Analysis and modeling of CD variation for statistical static timing

Brian Cline, Kaviraj Chopra, David Blaauw, Yu Cao

Research output: Chapter in Book/Report/Conference proceedingConference contribution

58 Scopus citations


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 (< 6.6mm × 5.7mm), the simple models provide comparable accuracy to that of the more complex ones, while incurring significantly less runtime and implementation difficulty. The results of this study demonstrate that correlation models for SSTA must be carefully tested on actual process data and must be used judiciously.

Original languageEnglish (US)
Title of host publicationProceedings of the 2006 International Conference on Computer-Aided Design, ICCAD
Number of pages7
StatePublished - 2006
Event2006 International Conference on Computer-Aided Design, ICCAD - San Jose, CA, United States
Duration: Nov 5 2006Nov 9 2006

Publication series

NameIEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD
ISSN (Print)1092-3152


Other2006 International Conference on Computer-Aided Design, ICCAD
Country/TerritoryUnited States
CitySan Jose, CA

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

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