本論文旨在探討應用液滴表面張力及微晶粒或基板固定座與液滴之接觸界面間界面張力於微晶粒之自我對位，進而對微液透鏡成形進行分析。本論文採用之分析工具為Surface Evolver程式，該程式常被用來探討在表面張力能及其他能量影響下之液滴外形。
在利用液滴使微晶粒於基板固定座自我對位研究方面，本論文首先探討微晶粒於空氣中平移、下壓、旋轉或傾斜時之液滴變形及微晶粒或基板固定座與液滴間之接觸特性。在液滴表面張力及接觸界面與液滴間之界面張力的影響下，液滴於微晶粒或基板固定座上之接觸線、邊緣溢出或無溼潤區域等現象亦予完整探討。藉由觀察接觸線及溼潤區域之精微變化，配合微晶粒回復力或回復扭矩之計算，得以準確預估微晶粒之自我對位。此外，由於液滴於空氣與流體中之表面張力或接觸界面張力不同，其與微晶粒或基板固定座間之接觸特性亦不同。而置於流體中之液滴及微晶粒，因浮力、流體靜液壓力及界面張力之效應，液滴之變形、回復力或回復扭矩亦均受影響，進而改變自我對位機制，本論文接著亦將予以深入分析。本論文提出之微晶粒於空氣或溶液中自我對位分析模型，不但可改進部分文獻之缺失，亦可計算微晶粒可移動之臨界值，以改善其自我對位之準確性。
微液透鏡研究大都係利用電潤濕效應，以控制微液透鏡與基板間的界面張力，來改變微液透鏡之曲率半徑，隨著微液透鏡焦距變化，可有不同放大效果。本論文在不同施載電壓區間所計算得接觸角與文獻之實驗結果相較極為脗合。本論文最後將探討以施載電壓準確控制微液透鏡成形之機制，分析施載電壓與微液透鏡曲率半徑、焦距、物距、像距、孔徑、放大率與焦距比數等之間的關係，以供進行微液透鏡光學設計之參考。
本論文所建立之微晶粒自我對位模型與微液透鏡成形研究，除可彌補文獻現有分析模型之不足外，亦有助於相關設計參數之準確掌握，對於流體自我組裝技術或微液透鏡光學設計之提升，將有相當助益。

This work is mainly to investigate the surface tension of the droplet and the interfacial tension between the microchip/binding site and the droplet to study the self-alignment of the microchip and the formation of the liquid microlens. The Surface Evolver Program is adopted as an analysis tool in this work, which is developed for analyzing the droplet formation due to surface tension energy and other energies.
On the study of the self-alignment of the microchip with the binding site using the droplet, this work explores firstly the droplet deformation and the contact characteristics between the microchip/binding site and the droplet when the microchip is subjected to translation, compression, yawing or rolling in air. Under the effects of the surface tension of the droplet and the interfacial tension between the droplet and its contact surface, the contact line, overflow and no wet regions of the droplet on the microchip/binding site are thoroughly demonstrated. By observing the details of changes in the contact line and the wetted area and calculating the restoring force and restoring torque, the self-alignment of the microchip can be estimated accurately. Moreover, because the surface tension or interfacial tension is different for the droplet in air and in solution, the contact characteristics between the microchip/binding site and the droplet is also different. For the droplet and the microchip in solution, due to the effects of buoyancy, hydrostatic pressure and interfacial tension, the deformation of the droplet, restoring force or restoring torque are also affected, and change the self-alignment of the microchip. These are all analyzed thoroughly in this work. The present analysis model for the self-alignment of the microchip in air or solution can not only improve some drawbacks in the literature, but also predict the critical values of restoring movements to improve the accuracy of the self-alignment of the microchip.
The liquid microlens research generally utilizes the electrowetting effect to control the interfacial tension between the liquid microlens and the substrate to change the radius of curvature of the liquid microlens. The changes in the focal lengths can cause different magnifications. The contact angles under different applied voltages calculated by the present model are in excellent agreement with the experimental results in the literature. This work finally elucidates the accurate control of the formation of the liquid microlens under the applied voltage and investigates the functional relationships between the applied voltage and the radius of curvature, focal length, object distance, image distance, the diameter of the entrance pupil, magnification and f-number, to be of much help for the optical design of liquid microlens.
The analysis models established for the self-alignment of the microchip and the study for the formation of the liquid microlens in this work are applied not only to supplement an analysis models discussed in the literature, but also to be helpful for accurately controlling the related design parameters. The computed results are useful to improve the fluidic self-assembly technique or the optical design of the liquid microlens.

Adamson, A. W. and Gast, A. P., 1997: Physical Chemistry of Surfaces, sixth ed. John Wiley & Sons, New York.
Berge, B. and Peseux, J., 2000, “Variable Focal Lens Controlled by an External Voltage: An Application of Electrowetting,” European Physical Journal E, Vol. 3, pp. 159–163.
Berthier, J., Brakke, K. A., Grossi, F., Sanchez, L. and Di Cioccio, L., 2010, “Self-alignment of Silicon Chips on Wafers: A Capillary Approach,” Journal of Applied Physics, Vol.108, No.5, pp.054905-1–10.
Bhatti, P., Hannaford, B. and Marbot, P.-H., 1993, “Microscopic Pick-and-place Teleoperation” Proceedings of the SPIE - The International Society for Optical Engineering, Vol. 1833, pp. 2–8.
Böhringer, K. F., Srinivasan, U. and Howe, R. T., 2001, “Modeling of Capillary Forces and Binding Sites for Fluidic Self-Assembly,” Proceedings of the IEEE Micro Electro Mechanical Systems (MEMS), pp.369–374.
Brakke, K. A., 1992, “The Surface Evolver,” Experimental Mathematics, Vol.1, No.2, pp.141–165.
Brakke, K. A., 1996: Surface Evolver Manual, Version 2.01. The Geometry Center. University of Minnesota.
Cabestany, J., Rojas, I. and Joya, G., 2011: Advances in Computational Intelligence, first ed. Spring Science + Business Media, New York.
Cheng, C. C., Chang, C. A. and Yeh, J. A., 2006, “Variable focus dielectric liquid droplet lens,” Optics Express, Vol. 14, No. 9, pp.4101–4106.
Eugene, H., 2002: Optics, fourth ed. Addison Wesley, San Francisco.
Fang, J. and Böhringer, K. F., 2005, “High Yield Batch Packaging of Micro Devices with Uniquely Orienting Self-assembly,” 18th IEEE International Conference on Micro Electro Mechanical Systems, pp.12–15.
Fang, J. and Böhringer, K. F., 2006, “Wafer-level Packaging Based on Uniquely Orienting Self-Assembly (the DUO-SPASS Processes),” Journal of Microelectro- mechanical Systems, Vol. 15, No. 3, pp.531–540.
Fearing, R. S., 1995, “Survey of Sticking Effects for Micro-parts,” IEEE International Conference on Intelligent Robots and Systems, Vol. 2, pp. 212–217.
Greiner, A., Lienemann, J., Korvink, J. G., Xiong, X., Hanein, Y. and Böhringer, K. F., 2002, “Capillary Forces in Micro-Fluidic Self-Assembly,” 2002 International Conference on Modeling and Simulation of Microsystems - MSM 2002, pp.198–201.
Greivenkamp, J. E., 2004: Field Guide to Geometrical Optics, SPIE Press, Bellingham, Washington.
Hessler, W., 1996, “How to Build Simple, Effective Pick-and-place Device,” Robotics Today, Vol. 9, No. 4, pp. 1–5.
Hsieh, W. H. and Chen, J. H., 2005, “Lens-Profile Control by Electrowetting Fabrication Technique,” IEEE Photonics Technology Letters, Vol. 17, No. 3, pp.606–608.
Inaba, H. and Sato, K., 1996, “Measurement of Interfacial Tension between Tetradecane and Ethylene Glycol Water Solution by Means of the Pendant Drop Method,” Fluid Phase Equilibria, Vol.125, No.1-2, pp.159–168.
Kang, M., Yue, R., Wu, J., Ouyang, F. and Liu, L., 2007, “Meniscus Pinned Variable-focus Liquid Lens Based on Electrowetting-on-dielectric,” Proceedings of the 2nd IEEE International Conference on Nano/Micro Engineered and Molecular Systems, pp. 357–360.
Karniadakis, G., Beskok, A. and Aluru, N., 2005: Microflows and Nanoflows： Fundamentals and Simulation, first ed., Spring Science + Business Media, New York.
Kim, J. M., Shin, Y. E. and Fujimoto, K., 2004, “Dynamic Modeling for Resin Self-Alignment Mechanism,” Microelectronics Reliability, Vol.44, No.6, pp.983–992.
Kim, J. M., Yasuda, K. and Fujimoto, K., 2005, “Resin Self-Alignment Processes for Self-Assembly Systems,” Journal of Electronic Packaging, Transactions of the ASME, Vol.127, No.1, pp.18–24.
Krupenkin, T., Yang, S. and Mach, P., 2003, “Tunable Liquid Microlens,” Applied Physics Letters, Vol.82, No.3, pp.316–318.
Kuiper, S. and Hendriks, B. H. W., 2004, “Variable-focus Liquid Lens for Miniature Cameras,” Applied Physics Letters, Vol. 85, pp. 1128–1130.
Kwon, S. and Lee, L.P., 2001, “Focal Length Control by Microfabricated Planar Electrodes-based Liquid Lens,” 11th International Conference on Solid-State Sensors and Actuators. Digest of Technical Papers, Vol.2, pp. 1348–1351.
Lienemann, J., Greiner, A. and Korvink, J.G., 2002, “Surface Tension Defects in Micro-Fluidic Self-Alignment,” Proceedings of the SPIE - The International Society for Optical Engineering, Vol. 4755, pp. 55–63.
Liu, C.-X., Park, J. and Choi, J.-W., 2008, “A Planar Lens Based on the Electrowetting of Two Immiscible Liquids,” Journal of Micromechanics and Microengineering, Vol. 18, pp. 035023-1–7.
Lu, Y., Xia, S., Liu, M. and Zhang, J., 2006, “Dynamic Simulation of MEMS Self-Assembly Using Capillary Force,” 1st IEEE International Conference on Nano/Micro Engineered and Molecular Systems, pp. 414–417.
Martin, B. R., Furnange, D. C., Jackson, T. N., Mallouk, T. E. and Mayer, T. S., 2001, “Self-alignment of Patterned Wafers Using Capillary Forces at a Water-air Interface,” Advanced Funtional Materials, Vol. 11, No. 5, pp. 381–386.
Mastrangeli, M., Ruythooren, W., Celis, J. P. and Van Hoof, C., 2011, “Challenges for Capillary Self-Assembly of Microsystems,” IEEE Transactions on Components, Packaging and Manufacturing Technology, Vol. 1, No. 1, pp.133–149.
Morris, C. J., Stauth, S. A. and Parviz, B. A., 2005, “Self-Assembly for Microscale and Nanoscale Packaging: Steps Toward Self-packaging,” IEEE Transactions on Advanced Packaging, Vol. 28, No. 4, pp. 600–611.
Morris, C. J. and Parviz, B. A., 2008, “Micro-scale Metal Contacts for Capillary Force-driven Self-assembly,” Journal of Micromechanics and Microengineering, Vol. 18, No. 1, pp.015022-1–10.
Mugele, F. and Baret, J.-C., 2005, “Electrowetting: from Basics to Applications,” Journal of Physics: Condensed Matter, Vol. 17, pp.R705-R774.
Myers, D., 1999: Surfaces, Interfaces, and Colloids, second ed., John Wiley & Sons, New York.
Neumann, W. A., David, R. and Zuo, Y., 2011: Applied Surface Thermodynamics, second ed., Taylor & Francis Group, Northwest Washington.
Ouyang, F., Wu, J., Kang, M., Yue, R. and Liu, L., 2007, “Planar Variable-Focus Liquid Lens Based on Electrowetting on Dielectric,” IEEE International Conference on Nano/Micro Engineered and Molecular Systems, pp. 834–837.
Owens, D. K. and Wendt, R. C., 1969, “Estimation of the Surface Free Energy of Polymers,” Journal of Applied Polymer Science, Vol.13, pp.1741-1747.
Ozkan, M., Kibar, O., Ozkan, C. S. and Esener, S. C., 2000a, “New Optical and Electric-field-assisted Fluidic Pick-and-place Technique,” Proceedings of the SPIE - The International Society for Optical Engineering, Vol.4089, pp.1021–1026.
Ozkan, M., Kibar, O., Ozkan, C. S. and Esener, S. C., 2000b, “Massively Parallel low-cost Pick-and-place of Optoelectronic Devices by Electrochemical Fluidic Processing,” Optics Letters, Vol.25, No.17, pp.1285–1287.
Park, J., Liu, C.-X. and Choi, J.-W., 2007, “A Planar Liquid Lens Design Based On Electrowetting,” The 6th IEEE Conference on Sensors, pp. 438–442.
Saeedi, E., Kim, S. S. and Parviz, B. A., 2007, “Self-Assembled Inorganic Micro-Display on Plastic,” 20th IEEE International Conference on Micro Electro Mechanical Systems, pp.755–758.
Sato, K., Hata, S. and Shimokohbe, A., 1999, “Self-Alignment of Microparts Using Water Surface Tension,” Proceedings of SPIE - The International Society for Optical Engineering, Vol.3892, pp.321–329.
Sato, K., Ito, K., Hata, S. and Shimokohbe, A., 2003, “Self-Alignment of Microparts Using Liquid Surface Tension - Behavior of Micropart and Alignment Characteristics,” Precision Engineering, Vol.27, No.1, pp.42–50.
Saurei, L., Mathieu, G. and Berge, B., 2004, “Design of an Autofocus Lens for VGA 1/4” CCD and CMOS Sensors,” Proceedings of SPIE, Vol. 5249, pp. 288–296.
Seo, S. W., Han, S., Seo, J. H., Kim, Y. M., Kang, M. S., Min, N. K., Choi, W. B. and Sung, M. Y., 2009, “Microelectromechanical-system-based Variable-focus Liquid Lens for Capsule Endoscopes,” Japanese Journal of Applied Physics, Vol.48, pp. 052404-1–4.
Smith, J. S., 2000, “High Density, Low Parasitic Direct Integration by Fluidic Self Assembly (FSA),” International Electron Devices Meeting 2000 Technical Digest, pp.201–204.
Srinivasan, U., Howe, R. T. and Lieprriann, D., 2001, ‘‘Microstructure to Substrate Self-Assembly Using Capillary Forces,” Journal of Microelectromechanical Systems, Vol.10, No.1, pp.17–24.
Srinivasan, U., Helmbrecht, M. A., Muller, R. S. and Howe, R. T., 2002, “MEMS : Some Self-Assembly Required,” Optics and Photonics News, Vol.13, No.11, pp.20–24+56.
Talghader, J. J., Tu, J. K. and Smith, J. S., 1995, “Integration of Fluidically Self-Assembled Optoelectronic Devices Using a Silicon-Based Process,” IEEE Photonics Technology Letters, Vol.7, No.11, pp.1321–1323.
Talghader, J. J., 1998, “Integration of LEDs and VCSELs Using Fluidic Self-Assembly,” Proceedings of SPIE - The International Society for Optical Engineering, Vol.3286, pp.86–95.
Tsai, C. G., Hsieh, C. M. and Yeh, J. A., 2007, “Self-Alignment of Microchips Using Surface Tension and Solid Edge,” Sensors and Actuators A: Physical, Vol.139, No.1–2, pp.343–349.
Tu, J. K., Talghader, J. J., Hadley, M. A. and Smith, J. S., 1995, “Fluidic Self-assembly of InGaAs Vertical Cavity Surface Emitting Lasers onto Silicon,” Electronics Letters, Vol.31, No.17, pp.1448–1449.
Vallet, M., Berge, B. and Vovelle, L., 1996, “Electrowetting of Water and Aqueous Solutions on Poly(ethylene Terephthalate) Insulating Films,” Polymer Vol. 37, pp.2465–2470.
Verheijen, H. J. J. and Prins, M. W. J., 1999, “Reversible Electrowetting and Trapping of Charge: Model and Experiments,” Langmuir, Vol.15, No.20, pp.6616–6620.
Verma, A. K., Hadley, M. A., Yeh, H. J. J. and Smith, J. S., 1995, “ Fluidic Self-Assembly of Silicon Microstructures,” Proceedings- Electronic Components and Technology Conference, pp.1263–1268.
Welters, W. J. J. and Fokkink, L. G. J., 1998, “Fast electrically switchable capillary effects,” Langmuir, Vol. 14, pp. 1535–1538.
Xiong, X., Hanein, Y., Fang, J., Wang, Y., Wang, W., Schwartz, D. T. and Böhringer, K. F., 2003, “Controlled Multibatch Self-Assembly of Microdevices,” Journal of Microelectromechanical Systems, Vol.12, No.2, pp.117–27.
Yang, S., Krupenkin, T. N., Mach, P. and Chandross, E. A., 2003, “Tunable and Latchable Liquid Microlens with Photopolymerizable Components,” Advanced Materials, Vol. 15, No.11, pp. 940–943.
Yang, J. T., Chen, J. C., Huang, K. J. and Yeh, J. A., 2006, “Droplet manipulation on a hydrophobic textured surface with roughened patterns,” Journal of Microelectro- mechanical Systems, Vol. 15, No. 3, pp.697–707.
Yeh, H. J. J. and Smith, J. S., 1994a, “Fluidic Self-Assembly for The Integration of GaAs Light-Emitting Diodes on Si Substrates,” IEEE Photonics Technology Letter, Vol. 6, No.6, pp.706–708.
Yeh, H. J. J. and Smith, J. S., 1994b, “Fluidic Self-Assembly of Microstructures and Its Application to The Integration of GaAs on Si,” Proceedings of the IEEE Micro Electro Mechanical Systems, pp.279–284.
Zill, D. G. and Cullen, M. R., 2000: Advanced Engineering Mathematics, second ed., Jones and Bartlett Publishers, Sudbury.
Zhu, Q., Wang, G. and Luo, L., 1998, “Optimization of Design and Manufacturing Parameters for Solder Joint Geometry and Self-Alignment in Flip-Chip Technology,” International Conference on Solid-State and Integrated Circuit Technology Proceedings, pp.554–558.