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Vectorial mask optimization methods for robust optical lithography

[+] Author Affiliations
Xu Ma

Beijing Institute of Technology, School of Optoelectronics, Key Laboratory of Photoelectronic Imaging Technology and System of Ministry of Education of China, Beijing, China

Yanqiu Li

Beijing Institute of Technology, School of Optoelectronics, Key Laboratory of Photoelectronic Imaging Technology and System of Ministry of Education of China, Beijing, China

Xuejia Guo

Beijing Institute of Technology, School of Optoelectronics, Key Laboratory of Photoelectronic Imaging Technology and System of Ministry of Education of China, Beijing, China

Lisong Dong

Beijing Institute of Technology, School of Optoelectronics, Key Laboratory of Photoelectronic Imaging Technology and System of Ministry of Education of China, Beijing, China

Gonzalo R. Arce

University of Delaware, Department of Electrical and Computer Engineering, Newark, Delaware 19716-3130

J. Micro/Nanolith. MEMS MOEMS. 11(4), 043008 (Nov 15, 2012). doi:10.1117/1.JMM.11.4.043008
History: Received July 18, 2012; Revised September 25, 2012; Accepted October 22, 2012
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Abstract.  Continuous shrinkage of critical dimension in an integrated circuit impels the development of resolution enhancement techniques for low k1 lithography. Recently, several pixelated optical proximity correction (OPC) and phase-shifting mask (PSM) approaches were developed under scalar imaging models to account for the process variations. However, the lithography systems with larger-NA (NA>0.6) are predominant for current technology nodes, rendering the scalar models inadequate to describe the vector nature of the electromagnetic field that propagates through the optical lithography system. In addition, OPC and PSM algorithms based on scalar models can compensate for wavefront aberrations, but are incapable of mitigating polarization aberrations in practical lithography systems, which can only be dealt with under the vector model. To this end, we focus on developing robust pixelated gradient-based OPC and PSM optimization algorithms aimed at canceling defocus, dose variation, wavefront and polarization aberrations under a vector model. First, an integrative and analytic vector imaging model is applied to formulate the optimization problem, where the effects of process variations are explicitly incorporated in the optimization framework. A steepest descent algorithm is then used to iteratively optimize the mask patterns. Simulations show that the proposed algorithms can effectively improve the process windows of the optical lithography systems.

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© 2012 Society of Photo-Optical Instrumentation Engineers

Citation

Xu Ma ; Yanqiu Li ; Xuejia Guo ; Lisong Dong and Gonzalo R. Arce
"Vectorial mask optimization methods for robust optical lithography", J. Micro/Nanolith. MEMS MOEMS. 11(4), 043008 (Nov 15, 2012). ; http://dx.doi.org/10.1117/1.JMM.11.4.043008


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