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

TitleRobust photomask design with defocus variation using inverse synthesis
Authors
Issue Date2008
Citation
The SPIE Lithography Asia 2008, Taipei, Taiwan, 4–6 November 2008. In SPIE Proceedings, 2008, v. 7140, abstract no. 7140-88 How to Cite?
AbstractWith 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 model-based 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 pixel-based 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 gradient-based 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.
DescriptionSession 13, no. 7140-88
Persistent Identifierhttp://hdl.handle.net/10722/62073

 

DC FieldValueLanguage
dc.contributor.authorJia, Nen_HK
dc.contributor.authorLam, EYen_HK
dc.date.accessioned2010-07-13T03:53:20Z-
dc.date.available2010-07-13T03:53:20Z-
dc.date.issued2008en_HK
dc.identifier.citationThe SPIE Lithography Asia 2008, Taipei, Taiwan, 4–6 November 2008. In SPIE Proceedings, 2008, v. 7140, abstract no. 7140-88-
dc.identifier.urihttp://hdl.handle.net/10722/62073-
dc.descriptionSession 13, no. 7140-88-
dc.description.abstractWith 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 model-based 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 pixel-based 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 gradient-based 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.languageengen_HK
dc.relation.ispartofSPIE Proceedings-
dc.titleRobust photomask design with defocus variation using inverse synthesisen_HK
dc.typeConference_Paperen_HK
dc.identifier.emailLam, EY: elam@eee.hku.hken_HK
dc.identifier.authorityLam, EY=rp00131en_HK
dc.identifier.hkuros158736en_HK
dc.identifier.volume7140-
dc.customcontrol.immutablesml 151002-

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