Statistical Clock Skew Analysis Considering Intra-Die Process Variations

  • Authors:
  • Aseem Agarwal;David Blaauw;Vladimir Zolotov

  • Affiliations:
  • University of Michigan, Ann Arbor;University of Michigan, Ann Arbor;Motorola, Inc., Austin, TX

  • Venue:
  • Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
  • Year:
  • 2003

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Abstract

With shrinking cycle times, clock skew has become an increasinglydifficult and important problem for high performance designs.Traditionally, clock skew has been analyzed using case-files whichcannot model intra-die process variations and hence result in a veryoptimistic skew analysis. In this paper, we present a statistical skewanalysis method to model intra-die process variations. We firstpresent a formal model of the statistical clock skew problem and thenpropose an algorithm which is based on propagation of joint probabilitydistribution functions in a bottom up fashion in a clock tree.The analysis accounts for topological correlations between pathdelays and has linear run time with the size of the clock tree. Theproposed method was tested on several large clock tree circuits,including a clock tree from a large industrial high-performancemicroprocessor. The results are compared with Monte Carlo simulationfor accuracy comparison and demonstrate the need for statisticalanalysis of clock skew.