精密單晶矽晶球可以透過計算同位素矽晶體中的原子數來確定亞佛加厥常數，在新制國際單位(New SI)中扮演重要的角色，但在精密球體的加工過程中，為了達到球體均勻地加工，必須瞭解球體於拋光製程中的運動狀態。本研究將化學機械拋光(Chemical mechanical polishing, CMP)導入球體拋光製程中，並針對三軸球體拋光系統進行力與力矩平衡式分析，瞭解球體於製程中的運動行為，並建立拋光軌跡動態數學模型。以三軸球體拋光監控系統及薄膜壓力感測器量測系統量測製程拋光功率與量化靜態負載力。實驗以黃玉石球進行參數測試後，再將最佳化製程參數應用於由直徑100 mm (4吋)單晶矽晶錠加工成之直徑94.9466 mm球體。透過奈米壓痕機械性質分析儀進行奈米刮痕實驗(Nano scratch test)，計算比材料移除能並預測體積材料移除率。以三次元座標量測儀(Coordinate Measurement Machine, CMM)量測半球體，並依據點資料計算得出真球度(Sphericity)。本研究完成研發三軸單晶矽晶球CMP製程，製程後真球度達3.6 μm，平均表面粗糙度Sa達5 nm。研究成果未來可應用於四軸(Four-cup)精密球體拋光機之研發，製造工業標準所需之新制國際單位標準球。

Precision monocrystalline silicon sphere plays an important role in the New International System of Unit (New SI) because it can determine the Avogadro constant by counting the atoms in an isotopic silicon crystal. In this study, chemical mechanical polishing (CMP) is applied on a three-cup sphere polishing process. Based on force-moment balance formulation, the study aims to develop a dynamic mathematical model of sphere polishing trajectory in a three-cup sphere polishing machine. Moreover, the three-cup sphere polishing monitoring system and the thin film pressure sensor measurement system have been established to measure the power signals and quantify the static load force of polishing. Experiments are initially carried out with topaz spheres then polishing parameters are adapted to monocrystalline silicon sphere with a diameter of 94.9466 mm which is manufactured from an ingot of diameter 100 mm (4”) cylinder. The material removal rate is predicted using specific energy of material removal based on nano-scratch tests by nano-indenter instrument. The sphericity is evaluated from the data points measured on the hemisphere by the coordinate measurement machine (CMM). Results of this study have developed a CMP process of monocrystalline silicon spheres to achieve the sphericity as 3.6 μm and the average surface roughness Sa as 5 nm. Future development can be used as a source for developing a four-cup machine for fabrication of new SI standard sphere for industrial reference.

[1] R. Davis, "The SI unit of mass," Metrologia, vol. 40, no. 6, p. 299, 2003.
[2] B. Wood and H. Bettin, "The Planck constant for the definition and realization of the kilogram," Annalen der Physik, vol. 531, no. 5, p. 1800308, 2019.
[3] A. Nicolaus, R. Meeß, and G. Bartl, "New Avogadro spheres for the redefinition of the kilogram," in Key Engineering Materials, 2014, vol. 613, pp. 17-25: Trans Tech Publ.
[4] F. Löffler, "Manufacturing Process Chain for Silicon Spheres," ed. Germany,: Physikalisch-Technische Bundesanstalt, 2015.
[5] R. Meeß, G. Hinzmann, and A. Lück, "Improved manufacturing process chain for silicon spheres," presented at the euspen’s 15th International Conference & Exhibition, Belgium, June 5, 2015.
[6] W. Angele, "Finishing high precision quartz balls," Precision Engineering, vol. 2, no. 3, pp. 119-122, 1980.
[7] A. Leistner and G. Zosi, "Polishing a 1-kg silicon sphere for a density standard," Applied optics, vol. 26, no. 4, pp. 600-601, 1987.
[8] A. Leistner and W. Giardini, "Fabrication and testing of precision spheres," Metrologia, vol. 28, no. 6, p. 503, 1991.
[9] 柴田順二, "球体のはなし," Journal of the Japan Society for Abrasive Technology, vol. 55, no. 12, pp. 746-747, 2011.
[10] Y. Peng et al., "Sphere precessions polishing method," Optical Engineering, vol. 60, no. 6, p. 064108, 2021.
[11] 廖紘毅, "銅膜晶圓化學機械拋光之終點偵測研究," 碩士, 機械工程系, 國立臺灣科技大學, 台北市, 2020.
[12] T. Kojima, M. Miyajima, F. Akaboshi, T. Yogo, S. Ishimoto, and A. Okuda, "Application of CMP process monitor to Cu polishing," IEEE transactions on semiconductor manufacturing, vol. 13, no. 3, pp. 293-299, 2000.
[13] T. K. Das, R. Ganesan, A. K. Sikder, and A. Kumar, "Online end point detection in CMP using SPRT of wavelet decomposed sensor data," IEEE transactions on semiconductor manufacturing, vol. 18, no. 3, pp. 440-447, 2005.
[14] H. Jeong, H. Kim, S. Lee, and D. Dornfeld, "Multi-Sensor Monitoring System in Chemical Mechanical Planarization (CMP) for Correlations with Process Issues," CIRP Annals, vol. 55, no. 1, pp. 325-328, 2006.
[15] H. Hocheng and Y.-L. Huang, "In Situ Endpoint Detection by Acoustic Emissions in Chemical–Mechanical Polishing of Metal Overlay," IEEE Transactions on Semiconductor Manufacturing, vol. 20, no. 3, pp. 306-312, 2007.
[16] 蔡岳勳, "電致動力應用於銅化學機械拋光平坦化效應研究," 碩士, 機械工程系, 國立臺灣科技大學, 台北市, 2015.
[17] H. Li, X. Lu, and J. Luo, "Motor power signal analysis for end-point detection of chemical mechanical planarization," Micromachines, vol. 8, no. 6, p. 177, 2017.
[18] 林昱銘, "電致動力輔助化學機械平坦化加工之雙向交錯式電極開發應用於矽導微孔晶圓研究," 碩士, 機械工程系, 國立臺灣科技大學, 台北市, 2017.
[19] Z. Qu et al., "Cu Layer thickness monitoring in CMP process by using eddy current sensor," in ICPT 2012-International Conference on Planarization/CMP Technology, 2012, pp. 1-5: VDE.
[20] S. Bourzgui, A. Roussy, G. Georges, E. Faivre, K. Labory, and A. Allard, "Device pattern impact on optical endpoint detection by interferometry for STI CMP," in ICPT 2017; International Conference on Planarization/CMP Technology, 2017, pp. 1-6: VDE.
[21] T. Fujita and K. Kitade, "Development of endpoint detection using optical transmittance and magnetic permeability based on skin effect in chemical mechanical planarization," Precision Engineering, vol. 57, pp. 95-103, 2019.
[22] D.Zeidler, M.Plotner, and K.Drescher, "Endpoint detection method for CMP of copper," Semiconductor and Microsystems Technology Laboratory, Dresden University of Technology, 01062 Dresden, Germany, 2000.
[23] W. J. Cote, J. E. Cronin, W. R. Hill, and C. A. Hoffman, "Endpoint detection apparatus and method for chemical/mechanical polishing," U.S. Patent No. 5,308,438, 1994.
[24] N. Kimura, F. Sakata, and T. Takahashi, "Polishing endpoint detection method," U.S. Patent No. 5,639,388, 1997.
[25] H.-C. Chen and S.-L. Hsu, "Chemical/mechanical planarization (CMP) endpoint method using measurement of polishing pad temperature," U.S. Patent No. 5,597,442, 1997.
[26] F. Zhang, "Chemical/mechanical polishing endpoint detection device and method," U.S. Patent No. 6,547,637, 2003.
[27] A. Bello and M. Wedlake, "Methods and systems for chemical mechanical planarization endpoint detection using an alternating current reference signal," U.S. Patent No. 10,343,253, 2019.
[28] N. E. Lustig, K. L. Saenger, and H.-M. Tong, "In-situ endpoint detection and process monitoring method and apparatus for chemical-mechanical polishing," U.S. Patent No. 5,433,651, 1995.
[29] T. Takahashi, K. Tohyama, and T. Takahashi, "Polishing apparatus having endpoint detection device," U.S. Patent No. 5,672,091, 1997.
[30] B. Swedek and A. N. Wiswesser, "Endpoint detection with light beams of different wavelengths," U.S. Patent No. 6,190,234, 2001.
[31] T. Matsuzaki, "CMP apparatus and method of polishing wafer using CMP," U.S. Patent No. 8,221,191, 2012.
[32] F.-S. Lee, C.-C. Chen, J.-C. Lee, and H.-C. Huang, "Method for endpoint detection for copper CMP," U.S. Patent No. 6,179,691, 2001.
[33] T. K. Das, R. Ganesan, A. K. Sikder, and A. J. I. t. o. s. m. Kumar, "Online end point detection in CMP using SPRT of wavelet decomposed sensor data," vol. 18, no. 3, pp. 440-447, 2005.
[34] Dayton, "Dayton Operating Instructions and Parts Manual," vol. Form 5S4031, ed. Niles, Illinois 60714 U.S.A.: Manufactured for Dayton Electric Mfg. Co.
[35] Modbus-Organization, "Modbus_Application_Protocol," vol. 1.1b3, ed. United States: The Modbus Organization, 2022.
[36] G. Thomas, "Introduction to the modbus protocol," The Extension, vol. 9, no. 4, pp. 1-4, 2008.
[37] Tekscan, "Calibration Quick Start Guide For Flexiforce Sensors," Rev 032415 ed. South Boston, United States: Tekscan Inc.
[38] Tekscan, "Tekscan FlexiForce Sensor A201 Manual," DS Rev I 062821 ed. South Boston, United States: Tekscan, Inc., 2021.
[39] C.-C. A. Chen, W.-C. Pu, and M. P. Trai, "Development on Advanced Chemical Mechanical Polishing Process for Manufacturing of Monocrystalline Silicon Sphere of Kilogram Prototype," Chinese Society of Mechanical Engineers, 2020.
[40] 陳炤彰, 卜偉晉, M. P. Trai, "先進化學機械拋光法於單晶矽球之質量原器製造研究" 科技部工程司109年度機械固力學門成果發表會, 21 Nov. 2021.
[41] Moore-Nanotech, "Nanotech 350FG Specification Overview," ed. United States: Moore Nanotechnology Systems, 2007.
[42] O. V. Zakharov, N. M. Bobrovsky, A. V. Kochetkov, S. N. Grigoriev, and I. N. Bobrovsky, "A sphericity measurement method based on the minimum measuring zone," in AIP Conference Proceedings, 2016, vol. 1785, no. 1, p. 040094: AIP Publishing LLC.