晶圓代工為台灣蓬勃發展之重點產業之一，本研究個案公司為GaAs(Gallium Arsenide)砷化鎵晶圓代工廠，近年來砷化鎵上下游產業極力發展作為光電元件之製程─VCSEL(Vertical Cavity Surface Emitting Laser)「垂直共振腔面射型雷射」。
VCSEL晶片上有數十至數千顆不等之發光頭，製程關鍵重點之一為將單位面積內放入最多之發光頭，可有效降低晶圓採購成本，而將發光頭平台(emitter mesa)剖面角度做到趨近垂直可幫助實現縮小晶片尺寸之目的並可進一步縮小模組尺寸，趨近於垂直的發光頭角度仰賴蝕刻製程參數之調配。
產業中常用實驗設計方法(Design of Experiments, DOE)作為優化製程參數的手法，本研究使用田口方法找出製程之關鍵因子，搭配反應曲面法取得最大化發光頭角度之參數，使個案公司提升VCSEL製程之競爭力及製程能力。
經實驗結果分析，影響發光頭平台角度之主要影響因子為反應氣體N2(氮氣)濃度、反應氣體BCl3(三氯化硼)及機台腔體壓力，透過反應曲面法及驗證實驗得出之優化參數組合為N2(氮氣)=7.7(sccm)， BCl3(三氯化硼)=30.17(sccm)，腔體壓力=1.3(mTorr)，而由此參數條件進行之製程可將原本71度之平台角度提升至84度，進而有效的減少發光頭之間距並縮小晶片之尺寸。

Wafer foundry is one of the most important and booming industries in Taiwan. The case-study company is a world-renowned GaAs-based foundry company and is vigorously developing a new technology called VCSEL (Vertical Cavity Surface Emitting Laser) for facial recognition, 3D sensing and AR/VR applications.in recent years.
There are many (up to 1000’s) light -emitting heads on a single VCSEL chip. One of the key points of the process is to put the largest number of light-emitting heads in a unit area, which can effectively reduce the cost of wafer procurement. The profile angle of emitter mesa approaching vertical can help to achieve the purpose of reducing the chip size and further reduce the cost and module size. As we know, the profile angle depends strongly on the adjustment of the etching process parameters.
This study adopted Taguchi method to determine the key factors, and applied Response Surface Methodology to optimize the etching process parameters to increase the emitter head angle.
The experimental result of this study shows that N2, BCl3 and pressure are the three key factors impacting the profile angles of emitter heads. The profile angle made by the original process was around 71~72 degree, by using the optimized parameters, the profile angle of 84 degree (near vertical) has been achieved, and the improved process is in better control and the standard deviation of the improved process is smaller than that of the original process.

史志洋. (2010). 利用實驗設計法改善測試機台造成 IC 晶粒破裂之問題---以A封測廠為例. (碩士). 國立交通大學, 新竹市
何文獻, 蔡進聰, 林清煌, & 周至宏. (2007). 應用反應曲面法與基因演算法於船體結構構件斷面尺寸之最佳化設計. [Optimal Section Scantling Design for Ship Structures Using Response Surface Method and Genetic Algorithm]. 中國造船暨輪機工程學刊, 26(1), 39-50.
呂政冀. (2009). 應用部分因子實驗設計進行LED磊晶之MOCVD製程最佳參數之研究. (碩士). 國立成功大學, 台南市.
李輝煌. (2019). 田口方法: 品質設計的原理與實務: 新北市:高立圖書有限公司.
邱威錡. (2019). 應用實驗設計法優化黑色矩陣線幅. (碩士). 國立成功大學, 台南市.
翁翎華. (2014). 應用反應曲面法建構茶葉低溫乾燥製程最佳化之研究. (碩士). 國立勤益科技大學, 台中市.
張秋貴. (2003). 應用實驗設計法調整蝕刻製程程式以改善晶圓允收測試之接觸窗阻值電性之研究. (碩士). 中原大學, 桃園縣.
張展榮. (2014). 以實驗設計法最佳化黃光製程對準之蝕刻參數. (碩士). 國立中興大學, 台中市.
陳昭吟. (2014). 應用田口方法改善半導體光罩之註記差. (碩士). 國立成功大學, 台南市.
陳寵文. (2007). 以田口方法探討光電廠去光阻劑回收系統運轉之最佳化. (碩士). 國立交通大學, 新竹市.
楊世豐. (2014). TFT LCD 乾蝕刻製程化學性側蝕法研究. (碩士). 國立交通大學, 新竹市.
黎正中. (2019). 實驗設計與分析. 新北市:高立圖書有限公司.
劉洺辰. (2018). 應用實驗設計法(DOE)改善人工水晶體製程良率. (碩士). 國立交通大學, 新竹市.
戴搖廷. (2014). 應用田口方法至 TFT-LCD 黑色矩陣檢測缺陷之參數設計. (碩士). 國立中興大學, 台中市.
蘇朝墩. (2002). 品質工程: 新北市:前程文化事業有限公司.
龔進安. (2016). 半導體蝕刻製程參數調整最佳化 –以P公司蝕刻製程為例. (碩士). 國立交通大學, 新竹市.
Aamir, M., Tu, S., Tolouei-Rad, M., Giasin, K., & Vafadar, A. (2020). Optimization and modeling of process parameters in multi-hole simultaneous drilling using taguchi method and fuzzy logic approach. Materials, 13(3), 680.
Alshraideh, H. (2011). Analysis and optimization of profile and shape response experiments. (Ph.D.). The Pennsylvania State University, Ann Arbor. ProQuest Dissertations & Theses A&I; SciTech Premium Collection database. (3483758)
Bahrami, M., Amiri, M. J., & Bagheri, F. (2019). Optimization of the lead removal from aqueous solution using two starch based adsorbents: Design of experiments using response surface methodology (RSM). Journal of Environmental Chemical Engineering, 7(1), 102793.
Bote, M. A., Naik, V. R., & Jagdeeshgouda, K. B. (2020). Optimization of spark ignition engine adopting Taguchi access and response surface methodology. Fuel, 280, 118530.
Dean, A., Voss, D., & Draguljić, D. (2017). Response Surface Methodology. In Design and Analysis of Experiments (pp. 565-614). Cham: Springer International Publishing.
Gasvoda, R. J., Zhang, Z., Wang, S., Hudson, E. A., & Agarwal, S. (2020). Etch selectivity during plasma-assisted etching of SiO2 and SiN x: Transitioning from reactive ion etching to atomic layer etching. Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, 38(5), 050803.
Hammoudi, A., Moussaceb, K., Belebchouche, C., & Dahmoune, F. (2019). Comparison of artificial neural network (ANN) and response surface methodology (RSM) prediction in compressive strength of recycled concrete aggregates. Construction and Building Materials, 209, 425-436.
Islam, M. N., & Pramanik, A. (2016). Comparison of Design of Experiments via Traditional and Taguchi Method. Journal of Advanced Manufacturing Systems, 15(03), 151-160.
Kwon, K.-S., & Lin, R.-M. (2005). Robust Damage Location in Structures Using Taguchi Method. Journal of Structural Engineering, 131(4), 629-642.
Mönch, L., Uzsoy, R., & Fowler, J. W. (2018a). A survey of semiconductor supply chain models part I: semiconductor supply chains, strategic network design, and supply chain simulation. International Journal of Production Research, 56(13), 4524-4545.
Mönch, L., Uzsoy, R., & Fowler, J. W. (2018b). A survey of semiconductor supply chain models part III: master planning, production planning, and demand fulfilment. International Journal of Production Research, 56(13), 4565-4584.
Montgomery, D. C. (2017). Design and Analysis of Experiments, 9th Edition.
Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2016). Response Surface Methodology: Process and Product Optimization Using Designed Experiments: John Wiley & Sons.
Nojiri, K. (2015). Dry Etching Technology for Semiconductors: Springer.
Polat, S., & Sayan, P. (2019). Application of response surface methodology with a Box–Behnken design for struvite precipitation. Advanced Powder Technology, 30(10), 2396-2407.
Shi, Z., Sun, X., Cai, Y., & Yang, Z. (2020). Robust Design Optimization of a Five-Phase PM Hub Motor for Fault-Tolerant Operation Based on Taguchi Method. IEEE Transactions on Energy Conversion, 35(4), 2036-2044. doi:10.1109/TEC.2020.2989438
Stevens, N. T., & Anderson-Cook, C. M. (2019). Design and analysis of confirmation experiments. Journal of Quality Technology, 51(2), 109-124.
Toyota, H., Asai, T., & Oku, N. (2017). Process optimization by use of design of experiments: Application for liposomalization of FK506. European Journal of Pharmaceutical Sciences, 102, 196-202.
Yang, A., Han, Y., Pan, Y., Xing, H., & Li, J. (2017). Optimum surface roughness prediction for titanium alloy by adopting response surface methodology. Results in Physics, 7, 1046-1050.
Yang, W. H., & Tarng, Y. S. (1998). Design optimization of cutting parameters for turning operations based on the Taguchi method. Journal of Materials Processing Technology, 84(1), 122-129.
Yolmeh, M., & Jafari, S. M. (2017). Applications of response surface methodology in the food industry processes. Food and Bioprocess Technology, 10(3), 413-433.
Yung, K. C., Wang, J., Huang, S. Q., Lee, C. P., & Yue, T. M. (2006). Modeling the Etching Rate and Uniformity of Plasma-Aided Manufacturing Using Statistical Experimental Design. Materials and Manufacturing Processes, 21(8), 899-906.
Zhang, F., Song, J., Dai, Y., & Xu, J. (2020). Semiconductor wafer fabrication production planning using multi-fidelity simulation optimisation. International Journal of Production Research, 58(21), 6585-6600.
Lyon, Apple's strategy towards 3D sensing is pushing VCSEL industry. Yole Development. July 26, 2018. http://www.yole.fr/VCSEL_IndustryOverview.aspx#.XyA4Np4zaUk
Lumentum, Multi-Junction VCSEL Array, Dec. 2020
https://www.lumentum.com/en/products/multi-junction-vcsel-array