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Conference Paper: Robust photomask design with defocus variation using inverse synthesis
Title  Robust photomask design with defocus variation using inverse synthesis 

Authors  
Issue Date  2008 
Citation  The SPIE Lithography Asia 2008, Taipei, Taiwan, 4–6 November 2008. In SPIE Proceedings, 2008, v. 7140, abstract no. 714088 How to Cite? 
Abstract  With continuous integrated circuit miniaturization, microlithography faces increasing challenges to meet the requirement of higher resolution in critical dimension (CD).Resolution enhancement technology (RET) is widely used in practice, particularly optical proximity correction (OPC). Many modelbased OPCs aim at minimizing the image shape distortion due to diffraction in the printed pattern. However, most of the existing algorithms do not take process variations, such as dose variation, focus variation, etc. into consideration. Our research focuses on the robustness of the mask design in the presence of certain process variations.
In this paper, we present a design method that involves a small increase in complexity over a typical inverse lithography approach, but can show better performance with process variations. We use focus variation as an illustration. We employ a pixelbased image representation by discretizing the mask and the printed pattern for the convenience of using an image synthesis approach. We also assume a coherent imaging system for the sake of simplicity, although the algorithm is expected to work for more general cases. Thus, the aerial image can be assumed to be the object convolved with a Gaussian kernel representing the amplitude spread function (ASF), which is then subjected to a sigmoid function that models the resist process. A gradientbased descent method for iterative optimization is used to search for the optimal mask that could generate the desired output pattern by deliberately predistorting input mask pattern.
To increase the robustness of the mask, we introduce a statistical formulation in the framework described above. First, we assume that the focus error is a stochastic variable following a Gaussian distribution. We then derive the defocus ASF. Then we take the expectation of all outputs under different focus error values as the final output to calculate the gradient vector in the optimization process. In this case, the predistortions of certain mask patterns under different focus errors are averaged by canceling and compensating each other. As a result, the optimized mask tends to perform better in a certain range of focus errors, with the necessary tradeoff that in the close proximity of no focus variations, the pattern fidelity suffers some errors. We present cases that such errors are tolerable, while the gain in fidelity for larger focus errors makes the algorithm more robust to focus errors. 
Description  Session 13, no. 714088 
Persistent Identifier  http://hdl.handle.net/10722/62073 
DC Field  Value  Language 

dc.contributor.author  Jia, N  en_HK 
dc.contributor.author  Lam, EY  en_HK 
dc.date.accessioned  20100713T03:53:20Z   
dc.date.available  20100713T03:53:20Z   
dc.date.issued  2008  en_HK 
dc.identifier.citation  The SPIE Lithography Asia 2008, Taipei, Taiwan, 4–6 November 2008. In SPIE Proceedings, 2008, v. 7140, abstract no. 714088   
dc.identifier.uri  http://hdl.handle.net/10722/62073   
dc.description  Session 13, no. 714088   
dc.description.abstract  With continuous integrated circuit miniaturization, microlithography faces increasing challenges to meet the requirement of higher resolution in critical dimension (CD).Resolution enhancement technology (RET) is widely used in practice, particularly optical proximity correction (OPC). Many modelbased OPCs aim at minimizing the image shape distortion due to diffraction in the printed pattern. However, most of the existing algorithms do not take process variations, such as dose variation, focus variation, etc. into consideration. Our research focuses on the robustness of the mask design in the presence of certain process variations. In this paper, we present a design method that involves a small increase in complexity over a typical inverse lithography approach, but can show better performance with process variations. We use focus variation as an illustration. We employ a pixelbased image representation by discretizing the mask and the printed pattern for the convenience of using an image synthesis approach. We also assume a coherent imaging system for the sake of simplicity, although the algorithm is expected to work for more general cases. Thus, the aerial image can be assumed to be the object convolved with a Gaussian kernel representing the amplitude spread function (ASF), which is then subjected to a sigmoid function that models the resist process. A gradientbased descent method for iterative optimization is used to search for the optimal mask that could generate the desired output pattern by deliberately predistorting input mask pattern. To increase the robustness of the mask, we introduce a statistical formulation in the framework described above. First, we assume that the focus error is a stochastic variable following a Gaussian distribution. We then derive the defocus ASF. Then we take the expectation of all outputs under different focus error values as the final output to calculate the gradient vector in the optimization process. In this case, the predistortions of certain mask patterns under different focus errors are averaged by canceling and compensating each other. As a result, the optimized mask tends to perform better in a certain range of focus errors, with the necessary tradeoff that in the close proximity of no focus variations, the pattern fidelity suffers some errors. We present cases that such errors are tolerable, while the gain in fidelity for larger focus errors makes the algorithm more robust to focus errors.   
dc.language  eng  en_HK 
dc.relation.ispartof  SPIE Proceedings   
dc.title  Robust photomask design with defocus variation using inverse synthesis  en_HK 
dc.type  Conference_Paper  en_HK 
dc.identifier.email  Lam, EY: elam@eee.hku.hk  en_HK 
dc.identifier.authority  Lam, EY=rp00131  en_HK 
dc.identifier.hkuros  158736  en_HK 
dc.identifier.volume  7140   
dc.customcontrol.immutable  sml 151002   