矽晶棒長晶製程製造的最前端製程，會依照客戶需求生長不同尺寸的晶棒，在指定矽晶棒尺寸的要求下，生長直徑的控制就非常重要，在良率高的情況能夠得到相對較低成本獲得更高的營收獲利，同時也可以穩住客戶的訂單需求，若良率低的情況下則會造成產能排程的擠壓，需要開更多的爐數來進行生長產出，成本高的情況在業界的產品競爭力會下降，且產品無法順利達交造成客戶訂單的流失，所以生長直徑不足會造成低良率及營收獲利與客戶訂單的損失。
長晶的製程有很多參數能夠控制晶棒生長，本研究運用六標準差設計的架構，首先將問題定義清楚，並於過程中特性要因圖找出相關因子，第一階段進行實驗設計工具進行統計分析，找出對實驗結果正向的參數組合進行確認，再搭配模擬軟體進行模擬驗證，第二階段探討比例-積分-微分(Proportional Integral Derivative, PID)控制器邏輯進行優化，使用三菱電機控制系統進行編輯研究適合參數，在PID控制器上將公式拆解使用Excel檔案進行公式上的驗證，以上兩種方式可用模擬取代實際驗證參數，降低實驗測試的成本與時間縮短，且晶棒不良浪費減少，廠內總共有A~J等產品，單以A產品製程月營收可增加約2.2百萬臺幣/月，同步提升機台有效產能利用，且每月需交付的產量皆能順利達交，後續平行展開至其它產品，達到公司與市場雙贏局面。

The front-end process of silicon ingot growth process will grow ingots of different sizes according to customer needs. Under the requirements of the specified silicon ingot size, the control of the growth diameter is very important. The pursuit of of high yield can relatively lower cost to obtain higher profit, and at the same time stabilize customer order demand. On the other hand, if yield rate is low, it will cause the squeeze of capacity scheduling, and more furnaces should be opened for growth and production. With higher cost, the competitiveness of products in the industry will decline, and the failure of smoothly deliver products would cause the loss of customer orders.
There are many parameters in the crystal growth process that can control the growth of the ingot. This study adopts the framework of the six sigma design. First, the problem is clearly defined, and the relevant factors are found in the characteristic factor diagram of the process. The next stage is the experimental design tool for statistics Analyze and find out the parameter combination that is positive to the experimental results for confirmation. Simulation software is then used for verification. This surtdy further discusses the proportional-integral-derivative (Proportional Integral Derivative, PID) controller logic optimization using the Mitsubishi Electric control system Edit and study the suitable parameters, disassemble the formula on the PID controller and use the Excel file to verify the formula. The above two methods can be used to replace the actual verification parameters with simulation, which can reduce the cost and time of experimental testing, and the waste of bad ingots. There are a total of A~J products in the factory, and the monthly revenue of product A alone can increase by about 2.2 million NTD/month, and simultaneously improve the effective capacity utilization of the machine with smoothly delivery tempo that achieves a win-win situation for the company and the market.

摘要 II
ABSTRACT III
誌謝 V
目錄 VI
圖目錄 1
表目錄 3
第一章 緒論 4
1.1 研究背景 4
1.2 研究動機 5
1.3 研究目的 6
1.4 研究架構 7
第二章文獻回顧 8
2-1 單晶生長製程 8
2-2 實驗設計 12
2-3 PID控制器 16
第三章 研究方法 19
3-1 定 義 20
3-2 量 測 21
3-3 分 析 23
3-4 改 善 26
3-5 控 制 27
第四章 個案分析 29
4-1個案背景 29
4-1-1製程說明 30
4-1-2生長爐的組成元件 31
4-2六標準差設計 34
4-2-1定義(Define) 34
4-2-2衡量(Measure) 34
4-2-3分析(Analyze) 36
4-2-4改善(Improve) 41
4-2-5 實際投入結果 46
4-2-6控制(Control) 49
第五章結論與未來研究方向 50
5-1結 論 50
5-2研究限制 50
5-2未來研究方向 50
參考文獻 52

英文文獻部分：
Baptista, A., Silva, F. J. G., Campilho, R. D. S. G., Ferreira, S., & Pinto, G. (2020). Applying DMADV on the industrialization of updated components in the automotive sector: a case study. Procedia Manufacturing, 51, 1332-1339.
Cheng, Z., & Lei, G. (2021). Control of Nonlinear Uncertain Systems by Extended PID. IEEE Transactions on Automatic Control, Vol. 66, 3840-3847.
Rotsch, C, F., Dropka, N., Kießling, F., & Rudolph, P. (2020). Semiconductor Crystal Growth under the Influence of Magnetic Fields. Cryst. Res. Technol. 55, 1900115.
Kashirskaya, E. N., Kurnasov, E. V., Kholopov, V. A., & Shmeleva A. G. (2017). Methodology for Assessing the Implementation of the Production Process, IEEE 978-1-5386-0777-0, 232-235.
Kusuma, H. H., Radzi, M., & Sudin, B. (2004). Numerical Modeling of Czochralski Single Crystal Growth Process. Annual Fundamental Science Seminar Ibnu Sina Institute for Fundamental Science Studies.
Luiten, W. (2018). Thermal Design for Six Sigma of an Imaging Device with Dynamic Thermal Management. Proceeding of 24rd International Workshop on Thermal Investigations of ICs and Systems, IEEE 978-1-5386-6759-0.
Lukanin, D. P., Kalaev, V. V., Makarov, Yu. N., Wetzel, T., Virbulis, J., & Ammon, W. (2004). Advances in the simulation of heat transfer and prediction of the melt-crystal interface shape in silicon CZ growth. Journal of Crystal Growth 266, 20-27.
Mukaiyama, Y., Artemyev, V. V. & Sueoka, K. (2022). Numerical analysis of constitutional supercooling in heavily doped silicon crystals grown using the Czochralski method. Journal of Crystal Growth 597, 126844.
Nagi, A., & Altarazi, S. (2017). Integration of Value Stream Map and Strategic Layout Planning into DMAIC Approach to Improve Carpeting Process, Journal of Industrial Engineering and Management, 10(1), 74-97.
Dogru, O., Velswamy, K., Ibrahim, F., Yuqi, W., Sundaramoorthy, A. S., Biao, H., Xu, S., Nixon, M., & Bell, N. (2022). Reinforcement learning approach to autonomous PID tuning. Computers and Chemical Engineering 161, 107760.
Pan, Z., Jiajia, C., Yan, S., Xiang, T., Tiejuan, X., & Tao, M. (2012). Design of a Control System for an Autonomous Vehicle Based on Adaptive-PID. Int J Adv Robotic Sy, 2012, Vol. 9, 44.
Padula, F., & Visioli, A. (2011). Tuning rules for optimal PID and fractional-order PID controllers. Journal of Process Control 21, 69-81.
Panichi, C., Citti, P., & Rosti, D. (2006). A new integrated approach to the design of a race car suspension. Proceeding of 4th International Conference on Axiomatic Design ICAD-2006, Firenze. Jun 13-16.
Sundari, A. S., Setyawati, E. P., & Rimantho, D. (2020). Quality Control Analysis of Tube Sandwich Using Six Sigma Method in PTXYZ. Materials Science and Engineering, Vol 847, 012015.
Praveen, V., & Pillai, A. S. (2016). Modeling and Simulation of Quadcopter using PID Controller. International Science Press. I J C T A, 9(15), 7151-7158.
Ren, J. C., Ding, L., & Yin, W. (2021). Modeling and application of Czochralski silicon single crystal growth process using hybrid model of data-driven and mechanism-based methodologies. Journal of Process Control 104, 74-85.
Shailesh, P., Sundarrajan, S., & Komaraiah, M. (2014). Optimization of process parameters of Al-Si alloy by centrifugal casting technique using Taguchi design of experiments. Procedia Materials Science 6, 812-820.
Manny, U., & Telford, J. K. (2009). Optimization by Design of Experiment Techniques. IEEEAC paper #1470, Version 4, 978-1-4244-2622-5.
Yin, W., & D, L., Cong-Cong, L., & Ren, J.C. (2021). Data-Driven Model Predictive Control of Cz Silicon Single Crystal Growth Process With V/G Value Soft Measurement Model. IEEE Transactuons On Semiconductor Manufacturing, Vol. 34, No. 3. 420-428.
 
中文文獻部分：
1.王書邵(2014)，柴氏長晶法之熱流場與液固界面形狀之數值分析，成功大學，碩士論文。
2.黃禮翼、藍崇文(2007)，利用電腦模擬對矽單晶提拉之熱場分析與應用，台灣大學，化工會刊，第54卷，第5期，P29。
3.謝邦彥、紀宏、王彥彭、陳慧菱(2008)，六標準差DOE手法於硬碟防震最佳化之研究，數據分析，第3卷，第6期，P65-78。
4.翁榮駿(2014)，應用六標準差方法探討半導體測試品質，淡江大學，碩士論文。
5.鄧澤民、蔡世華、鄭呈偉、胡宇方(2018)，風險評估與實驗設計在製藥開發之應用，化工會刊，第65卷，第1期，P42-51。
6.黃臣鴻(2003)，PCABS合膠機械性質之射出成型條件最佳化，中央大學，碩士論文。
7.吳泰元(2020)，運用田口法探討自動化面板重合精度最佳化製程之研究，成功大學，碩士論文。
8.劉威志(2021)，運用田口方法分析ABS塑膠材料之射出成型參數對拉伸強度的影響，中央大學，碩士論文。
9.李楊正(2020)，利用田口法探討放電加工鎳基合金Rene108之最佳參數組合，屏東科技大學，碩士論文。
10.楊永弘(2021)，應用8D手法提升機台使用率，清華大學，碩士論文。
11.邱創鈞、莊禮帆(2009)運用田口方法於迴轉成型塑膠發泡製程最佳化設計，虎尾科技大學，碩士論文。
12.黃奇、黃志豪、呂政芳(2008)，解析PID控制器設計，化工會刊，第55卷，第2期，P18-34。
13.李佩蓉(2015)最佳自動調諧模糊PID控制器在生物反應器之應用，臺灣大學，碩士論文。
14.張茂青(2008)應用田口氏方法調整PID控制器，臺灣大學，碩士論文。
15.呂奇璜、廖本右(2020)射出成型機加熱料管之自調整PID溫度控制，能源科技專題，科儀新知223期。
16.簡富禎，決策分析與管理：紫式決策分析以全面提升決策品質(第二版)。
17.桑慧敏(2017)，一生受用的統計學大數據分析之鑰，高立書局。
18.蘇朝墩(2009)，六標準差，前程文化出版社。
19.蘇朝墩(2010)，品質工程，前程文化出版社。
20.蘇朝墩(2012)，品質管理，前程文化出版社。
21.林明獻-編(2020)，矽晶圓半導體材料技術(6版)，全華圖書。
 
網路資源部分：
1.全球半導體矽晶圓需求量(富士經濟, 2022) (https://www.moea.gov.tw/MNS/doit/industrytech/IndustryTech.aspx?menu_id=13545&it_id=436)
2.矽晶圓未來趨勢(https://www.inside.com.tw/article/25155-sas-globalwafers-long-term-chip-orders-2022)
3.DMAIC解說 (https://experience.dropbox.com/zh-tw/resources/dmaic)
4.晶體製造解說(https://zh.wikipedia.org/wiki/%E6%99%B6%E5%9C%93#%E8%A3%BD%E9%80%A0%E9%81%8E%E7%A8%8B)
5.實驗設計解說 (http://www.tynesys.com/doe/index.html)
6.模擬熱場圖面 (https://xueqiu.com/4886417478/165019366)
7.特性要因分析圖 (https://www.researchmfg.com/2012/03/cause-effect-analysis/)
8.矽晶圓製造業資源化應用技術手冊(https://riw.tgpf.org.tw/ReadFile/?p=Publish&n=06bb70d3-04c8-4029-9d02-654db04da568.pdf)