Multilevel tree fusion for robust clock networks

Abstract

Abstract-Recent improvements in clock-tree and mesh-based topologies maintain a healthy competition between the two. Trees require much smaller capacitance, but meshes are naturally robust against process variation and can accommodate late design changes. Cross-link insertion has been advocated to make trees more robust, but is limited in practice to short distances. In this work we develop a novel non-tree topology that fuses several clock trees to create large-scale redundancy in a clock network. Empirical validation shows that our novel clock-network structure incrementally enhances robustness to satisfy given variation constraints. Our implementation called Contango3.0 produces robust clock networks even for challenging skew limits, without parallel buffering used by other implementations. It also offers a fine trade-off between power and robustness, increasing the capacitance of the initial tree by less than 60%, which results in 2.3× greater power efficiency than mesh structures.

Algorithmic tuning of clock trees and derived non-tree structures

“…The mean and variance of Skew ( , ) can be derived from the mean and variance of ( , ) as explained in [16]. For a clock network with > 1 redundant paths per sink (illustrated in Figure 2a), one can obtain…”

“…After performing initial-tree construction according to [15], the impact of variation on skew between eligible sink pairs is analyzed [16]. Eligible sink pairs are often geometrically close, but they can be distant in the tree, i.e., the shortest tree-path connecting them can traverse many tree edges.…”

“…The clock-network structure proposed in [16] is similar to traditional trees except for possible cycles that close at critical sinks. To leverage the efficacy of existing tree-optimization techniques [15], each critical sink is split (cloned) and its input capacitance is distributed among the resulting splinter sinks.…”

“…Due to this averaging effect, nominal skew optimization with splinter-sinks is both reliable and effective. Further details are discussed in [16].…”

“…Empirical evaluation in [16] indicates that the multilevel fusion topology exhibits sufficient flexibility to incrementally improve clock-network robustness based on variational analysis. A given local skew limit can be satisfied with only a modest increase in total capacitance.…”