Articles

Fast pixel-based mask optimization for inverse lithography

[+] Author Affiliations
Yuri Granik

Mentor Graphics Corporation, 1001 Ridder Park Drive, San Jose, California 95131

J. Micro/Nanolith. MEMS MOEMS. 5(4), 043002 (December 13, 2006). doi:10.1117/1.2399537
History: Received September 22, 2005; Revised August 14, 2006; Accepted August 21, 2006; Published December 13, 2006
Text Size: A A A

The direct problem of optical microlithography is to simulate printing features on the wafer under the given mask, imaging system, and process characteristics. The goal of inverse problems is to find the best mask, imaging system, or process to print the given wafer features. In this study, we proposed the strict formalization and fast solution methods of inverse mask problems. We stated inverse mask problems (or “layout inversion” problems) as nonlinear, constrained minimization problems over a domain of mask pixels. We considered linear, quadratic, and nonlinear formulations of the objective function. The linear problem is solved by an enhanced version of the Nashold projections. The quadratic problem is addressed by eigenvalue decompositions and quadratic programming methods. The general nonlinear formulation is solved by the local variations and gradient descent methods. We showed that the gradient of the objective function can be calculated analytically through convolutions. This is an important practical result because it enables layout inversion on a large scale in order of MlogM operations for M pixels.

Figures in this Article
© 2006 Society of Photo-Optical Instrumentation Engineers

Citation

Yuri Granik
"Fast pixel-based mask optimization for inverse lithography", J. Micro/Nanolith. MEMS MOEMS. 5(4), 043002 (December 13, 2006). ; http://dx.doi.org/10.1117/1.2399537


Tables

Access This Article
Sign in or Create a personal account to Buy this article ($20 for members, $25 for non-members).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging & repositioning the boxes below.

Related Journal Articles

Related Book Chapters

Topic Collections

Advertisement
  • Don't have an account?
  • Subscribe to the SPIE Digital Library
  • Create a FREE account to sign up for Digital Library content alerts and gain access to institutional subscriptions remotely.
Access This Article
Sign in or Create a personal account to Buy this article ($20 for members, $25 for non-members).
Access This Proceeding
Sign in or Create a personal account to Buy this article ($15 for members, $18 for non-members).
Access This Chapter

Access to SPIE eBooks is limited to subscribing institutions and is not available as part of a personal subscription. Print or electronic versions of individual SPIE books may be purchased via SPIE.org.