An analytical approach to efficient circuit variability analysis in scaled CMOS design

Process variations have become increasingly important for scaled technologies starting at 45nm. The increased variations are primarily due to random dopant fluctuations, line-edge roughness and oxide thickness fluctuation. These variations greatly impact all aspects of circuit performance and pose a grand challenge to future robust IC design. To improve robustness, efficient methodology is required that considers effect of variations in the design flow. Analyzing timing variability of complex circuits with HSPICE simulations is very time consuming. This thesis proposes an analytical model to predict variability in CMOS circuits that is quick and accurate. There are several analytical models to estimate nominal delay performance but very little work has been done to accurately model delay variability. The proposed model is comprehensive and estimates nominal delay and variability as a function of transistor width, load capacitance and transition time. First, models are developed for library gates and the accuracy of the models is verified with HSPICE simulations for 45nm and 32nm technology nodes. The difference between predicted and simulated σ/μ for the library gates is less than 1%. Next, the accuracy of the model for nominal delay is verified for larger circuits including ISCAS'85 benchmark circuits. The model predicted results are within 4% error of HSPICE simulated results and take a small fraction of the time, for 45nm technology. Delay variability is analyzed for various paths and it is observed that non-critical paths can become critical because of Vth variation. Variability on shortest paths show that rate of hold violations increase enormously with increasing Vth variation.