In this paper, we propose a novel stochastic method for analyzing the voltage drop variations of on-chip power grid networks with log-normal leakage current variations. The new method, called StoEKS, applies Hermite polynomial chaos (PC) to represent the random variables in both power grid networks and input leakage currents. But different from the existing Hermit PC based stochastic simulation method, extended Krylov subspace method (EKS) is employed to compute variational responses using the augmented matrices consisting of the coefficients of Hermite polynomials. Our contribution lies in the combination of the statistical spectrum method with the extended Krylov subspace method to fast solve the variational circuit equations for the first time. Experimental results show that the proposed method is about two-order magnitude faster than the existing Hermite PC based simulation method and more order of magnitudes faster than Monte Carlo methods with marginal errors. StoEKS also can analyze much larger circuits than the exiting Hermit PC based methods.
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