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

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, our timing methodology has implemented block-based statistical timing analysis (StTA) (for path selection) and path-based StTA (for timing accuracy). We verified our method by comparing our results to SPICE using ten ISCAS85 benchmark circuits. The average errors in the circuit-delay mean and standard deviation (SD) are 1.47% and -1.15% respectively. We also compared our method with traditional quadratic delay models and achieve significant accuracy improvement and consume 38% less run time.