快速熱程序系統之燈組配置與控制系統設計

Abstract

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