Fast Simulation Of The Process Variation Of Power Network Analysis Methods

With the rapid development of integrated circuits, the process variations affect the performance of the integrated circuits more and more seriously. The process variation in power grid make the delay and voltage distribution uncertain, so it will reduce the performance of the overall chip. Circuit simulation under process variation has become an essential tool in modern integrated circuit design, the increase of frequency and scale of integrated circuit bring great challenges into circuit simulation. In this paper, we focus the research area at two directions, one is setup the model of integrated circuits, and the other is solving the equation of circuit rapidly and exactly.In this paper, a Stochastic Non-Homogeneous Arnoldi method (SNHAR) is proposed for the analysis of the on-chip power grid networks in the presence of process variations. In SNHAR method, the polynomial chaos based stochastic method is employed to handle the variations of power grids. Different with StoEKS, we propose the Kronecker products to deal with the Hermite polynomial chaos to setup the big augment system equations, the systematic approach of matrix equation improve the efficiency in setup the model of circuit with process variations.Different from the existing StoEKS method which uses extended Krylov Subspace (EKS) method to compute the coefficients of the polynomial chaos, a computation-efficient and numerically stable Non-Homogeneous Amoldi (NHAR) method is proposed in SNHAR method to compute the coefficients of the polynomial chaos. Compared with EKS method, NHAR method has superior numerical stability and can achieve remarkably higher accuracy with even lower computational cost. As a result, SNHAR can capture the stochastic characteristics of the on-chip power grid networks with higher accuracy, but lower computational cost than StoEKS.