Analysis and modeling of CD variation for statistical static timing

  • Authors:
  • Brian Cline;Kaviraj Chopra;David Blaauw;Yu Cao

  • Affiliations:
  • University of Michigan, Ann Arbor, MI;University of Michigan, Ann Arbor, MI;University of Michigan, Ann Arbor, MI;Arizona State University, Tempe, AZ

  • Venue:
  • Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
  • Year:
  • 2006

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Abstract

Statistical static timing analysis (SSTA) has become a key method for analyzing the effect of process variation in aggressively scaled CMOS technologies. Much research has focused on the modeling of spatial correlation in SSTA. However, the vast majority of these works used artificially generated process data to test the proposed models. Hence, it is difficult to determine the actual effectiveness of these methods, the conditions under which they are necessary, and whether they lead to a significant increase in accuracy that warrants their increased runtime and complexity. In this paper, we study 5 different correlation models and their associated SSTA methods using 35420 critical dimension (CD) measurements that were extracted from 23 reticles on 5 wafers in a 130nm CMOS process. Based on the measured CD data, we analyze the correlation as a function of distance and generate 5 distinct correlation models, ranging from simple models which incorporate one or two variation components to more complex models that utilize principle component analysis and Quad-trees. We then study the accuracy of the different models and compare their SSTA results with the result of running STA directly on the extracted data. We also examine the trade-off between model accuracy and run time, as well as the impact of die size on model accuracy. We show that, especially for small dies (