Statistical modeling and simulation of threshold variation under dopant fluctuations and line-edge roughness

Yun Ye, Frank Liu, Sani Nassif, Yu Cao

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

46 Scopus citations


The threshold voltage (Vth) of a nanoscale transistor is severely affected by random dopant fluctuations and line-edge roughness. The analysis of these effects usually requires atomistic simulations that are too expensive computationally for statistical circuit design. In this work, we develop an efficient SPICE simulation method and statistical transistor model that accurately predict threshold variation as a function of dopant fluctuations and gate length change caused by sub-wavelength lithography and gate etching process. By understanding the physical principles of atomistic simulations, we (a) identify the appropriate method to divide a non-uniform gate into slices in order to map those fluctuations into the device model; (b) extract the variation of Vth from the strong-inversion region instead of the leakage current, benefiting from the linearity of the saturation current with respect to Vth; and (c) propose a compact model of Vth variation that is scalable with gate size and the amount of dopant and gate length fluctuations. The proposed SPICE simulation method is fully validated against atomistic simulation results. Given the post-lithography gate geometry, this approach correctly models the variation of device output current in all operating regions. Based on the new results, we further project the amount of Vth variation at advanced technology nodes, to help shed light on the challenges of future robust circuit design.

Original languageEnglish (US)
Title of host publicationProceedings of the 45th Design Automation Conference, DAC
Number of pages6
StatePublished - 2008
Event45th Design Automation Conference, DAC - Anaheim, CA, United States
Duration: Jun 8 2008Jun 13 2008

Publication series

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


Other45th Design Automation Conference, DAC
Country/TerritoryUnited States
CityAnaheim, CA


  • Atomistic simulations
  • Line-edge roughness
  • Non-rectangular gate
  • Predictive modeling
  • Random dopant fluctuations
  • SPICE simulation
  • Threshold variation

ASJC Scopus subject areas

  • Hardware and Architecture
  • Control and Systems Engineering


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