Statistical decoupling capacitance allocation by efficient numerical quadrature method

In this paper, we propose a novel statistical decap allocation method to reduce the voltage drop noise in the presence of variational leakage current sources. The new method can derive the closed form of decoupling capacitance (decaps) in terms of variational parameters from the variational leakage currents. It treats the deterministic decap method as a black box and can work with any existing simulation-based methods. The new method employs the orthogonal polynomials to represent the variational gate leakages in a closed form first. Decap distributions are then computed by a fast multi-dimentional Gaussian quadrature method with sparse grid technique. Experimental results show that the proposed method can deliver order of magnitudes speedup over the Monte Carlo method with almost the same accurancy.