Fast statistical analysis of RC nets subject to manufacturing variabilities

This paper proposes a highly efficient methodology for the statistical analysis of RC nets subject to manufacturing variabilities, based on the combination of parameterized RC extraction and structure-preserving parameterized model order reduction methods. The sensitivity-based layout-to-circuit extraction generates first-order Taylor series approximations of resistances and capacitances with respect to multiple geometric parameter variations. This formulation becomes the input of the parameterized model order reduction, which exploits the explicit parameter dependence to produce a linear combination of multiple non-parameterized transfer functions weighted by the parameter variations. Such a formulation enables a fast computation of statistical properties such as the standard deviation of the transfer function given the process spreads of the technology. Both the extraction and the reduction techniques avoid any parameter sampling. Therefore, the proposed method achieves a significant speed up compared to the Monte Carlo approaches.