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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 3 — Jan. 31, 2011
  • pp: 2165–2180

Pixel-based OPC optimization based on conjugate gradients

Xu Ma and Gonzalo R. Arce  »View Author Affiliations


Optics Express, Vol. 19, Issue 3, pp. 2165-2180 (2011)
http://dx.doi.org/10.1364/OE.19.002165


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Abstract

Optical proximity correction (OPC) methods are resolution enhancement techniques (RET) used extensively in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. In pixel-based OPC (PBOPC), the mask is divided into small pixels, each of which is modified during the optimization process. Two critical issues in PBOPC are the required computational complexity of the optimization process, and the manufacturability of the optimized mask. Most current OPC optimization methods apply the steepest descent (SD) algorithm to improve image fidelity augmented by regularization penalties to reduce the complexity of the mask. Although simple to implement, the SD algorithm converges slowly. The existing regularization penalties, however, fall short in meeting the mask rule check (MRC) requirements often used in semiconductor manufacturing. This paper focuses on developing OPC optimization algorithms based on the conjugate gradient (CG) method which exhibits much faster convergence than the SD algorithm. The imaging formation process is represented by the Fourier series expansion model which approximates the partially coherent system as a sum of coherent systems. In order to obtain more desirable manufacturability properties of the mask pattern, a MRC penalty is proposed to enlarge the linear size of the sub-resolution assistant features (SRAFs), as well as the distances between the SRAFs and the main body of the mask. Finally, a projection method is developed to further reduce the complexity of the optimized mask pattern.

© 2011 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(110.4980) Imaging systems : Partial coherence in imaging
(110.5220) Imaging systems : Photolithography

ToC Category:
Image Processing

History
Original Manuscript: November 10, 2010
Revised Manuscript: December 25, 2010
Manuscript Accepted: December 26, 2010
Published: January 20, 2011

Citation
Xu Ma and Gonzalo R. Arce, "Pixel-based OPC optimization based on conjugate gradients," Opt. Express 19, 2165-2180 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-2165


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