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

Yun Ye, Frank Liu, Min Chen, Sani Nassif, Yu Cao

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


The threshold voltage (V th) of a nanoscale transistor is severely affected by random dopant fluctuations and line-edge roughness. The analysis of these effects usually requires atomistic simulations which are too expensive in computation for statistical design. In this work, we develop an efficient SPICE simulation method and statistical variation model that accurately predict threshold variation as a function of dopant fluctuations and gate length change caused by lithography and the etching process. By understanding the physical principles of atomistic simulations, we: 1) identify the appropriate method to divide a nonuniform gate into slices in order to map those fluctuations into the device model; 2) extract the variation of V th from the strong-inversion region instead of the leakage current, benefiting from the linearity of the saturation current with respect to V th ; 3) propose a compact model of V th variation that is scalable with gate size and the amount of dopant and gate length fluctuations; and 4) investigate the interaction with non-rectangular gate (NRG) and reverse narrow width effect (RNWE). The proposed SPICE simulation method is validated with 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 V th variation at advanced technology nodes, helping shed light on the challenges of future robust circuit design.

Original languageEnglish (US)
Article number5439902
Pages (from-to)987-996
Number of pages10
JournalIEEE Transactions on Very Large Scale Integration (VLSI) Systems
Issue number6
StatePublished - Jun 2011


  • Atomistic simulation
  • gate slicing
  • line-edge roughness
  • non-rectangular gate
  • random dopant fluctuations
  • threshold voltage
  • variation

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Electrical and Electronic Engineering


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