Optimization of Lens Adjustment in Semiconductor Lithography Equipment Using Quadratically Constrained and Second-Order Cone Programming
The present paper considers optimization of lens adjustment in semiconductor lithography equipment. For improving productivity, the laser irradiation power of recent semiconductor lithography equipment has been boosted, which causes significant aberration due to heating during exposure. The aberrati...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
The Japan Society of Mechanical Engineers
2010-08-01
|
| Series: | Journal of Advanced Mechanical Design, Systems, and Manufacturing |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/jamdsm/4/4/4_4_785/_pdf/-char/en |
| _version_ | 1828763744218382336 |
|---|---|
| author | Yuji SHINANO Toshiyuki YOSHIHARA Ryuhei MIYASHIRO Youzou FUKAGAWA |
| author_facet | Yuji SHINANO Toshiyuki YOSHIHARA Ryuhei MIYASHIRO Youzou FUKAGAWA |
| author_sort | Yuji SHINANO |
| collection | DOAJ |
| description | The present paper considers optimization of lens adjustment in semiconductor lithography equipment. For improving productivity, the laser irradiation power of recent semiconductor lithography equipment has been boosted, which causes significant aberration due to heating during exposure. The aberration of the equipment must be measured or estimated in order to adjust the positions and orientations of the lenses. Since this adjustment is performed sequentially during exposure, the optimization problem to obtain optimal lens adjustment should be solved within a time as short as 100 ms. Although the problem of calculating the optimal lens adjustment can be naturally formulated as a convex minimization problem, in such a formulation the objective function is convex but includes several nondifferentiable points. Hence, optimization methods based on derivatives cannot be applied. Other approaches using derivative-free optimization or meta-heuristic methods cannot guarantee that the obtained solutions are truly optimal. Therefore, we formulate the optimization problem as quadratically constrained and second-order cone programming problems, which can be handled by solvers using an interior point method. Using the proposed formulations, computational experiments demonstrate that the optimal lens adjustment is obtained in a practical computational time, which is much less than 100 ms. |
| first_indexed | 2024-12-11T02:06:47Z |
| format | Article |
| id | doaj.art-cce01d0d9c284619b242f4a99537699b |
| institution | Directory Open Access Journal |
| issn | 1881-3054 |
| language | English |
| last_indexed | 2024-12-11T02:06:47Z |
| publishDate | 2010-08-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Journal of Advanced Mechanical Design, Systems, and Manufacturing |
| spelling | doaj.art-cce01d0d9c284619b242f4a99537699b2022-12-22T01:24:22ZengThe Japan Society of Mechanical EngineersJournal of Advanced Mechanical Design, Systems, and Manufacturing1881-30542010-08-014478579310.1299/jamdsm.4.785jamdsmOptimization of Lens Adjustment in Semiconductor Lithography Equipment Using Quadratically Constrained and Second-Order Cone ProgrammingYuji SHINANO0Toshiyuki YOSHIHARA1Ryuhei MIYASHIRO2Youzou FUKAGAWA3Konrad-Zuse-Zentrum für Informationstechnik BerlinSemiconductor Production Equipment PLM Center 2, CANON INC.Institute of Engineering, Tokyo University of Agriculture and TechnologySemiconductor Production Equipment PLM Center 2, CANON INC.The present paper considers optimization of lens adjustment in semiconductor lithography equipment. For improving productivity, the laser irradiation power of recent semiconductor lithography equipment has been boosted, which causes significant aberration due to heating during exposure. The aberration of the equipment must be measured or estimated in order to adjust the positions and orientations of the lenses. Since this adjustment is performed sequentially during exposure, the optimization problem to obtain optimal lens adjustment should be solved within a time as short as 100 ms. Although the problem of calculating the optimal lens adjustment can be naturally formulated as a convex minimization problem, in such a formulation the objective function is convex but includes several nondifferentiable points. Hence, optimization methods based on derivatives cannot be applied. Other approaches using derivative-free optimization or meta-heuristic methods cannot guarantee that the obtained solutions are truly optimal. Therefore, we formulate the optimization problem as quadratically constrained and second-order cone programming problems, which can be handled by solvers using an interior point method. Using the proposed formulations, computational experiments demonstrate that the optimal lens adjustment is obtained in a practical computational time, which is much less than 100 ms.https://www.jstage.jst.go.jp/article/jamdsm/4/4/4_4_785/_pdf/-char/ensemiconductor lithographyaberrationoptimum designsystem engineeringoptical instrumentprecision instrumentsecond order cone programmingquadratically constrained programmingengineering optimization |
| spellingShingle | Yuji SHINANO Toshiyuki YOSHIHARA Ryuhei MIYASHIRO Youzou FUKAGAWA Optimization of Lens Adjustment in Semiconductor Lithography Equipment Using Quadratically Constrained and Second-Order Cone Programming Journal of Advanced Mechanical Design, Systems, and Manufacturing semiconductor lithography aberration optimum design system engineering optical instrument precision instrument second order cone programming quadratically constrained programming engineering optimization |
| title | Optimization of Lens Adjustment in Semiconductor Lithography Equipment Using Quadratically Constrained and Second-Order Cone Programming |
| title_full | Optimization of Lens Adjustment in Semiconductor Lithography Equipment Using Quadratically Constrained and Second-Order Cone Programming |
| title_fullStr | Optimization of Lens Adjustment in Semiconductor Lithography Equipment Using Quadratically Constrained and Second-Order Cone Programming |
| title_full_unstemmed | Optimization of Lens Adjustment in Semiconductor Lithography Equipment Using Quadratically Constrained and Second-Order Cone Programming |
| title_short | Optimization of Lens Adjustment in Semiconductor Lithography Equipment Using Quadratically Constrained and Second-Order Cone Programming |
| title_sort | optimization of lens adjustment in semiconductor lithography equipment using quadratically constrained and second order cone programming |
| topic | semiconductor lithography aberration optimum design system engineering optical instrument precision instrument second order cone programming quadratically constrained programming engineering optimization |
| url | https://www.jstage.jst.go.jp/article/jamdsm/4/4/4_4_785/_pdf/-char/en |
| work_keys_str_mv | AT yujishinano optimizationoflensadjustmentinsemiconductorlithographyequipmentusingquadraticallyconstrainedandsecondorderconeprogramming AT toshiyukiyoshihara optimizationoflensadjustmentinsemiconductorlithographyequipmentusingquadraticallyconstrainedandsecondorderconeprogramming AT ryuheimiyashiro optimizationoflensadjustmentinsemiconductorlithographyequipmentusingquadraticallyconstrainedandsecondorderconeprogramming AT youzoufukagawa optimizationoflensadjustmentinsemiconductorlithographyequipmentusingquadraticallyconstrainedandsecondorderconeprogramming |