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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 23 — Nov. 12, 2007
  • pp: 15066–15079

Generalized inverse lithography methods for phase-shifting mask design

Xu Ma and Gonzalo R. Arce  »View Author Affiliations

Optics Express, Vol. 15, Issue 23, pp. 15066-15079 (2007)

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Optical proximity correction (OPC) and phase shifting masks (PSM) are resolution enhancement techniques (RET) used extensively in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. In this paper, we develop generalized gradient-based RET optimization methods to solve for the inverse lithography problem, where the search space is not constrained to a finite phase tessellation but where arbitrary search trajectories in the complex space are allowed. Subsequent mask quantization leads to efficient design of PSMs having an arbitrary number of discrete phases. In order to influence the solution patterns to have more desirable manufacturability properties, a wavelet regularization framework is introduced offering more localized flexibility than total-variation regularization methods traditionally employed in inverse problems. The proposed algorithms provide highly effective four-phase PSMs capable of generating mask patterns with arbitrary Manhattan geometries. Furthermore, a double-exposure optimization method for general inverse lithography is developed where each exposure uses an optimized two-phase mask.

© 2007 Optical Society of America

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(100.3190) Image processing : Inverse problems
(100.7410) Image processing : Wavelets
(220.3740) Optical design and fabrication : Lithography

ToC Category:
Optical Design and Fabrication

Original Manuscript: August 15, 2007
Revised Manuscript: September 21, 2007
Manuscript Accepted: October 26, 2007
Published: October 31, 2007

Xu Ma and Gonzalo R. Arce, "Generalized inverse lithography methods for phase-shifting mask design," Opt. Express 15, 15066-15079 (2007)

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