Clock Tree Synthesis Considering Slew Effect on Supply Voltage Variation

Abstract

This work tackles a problem of clock power minimization within a skew constraint under supply voltage variation. This problem is defined in the ISPD 2010 benchmark. Unlike mesh and cross link that reduce clock skew uncertainty by multiple driving paths, our focus is on controlling skew uncertainty in the structure of the tree. We observe that slow slew amplifies supply voltage variation, which induces larger path delay variation and skew uncertainty. To obtain the optimality, we formulate a symmetric clock tree synthesis as a mathematical programming problem in which the slew effect is considered by an NLDM-like cell delay variation model. A symmetry-to-asymmetry tree transformation is proposed to further reduce wire loading. Experimental results show that the proposed four methods save up to 20% of clock tree capacitance loading. Beyond controlling slew to suppress supply-voltage-variation-induced skew, we also discuss the strategies of clock tree synthesis under variant variation scenarios and the limitations of the ISPD 2010 benchmark.