旋轉塗佈薄膜的流體力學與質量傳輸數值研究

Numerical Study of Fluid Mechanics and Mass Transfer of Spin Coating of Thin Films

謝采倫(Tsai-Lun Hsieh)

指導教授 ： 李雨

國立臺灣大學/工學院/應用力學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202203126

摘要

以旋轉塗佈（簡稱旋塗）方式在一平面（基材）上產生一層微米量級均勻薄膜，是工業（如半導體產業）上常用且有效的製造方法，其中薄膜厚度及其均勻度為此方法所最著重的兩項指標；了解旋塗過程中的流體力學及質量傳輸行為是達成此兩項指標的關鍵。旋塗過程的特色為用以旋塗在平面上的液體其所佔空間隨時隨地都在改變、且與液體上方空氣亦有動量與質量交換。本研究在旋轉軸對稱的前題下，利用包含質量傳輸的計算流體力學來探討相關的物理、並透過COMSOL Multiphysics軟體中的移動網格法(Moving Mesh Method)與相場法(Phase Field Method)來處理旋塗液的移動邊界問題，及濃物質質傳(Transport of Concentrated Species)模組來納入旋塗液中的溶劑揮發效應。
就旋塗過程中不包含或包含質傳效應的狀況，本文計算結果與文獻中多項理論與實驗結果驗證無誤，可確信本文利用COMSOL Multiphysics軟體所開發的計算模組可用來設定旋塗參數及產品開發，並獲致詳細流場及濃度場資料。就旋塗過程的物理現象，本文結果顯示以牛頓流體進行旋塗所形成薄膜，除邊緣珠(edge bead)區域外其表面分佈均勻性高，流體黏度越小和基材轉速越快所形成的膜會越薄、且降低邊緣珠對整體薄膜均勻性的不良影響；剪切稀化或增稠的非牛頓流體效應會導致薄膜表面均勻性降低。因旋塗液多由揮發性溶劑與固體溶質所組成，含質傳的計算結果顯示薄膜厚度減少機制有二：旋塗初期由離心力主導、將旋塗液由旋塗平面邊緣甩出導致厚度快速減少，其後因溶劑蒸發引致薄膜厚度持續下降，至溶劑揮發殆盡。伴隨溶劑蒸發，旋塗液中固體含量提高，使得流體黏度急劇增加、擴散係數快速下降，二者均會大幅影響流動行為。旋塗薄膜最終厚度與旋轉角速度之平方根成反比關係，其間係數與旋塗液中初始固體溶質濃度呈指數上升關係。

關鍵字

旋轉塗佈 ； 移動網格 ； 相場法 ； 濃物質質傳 ； 薄膜厚度

並列摘要

Spin coating is a common and effective manufacturing process in industries (such as semiconductor manufacturing) for generating a uniform thin film with micron size on a flat surface (substrate). The thickness and the uniformity of the fabricated thin film are the two indices for the success of a given spin coating process. Understanding the behavior of fluid flow and mass transfer throughout the process are crucial for the achievement of a precise thickness with allowable uniformity. The characteristics of spin coating in fluid mechanics analysis are that the shape of the coating liquid is changing with time and space, and there are momentum and mass transport between the liquid and the air above. Under the rotational symmetric assumption, the physics of spin coating process is investigated here using computational fluid mechanics with mass transfer. Moving Mesh Method and Phase Field Method were employed for handling the moving boundary, and Transport of Concentrated Species Analysis was employed for treating the solvent evaporation of the coating liquid, via the aid of the software, COMSOL Multiphysics.
The present calculation developed for spin coating process via COMSOL was validated via several theoretical and experimental results in the literature without and with mass transfer, and thus is capable for parametric optimization of a given process, related product development, as well as visualizing detailed flow and concentration field. As for the physics of spin coating, the present study shows that the thin film has a good uniformity in thickness, besides the edge bead region. Thinner film with smaller edge bead region can be obtained using a larger spinning speed and less viscous liquid. The film uniformity is reduced for a non-Newtonian liquid, due to both the shear thinning and shear thickening effects. There are two mechanisms for reducing the film thickness during the process of spin coating of violate liquid: (1) a large amount of the liquid on the substrate was flung radially outward by the centrifugal force, and thus the film thickness reduces rapidly in the initial period, (2) the thickness reduces continuously as a result of solvent volatilization, and such a mechanism dominates in a later period. Both the viscosity increases and the mass diffusivity reduces rapidly, for the coating liquid, as a result of solvent volatilization, and such property changes are crucial for the fluid flow. The final film thickness is inverse proportional to the square root of spinning speed, with the proportional constant increases exponentially with the initial solute concentration of the coating liquid.

並列關鍵字

Spin coating ； Moving mesh ； Phase-field method ； Transport of concentrated species ； Film thickness

參考文獻

Cohen, E. and E.J. Lightfoot, Coating Processes. Kirk-Othmer Encyclopedia of Chemical Technology, 2011.

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Norrman, K., A. Ghanbari-Siahkali, and N.B. Larsen, 6 Studies of spin-coated polymer films. Annual Reports Section "C" (Physical Chemistry), 2005. 101: p. 174.

Lorenz, H., et al., High-aspect-ratio, ultrathick, negative-tone near-UV photoresist and its applications for MEMS. Sensors and Actuators A: Physical, 1998. 64(1): p. 33-39.

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