週期性結構液膜平坦化之解析解

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：71

、訪客IP：18.118.162.180

姓名

蕭裕璋(Yu-chang Hsiao) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

週期性結構液膜平坦化之解析解
(2-D analytical solution of film planarizatsion for spin coating)

相關論文

★ 化學機械研磨流場模擬實驗研究	★ 變轉速之旋轉塗佈實驗研究
★ 微小熱點之主動式冷卻	★ 大尺寸晶圓厚膜塗佈
★ 科氏力與預塗薄膜對旋轉塗佈之影響	★ 微液滴對微熱點之冷卻
★ 大尺寸晶圓之化學機械研磨實驗研究	★ 液晶顯示器旋轉塗佈研究
★ 流體黏度對旋塗減量之影響	★ 微熱點與微溫度感測器製作
★ 高溫蓄熱器理論模擬	★ 熱氣泡式噴墨塗佈
★ 注液模式對旋轉塗佈之影響	★ 磁流體旋塗不穩定之研究
★ TFT-LCD狹縫式塗佈研究	★ 彩色濾光片噴塗研究

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

至系統瀏覽論文 ( 永不開放)

摘要(中)

週期性二維液膜解析解用以計算液膜平坦化之程度與描述液膜之分佈。在半導體的製程中，應用旋轉塗佈可得微米級之薄膜，再逐步逐層的經過沉積、顯影與蝕刻等步驟，製得半導體之元件。在一個有週期性結構的晶圓上旋塗薄膜，並以一個非線性的偏微分方程式描述其流體行為。取結構上的一小部分，分做四個子區塊，可以將非線性的偏微分方程式線性化，且首先解出其符號解，以一個無因次參數描繪不同條件下的平坦度。是表示離心力與表面張力的比，當趨近於無窮大，表面張力趨近於零，液膜是順形液膜，即在每一個位置液膜厚度一樣。當趨近於零，表面張力趨近無窮大，則得到平坦液膜。窄形或方形特徵中，低時，X方向間距越小，平坦度越差；相對於Y方向間距越小，平坦度越好。特徵高度對平坦度則不會有太大影響。此外，於大部分情形中，高時，平坦度就固定在-25%，不再隨變化了。文獻中一維模型解析解視結構在Y方向為無窮遠，故其解析解只適於窄形結構。本論文所提之二維模型不僅適用於窄形的結構，對於方形或長形結構亦可考慮到在其Y方向結構的變化而加以描繪。

摘要(英)

This thesis is the first one to present “a 2-D analytical solution of film planarizatsion for spin coating”. This analytical solution is used for predicting the degree of planarization (abbreviated as DOP), and describing the film distribution. Among semiconductor manufacturing process, utilizing spin coating can obtain the micro-thick film, and help other process to produce the elements. The thin film on the wafer which has period structures is coated by spin coating. We can describe the phenomenon by four order partial differential equation. And it can be used to solve out the symbolic solution by linearizing the partial differential equation at four subregions which is the part of the period structure. We describe the DOP by using the governing dimensionless parameter at different conditions. The represents the ratio of centrifugal force to surface tension force during spin coating. When approach to infinite, surface tension is zero, and the film is always conformal. When approach to zero, surface tension is infinite, and the film is planar The DOP of narrow rectangular or square feature decreases with decrease of the space between two features on X direction. A comparison shows that DOP will increase with decrease of the space between two features on Y direction. And for height of the feature, DOP changes slightly with increase of the .Finally, for the most conditions, no matter how the features and parameters change, at high , DOP will steady at -25% and not change with any more.

關鍵字(中)

★ 平坦化
★ 旋轉塗佈

關鍵字(英)

★ planarization
★ spin coating

論文目次

摘要………………………………………………………………………i
英文摘要…………………………………………………………………ii
致謝……………………………………………………………………iii
目錄……………………………………………………………………iv
圖目錄…………………………………………………………………vi
符號表…………………………………………………………………vii
第一章緒論………………………………………………………………1
1-1 簡介……………………………………………………1
1-2 文獻回顧………………………………………………2
1-3 解析解研究之演………………………………………4
第二章旋塗液膜平坦化之解析解………………………………………8
2-1 統御方程式……………………………………………8
2-2 解析解………………………………………………………12
第三章結果與討論……………………………………………………17
3-1 邊界條件的探討…………………………………………………17
3-2 各種特徵對的影響………………………………………………18
第四章結論……………………………………………………………24
參考文獻…………………………………………………………………25
附圖………………………………………………………………………29
附錄週期性旋塗液膜平坦化之解析解的符號解……………………46

參考文獻

1. A. G. Emslie, F. T. Bonner, and L. G. Peck, Flow of a Viscous Liquid on a Rotating Disk, J. Appl. Phy., Vol. 29, pp. 858-862 (1958).
2. E.Momoniat. D.P. Mason, Ivestigation of the Coriolis Force on a Thin Fluid Film on a Rotating Disk, J.Appl.Phys.,Vol 31, No.6,pp963-968(1960).
3. A. Acrivos, M. J. Shah, and E. E. Petersen, On the Flow of a Non-Newtonian Liquid on a Rotating Disk, J. Appl. Phys., Vol. 31, p. 963-968 (1960).
4. M. Yanagisawa, Slip Effect for Thin Liquid Film on a Rotating Disk, J. Appl. Phys., Vol. 61, pp. 1034(1978).
5. H. P. Greenspan and L. N. Howard, On a Time-Dependent Motion of a Rotating Disk, J. Fluid Mech., Vol. 17, pp. 385-404 (1963).
6. E. R. Benton, On the Flow due to a Rotating Disk, J. Fluid Mech., Vol. 24, pp. 781-800 (1966).
7. B. G. Higgins, Film Flow on a Rotating Disk, Phys. Fluids, 29, 3522 (1986).
8. L . K. White, Approximating Spun-on, Thin Film Planarization Properties on Complex Topography, J. Electrochem. Soc., Vol. 132, pp. 168-172 (1985).
9. C. J. Lawrence, The Mechanics of Spin Coating of Polymer Films, Phys. Fluids, 31, 2786 (1988).
10. D. E. Bornside and R. A. Brown, The Effect of Gas Phase Convection on Mass Transfer in Spin Coating, J. Appl. Phys., 73, 585 (1993).
11. A. Oztekin, D. E. Bornside, and R. A. Brown, The Connection Between Hydrodynamic Stability of Gas Flow in Spin Coating and Coated Film Uniformity, J. Appl. Phys., 77, 2297 (1995).
12. M. L. Forcada, and C. M. Mate, The Flow of Thin Lubricant Films on Rotating Disks, Wear, Vol. 168, pp. 21(1993).
13. C. T. Wang and S. C. Yeu, Theoretical Analysis of Film Uniformity in Spinning Processes, Chem. Eng. Sci., Vol. 50,pp.989(1995).
14. J. H. Hwang and F. Ma, On the Flow of a Thin Liquid Film over a Rough Rotating Disk, J. Appl. Phys. Vol. 66, pp. 388(1989).
15. J. H. Hwang and F. Ma, The Effect of Air Shear on the Flow of a Thin Liquid Film Over a Rough Rotating Disk, ASME J. Appl. Phys., Vol. 112, pp. 165(1990).
16. B. S. Dandapat and P. C. Ray, The Effect of Thermocapillarity on the Flow of a Thin Liquid Film on a Rotating Disk, J. Phys. D: Appl. Phys., 27, 2041 (1994).
17. P.C. Sukanek, A Model for Spin Coating with Topography , J. Electrochem. Soc., 136, 3019 (1989).
18. P.C. Sukanek, Dependence of Film Thickness on Speed in Spin Coating, J. Electrochem. Soc., 138, 1712 (1991).
19. P.C. Sukanek, Anomalous Speed Dependence in Polyimide Spin Coating, J. Electrochem. Soc., 144, 3959 (1997).
20. L. E. Stillwagon and R. G. Larson, Leveling of Thin Films over Uneven Substrates During Spin Coating, Phys. Fluids A2, 1937 (1990).
21. L. M. Peurrung and D. B. Graves, Film Thickness Profiles over Topography in Spin Coating, J. Electrochem. Soc., 138, 2115 (1991).
22. F. C. Chou, P. Y. Wu and S. C. Gong, Analytical Solutions of Film Planarization during Spin Coating, Jpn. J. Appl. Phys., 37, 4321 (1998).
23. P. Y. Wu, F. C. Chou, and S. C. Gong, Analytical Solutions of Film Planarization for Periodic Features, (Submitted to J. Applied Phys.).
24. 吳培瑛，旋轉塗佈液膜平坦化之解析解，國立中央大學機械工程研究所博士論文 (1999)
25. L. M. Manske, and D. B. Graves, Origins of Asymmetry in Spin-Cast Films over Topography, Proc. SPIE, Vol. 1463, pp. 414-422 (1991).
26. L. M. Peurrung, and D. B. Graves, Film Thickness Profiles over Topography in Spin Coating, J. Electrochem. Soc., Vol. 138, pp. 2115-2124 (1991).
27. L. M. Peurrung, and D. B. Graves, Spin Coating over Topography, IEEE Transact. Semiconductor Manufacturing, Vol. 6, pp. 72-76. (1993).
28. S. Middleman, The Effect of Induced Air-Flow on the Spin Coating of Viscous Liquid, J. Appl. Phys., 62, 2530 (1987).
29. T. J. Rehg and B. G. Higgins, The Effect of Inertia and Interfacial Shear on Film Flow on a Rotating disk, Phys. Fluids, 31, 1360 (1988).
30. W. H. McConnell, On the Rate of Thinning of Thin liquid Films on a Rotating disk, J. Appl. Phys., 64, 2232 (1988).
31. J. H. Hwang and F. Ma, On the Flow of a Thin Liquid Film over a Rough Rotating Disk, J. Appl. Phys., 66, 388 (1989).
32. F. Ma and J. H. Hwang, Stochastic Simulation of the Flow of a Thin Liquid Film over a Rough Rotating Disk, J. Appl. Phys., 66, 5026 (1989).
33. 林建宏,旋轉塗佈液膜平坦化之二維解析解,國立中央大學機械工程研究所碩士論文(2005)
34. D. E. Bornside, Mechanism for the local Planarization of Microscopically Rough Surface by Drying Thin Films of Spin-Coated Polymer/Solvent Solutions, J. Electrochem. Soc., 137, 2589 (1990).
35. A. Schiltz, An Empirical Model for Planarization with Polymer Solutions, Jpn. J. Appl. Phys., 34, 4185 (1995).

指導教授

周復初(Fu-chu Chou)

審核日期

2008-5-26

推文