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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳中平 | zh_TW |
| dc.contributor.advisor | Chung-Ping Chen | en |
| dc.contributor.author | 朱冠穎 | zh_TW |
| dc.contributor.author | Guan-Ying Chu | en |
| dc.date.accessioned | 2023-08-01T16:31:45Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-08-01 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-07-07 | - |
| dc.identifier.citation | [1] Abiola Ayodele. Dry Etching vs Wet Etching: Everything You Need To Know, 2021.
[2] R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. Van der Vorst. Templates for the solution of linear systems: building blocks for iterative methods. SIAM, 1994. [3] Y.Chen, T.A.Davis, W.W.Hager, and S.Rajamanickam. Algorithm887: Cholmod, supernodal sparse cholesky factorization and update/downdate. ACM Transactions on Mathematical Software (TOMS), 35(3):1–14, 2008. [4] A.H.-D.Cheng and D.T.Cheng. Heritage and early history of the boundary element method. Engineering analysis with boundary elements, 29(3):268–302, 2005. [5] Dale R. Durran. Numerical Methods for Fluid Dynamics With Applications to Geo- physics. Springer, New York, 2010. [6] M. de Mier Torrecilla. Introduction to numerical simulation of fluid flows. San Petersburgo (Rusia), 2004. [7] F. H. Dill, A. R. Neureuther, J. A. Tuttle, and E. J. Walker. Modeling projection printing of positive photoresists. IEEE Transactions on Electron Devices, 22(7):456– 464, 1975. [8] S. D' Silva, T. Mülders, H.-J. Stock, and A. Erdmann. Modeling the impact of shrinkage effects on photoresist development. Journal of Micro/Nanopatterning, Materials, and Metrology, 20(1):014602–014602, 2021. [9] J. R. Gilbert, C. Moler, and R. Schreiber. Sparse matrices in matlab: Design and implementation. SIAM journal on matrix analysis and applications, 13(1):333–356, 1992. [10] Y. Granik. Analytical solutions for the deformation of a photoresist film. In Optical Microlithography XXXII, volume 10961, pages 59–89. SPIE, 2019. [11] P.Gröning, L.Nilsson, P.Ruffieux, R.Clergereaux, and O.Gröning. Encyclopedia of Nanoscience and Nanotechnology, volume 1, pages 547–579. American Scientific Publishers, 2004. [12] C. Mack. Semiconductor Lithography (Photolithography)-The Basic Process,2018. [13] T. A. Manteuffel. An incomplete factorization technique for positive definite linear systems. Mathematics of computation, 34(150):473–497, 1980. [14] MEMS, Nanotechnology Exchange. Lithography, 2018. [15] RandallJ. LeVeque. Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-dependent Problems. Society for Industrial and Applied Mathematics, USA, 2007. [16] Y. Saad. Iterative methods for sparse linear systems. SIAM, 2003. [17] K. Saga, H. Kuniyasu, T. Hattori, K. Saito, I. Mizobata, T. Iwata, and S. Hirae. Ef- fect of wafer rotation on photoresist stripping in supercritical co2. In Solid State Phenomena, volume 134, pages 355–358. Trans Tech Publ, 2008. [18] N. Sahu, B. Parija, and S. Panigrahi. Fundamental understanding and modeling of spin coating process: A review. Indian Journal of Physics, 83(4):493–502, 2009. [19] San Joaquin Delta College. Numerical methods for solving differential equations. https://web.archive.org/web/20090212005921/http: //calculuslab.deltacollege.edu/ODE/7-C-2/7-C-2-h.html, 2023. [2023-06-19]. [20] C. E. Scheidegger, J. L. D. Comba, and R. D. da Cunha. Navier-stokes on pro- grammable graphics hardware using smac. In Proceedings. 17th Brazilian Sympo- sium on Computer Graphics and Image Processing, pages 300–307. IEEE, 2004. [21] 朱佳仁. 工程流體力學. 科技圖書, 臺灣, 2012. [22] 林沛諄. Microlithography Simulation and the Transmission and Analysis of Bio-signal. 2012. [23] 林沛諄. Lithography Optimization considering Post-Exposure Bake and the Photo- Acid Effect for 10-nm Node and Beyond. 2016. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/88035 | - |
| dc.description.abstract | 2023年GTC 2023 Keynote Nivida展示了新技術culitho，這項科技可以幫助IC製造公司在光罩製作以及圖案投影，在這項技術還沒有被實現時，根據Nivida公布執行這項模擬會消耗百億個cpu小時，資料中心需要全年無休來做光罩產生。由此可知，隨著製程3奈米節點後繼續縮小，IC製造公司越是需要需要更精確且多種物理及化學模擬，預測IC製造時可能會發生的問題，才有辦法在現實中做一些補償，以降低生產成本。由於模擬實際現象需要多種物理方程式，本論文只針對曝光烘乾後的流程，也就是微影溶解。在我們的研究中，利用finite difference method 離散化Navier-stokes equation 以及concentration equation，並利用迭代法加速求解稀疏線性系統，可以看到我們的結果在輸入資料量很大時，記憶體使用量以及運算時間有顯著的效果。 | zh_TW |
| dc.description.abstract | In the 2023 GTC Keynote, Nvidia presented a new technology called culitho, which can assist IC manufacturing companies in mask fabrication and pattern projection. Before the implementation of this technology, according to Nvidia's disclosure, performing simulations for these purposes would consume billions of CPU hours, requiring data centers to operate continuously throughout the year for mask generation. This indicates that as the process node continues to shrink beyond the 3-nanometer threshold, IC manufacturing companies increasingly require more precise and diverse physical and chemical simulations to predict potential issues during IC fabrication. These simulations enable them to make compensations in the real world, ultimately reducing production costs. Given that simulating real-world phenomena involves multiple physical equations, this paper focuses solely on the post-exposure baking process, specifically lithography dissolution. In our research, we discretize the Navier-Stokes equation and concentration equation using the finite difference method. We employ an iterative method to accelerate the solution of the sparse linear system. Our results demonstrate significant improvements in memory usage and computation time when dealing with large input datasets. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-08-01T16:31:45Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-08-01T16:31:45Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i
Acknowledgements iii 摘要 v Abstract vii Contents ix List of Figures xiii List of Tables xv Chapter 1 Introduction 1 1.1 Background............................... 1 1.1.1 Process Flow of the Lithography ................... 1 1.2 Previous work ............................. 2 1.3 Contribution .............................. 4 1.4 Motivation ............................... 4 1.5 Thesis Organization ............. 5 Chapter 2 Naiver Stokes and Concentration Equation 7 2.1 Transport Equation ........................... 7 2.1.1 Control Volume ............... 8 2.1.2 Reynold’s Transport Theorem .................... 8 2.2 Incompressible Navier Stokes Equation .................... 9 2.2.1 Momentum Equation ........................ 9 2.2.2 Continuity Equation.......................... 10 2.3 Concentration Equation ........................... 10 2.4 Non-Dimensional Equation ........................... 11 2.5 Problem Formulation ........................... 12 Chapter 3 Finite Difference Method 15 3.1 Truncation Error ............................ 15 3.2 Basic Numerical Method........................ 16 3.3 Runge-Kutta Method.......................... 17 3.3.1 2-StageRunge-KuttaMethod..................... 18 3.3.2 Adaptive Runge-Kutta Method.................... 18 3.3.3 Strong Stability Perserving Runge–Kutta (SSPRK) Method ........................... 19 3.3.4 Diagonally Implicit Runge–Kutta (DIRK) Method ........................... 20 3.4 Multistep Method............................ 20 3.4.1 Explicit Adams-Bashforth Method .................. 21 3.4.2 Implicit Adams-Moulton Method................... 21 3.4.3 Backward Differentiation Formulae (BDF) ........................... 22 3.5 Stiffness Ordinary Differential Equation ........................... 22 3.6 Predictor Corrector Method ...................... 23 Chapter 4 Methodology 25 4.1 Simulator Framework ......................... 25 4.2 Numerical Method ........................... 27 4.3 Rotating System ............................ 28 4.4 Staggered Grid ............................. 30 4.5 Boundary Condition .......................... 30 4.6 Sparse Linear System.......................... 32 4.6.1 Pressure Poisson Equation ...................... 32 4.6.2 Sparse Matrix ............................. 34 4.6.3 Iterative Method............................ 35 Chapter 5 Experimental Result 37 5.1 Analytical Solution vs Numerical Solution ........................... 37 5.2 Performance of the Simulator ..................... 39 5.3 Simulation Result ............................ 41 5.3.1 Flow over an Object Case ....................... 41 5.3.2 Flow over Multiple Objects Case ................... 41 5.3.3 Flow over an Object Case in Millimeter Scale ........................... 42 Chapter 6 Conclusion and Future Work 47 6.1 Conclusion ............................... 47 6.2 Future Work .............................. 47 6.2.1 3D Model............................... 47 6.2.2 More Application ........................... 48 References 49 Appendix A — Vector Operation 53 | - |
| dc.language.iso | en | - |
| dc.subject | 預測-校正方法 | zh_TW |
| dc.subject | 流體動力學模擬 | zh_TW |
| dc.subject | 納維斯托克斯方程式 | zh_TW |
| dc.subject | 濃度方程式 | zh_TW |
| dc.subject | 顯影溶解 | zh_TW |
| dc.subject | Navier Stokes equation | en |
| dc.subject | Fluid dynamics simulation | en |
| dc.subject | Predictor-corrector method | en |
| dc.subject | Development dissolution | en |
| dc.subject | Concentration equation | en |
| dc.title | NiCE-sim：一個使用Navier-Stokes和濃度方程的非均勻旋轉微影模擬器 | zh_TW |
| dc.title | NiCE-sim: A Non-Uniform Simulator for Spin Development Using Navier-Stokes and Concentration Equations | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 蔡坤諭;胡璧合;陳奕傑 | zh_TW |
| dc.contributor.oralexamcommittee | Kuen-Yu Tsai;Pi-Ho Hu;Yi-Jie Chen | en |
| dc.subject.keyword | 流體動力學模擬,納維斯托克斯方程式,濃度方程式,顯影溶解,預測-校正方法, | zh_TW |
| dc.subject.keyword | Fluid dynamics simulation,Navier Stokes equation,Concentration equation,Development dissolution,Predictor-corrector method, | en |
| dc.relation.page | 53 | - |
| dc.identifier.doi | 10.6342/NTU202300972 | - |
| dc.rights.note | 未授權 | - |
| dc.date.accepted | 2023-07-11 | - |
| dc.contributor.author-college | 電機資訊學院 | - |
| dc.contributor.author-dept | 電子工程學研究所 | - |
| 顯示於系所單位： | 電子工程學研究所 | |
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