Accurate Standard Cell Characterization and Statistical Timing Analysis using Multivariate Adaptive Regression Splines

Taizhi Liu,  Chang-Chih Chen,  Linda Milor
Georgia Institute of Technology


This paper proposes a methodology for standard cell characterization which contains three models: an input capacitance model, a sensitivity model for variational resistive-capacitive loads, and gate and interconnect delay models via multivariate adaptive regression splines (MARS). Our MARS-based methodology has several advantages. Firstly, MARS captures nonlinearities and interactions for high-dimensional problems. Secondly, MARS is an adaptive and intelligent procedure that can ‘filter out’ negligible parameters without manual intervention while characterizing a complex cell with over 40 devices. Thirdly, we extend our work to path-delay estimations, which achieve significant accuracy for each sample and thus only requires a small sample size for accurate path-delay distribution estimation. We verified our method by comparing our results to SPICE using paths in ten ISCAS85 benchmark circuits. The average errors in the circuit-delay mean and standard deviation (SD) are 0.71% and 1.25%, respectively, and the computational complexity is linear as a function of path depth and sample size. We also compared our method with traditional quadratic delay models and achieve significant accuracy improvement and consume 38% less run time.