臺灣博碩士論文加值系統

在回火、氮化與氧化等半導體製程中，快速熱程序(RTP)製程已成為傳統爐腔系統外的其他選擇。本論文探討快速熱程序系統之燈組配置與控制系統設計問題，所研究的RTP系統具有四個同軸對稱的燈組，其中三個燈組位於晶圓上方，另一個則環繞著晶圓。文中以溫度均勻的充分必要條件及視界因數(view factor)之特性為基礎，提出一種決定燈組幾何參數的方法，以使系統具備使晶圓溫度分佈均勻之能力。之後我們針對所設計出的RTP系統，提出以最少平方誤差前饋控制器加上輸出回授正比積分控制器作為其溫度控制器的方法。其中最少平方誤差前饋控制器之設計係使用系統的高階非線性模型，而在均勻的穩態溫度上所得到的線性化系統模型經模式簡化後則用來作輸出回授正比積分控制器之設計；至於正比積分控制器之增益矩陣設計則採用線性二次調節程序(LQR)加以完成。本論文除了探討系統穩健性與溫控性能之權衡方法外，也以模擬結果驗證所提方法之溫度追蹤穩健性與均勻度。

Rapid thermal processing (RTP) has become an alternative to the traditional furnace-based batch processing in semiconductor manufacturing processes such as annealing, nitridation and oxidation. We study design of temperature control system and lamp configuration for RTP systems. We consider a configuration consists of four concentric circular lamp zones, three of them above the wafer and one circumvallating the wafer. We propose a method to determine the geometric parameters, the width, height and radius, of the lamp zones so that the configuration designed has the capacity to achieve uniform temperature on the wafer. The method is based on a necessary and sufficient condition for uniform temperature tracking and analytic expressions of the view factors. For the designed lamp configuration, we proposes a control system consisting of a least square feedforward controller and an output feedback proportional plus integral (PI) controller. A high-order nonlinear model describing the temperature dynamics of the RTP system is used for the feedforward controller design. A balanced reduced model, obtained from a linear model around a desired uniform steady-state temperature, is used for the design of the MIMO PI controller. The PI controller gain matrices are designed using an LQR based procedure. Tradeoff between robustness and performance of the system is discussed. Simulation results show the control system designed yields robust temperature tracking with good uniformity for a wide temperature range.
Acknowledgement ii
Chapter 1: Introduction 1
1.1 Background 1
1.2 General Description on Our Lamp Configuration and Control System 2
1.3 Notations 4
Chapter 2: RTP System Model 5
2.1 System Description 5
2.1.1 The RTP System Considered 5
2.1.2 A Dynamic System Model 5
2.2 Temperature Uniformity Condition 7
Chapter 3: Lamp Configuration Design 9
3.1 The View Factor: Formulas and Properties 9
3.1.1 View Factor on the Wafer Surface 9
View Factors Associated with Lamps 1-3 9
View Factors Associated with Lamp 4 11
3.1.2 View Factor on the Wafer Edge 11
3.2 Lamp Design for Uniform Temperature Tracking 12
3.2.1 Constraints on the View Factors 12
3.2.2 Design to Minimize the Variation of View Factors 14
3.2.3 Design Procedure and Examples 16
3.2.4 Least Square Open-Loop Control 19
3.2.5 Discussions 22
Chapter 4: Control System Description 23
4.1 Control System Structure 23
4.1.1 Least Square Feedforward Controller 23
4.1.2 A Model for Sensor Locations and PI Controller Design 24
4.1.3 The Overall Control System 25
4.2 Sensor Locations and Steady-State Performance 26
4.2.1 Effects of Sensor Locations on Steady-State Error 26
4.2.2 Selecting Sensor Locations 29
Chapter 5: Controller Design 31
5.1 Design of Gain Matrices Based on a Reduced Model 31
5.1.1 Model Reduction via Balanced Realization 31
5.1.2 Stability Consideration 32
5.1.3 Design of K and G 33
5.1.4 Performance Analysis 35
5.2 Design Procedure and Simulation Results 37
5.2.1 Design Procedure 37
5.2.2 Simulation Results 38
Chapter 6: Conclusion 45
Reference 47
Appendix:
A 51
B 53
C 57
D 59
E 62
F 65
G 66

Cover
摘要（中文）
Abstract
Acknowledgement
Content
Chatper 1: Introduction
1.1 Background
1.2 General Description on Our Lamp Configuration and Control System
1.3 Notations
Chapter 2: RTP System Model
2.1 System Description
2.2 Temperature Uniformity Condition
Chapter 3: Lamp Configuration Design
3.1 The View Factor: Formulas and Properties
3.2 Lamp Design for Uniform Temperature Tracking
Chapter 4: Control System Description
4.1 Control System Structure
4.2 Sensor Locations and Steady-State Performance
Chatper 5: Controller Design
5.1 Design of Gain Matrices Based on a Reduced Model
5.2 Design Procedure and Simulation Results
Chapter 6: Conclusion
Reference
Appendix
Vita
Publish List

[1] R. B. Fair, Rapid Thermal Processing: Science and Technology, Academic Press, 1993.
[2] L. Peters, “The hottest topic in RTP,” Semiconductor International, pp. 56-62, Aug. 1991.
[3] P. Singer, “Rapid thermal processing: a progress report,” Semiconductor International, pp. 64-69, May 1993.
[4] P. P. Apte and K.C. Saraswat, “Rapid thermal processing uniformity using multivariable control of a circularly symmetric 3 zone lamp,” IEEE Trans. Semicond. Manufact., vol. 5, no. 3, pp. 180-188, Aug. 1992.
[5] S. A. Norman, “Wafer temperature control in rapid thermal processing,” Ph. D. dissertation, Stanford University, 1992.
[6] S. A. Norman and S. P. Boyd, “Multivariable feedback control of semiconductor wafer temperature,” Proceedings of the American Control Conference, pp. 811-816, 1992.
[7] H. A. Lord, “Thermal and stress analysis of semiconductor wafers in a rapid thermal processing oven,” IEEE Trans. Semicond. Manufact., vol. 1, no. 3, pp. 105-114, Aug. 1988.
[8] C. D. Schaper, M.M. Moslehi, K.C. Saraswat, and T. Kailath, “Modeling, identification, and control of rapid thermal processing systems,” J. Electrochem. Soc., vol. 141, no. 11, pp. 3200-3209, Nov. 1994.
[9] C. D. Schaper, “Real-time control of rapid thermal processing semiconductor manufacturing equipment,” Proceedings of the American Control Conference, pp. 2985-2989, Jun. 1993.
[10] C. Schaper, M. Moslehi, K. Saraswat and T. Kailath, “Control of MMST RTP: repeatability, uniformity, and integration for flexible manufacturing,” IEEE Trans. Semicond. Manufact., vol. 7, no. 2, pp. 202-219, May 1994.
[11] S. Belikov and B. Friedland, “Closed-loop adaptive control for rapid thermal processing,” Proceedings of the 34th conference on decision and control, pp. 2476-2481, Dec. 1995.
[12] W. Kosonocky, M. Kaplinsky, N. McCaffrey, E. Hou, C. Manikopoulos, N. Ravindra, S. Belikov, J. Li, and V. Patel, “Multi-wavelength imaging pyrometer,” Proceedings, SPIE Symposium on Optical Engineering in Aerospace Sensing, Vol. 2225, pp. 26-43, Orlando, FL, Apr. 1994.
[13] J. D. Stuber, T. F. Edgar, J. K. Elliott, and T. Breedijk, “Model-based control of rapid thermal processes,” IEEE Proceedings of the 33rd Conference on Decision and Control, pp.79-85, Dec. 1994.
[14] Y. M. Cho and P. Gyugyi, “Control of rapid thermal processing: A system theoretic approach,” IEEE Trans. Semicond. Manufact., vol. 5, no. 6, pp. 644-653, Nov. 1997.
[15] C. D. Schaper, T. Kailath, and Y. J. Lee, “Decentralized control of wafer temperature for multizone rapid thermal processing systems,” IEEE Trans. Semicond. Manufact., vol. 12, no. 2, pp. 193-199, May 1999.
[16] J. X. Xu, Y. Chen, T. M. Lee, S. Yamamoto, “Temperature iterative learning control with application to RTPCVD thickness control,” Automatica, vol. 35, pp. 1535-1542, 1999.
[17] F. Roozeboom and N. Parekh, “Rapid thermal processing systems: A review with emphasis on temperature control”, J. Vac. Sci. Technol., Vol. B8, No. 6, pp. 1249-1259, Nov./Dec. 1990.
[18] F. Y. Sorrell, S. Yu, and W. J. Kiether, “Applied RTP optical modeling: An argument for model-based control,” IEEE Trans. Semicond. Manufact., vol. 7, no. 4, pp. 454-459, Nov. 1994.
[19] F. L. Degertekin, J. Pei, B. T. Khuri-Yakub, and K. C. Saraswat, “In situ acoustic temperature tomography of semiconductor wafers,” Appl. Phys. Lett., Vol. 64, No. 11, pp. 1338-1340, Mar. 1994.
[20] Y. J. Lee, B. T. Khuri-Yakub, and K. Saraswat, “Temperature measurement in rapid thermal processing using the acoustic temperature sensor,” IEEE Trans. Semicond. Manufact., vol. 9, no. 1, pp. 115-121, Feb. 1996.
[21] V. M. Donnelly and J. A. McCaulley, “Infrared-laser interferometric thermometry: a nonintrusive technique for measuring semiconductor wafer temperatures”, J. Vac. Sci. Technol., Vol. A8, No. 1, pp. 84-92, Jan./Feb. 1990.
[22] B. J. Cho, P. Vandenabeele and K. Maex, “Development of a hexagonal-shaped rapid thermal processor using a vertical tube,” IEEE Trans. Semicond. Manufact., vol. 7, no. 3, pp. 345-353, Aug. 1994.
[23] J. P. , K. Ullrich, J. Peroldt and G. Eichhorn, “New lamp arrangement for rapid thermal processing,” Applied Surface Science, vol. 69, pp. 193-197, 1993.
[24] Y. M. Cho, A. Paulraj, T. Kailath, and G. Xu, “A contribution to optimal lamp design in rapid thermal processing,” IEEE Trans. Semicond. Manufact., vol. 7, no. 1, pp. 34-41, Feb. 1994.
[25] Y. K. Jan and C. A. Lin, “Lamp configuration design for rapid thermal processing systems,” IEEE Trans. Semicond. Manufact., vol. 11, no. 1, pp. 75-84, Feb. 1998.
[26] G. L. Young and K.A. Mcdonald, “Effect of radiation shield angle on temperature and stress profiles during rapid thermal annealing,” IEEE Trans. Semicond. Manufact., vol. 3, no. 4, pp. 176-182, Nov. 1990.
[27] F. Y. Sorrel, M. J. Fordham, M. C. , and J. J. Wortman, “Temperature uniformity in RTP furnaces,” IEEE Trans. On Electron Devices, vol. 39, no. 1, pp. 75, Jan. 1992
[28] S. A. Campbell and K.L. Knutson, “Transient effects in rapid thermal processing,” IEEE Trans. Semicond. Manufact., vol. 5, no. 4, pp. 302-307, Nov. 1992.
[29] R. H. Perkins, T. J. Riley, and R. S. Gyurcsik, “Thermal uniformity and stress minimization during rapid thermal processes,” IEEE Trans. Semicond. Manufact., vol. 8, no. 3, pp. 272-279, Aug. 1995.
[30] J. R. Howell, Radiation configuration factor, New York: McGraw-Hill, 1982.
[31] A. N. Kolmogorov and S. V. Fomin, Introductory real analysis, New York: Dover, 1970.
[32] SystemBuild/WS V2.4 User’s Guide. MDG002-111.
[33] C. Hill, S. Jones and D. Boys, “Rapid thermal annealing- theory and practice,” in Reduced Thermal Processing for ULSI, NATO ASI Series B: Physics, pp.143-180, 1989.
[34] C. A. Desoer and M. Vidyasagar, “Feedback systems: input-output properties,” pp. 59, Academic Press, New York, 1975.
[35] K. Zbou, F. C. Doyle and K. Glover, Robust and Optimal Control, Prentice-Hall, 1995.
[36] B. A. Francis, Lecture Notes in Control and Information Sciences, Springer-Verlag, 1987.
[37] T. Kailath, Linear Systems, Prentice-Hall, 1980.
[38] G. H. Golub and C. F. Van Loan, Matrix Computations, Johns Hopkins University Press, 1989.