Robust Clock Tree Synthesis with timing yield optimization for 3D-ICs

Abstract

3D integration has new manufacturing and design challenges such as timing corner mismatch between tiers and device variation due to Through Silicon Via (TSV) induced stress. Timing corner mismatch between tiers is caused because each tier is manufactured in independent process. Therefore, inter-die variation should be considered to analyze and optimize for paths spreading over several tiers. TSV induced stress is another challenge in 3D Clock Tree Synthesis (CTS). Mobility variation of a clock buffer due to stress from TSV can cause unexpected skew which degrades overall chip performance. In this paper, we propose clock tree design methodology with the following objectives: (a) to minimize clock period variation by assigning optimal z-location of clock buffers with an Integer Linear Program (ILP) formulation, (b) to prevent unwanted skew induced by the stress. In the results, we show that our clock buffer tier assignment reduces clock period variation up to 34.2%, and the most of stress-induced skew can be removed by our stress-aware CTS. Overall, we show that performance gain can be up to 5.7% with our robust 3D CTS.