Quadratic Backward Propagation of Variance for Nonlinear Statistical Circuit Modeling

Accurate statistical modeling and simulation are keys to ensure that integrated circuits (ICs) meet the specifications over the stochastic variations that are inherent in IC manufacturing technologies. Backward propagation of variance (BPV) is a general technique for statistical modeling of semiconductor devices. However, the BPV approach assumes that statistical fluctuations are not large so that variations in device electrical performances can be modeled as linear functions of process parameters. With technology scaling, device performance variability over manufacturing variations becomes nonlinear. In this paper, we extend the BPV technique to take into account these nonlinearities. We present the theory behind the technique and apply it to specific examples. We also investigate the effectiveness of several possible solution algorithms.