way. It avoids the sampling operations in the existing spectral stochastic method [1] that is based on the Hermite orthogonal-polynomial representation of variational capacitances. In this paper, Cui et al. obtain the coefficients of orthogonal polynomials for capacitances of an enlarged potential coefficient system.

This method involves a first-order form using Taylor expansion and orthogonal decomposition. It derives an augmented potential coefficient matrix consisting of the coefficients of the polynomials, and then solves the corresponding system to obtain the variational capacitance values in the orthogonal-polynomial form. The method needs to set up the augmented equation only once, and can exploit the sparsity and low-rank property to speed up the extraction process.

Experimental results show that this method is two orders of magnitude faster than the recently proposed statistical capacitance-extraction method--based on the spectral stochastic collocation method (SSCM), and many orders of magnitude faster than the Monte Carlo method for several practical interconnect structures.