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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 24 — Nov. 24, 2008
  • pp: 20126–20141

PSM design for inverse lithography with partially coherent illumination

Xu Maa and Gonzalo R. Arceb  »View Author Affiliations

Optics Express, Vol. 16, Issue 24, pp. 20126-20141 (2008)

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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. Recently, a set of gradient-based PSM optimization methods have been developed to solve for the inverse lithography problem under coherent illumination. Most practical lithography systems, however, use partially coherent illumination due to non-zero width and off-axis light sources, which introduce partial coherence factors that must be accounted for in the optimization of PSMs. This paper thus focuses on developing a framework for gradient-based PSM optimization methods which account for the inherent nonlinearities of partially coherent illumination. In particular, the singular value decomposition (SVD) is used to expand the partially coherent imaging equation by eigenfunctions into a sum of coherent systems (SOCS). The first order coherent approximation corresponding to the largest eigenvalue is used in the PSM optimization. In order to influence the solution patterns to have more desirable manufacturability properties and higher fidelity, a post-processing of the mask pattern based on the 2D discrete cosine transformation (DCT) is introduced. Furthermore, a photoresist tone reversing technique is exploited in the design of PSMs to project extremely sparse patterns.

© 2008 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: October 2, 2008
Revised Manuscript: November 10, 2008
Manuscript Accepted: November 18, 2008
Published: November 21, 2008

Xu Ma and Gonzalo R. Arce, "PSM design for inverse lithography with partially coherent illumination," Opt. Express 16, 20126-20141 (2008)

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