本論文致力於在高精度無光罩曝光系統下，開發光阻（Photoresist, PR）在曝光與顯影後之三維形貌的預測與模擬方法，目標是透過對紫外 (Ultraviolet, UV) 光在光阻中的劑量分佈和顯影時間的控制，成功在光阻層中製造出各種形貌的三維微結構，同時進行製程參數的優化，更精確地控制所製作之三維微結構的形貌。本研究之無光罩UV曝光系統是基於數位微反射鏡裝置（Digital Micromirror Device, DMD），透過軟體的數位控制，精準地調節投射在光阻層上的紫外光劑量。
針對光阻的數值模擬，首先通過經驗模型（Empirical Model）建立了光阻劑量、深度和顯影時間之間的數值關係，進而描述光阻在UV曝光後的溶解速率特性；接著基於Eikonal方程式之光阻顯影的數值模擬，達成曝光顯影後光阻之三維形貌的預測。同時，本文將利用實驗室開發的步進式斜掃描演算法 (Obliquely Scanning and Step Strobe-lighting , OS3L)，結合紫外光光源的頻閃和DMD光點陣列的斜掃描，針對任意形狀的三維微結構建立了一套數值最佳化的軟體。在數值最佳化的策略中，使模擬結果與目標形貌的誤差最小化，進而獲得曝光點密度分佈和最佳的實驗製程參數。在得到紫外光圖案化的點分佈後，透過軟體處理DMD串列圖檔，實現對曝光劑量的空間分佈進行精準控制。最終，在光阻顯影後，能夠獲得所需特徵尺寸的三維微結構。
總而言之，本研究基於DMD的無光罩曝光技術，針對高精度三維微結構的製造需求，透過數值模擬和最佳化方法，實現了對曝光劑量以及顯影時間的準確控制，從而提高了三維微結構的製造精度。

This paper is dedicated to developing a simulation method for postexposure development of photoresist in a high-precision maskless exposure system. By controlling the dose distribution and development time, various three-dimensional (3D) microstructures were successfully fabricated, and process parameters were optimized to achieve more precise 3D microstructures.This method utilizes maskless lithography technology based on digital
micromirror devices (DMD) and employs digital control via software to precisely adjust the UV dose projected onto the photoresist layer.
For the numerical simulation of the photoresist, the relationship between the photoresist dose, depth, and development time was first established through empirical model, describing the dissolution rate characteristics of the photoresist after exposure. Then, by convoluting the dose of a single pixel of the DMD with the exposure point density distribution, the surface dose during photoresist exposure is obtained. Finally, combining this with the numerical simulation of photoresist development based on the Eikonal equation, the 3D morphology of the photoresist after exposure and development was achieved.
Moreover, this paper utilizes a Obliquely Scanning and Step Strobe-lighting Algorithm developed in the laboratory, combined with the stroboscopic UV light source and the oblique scanning of the DMD light point array, to establish a numerically optimized software system for arbitrary shaped 3D microstructures. In the numerical optimization strategy, the error between the simulation results
and the target morphology is minimized, thereby obtaining the exposure point density distribution and optimal experimental process parameters. After obtaining the UV patterned point distribution, the DMD sequence images are processed through software to achieve precise control over the spatial distribution of the exposure dose. Ultimately, after photoresist development, the desired feature sizes of 3D microstructures can be obtained.
In conclusion, the DMD-based maskless exposure technology combines high precision with the manufacturing needs of 3D microstructures. Through numerical simulation and optimization methods, accurate control over exposure dose and development time is realized, thereby improving the manufacturing precision of 3D microstructures.

[1] K. Takahashi, and J. Setoyama, “A UV‐Exposure System using DMD.” Electron. Comm. Jpn. Pt. II, Vol. 83(7), pp. 56-58, March 2000.
[2] 簡弘量, “光點陣列斜掃描無光罩式微影系統開發,” 國立成功大學機械工程學系博士論文, 2020.
[3] K. F. Chan, Z. Feng, R. Yang, A. Ishikawa and W. Mei, “High-Resolution Maskless Lithography.” J. Microlithogr. Microfabr. Microsyst., Vol. 2(4), pp. 331-339, 2003.
[4] K. Zhong, Y. Gao, F. Li, N. Luo, and W. Zhang, “Fabrication of continuous relief micro-optic elements using real-time maskless lithography technique based on DMD.” Opt. & Laser Technol., Vol. 56, pp. 367-371, 2014.
[5] Dill, F.H., et al., “Characterization of Positive Photoresist.” IEEE Transactions on Electron Devices, Vol. ED-22, No.7, pp 445-452, July 1975.
[6] X. Ma, Y. Kato, F. Kempen, Y. Hirai, T. Tsuchiya, F. Keulen, and O. Tabata, “Multiple patterning with process optimization method for maskless DMD-based grayscale lithography.” Procedia Eng., Vol. 120, pp. 1091-1094, 2015.
[7] M. N. Hasan, D.-H. Dinh, H.-L. Chien, and Y.-C. Lee, “Maskless Beam Pen Lithography Based on Integrated Microlens Array and Spatial-Filter Array.” Opt. Eng., Vol. 56, 115104, 2017.
[8] D.-H. Dinh, H.-L. Chien, and Y.-C. Lee, “Maskless Lithography Based on Digital Micromirror Device (DMD) and Double Sided Microlens and Spatial-Filter Array.” Opt. & Laser Technol., Vol. 113, pp. 407-415, 2019.
[9] H. Zhang, and S. Wen, “Microlens Array Based Three-dimensional Light Field Projection and Possible Applications in Photolithography.” Proc., Vol. 11175, Optifab 2019.
[10] H.-L. Chien and Y.-C. Lee, “Three Dimensional Maskless Ultraviolet Exposure System Based on Digital Light Processing.” Int. J. Precis. Eng. Manuf., Vol. 21, pp. 937-945, 2020.
[11] DILL, Frederick H., et al. “Characterization of positive photoresist.” IEEE Transactions on electron devices, 1975.
[12] P. Trefonas III, and B. K. Daniels. “ New principle for image enhancement in single layer positive photoresists.” Advances in Resist Technology and Processing IV, SPIE, Vol. 771, 1987.
[13] Robertson, S. A., Stevenson, J. T. M., Holwill, R. J., Thirsk, M., Daraktchiev, I. S., & Hansen, S. G., “Photoresist dissolution rates: a comparison of puddle, spray, and immersion processes.” SPIE, Vol. 1464, pp. 232-244, 1991.
[14] Chris A. Mack, “Development of Positive Photoresist.” J. Electrochem. Soc., Vol. 134, No. 1, pp 148-152, 1987.
[15] Chris A. Mack, “A New Kinetic Model to Describe Photoresist Development.” J. Electrochem. Soc., Vol. 139, No. 4, pp L35-L37, 1992.
[16] Graham Arthur, G., Mack, C.A., Martin, B., “A New Development Model for Lithography Simulation.” Olin Microlithography Seminar, pp. 55-66, 1997.
[17] Ralph R Dammel, “Theoretical Basis For A New Development Rate Model For Positive Photoresists.” J. Photopolym. Sci. Tec., Vol. 10, No. 3, pp. 379-386, 1997.
[18] Huang, Jian-Ping, T. K. Kwei, and Arnost Reiser. “On the molecular Mechanism of positive novolac resists.” Advances in Resist Technology and Processing VI., SPIE, Vol. 1086, pp.74-84, 1989.
[19] J. A. Sethian, “A fast marching level set method for monotonically advancing fronts.” Proc. Natl. Acad. Sci., Vol. 93, No.4, 1996.
[20] Yoshikazu Hirai, Yoshiteru Inamoto, Koji Sugano, Toshiyuki Tsuchiya and Osamu Tabata, “Moving mask UV lithography for three-dimensional structuring.” J. Micromech. Microeng, vol. 17, No.2, 2006.
[21] Y. Hirai, K. Sugano, T. Tsuchiya, and O. Tabata, “A three-dimensional microstructuring technique exploiting the positive photoresist property.” J. Micromech. Microeng., vol. 20, 2010.
[22] Xiaoxu Ma, Yoshiki Kato, Floris van Kempen, Yoshikazu Hirai, Toshiyuki Tsuchiya, Fred van Keulen, and Osamu Tabata, “Experimental study of numerical optimization for 3-D microstructuring using DMD-based grayscale lithography.” J. Microelectromech. Syst., Vol. 24 No.6, 2015.
[23] 許永昕, “利用斜掃描與頻閃技術之高精度無光罩式微影系統的開發與應用,” 國立成功大學機械工程學系博士論文, 2023。
[24] 李汶峰, “數位光學暨光點陣列畸變校正應用於高精度無光罩微影曝光,” 國立成功大學機械工程學系碩士論文, 2023。
[25] Meyer, P., A. El-Kholi, and J. Schulz. “Investigations of the development rate of irradiated PMMA microstructures in deep X-ray lithography.” Microelectronic Engineering, 2002.
[26] J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” J. Comput., vol. 7, pp. 308-313, 1965.
[27] Helmsen, John Joseph, et al. “Two new methods for simulating photolithography development in 3D.”Optical Microlithography IX., Vol. 2726. SPIE, 1996.
[28] Sethian, James A. “A fast marching level set method for monotonically advancing fronts.” proceedings of the National Academy of Sciences,1996.
[29] Savic, Marko, et al. “Lung nodule segmentation with a region-based fast marching method.” Sensor,2021.
[30] Garrido, Santiago, David Alvarez, and Luis E. Moreno. “Marine applications of the fast marching method.” Frontiers in Robotics and AI ,2020.
[31] Syu, Yong-Sin, et al. “Maskless lithography for large area patterning of three-dimensional microstructures with application on a light guiding plate.” Optics Express, 2023.
[32] Chung, C. K., Sher, K. L., Syu, Y. J., & Cheng, C. C.. “Fabrication of cone-like microstructure using UV LIGA-like for light guide plate application.” Microsystem technologies, vol. 16, pp.1619-1624, 2010.
[33] 蔣明澤, “以數位光學斜掃描為基礎之無光罩微影技術應用於大面積任意圖形三維微結構之製作,” 國立成功大學機械工程學系碩士論文, 2023。
[34] H. Niederreiter, “Low-Discrepancy and Low-Dispersion Sequence,” J. Number Theory., vol. 30, pp. 51-70, 1998.