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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 28 — Oct. 1, 2011
  • pp: 5567–5576

Optimal 3D phase-shifting masks in partially coherent illumination

Xu Ma, Gonzalo R. Arce, and Yanqiu Li  »View Author Affiliations

Applied Optics, Vol. 50, Issue 28, pp. 5567-5576 (2011)

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Gradient-based phase-shifting mask (PSM) optimization methods have emerged as an important tool in computational lithography to solve for the inverse lithography problem under the thin-mask assumption, where the mask is considered a thin two-dimensional object. As the critical dimension printed on the wafer shrinks into the subwavelength regime, thick-mask effects become prevalent and thus these effects must be taken into account in PSM optimization methods. Thick-mask effects are particularly aggravated and pronounced in etching profiles with abrupt discontinuities and trench depths. PSM methods derived under the thin-mask assumption have inherent limitations and perform poorly in the subwavelength scenario. This paper focuses on developing three-dimensional PSM optimization methods that can overcome the thick-mask effects in lithography systems with partially coherent illumination. The boundary layer model is exploited to simplify and characterize the thick-mask effects, leading to a gradient-based PSM optimization method. Several illustrative simulations are presented.

© 2011 Optical Society of America

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(100.3190) Image processing : Inverse problems
(110.4980) Imaging systems : Partial coherence in imaging
(110.5220) Imaging systems : Photolithography

ToC Category:
Imaging Systems

Original Manuscript: May 12, 2011
Revised Manuscript: June 28, 2011
Manuscript Accepted: July 12, 2011
Published: September 30, 2011

Xu Ma, Gonzalo R. Arce, and Yanqiu Li, "Optimal 3D phase-shifting masks in partially coherent illumination," Appl. Opt. 50, 5567-5576 (2011)

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