當IC尺寸日益縮小，半導體製程日益精密，為維持製程高良率，必須採用逐片檢測先進製程控制模式。而此模式必須獲得每片晶圓之品質量測值，但此做法將耗費大量時間與成本。由於虛擬量測可即時推估每片晶圓的製程品質，而不需要實際量測，因此，虛擬量測為達成逐片檢測先進製程控制模式的可行方案。而要將虛擬量測應用至逐片檢測先進製程控制模式，推估精度與速度必須同時考量。對於模擬半導體及TFT-LCD製程，具備二個隱藏層的倒傳遞類神經網路被廣為運用。但該網路需耗費大量建模時間，相較而言，徑向基底函數類神經網路只有一個參數需要調整，所以訓練速度較快。因此，本論文採用徑向基底函數網路建構虛擬量測架構，並設計模型參數調整器，可對模型參數進行調整，以提高推估精度。其次，為瞭解是否有其它演算法可作為虛擬量測之即時性應用，針對另外四種演算法，進行虛擬量測精度與速度之評估。除此，亦提出相關理論背景與實作上的考量，並律定R2R控制之即時性需求，作為評估虛擬量測是否可應用於逐片檢測先進製程控制模式之標準。另外，為提昇類神經虛擬量測推估精度，本論文提出以類神經網路為基之逐步選取法。此方法有別於傳統以複迴歸為基之逐步選取法，係利用以複迴歸為基之逐步選取法篩選變數作為初始解，並運用類神經網路建構模型，且採用不同之變數篩選程序，以找出對於提昇類神經虛擬量測推估精度最具貢獻之變數。本論文所提出之方法，可滿足逐片檢測先進製程控制模式之精度與即時性需求。因此，當運用於半導體及TFT-LCD 等製程，可有效提昇製程能力及生產效率。

As the dimension of electronic devices shrink increasingly, wafer-to-wafer (W2W) advanced process control (APC) becomes more essential for critical production stages in improving yield rate. W2W APC requires the metrology values of each wafer; however, it will be time-consuming and highly expensive. Virtual metrology (VM) can be used to real-time conjecture the processing quality of each wafer by using the process data without conducting actual metrology. Therefore, VM is a good solution for W2W APC. To implement VM in W2W APC, both conjecture-accuracy and real-time requirements need to be considered. For modeling semiconductor or TFT-LCD production process, two-hidden-layered back-propagation neural network (BPNN-II) was widely adopted. But BPNN-II requires too much modeling execution time. Comparing to BPNN-II, radial basis function neural network (RBFN) has only one parameter needed to be adjusted and thereby has a faster learning speed. Therefore, the RBFN-based VM scheme is proposed. Moreover, a model parameter coordinator (MPC) is designed to adjust the parameters of VM model for enhancing the conjecture accuracy. Next, to find out if other algorithms can also be adopted for the real-time VM application, four VM algorithms are evaluated to test and verify the accuracy and real-time requirements. And, the theoretical backgrounds and implementation considerations are presented. Besides, the real-time requirements for applying VM in fab-wide R2R control are proposed as the criteria of evaluating whether NN-based VM algorithms can be applied in W2W APC. Further, to improve the NN-based VM conjecture accuracy, an advanced method called neural-network-based stepwise selection (NN-based SS), is proposed. The proposed method is quite different with the traditional multi-regression-based SS (MR-based SS). NN-based SS utilizes the selected variables of MR-based SS as the initial sets and starts with backward elimination to remove multiple variables repeatedly. Moreover, the designated NN algorithm is applied to run the NN-based SS process for finding the key-variables that have dominant contributions to enhance the VM conjecture accuracy. The proposed methods can satisfy the accuracy and real-time requirements of W2W APC. Thus, applying these proposed techniques in semiconductor and TFT-LCD processes, the process capability and production efficiency can be enhanced.

[1] Y.-C. Chang and F.-T. Cheng, “Application development of virtual metrology in semiconductor industry,” in Proc. 31st Annual Conference IEEE Industrial Electronics, Raleigh, NC, Nov. 2005, pp. 124-129.
[2] J. Moyne, E. del Castillo, and A.M. Hurwitz, Run-to-Run Control in Semiconductor Manufacturing, Boca Raton, FL: CRC Press, 2001.
[3] P.-H. Chen, S. Wu, J. Lin, F. Ko, H. Lo, J. Wang, C.-H. Yu, and M.-S. Liang, “Virtual metrology: a solution for wafer to wafer advanced process control,” in Proc. 2005 International Symposium on Semiconductor Manufacturing, Sept. 2005, pp. 155-157.
[4] A. Weber, “Virtual metrology and your technology watch list: ten things you should know about this emerging technology,” Future Fab International, issue 22, section 4, pp. 52-54, Jan. 2007.
[5] F.-T. Cheng, H.-C. Huang, and C.-A. Kao, “Dual-phase virtual metrology scheme,” IEEE Transactions on Semiconductor Manufacturing, vol. 20, no. 4, pp. 566-571, Nov. 2007.
[6] Y.-C. Su, T.-H. Lin, F.-T. Cheng, and W.-M. Wu, "Accuracy and real-time considerations for implementing various virtual metrology algorithms," to appear in IEEE Transactions on Semiconductor Manufacturing.
[7] D. Strokes and G. S. May, “Real-time control of reactive ion etching using neural networks,” IEEE Transactions on Semiconductor Manufacturing, vol. 13, no. 4, pp. 469-480, Nov. 2000.
[8] S. G. Asim Roy and R. Miranda, “An algorithm to generate radial basis function (RBF)-like nets for classification problem, “Neural Networks, vol. 8, issue 2, pp. 179-201, 1995.
[9] M.-H. Hung, T.-H. Lin, F.-T. Cheng, and R.-C. Lin, “A novel virtual metrology scheme for predicting CVD thickness in semiconductor manufacturing,” IEEE/ASME Transactions on Mechatronics, vol. 12, no. 3, pp. 308-316, June 2007.
[10] F.-T. Cheng, Y.-T. Chen, Y.-C. Su, and D.-L. Zeng, “Evaluating reliance level of a virtual metrology system,” IEEE Transactions on Semiconductor Manufacturing, vol. 21, no. 1, pp. 92-103, Feb. 2008.
[11] D. R. Anderson, D. J. Sweeney, T. A. Williams, and J.-C. Chen, Statistics for Business and Economics- A Practical Approach, Singapore: Thomson, 2006.
[12] S. Chatterjee, A. S. Hadi, and B. Price, Regression Analysis by Example, New York: Wiley, 2000.
[13] Y.-C. Su, M.-H. Hung, F.-T. Cheng, and Y.-T. Chen, “A processing quality prognostics scheme for plasma sputtering in TFT-LCD manufacturing,” IEEE Transactions on Semiconductor Manufacturing, vol. 19, no. 2, pp. 183-194, May 2006.
[14] Y. S. Hwang and S. Y. Bang, “An efficient method to construct a radial basis function neural network classifier,” Neural Network, vol. 10, no. 8, pp. 1495-1503, 1997.
[15] S. Haykin, Neural Networks-A Comprehensive Foundation, Prentice Hall, NJ:07458, 1999.
[16] B. Kim and K. Park, “Modeling plasma etching process using a radial basis function network,” Microelectronic Engineering, vol. 77, pp. 150-157, 2005.
[17] D. Han, S. B. Moon, K. Park, B. Kim, K. K. Lee, and N. J. Kim, “Modeling of plasma etching process using radial basis function network and genetic algorithm,” Vacuum, vol. 79, pp. 140-147, 2005.
[18] J. Han and K. Micheline, Data Mining: Concepts and Techniques, San Francisco: Morgan Kaufman, 2001.
[19] A. K. Jain, K. Nandakumar, and A. Ross, “Score normalization in multimodal biometric systems,” Pattern Recognition, 2005.
[20] S. Chen, C.F.N. Cowan, and P. M. Grant, "Orthogonal least squares learning algorithm for radial basis function networks," IEEE Transactions on Neural Networks, vol. 2, no. 2, pp. 302-309, Mar. 1991.
[21] W. R. Dillon and M. Goldstein, Multivariate Analysis Methods and Applications, New York: Wiley, 1984.
[22] T. W. Anderson, An Introduction to Multivariate Statistical Methods, New York: Wiley, 1984.
[23] M. Asada, “Wafer yield prediction by the Mahalanobis–Taguchi system,” in Proc. IEEE International Workshop on Statistical Methodology, 2001, pp. 25–28.
[24] G. Taguchi, S. Chowdhury, and Y. Wu, The Mahalanobis-Taguchi System, New York: McGraw-Hill, 2001.
[25] C. D. Himmel and G. S. May, “Advantages of plasma etch modeling using neural networks over statistical techniques,” IEEE Transactions on Semiconductor Manufacturing, vol. 6, no. 2, pp. 103-111, May 1993.
[26] B. Kim and S. Park, “An optimal neural network plasma model: a case study,” Chemometrics and Intelligent Laboratory Systems, vol. 56, pp. 39-50, Jan. 2001.
[27] B. Kim, D. W. Kim, and G. T. Park, “Prediction of plasma etching using a polynomial neural network,” IEEE Transactions on Plasma Science, vol. 31, no. 6, pp. 1330-1336, Dec. 2003.
[28] B. Kim and G. T. Park, “Modeling plasma equipment using neural networks,” IEEE Transactions on Plasma Science, vol. 29, pp. 8-12, Feb. 2001.
[29] R. P. Hern’andez, J. A. Gallegos, and J. A. Hern’andez Reyes, “Simple recurrent neural network: a neural network structure for control systems,” Neurocomputing, vol. 23, pp. 277-289, July 1998.
[30] P. H. Brown., Measurement, Regression, and Calibration, New York: Oxford University Press, 1998.
[31] M. Negnevitsky, Artificial Intelligence- A Guide to Intelligent Systems, Addison-Wesley: 2nd ed., 2005.
[32] I. S. Markham and T. R. Rakes, “The effect of sample size and variability of data on the comparative performance of artificial neural networks and regression,” Computers and Operations Research, vol. 25, no. 4, pp. 251-263, 1998.
[33] M. T. Hagan, H. B. Demuth, and M. Beale, Neural Network Design, Boston: PWS, 1998.
[34] Y.-T. Huang, F.-T. Cheng, and Y.-T. Chen, “Importance of data quality in virtual metrology,” in Proc. 32th Annual Conference of the IEEE Industrial Electronics Society, Paris, France, Nov. 2006, pp. 3727-3732.
[35] L. Xu and W. Zhang, “Comparison of different methods for variable selection,” Analytica Chimica Acta, vol. 446, pp.477–483, 2001.
[36] T. Matsuura, “An application of neural network for selecting feature variables in machinery diagnosis,” Journal of Materials Processing Technology, vol. 157–158, pp. 203–207, 2004.
[37] E. W. Steyerberg, J. C. Eijkemans, J. Dik, and F. Habbema, “Stepwise selection in small data sets: a simulation study of bias in logistic regression analysis,” Journal of Clinical Epidemiology, vol. 52, no. 10, pp. 935–942, 1999.
[38] D. G. Montgomery, E. A. Peck, and G. G. Vining, Introduction to Linear Regression Analysis, 3rd Ed., New York: Wiley, 2001.
[39] Z. K. Timothy, Multiple Regression and Beyond, Austin: Allyn & Bacon, 2005.
[40] G. R. Pasha, “Selection of variables in multiple regression using stepwise regression,” Journal of Research (Science), vol. 13, no. 2, pp. 119–127, Dec. 2002.
[41] D. C. Montgomery, Design and Analysis of Experiments, 6th ed., New York: Wiley, 2005.