# Timing Uncertainty in 3-D Clock Trees Due to Process Variations and Power Supply Noise

Xu, H.; Pavlidis, V. F. ; Tang, X. ; Burleson, W. ; De Micheli, G.

### Abstract

Clock distribution networks are affected by different sources of variations. The resulting clock uncertainty significantly affects the frequency of a circuit. To support this analysis, a statistical model of skitter, which consists of clock skew and jitter, for 3-D clock trees is introduced. The effect of skitter on both the setup and hold time slacks is modeled. The variation of skitter is shown to be underestimated up to 36% if process variations and dynamic power supply noise are considered separately, which highlights the importance of this unified treatment. Potential scenarios of supply noise in 3-D integrated circuits (ICs) are investigated. 3-D circuits generated from industrial benchmarks are simulated to show the skitter under these scenarios. The mean and standard deviation of skitter can vary up to 60% and 51%, respectively, due to the different amplitudes and phases of supply noise. The tradeoff between skitter and the power consumed by clock trees is also shown. A set of guidelines are presented to decrease skitter in 3-D ICs. By applying these guidelines to industrial benchmarks, simulations show a decrease in the mean skitter up to 31%.