Modeling of intra-die process variations for accurate analysis and optimization of nano-scale circuits

Sarvesh Bhardwaj, Sarma Vrudhula, Praveen Ghanta, Yu Cao

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

34 Scopus citations


This paper proposes the use of Karhunen-Loève Expansion (KLE) for accurate and efficient modeling of intra-die correlations in the semiconductor manufacturing process. We demonstrate that the KLE provides a significantly more accurate representation of the underlying stochastic process compared to the traditional approach of dividing the layout into grids and applying Principal Component Analysis (PCA). By comparing the results of leakage analysis using both KLE and the existing approaches, we show that using KLE can provide up to 4-5x reduction in the variability space (number of random variables) while maintaining the same accuracy. We also propose an efficient leakage minimization algorithm that maximizes the leakage yield while satisfying probabilistic constraints on the delay.

Original languageEnglish (US)
Title of host publication2006 43rd ACM/IEEE Design Automation Conference, DAC'06
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)1595933816, 1595933816, 9781595933812
StatePublished - 2006
Externally publishedYes
Event43rd Annual Design Automation Conference, DAC 2006 - San Francisco, CA, United States
Duration: Jul 24 2006Jul 28 2006

Publication series

NameProceedings - Design Automation Conference
ISSN (Print)0738-100X


Conference43rd Annual Design Automation Conference, DAC 2006
Country/TerritoryUnited States
CitySan Francisco, CA


  • Correlations
  • Intra-die
  • Karhunen-Loeve
  • Leakage
  • Process variations
  • Statistical


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