Abstract
This chapter introduces a framework of disturbance rejection controller for discrete-time Run-to-Run (R2R) control system in semiconductor manufacturing environments. While we discussed the source of uncertainty and disturbance in wafer fabrication process, the photolithography process as one of the cutting-edge steps in wafer fabrication is selected for illustrating the power of disturbance rejection algorithm for compensating the misalignment. Along with this case study, some classification of disturbance rejection control algorithm with the structure of control plant is discussed.
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- 1.
Static model: \(y_t = F(u_{t-1})\); Dynamic model: \(y_t = F(y_{t-1}, u_{t-1})\).
- 2.
The surface of a wafer can be partitioned into smaller part for increase the accuracy of measurement the overlay error, each partition is called a field.
- 3.
Regards to notation in the beginning of this section \(\mathbf x _t\) is equivalent to \(S_t\); \(\mathbf u _t\) is \(A_t\); \(\mathbf y _t\) is \(O_t\); \(P(\mathbf x _t|\mathbf x _{t-1},\mathbf u _{t-1})\) is \(R(S_{t}|S_{t-1}, A_{t-1})\); and \(E_t\) is \(R(S_t, A_t)\).
References
Åström, K.J., Wittenmark, B.: Adaptive Control. Courier Corporation (2013)
Bode, C., Ko, B., Edgar, T.: Run-to-run control and performance monitoring of overlay in semiconductor manufacturing. Control Eng. Pract. 12(7), 893–900 (2004)
Chen, Y., Moore, K.L., Ahn, H.S.: Iterative learning control. In: Encyclopedia of the Sciences of Learning. Springer, pp. 1648–1652 (2012)
Chiang, Y.C., Cheng, C.C.: Terminal adaptive output feedback variable structure control. In: IET Control Theory & Applications (2018)
Chien, C.F., Hsu, C.Y.: Unison analysis to model and reduce step-and-scan overlay errors for semiconductor manufacturing. J. Intell. Manuf. 22(3), 399–412 (2011)
Chien, C.F., Chang, K.H., Chen, C.P.: Design of a sampling strategy for measuring and compensating for overlay errors in semiconductor manufacturing. Int. J. Prod. Res. 41(11), 2547–2561 (2003)
Chien, C.F., Chang, K.H., Chen, C.P., Lin, S.L.: Overlay error model, sampling strategy and associated equipment for implementation. US Patent 6,975,974 (2005)
Chien, C.F., Chen, Y.J., Hsu, C.Y., Wang, H.K.: Overlay error compensation using advanced process control with dynamically adjusted proportional-integral R2R controller. IEEE Tran. Autom. Sci. Eng. 11(2), 473–484 (2014)
Da Silva, F.D.C., De Oliveira, J.B., De Araujo, A.D.: Robust interval adaptive pole-placement controller based on variable structure systems theory. In: 2017 25th International Conference on Systems Engineering (ICSEng). IEEE, pp. 45–54 (2017)
Duarte-Mermoud, M.A., Aguila-Camacho, N., Gallegos, J.A., Travieso-Torres, J.C.: Fractional-order model reference adaptive controllers for first-order integer plants. In: New Perspectives and Applications of Modern Control Theory. Springer, pp. 121–151 (2018)
El Chemali, C., Freudenberg, J., Hankinson, M., Collison, W., Ni, T.: Critical dimension control of a plasma etch process by integrating feedforward and feedback run-to-run control. J. Vac. Sci. Technol. B: Microelectron. Nanometer Struct. Process. Meas. Phenom. 21(6), 2304–2312 (2003)
Gamez, D.: Progress in machine consciousness. Conscious. Cogn. 17(3), 887–910 (2008)
Ganesan, R., Das, T.K., Ramachandran, K.M.: A multiresolution analysis-assisted reinforcement learning approach to run-by-run control. IEEE Trans. Autom. Sci. Eng. 4(2), 182–193 (2007)
Ge, S.S., Hang, C.C., Lee, T.H., Zhang, T.: Stable Adaptive Neural Network Control, vol 13. Springer Science & Business Media (2013)
Giarratano, J.C., Riley, G.: Expert Systems: Principles and Programming. Brooks/Cole Publishing Co. (1989)
Gong, Q., Yang, G., Pan, C., Chen, Y.: Performance analysis of single ewma controller subject to metrology delay under dynamic models. IISE Trans. 50(2), 88–98 (2018)
Gong, Q.S., Yang, G.K., Pan, C.C., Lee, M.S.: Stability and control performance analysis of double ewma controller with metrology delay. IEEE Trans. Semicond. Manuf. 29(1), 9–16 (2016)
Good, R.P., Qin, S.J.: On the stability of MIMO EWMA run-to-run controllers with metrology delay. IEEE Trans. Semicond. Manuf. 19(1), 78–86 (2006)
Gross, E.: On the Bellman’s principle of optimality. Phys. A: Stat. Mech. Appl. 462, 217–221 (2016)
Guo, B.Z., Zhao, Z.L.: On convergence of tracking differentiator. Int. J. Control 84(4), 693–701 (2011)
Guo, B.Z., Zhao, Z.L.: Extended state observer. In: Active Disturbance Rejection Control for Nonlinear Systems: An Introduction, pp. 93–154 (2016)
Haddad, W.M., Chellaboina, V.: Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach. Princeton University Press (2011)
van Hee, K.M., Hee, K.: Bayesian Control of Markov Chains, vol. 95. Mathematisch centrum Amsterdam, The Netherlands (1978)
Heirung, T.A.N., Ydstie, B.E., Foss, B.: Dual adaptive model predictive control. Automatica 80, 340–348 (2017)
Huang, M., Wang, X., Lu, Z., Ma, L., Su, H., Wang, L.: Multiple model adaptive control for a class of nonlinear systems with unknown control directions. Int. J. Control 1–13 (2018)
Huang, Y., Xue, W.: Active disturbance rejection control: methodology and theoretical analysis. ISA Trans. 53(4), 963–976 (2014)
Jang, J.S., Sun, C.T.: Neuro-fuzzy modeling and control. Proc. IEEE 83(3), 378–406 (1995)
Khakifirooz, M., Chien, C.F., Chen, Y.J.: Bayesian inference for mining semiconductor manufacturing big data for yield enhancement and smart production to empower industry 4.0. Appl. Soft Comput. 68, 990–999 (2018)
Khakifirooz, M., Fathi, M., Chien, C.F.: Modelling and decision support system for intelligent manufacturing: an empirical study for feedforward-feedback learning-based run-to-run controller for semiconductor dry-etching process. Int. J. Ind. Eng. Theory Appl. Pract. 25(6) (2018)
Khakifirooz, M., Chien, C.F., Fathi, M.: Compensating misalignment using dynamic random-effect control system: a case of high-mixed wafer fabrication. IEEE Trans. Autom. Sci. Eng. (2019)
Khakifirooz, M., Cayard, D., Chien, C.F., Fathi, M.: A system dynamic model for implementation of industry 4.0. In: 2018 International Conference on System Science and Engineering (ICSSE). IEEE, pp. 1–6, June 2018
Kuo, H.F., Faricha, A.: Artificial neural network for diffraction based overlay measurement. IEEE Access 4, 7479–7486 (2016)
Liptk, B.: Process Control: Instrument Engineers Handbook (2013)
Lynn, S.A., MacGearailt, N., Ringwood, J.V.: Real-time virtual metrology and control for plasma etch. J. Process Control 22(4), 666–676 (2012)
Mitchell, M.: An Introduction to Genetic Algorithms. MIT Press (1998)
Monahan, G.E.: State of the art-a survey of partially observable Markov decision processes: theory, models, and algorithms. Manag. Sci. 28(1), 1–16 (1982)
Moreau, W.M.: Semiconductor Lithography: Principles, Practices, and Materials. Springer Science & Business Media (2012)
Moyne, J., Del Castillo, E., Hurwitz, A.M.: Run-to-Run Control in Semiconductor Manufacturing. CRC Press (2000)
Ortega, R., Perez, J.A.L., Nicklasson, P.J., Sira-Ramirez, H.J.: Passivity-Based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications. Springer Science & Business Media (2013)
Park, S.J., Lee, M.S., Shin, S.Y., Cho, K.H., Lim, J.T., Cho, B.S., Jei, Y.H., Kim, M.K., Park, C.H.: Run-to-run overlay control of steppers in semiconductor manufacturing systems based on history data analysis and neural network modeling. IEEE Trans. Semicond. Manuf. 18(4), 605–613 (2005)
Rico-Azagra, J., Gil-Martínez, M., Rico, R., Maisterra, P.: Qft bounds for robust stability specifications defined on the open-loop function. Int. J. Robust Nonlinear Control 28(3), 1116–1125 (2018)
Rugh, W.J., Shamma, J.S.: Research on gain scheduling. Automatica 36(10), 1401–1425 (2000)
Schreier, M.: Modeling and adaptive control of a quadrotor. In: 2012 International Conference on Mechatronics and Automation (ICMA). IEEE, pp. 383–390 (2012)
Sullivan, N.T.: Semiconductor pattern overlay. In: Handbook of Critical Dimension Metrology and Process Control: A Critical Review. International Society for Optics and Photonics, vol. 10274, p. 102740C (1994)
Sun, L., Lu, J., Liu, Y., Huang, T., Alsaadi, F.E., Hayat, T.: Variable structure controller design for Boolean networks. Neural Netw. 97, 107–115 (2018)
Tan, Y., Moase, W., Manzie, C., Nešić, D., Mareels, I.: Extremum seeking from 1922 to 2010. In: 2010 29th Chinese Control Conference (CCC). IEEE, pp. 14–26 (2010)
Tanaka, T., Esfahani, P.M., Mitter, S.K.: LQG control with minimum directed information: semidefinite programming approach. IEEE Trans. Autom. Control 63(1), 37–52 (2018)
Thie, P.R.: Markov Decision Processes. Comap, Incorporated (1983)
Utkin, V., Guldner, J., Shi, J.: Sliding Mode Control in Electro-Mechanical Systems. CRC Press (2009)
Vassilyev, S., Kelina, A.Y., Kudinov, Y., Pashchenko, F.: Intelligent control systems. Procedia Comput. Sci. 103, 623–628 (2017)
Wan, L., Tan, F., Th, P.A.N.: Online estimation of time-varying metrology delay and run-to-run control co-design. Control Theory Appl. 1, 012 (2016)
Wang, Y., Zheng, Y., Fang, H., Wang, Y.: Armax model based run-to-run fault diagnosis approach for batch manufacturing process with metrology delay. Int. J. Prod. Res. 52(10), 2915–2930 (2014)
Wu, W.M., Cheng, F.T., Lin, T.H., Zeng, D.L., Chen, J.F.: Selection schemes of dual virtual-metrology outputs for enhancing prediction accuracy. IEEE Trans. Autom. Sci. Eng. 8(2), 311–318 (2011)
Xie, J., Yang, D., Zhao, J.: Multiple model adaptive control for switched linear systems: a two-layer switching strategy. Int. J. Robust Nonlinear Control 28(6), 2276–2297 (2018)
Zheng, Y., Wong, D.S.H., Wang, Y.W., Fang, H.: Takagi-Sugeno model based analysis of EWMA RtR control of batch processes with stochastic metrology delay and mixed products. IEEE Trans. Cybern. 44(7), 1155–1168 (2014)
Zimmermann, H.J.: Fuzzy control. In: Fuzzy Set Theory-and Its Applications. Springer, pp. 203–240 (1996)
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Khakifirooz, M., Fathi, M., Pardalos, P.M. (2019). Disturbance Rejection Run-to-Run Controller for Semiconductor Manufacturing. In: Blondin, M., Pardalos, P., Sanchis Sáez, J. (eds) Computational Intelligence and Optimization Methods for Control Engineering. Springer Optimization and Its Applications, vol 150. Springer, Cham. https://doi.org/10.1007/978-3-030-25446-9_13
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