Efficient Process Variation Characterization by Virtual Probe

  • Jun TaoEmail author
  • Wangyang Zhang
  • Xin LiEmail author
  • Frank Liu
  • Emrah Acar
  • Rob A. Rutenbar
  • Ronald D. Blanton
  • Xuan ZengEmail author


In this chapter, we propose a new technique, referred to as virtual probe (VP), to efficiently measure, characterize, and monitor spatially correlated inter-die and/or intra-die variations in nanoscale manufacturing process. VP exploits recent breakthroughs in compressed sensing to accurately predict spatial variations from an exceptionally small set of measurement data, thereby reducing the cost of silicon characterization. By exploring the underlying sparse pattern in spatial frequency domain, VP achieves substantially lower sampling frequency than the well-known Nyquist rate. In addition, VP is formulated as a linear programming problem and, therefore, can be solved both robustly and efficiently. Our industrial measurement data demonstrate the superior accuracy of VP over several traditional methods including two-dimensional interpolation, Kriging prediction, and k-LSE estimation.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.State Key Laboratory of ASIC and System, School of MicroelectronicsFudan UniversityShanghaiChina
  2. 2.Cadence Design Systems, Inc.PittsburghUSA
  3. 3.Department of Electrical and Computer EngineeringDuke UniversityDurhamUSA
  4. 4.IBM Research LaboratoryAustinUSA
  5. 5.IBM T. J. Watson Research CenterYorktown HeightsUSA
  6. 6.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  7. 7.Department of Electrical and Computer EngineeringCarnegie Mellon UniversityPittsburghUSA

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