Stochastic Delay Characterization for Multicoupled RLC Interconnects Under Process Variations

Abstract

The characterization of interconnect delay metrics in terms of process variations is an important but complicated task for statistical timing analysis in today’s integrated circuits (ICs). This paper presents a stochastic delay characterization framework for multicoupled interconnects in the presence of process variation. The proposed method starts with deriving the stochastic nodal equations for the RLC network that models multicoupled interconnects. By employing polynomial chaos (PC) expansion, a nonsampling-based stochastic prediction method, we further represent the voltage responses of network nodes as a series of orthogonal polynomials of random variables. During the expansion procedure, we use an adaptive approximation algorithm to reduce the number of required sampling points. We then use a stochastic collocation method to estimate the coefficients in the PC expansion model. With the voltage response determined as an expression of a multi-dimensional polynomial of random variables, the stochastic properties of the delay of multicoupled interconnects can be predicted. The proposed method not only takes into account the strong correlations among process variations, but also extracts an explicit delay representation for multicoupled interconnects in terms of process variations. Experimental results demonstrate that the delay characteristics predicted by the proposed method match well with the results by the brute-force Monte-Carlo method. Moreover, a significant speedup over the Monte-Carlo method has been achieved by the proposed delay characterization framework.