Balanced truncation model reduction for laser heating wafer model in frequency restricted domain
Modeling and simulating laser heating phenomena are crucial for optimizing manufacturing processes and ensuring high-quality final products. A major challenge in semiconductor manufacturing is achieving accurate, real-time temperature control during wafer heating. To reduce the computational burden...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Franklin Open |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S277318632400121X |
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| author | Md. Saiduzzaman Md. Shafiqul Islam Md. Sumon Hossain M. Monir Uddin Mohammad Osman Gani |
| author_facet | Md. Saiduzzaman Md. Shafiqul Islam Md. Sumon Hossain M. Monir Uddin Mohammad Osman Gani |
| author_sort | Md. Saiduzzaman |
| collection | DOAJ |
| description | Modeling and simulating laser heating phenomena are crucial for optimizing manufacturing processes and ensuring high-quality final products. A major challenge in semiconductor manufacturing is achieving accurate, real-time temperature control during wafer heating. To reduce the computational burden of complex mathematical models, low-dimensional reduced models can be employed. In this paper, we develop a mathematical model for laser heating in silicon wafers. For model reduction, we use the balanced truncation method, considering both frequency-unrestricted and restricted cases. Additionally, the rational Krylov subspace method is applied to solve high-dimensional sparse matrix equations. To gain key physical insights, we use the COMSOL Multiphysics package. Finally, some numerical experiments are conducted using MATLAB to validate the proposed approach. |
| format | Article |
| id | doaj-art-e4294bce533043dd8e41df760c5e4d9b |
| institution | OA Journals |
| issn | 2773-1863 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Franklin Open |
| spelling | doaj-art-e4294bce533043dd8e41df760c5e4d9b2025-08-20T01:58:34ZengElsevierFranklin Open2773-18632024-12-01910019110.1016/j.fraope.2024.100191Balanced truncation model reduction for laser heating wafer model in frequency restricted domainMd. Saiduzzaman0Md. Shafiqul Islam1Md. Sumon Hossain2M. Monir Uddin3Mohammad Osman Gani4Department of Mathematics, International University of Business Agriculture and Technology, BangladeshDepartment of Mathematics, International University of Business Agriculture and Technology, BangladeshDepartment of Mathematics and Physics, North South University, Bangladesh; Corresponding author.Department of Mathematics and Physics, North South University, BangladeshDepartment of Mathematics, Jahangirnagar University, BangladeshModeling and simulating laser heating phenomena are crucial for optimizing manufacturing processes and ensuring high-quality final products. A major challenge in semiconductor manufacturing is achieving accurate, real-time temperature control during wafer heating. To reduce the computational burden of complex mathematical models, low-dimensional reduced models can be employed. In this paper, we develop a mathematical model for laser heating in silicon wafers. For model reduction, we use the balanced truncation method, considering both frequency-unrestricted and restricted cases. Additionally, the rational Krylov subspace method is applied to solve high-dimensional sparse matrix equations. To gain key physical insights, we use the COMSOL Multiphysics package. Finally, some numerical experiments are conducted using MATLAB to validate the proposed approach.http://www.sciencedirect.com/science/article/pii/S277318632400121XLaser heating waferBalanced truncationLyapunov equationsGramiansRational Krylov subspace |
| spellingShingle | Md. Saiduzzaman Md. Shafiqul Islam Md. Sumon Hossain M. Monir Uddin Mohammad Osman Gani Balanced truncation model reduction for laser heating wafer model in frequency restricted domain Franklin Open Laser heating wafer Balanced truncation Lyapunov equations Gramians Rational Krylov subspace |
| title | Balanced truncation model reduction for laser heating wafer model in frequency restricted domain |
| title_full | Balanced truncation model reduction for laser heating wafer model in frequency restricted domain |
| title_fullStr | Balanced truncation model reduction for laser heating wafer model in frequency restricted domain |
| title_full_unstemmed | Balanced truncation model reduction for laser heating wafer model in frequency restricted domain |
| title_short | Balanced truncation model reduction for laser heating wafer model in frequency restricted domain |
| title_sort | balanced truncation model reduction for laser heating wafer model in frequency restricted domain |
| topic | Laser heating wafer Balanced truncation Lyapunov equations Gramians Rational Krylov subspace |
| url | http://www.sciencedirect.com/science/article/pii/S277318632400121X |
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