A Multiple Level Network Approach for Clock Skew Minimization with Process Variations

Makoto Mori, Hongyu Chen, Bo Yao and Chung-Kuan Cheng
July 28, 2003

In this paper, we investigate the effect of multilevel network for clock skew. We first define the simplified RC circuit model of a hybrid clock mesh/tree structure. The skew reduction effect of shunt segment contributed by the mesh is derived analytically from the simplified model. The result indicates that the skew decreases proportionally to the exponential of -R1/R, where R1 is the driving resistance of a leaf node in the clock tree and R is the resistance of a mesh segment. Based on our analysis, we propose a hybrid multi-level mesh and tree structure for global clock distribution. A simple optimization scheme is adopted to optimize the routing resource distribution of the multi-level mesh. Experimental results show that by adding a mesh to the bottom-level leaves of an H-tree, the clock skew can be reduced from 29.2 ps to 8.7 ps, and the multi-level networks with same total routing area can further reduce the clock skew by another 30%. We also discuss the inductive effect of mesh in the appendix. When the clock frequency is less than 4 GHz, our RC model remains valid for clock meshes with grounded shielding or using differential signals.

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