本論文主要針對半導體製程生產時所面臨的兩大問題:晶圓量測時間的延遲以及在半導體特有的多量少樣混合產品。根據上述問題，提出修正EWMA控制器使得產品品質可以滿足產品規格。
首先，我們直接以數學模式來分析量測時間的延遲對控制上的影響，提供一個控制上的指導方針，並且使用VM (Virtual Metrology) 來決解延遲之問題；並且在化學氣相沉積製程中加以分析各個建模方法對VM效果之比較，發現以Stepwise最佳之方法。
而在混合產品生產的問題，主要是以統計學之方法ANCOVA來解決，利用ANCOVA可以分析出各個產品對機台的特性，加以修正誤差項，來達到提升控制效能和品質。

Two problems encountered in many semiconductor manufacturing are metrology delay caused by the equipments and mixture products on producing. For this thesis, we develop some controllers to eliminate the influences of two problems.
First, focusing on the metrology delay problem, we deriver an analytic formula of the performance for a single EWMA controller and provide the guideline to reduce the effects of metrology delay system. Additionally, we provide VM (Virtual Metrology) system to solve it and analyze the performance of VM of modeling methods. Finally, we suggest Stepwise method to plug in VM system.
Mixed-product production can reduce amount of cost and time in semiconductor manufacturing. However, each product has a different I-O model and it is a big challenge to run-to-run control. In order to solve it, we use an ANCOVA model to deal with the characteristic of mixed products in different platforms, and to correct the modeling error due to mixed products in order to impove the controller performance and quality.

1. Sachs, E., Guo, R. S., Ha , S. and Hu, A. and Ingolfsson A. (1991). “Process control system for VLSI fabrication.” IEEE Transactions on Semiconductor Manufacturing, 4, pp. 134-143.
2. Sachs, E., Hu, A. and Ingolfsson A. (1995). “Run by Run Process Control: Combining SPC and Feedback Control”. IEEE Transactions on Semiconductor Manufacturing, 8, pp. 26-43.
3. Tedder L. L. and Rubloff G. W.( 1996), ”Dynamic rate and thickness metrology during poly-Si rapid thermal chemical vapor deposition from SiH4 using real time in situ mass spectrometry”, J. Vac. Sci. Technol. A 14(2), pp. 267-270.
4. Moyne, J., E.D. Castillo, and A.M. Hurwitz (2001). Run-to-Run Control in Semiconductor Manufacturing. CRC Press, Florida.
5. Castillo E. D.(2002), Statistical Process Adjustment for Quality Control. John-Wiley and Sons, New York.
6. Seborg, D.E., Edgar T.F., Mellichamp D.A.(2004), Process Dynamics and Control, Wiley.
7. Chen A., Guo R. S.(2001), “Age-based double EWMA controller and its application to CMP processes”, IEEE Trans. Semicond. Manuf. 14(1), pp11-19
8. Wang J., He Q.P., Qin S.J., Bode C.A., Purdy M.A. (2005), Recursive least squares estimation for Run-to-Run control with metrology delay and its application to STI etch process, IEEE Trans. Semicond. Manuf., 18 (2) ,pp.309–319.
9. Tseng S. T., Chou R. J., and Lee S.P.(2002), “A study on a multivariate EWMA controller”, IIE transactions, 34, pp.541-549.
10. Zheng, Y., Lin, Q.H., Wong, D.S.H. and Jang, S.S. (2006).” Stability and performance analysis of mixed product Run-to-Run control”, Journal of Process control, 16, pp.431-443.
11. Ingolfsson, A. and Sachs, E. (1993). “Stability and sensitivity of an EWMA controller.” Journal of Quality Technology, 25, pp. 271-287.
12. Box G. E. P. and Jenkins G. M.(1963), “Further contributions to adaptive quality control : Simultaneous estimation of dynamics, nonzero costs”, Bull. Int Statist. Inst., pp.943-947.
13. Jury E. I.(1962), “A simplified stability criterion for linear discrete systems”. IRE Proceedings, 50(6), pp. 1493-1500.
14. Adivikolanu S. and Zafiriou E.(1998),” Robust run-to-run control for semiconductor manufacturing: an internal model control approach”. Proceedings of the American Control Conference, 6, pp. 3687-3691.
15. Adivikolanu S. and Zafiriou E. S(2000).”Extensions and performance/robustness tradeoffs of the EWMA run-to-run controller by using the internal model control structure”, IEEE Trans. Electronics Packaging Manufacturing, Vol. 23, No. 1, Jan., pp.56-68.
16. Castillo E. D., and Hurwitz, A.M.(1997), "Run-to-Run Process Control: Literature Review and Extensions", Journal of Quality Technology, Vol.29 No.2, pp.184-196.
17. Smith, T.H. and Boning, D.S.(1997), "A Self-Tuning EWMA Controller Utilizing Artificial Neural Network Function Approximation Techniques", IEEE Transactions on Components, Packaging, and Manufacturing Technology, Part C, Vol.20 No.2, pp.121-132.
18. Castillo E. D. and Yeh, J.Y.(1998), "An Adaptive Run-to-Run Optimizing Controller for Linear and Nonlinear Semiconductor Processes", IEEE Transactions on Semiconductor Manufacturing,Vol.11 No.2,p285-p295.
19. Good R. and Qin S. J.(2002), “Stability analysis of double EWMA run-to-run control with metrology delay”, in Proc. Amer. Control Conf., Anchorage AK pp.2156-2161.
20. Good R. and Qin S. J.(2006), “On the Stability of MIMO run-to-run controllers with metrology delay”, IEEE Trans. Semicond. Manuf. 19(1):78-86.
21. Tseng S.T., Chou R.J., Lee S.P. (2002), “Statistical design of double EWMA controller”, Appl. Stochastic Models Bus. Indust., 18 (3), pp.313–322.
22. Tseng S.T., Hsu N.J. (2005), “Sample-Size determination for achieving asymptotic stability of a double EWMA control scheme”, IEEE Trans. Semicond. Manuf., vol 18 (1), pp.104–111.
23. Edgar, T.F., Butler, S.W., Campbell, W.J., Pfeifer, Bode, C., Hwang, S.B., Balakrisnan, K.S. and Hahn, J.(2000), "Automatic Control in Microelectronic Manufacturing: Practices, Challenges, and Possibilities", Automatica, Vol.36 Issue 11, pp.1567-1603.
24. Firth S.K.(2002), “Just-In-Time Adaptive Disturbance Estimation for Run-To-Run Control in Semiconductor Processes”, Ph.D. thesis, U. of Texas, Austin.
25. Edgar F., Firth S.K., Bode C., Martinenz V.(2004), “Multi-product Run-to-Run control for high-mix fabs”, AEC/APC Asia, Hsinchu, Taiwan.
26. Toprac A., Wang Y.(2004), “Solving the high-mix control problem”, AEC/APC Asia, Hsinchu, Taiwan.
27. Montgomery D.C.(1997), “Design an Analysis of Experiments, 4th edition”, John Wiley & Sons, New York.
28. Telfeyan R., Moyne J., Chaudhry N., Pugmire J., Shellman S., Boning D., Moyne W., Hurwitz A.(1995), Taylor J., “A Multi-Level Approach to the Control of a Chemical Mechanical Planarization Process”, 42nd National Symposium of the American Vacuum Society, Minneapolis.
29. Boning D., Moyne W., T. Smith, et. al.(1996), “Run by Run control of Chemical Mechanical Polishing”, IEEE Transactions on components packaging and manufacturing technology part c, vol.19, no. 4, October.
30. Nital S. Patel et al.(2000), “Device Dependent Control of Chemical-Mechanical Polishing of Dielectric Films”, IEEE Transactions on Semiconductor Manufacturing, vol. 13, no. 3, pp. 331-343.
31. Glade,B; Moller, S.(1999), ” Automatic monitoring and analysis of engineering experiment”， IEEE International Symposium on Semiconductor Manufacturing Conference, Proceedings, pp. 423-426.
32. Mejdell T. , Skogestad S. (1993), “Output Estimation Using Multiple Secondary Measurements: High-purity Distillation”, AIChE J. 39 (10) pp.1641-1653
33. Morari, M.; Stephanopoulos, G. (1980),”Optimal Selection of Secondary Measurements within the Framework of State Estimation in the Presence of Persistent Unknown Disturbances”. AIChE J.,26, 247
34. 交大應化無機薄膜實驗室http://chiuserv.ac.nctu.edu.tw/~htchiu/cvd/home.html.
35. Box G. E. P. and Jenkins G. M., “Time Series Analysis Forecasting And Control third edition”, Prentice Hall Inc. 1994, pp.78-90.
36. Harris, T.J., (1989) “Assessment of control loop performance”, Canadian Journal of Chemical Engineering, 67, 5, pp. 856-861.
37. Ko F., “Advanced Process Control through Virtual Metrology”, AEC/APC Asia, Hsin-Chu, 2005.
38. Moyne, J, “Fab-Wide Virtual Metrology and Feedback Control”, AEC/APC Asia, Taipei, 2006.
39. Stefani. J.A., Poarch, S., Saxena and Mozuner, P. (1996), “Advanced process control of a CVD tungsten reactor”, IEEE trans. Semiconduct, Manufact., 9, pp. 366-383.
40. 蕭宏，半導體製程技術導論，台灣培生教育出版公司,台北，2001.
41. Schliwinski, H. J., Schnakenberg, U.; Windbracke, W.; Neff, H.; Lange, P., Thermal annealing effects on the mechanical properties of plasma-enhanced chemical vapor deposited silicon oxide films, Journal of the Electrochemical Society, v 139, n 6, June 1992, p 1730-5