不論是筆記型電腦或數位相機等消費性電子產品在現代人的生活中皆是不可或缺的必需品，並往輕薄短小的目標邁進。因此，如何在矽晶圓上製作奈米尺寸之圖案，成為縮小電子元件之關鍵技術。
本論文提出的掃描探針微影術(Scanning probe lithography, SPL)，是應用原子力顯微鏡(Atomic force microscope, AFM)的陽極氧化效應(Anodic oxidation)，直接在矽晶圓表面上定義線寬，改良以往光學微影(Optical lithography)在光學繞射的困境，並利用田口實驗規劃控制因子及水準值，定出品質特性規範，再依照田口直交表(Orthogonal array)進行實驗。
由於田口方法(Taguchi method)是針對單一品質進行設計，就製程而言，往往無法達到整體品質特性之最佳化。因此，本論文結合灰關聯分析(Grey relational analysis) 和模糊推論系統(Fuzzy inference system)來整合多品質特性。利用灰關聯分析將數據正規化，並透過模糊推論系統(Fuzzy inference system)來整合多品質特性問題。並且利用田口方法的訊號雜訊比(Siganl to noise ratio, S/N)以及變異數分析(Analysis of variance)的結果進行探討，藉此找出對製程影響最大的顯著因子。最後利用倒傳遞類神經網路(Back-propagation neural network)結合擬牛頓法(BFGS)建構出預測製程的預測系統，以模擬實驗結果。
本論文經過多品質最佳化設計後，成功在矽晶圓上製作出寬度68奈米且均勻度良好的氧化矽線，將成為有利於縮小電子元件之技術。

Consumer electronics, ranging from notebooks to digital cameras, are considered as necessities in modern life. The trend for these products to become smaller, thinner, and lighter due to consumer demand and convenience introduces key technological advancement to sketch a pattern in nano-scale on silicon wafer surface.
The scanning probe lithography mentioned in this study used the anodic oxidation effect of the atomic force microscope to define the line width on the silicon wafer surface to resolve the problem of optical diffraction. We also utilized the Taguchi method to obtain factors and quality value to ensure quality characteristics followed by experimentation with orthogonal array.
Since Taguchi Method was initially designed for single quality characteristic, the method could not allow us to obtain multi-quality characteristics. We therefore combined grey relational analysis and fuzzy inference system for multi-quality characteristics. We used the grey relational analysis to normalize the experimental data and the fuzzy inference system to acquire multi-quality characteristics. From analyzing the signal-to-noise ratio and variance, we noted significant factors that affected the lithography process. Lastly, a prediction system was established to simulate the results by using back-propagation neural network with BFGS algorithm.
We had successfully produced evenly distributed silicon oxide lines of a 68nm width on the silicon wafer surface. This study can contribute to current techniques in producing desirable electronics for the market.

[1].M. T. Browne, P. Charalambous, and V. A. Kudryashov, “The proximity effect in e-beam nanolithography”, Microelectronic Engineering, Vol. 13, pp.221-224 (1991)
[2].F. Cerrina, “Recent advances in x-ray lithography”, Japanese Journal of Applied Physics, Vol. 31, No. 12B, pp. 4178-4184 (1992)
[3].G. Binnig, H. Rohrer, C. Gerber, and E. Weibel, “7 × 7 reconstruction of Si (111) resolved in real space”, Physical Review Letters, Vol. 50, pp. 120-123 (1983)
[4].G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope”, Physical Review Letters, Vol. 56, pp. 930-933 (1986)
[5].M. A. McCord, R. F. W. Pease, “High resolution, low-voltage probes from a field emission source close to the target plane”, The Journal of Vacuum Science and Technology B, Vol. 3, pp.198-201 (1985)
[6].M. A. McCord, and R. F. W. Pease, “Lithography with the scanning tunneling microscope”, The Journal of Vacuum Science and Technology B, Vol. 4, No. 1, pp. 86-88 (1986)
[7].J. A. Dagata, J. Schneir, and H. H. Harary, “Modification of hydrogen-passivated silicon by a scanning tunneling microscope operating in air”, Applied Physics Letters, Vol. 56, pp. 2001-2003 (1990)
[8].H. Sugimura, T. Uchida, N. Kitamura, and H. Masuhara, “Nanofabrication of titanium surface by tip-induced anodization in scanning tunneling microscopy”, Japanese Journal of Applied Physics, Vol. 32, pp. L553-L555 (1993)
[9].L. Tsau, D. Wang, and K. L. Wang, “ Nanometer scale patterning of silicon (100) surfaces by an atomic force microscope operating in air”, Applied Physics Letters, vol. 64, pp. 2133-2135 (1994)
[10].E. S. Snow, and P. M. Cambell, “Fabrication of Si nanostructures with an atomic force microscope”, Applied Physics Letters, Vol. 64, No.15, pp. 1932-1934 (1994)
[11].T. Teuschler, K. Mahr, S. Miyaxaki, M. Hundhausen, and L. Ley, “Nanometer-scale field-induced oxidation of Si(111) : H by a conducting-probe scanning force microscop : doping dependence and kinetics,” Applied Physics Letters, Vol. 67, No.21, pp. 3144-3146 (1995)
[12].A. E. Gordon, R. T. Fayfield, D. D. Litfin, and T. K. Higman, “Mechanisms of surface anodization produced by scanning probe microscopes”, The Journal of Vacuum Science and Technology B, Vol. 13, No. 6, pp. 2805-2808 (1995)
[13].D. Stievenard, P. A. Fontaine, and E. Bubois, “Nanooxidation using a scanning probe microscope : an analytical model based on field induced oxidation”, Applied Physics Letters, Vol. 70, No. 24, pp. 3272-3274 (1997)
[14].N. Cabrera, and N. F. Mott, “Theory of the oxidation of metals”, Reports on Progress in Physics, Vol. 12, PP. 163-184 (1948)
[15].P. Avouris, T. Hertel, and R. Martel, “Atomic force microscope tip-induced local oxidation of silicon : kinetics, mechanism, and nanofabrication”, Applied Physics Letters, Vol. 71, No. 2, pp. 285-287 (1997)
[16].F. Marchi, V. Bouchiat, H. Dallaporta, V. Safarov, D. Tonneau, and P. Doppelt, “Growth of silicon oxide on hydrogenated silicon during lithography with an atomic force microscope”, Journal of Vacuum Science & Technology B : Microelectronics and Nanometer Structures, Vol. 16, pp. 2952-2956 (1998)
[17].R. Garcia, Montserrat, and H. Rohrer, “Pattering of silicon surfaces with noncontact atomic force microscope : field-induced formation of nanometer-size water bridges”, Journal of Applied Physics, Vol. 86, No. 4, pp. 1898-1903 (1999)
[18].M. Tello, and R. Garcia, “Nano-oxidation of silicon surfaces : comparison of noncontact and contact atomic-force microscopy methods”, Applied Physics Letters, Vol. 79, No. 3, pp. 424-426 (2001)
[19].H. Uchida, T. Okada, K. H. Shin, and M. Inoue, “Local anodization of permalloy film by atomic force microscope”, Journal of Magnetism and Magnetic Materials, Vol.316 pp. e67-e70 (2007)
[20].L. Wonbae, k. Hyunsook, L. Haiwon, and H. Masahiko, “Atomic force microscope anodization lithography using organic molecular assembly and ferritin” Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 313, pp. 402-406 (2008)
[21].H. Jiwon, K. Daiji, I. Takashi, M. Kuniaki, and S. Hiroyuki, “Scanning probe anodization patterning of Si substrates covered with a self-assembled monolayer dependent on surface hydrophilicity”, Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, Vol. 27, pp. 928-933 (2009)
[22].R. Jeyapaul, P. Shahabudeen, and K. Krishnaiah, “Quality management research by considering multi-response problems in the Taguchi method –a review”, International Journal of Advanced Manufacturing Technology, Vol. 26, pp. 1331-1337 (2005)
[23].C. L. Lin, W. D. Chou, and J. L. Lin, “Optimization of the electrical discharge machining process based on the Taguchi method with fuzzy logics”, Journal of Science and Technology, Vol. 10, No. 2, pp. 119-127 (2001)
[24].Lu, Dawei, and J. Antony, “Optimization of multiple responses using a fuzzy-rule based inference System”, Taylor & Francis , Vol. 40, No. 7, pp. 1613-1625 (2002)
[25].C. L. Lin, “Use of the Taguchi method and grey relational analysis to optimize turning operations with multiple performance characteristics”, Materials and Manufacturing Processes, Vol. 19, No. 2, pp. 209-220 (2004)
[26].S. Dutta, and S. Hekhar, “Bond-rating : A non-conservative application of neural networks”, Proceedings of the IEEE International Conference on Neural Networks, Vol. 11, pp. 443-450 (1988)
[27].A. N. Refenes, B. M. Azema, and S. A. Karoussos, “Currency exchange rate prediction and neural network design strategies”, Neural Computing and Applications, Vol. 1, pp. 46-58 (1993)
[28].E. Dubois, and J. L. Budendorff, “Kinetics of scanned probe oxidation : space-charge limited growth”, Journal of Applied Physics, Vol. 87, No. 11, pp. 8148-8154 (2000)
[29].F. Te-Hua “Mechanisms of nanooxidation of Si(100) form atomic force microscopy”, Microelectronics Journal, Vol. 35 pp. 701–707 (2004)
[30].L. Ley, T. Teuschler, K. Mahr, S. Miyazaki, and M. Hundhausen, “Kinetics of field-induced oxidation of hydrogen-terminated Si (111) by means of a scanning force microscope”, The Journal of Vacuum Science and Technology B, vol.14, pp. 2845-2849 (1996)
[31].D. Stievenard, P. A. Fontaine, and E. Bubois, “Nanooxidation using a scanning probe microscope : an analytical model based on field induced oxidation”, Applied Physics Letters, Vol. 70, No. 24, pp. 3272-3274 (1997)
[32].D. Julong, “Introduction to grey system theory”, The Journal of Grey System, Vol. 1, pp. 1-24 (1989)
[33].李輝煌，“田口方法品質設計的原理與實務”，高立圖書有限公司，2008.
[34].蘇朝敦，“產品穩健設計”，三民書局，2003.
[35].T. H. Fang, “Mechanisms of nanooxidation of Si(100) from atomic force microscopy”, Microelectronics Journal, Vol. 35, pp. 701-707 (2004)
[36].L. A. Zadeh, “Information and control”, Fuzzy Sets, Vol. 8, pp.338-353 (1965)
[37].Y. S. Tarng, W. H. Yang, and S. C. Juang, “The set of fuzzy logic in the Taguchi method for the optimization of the submerged arc welding process”, International Journal of Advanced Manufacturing Technology, Vol. 16, pp. 688-694 (2000)
[38].葉怡成，“類神經網路模式應用與實作”，儒林圖書有限公司，1997
[39].葉怡成，“應用類神經網路”，儒林圖書有限公司，2001
[40].羅華強，“類神經網路 : MATLAB的應用”，高立圖書有限公司，2005
[41].林明獻，“矽晶圓半導體材料技術”，全華科技圖書股份有限公司，2003
[42].E. Allgower, and K. Georg, “Simplical and continuation method for approximation fixed point and solutions to system of equations”, SIAM Review, Vol.22, pp.28-84, (1980)
[43].R. P. Brent, “Some efficient algorithms for solving systems of nonlinear equations”, SIAM Journal on Numerical Analysis, Vol. 10, pp. 327-344 (1873)