臺灣博碩士論文加值系統

本研究的主要目的，在於提出一個具處理雙反應多變量 (multiple-input dual-output，MIDO) 且適用於R2R (Run-to-Run) 製程的最佳化控制器。本控制器稱為「雙反應最適化控制器」(adaptive dual-response optimizing controller，ADROC)；該控制器在製程批次行進間，可不斷地提供製程 (機台) 最適合的操作參數 (recipe)，讓製程反應值達到最佳化的要求。本控制器針對二階 (second-order) 的多變量非線性製程模型加以設計，但限制製程模型所關注之反應值必須簡化為兩個：主要反應值與次要反應值。
在實際製程中，製程常因為機台需要暖機或是長久使用之損耗，甚至電壓、電流等外部因素，導致製程隨著時間有飄移 (drift) 的現象，這使得製程在控制上，為了達到最佳化的需求，必須因應這些變化不停地修正操作參數。如此，ADROC控制器在設計上，嵌入了ST控制器的線上估計技術 (on-line estimation technique) ，在機台行進間將控制模型的參數做出最適合的調整，然後整合雙反應系統演算法 (dual response systems) 計算出最佳的操作參數回饋給機台。除此之外，本研究為了增進ADROC的控制效能並且避免過度控制的疑慮，提出「即時反應過濾器」(responsive filter) 嵌入ADROC中，進一步提高ADROC實務製程上之適用性。
在模擬實作的部分，本研究針對半導體製程中的晶圓平坦化製程，CMP製程，來做為ADROC的模擬實作模型。由於CMP製程中，晶圓的移除率 (removal rate) 以及表面的不平整度 (within-wafer non-uniformity) 是極重要的兩個反應值，所以本研究藉由此具雙反應值特性的R2R製程，來測試ADROC對於雙反應多變量製程模型的控制表現。

This research presents an optimization-based, multiple-input dual-output Run-to-Run (R2R) controller for chemical mechanical planarization (CMP) process of semiconductor manufacturing. This controller, termed adaptive dual-response optimizing controller (ADROC), can serve as a process optimizer as well as a recipe regulator between consecutive runs of wafer fabrication. It is assumed that the equipment model could be appropriately described by a pair of second-order polynomial (transfer) functions in terms of a set of control variables. Of practical relevance is to consider a drifting effect in the equipment model since in common semiconductor practice the process tends to drift due to machine ageing and tool wearing. Between production batches, the “true” process parameters in the underlying model are, in essence, time varying or initially unknown. In the ADROC, an on-line estimation technique is implemented in a self-tuning (ST) control manner for the adaptation purpose. Subsequently, an ad hoc global optimization algorithm based on the dual response approach, arising from the response surface methodology (RSM) literature, is used to seek the optimum recipe (i.e., the optimal values of control variables for the set-point of machine tool control) within the acceptability region for the execution of next run. In addition, a responsive filter specifically designed for the ADROC will be activated to compensate for the over-control problem and drifting dynamic as long as drifting effects are found to occur significantly in the process under control. The main components of the ADROC are described and its control performance will be assessed. Three different chemical mechanical planarization (CMP) processes will be demonstrated through simulated (constructed upon the real equipment models) to illustrate the ADROC in the research. It reveals from the simulation analysis that the ADROC can provide excellent control actions for the MIDO R2R situations even though the process exhibits complicated, nonlinear interaction effects between control variables, and the drifting disturbances.

TABLE OF CONTENTS
摘要........................................................ii
ABSTRACT...................................................iii
TABLE OF CONTENTS............................................v
LIST OF FIGURES AND TABLES.................................vii
ABBREVIATIONS.............................................viii
Chapter
1. INTRODUCTION..............................................1
1.1 Semiconductor Manufacturing Process......................4
1.2 Run-to-Run Control and Its Problem Statement.............5
1.3 Research Objective.......................................7
1.4 Organization of the Dissertation.........................7
2. A REVIEW OF EXISTING RUN-TO-RUN CONTROLLERS AND DUAL RESPONSE SYSTEMS.............................................8
2.1 SPC/EPC Integration......................................9
2.2 The Run-to-Run Controller Literature Review.............10
2.3 Exponential Weighted Moving Average Based (EWMA-based) Controller..................................................13
2.4 Multivariate Self-Tuning (ST) Controller................20
2.4.1 R2R Process Modeling..................................21
2.4.2 Numerical Optimization Algorithms to Self-tuning Control.....................................................24
2.4.3 Recursive Least Squares (RLS) Algorithm...............26
2.4.4 Discussion of Self-tuning Controller..................28
2.5 Dual Response Systems...................................29
2.6 Summary.................................................31
3. ADAPTIVE OPTIMIZING CONTROL..............................32
3.1 Static Model Description................................33
3.1.1 Optimality Condition in Dual Response Systems.........33
3.1.2 Degeneracy in Dual Response Systems...................36
3.1.3 A Decomposition Technique for Degenerate Problem.....................................................38
3.1.4 Dual ResponseⅡ (DR2) Algorithm.......................41
3.2 Control Model Description...............................43
3.2.1 Multiple-Input Dual-Output Control Model..............44
3.2.2 On-Line Estimation Technique..........................46
3.2.3 ADROC Algorithm.......................................48
3.2.4 Responsive Filter in the ADROC........................50
3.2.5 Full ADROC Algorithm..................................52
3.3 Experimental Study......................................54
4. ADROC PERFORMANCE EVALUATION.............................56
4.1 Chemical Mechanical Planarization Process...............56
4.2 Performance Measures....................................58
4.3 An Almost Linear 4x2 CMP Process........................60
4.4 A Nonlinear 3x2 CMP Process.............................74
4.5 A Nonlinear 6x2 CMP Process.............................78
4.6 4x2 CMP Process Simulation with Responsive Filter.......81
5. CONCLUSIONS AND FUTURE RESEARCH..........................83 5.1 Conclusions.............................................83
5.2 Future Research.........................................85
REFERENCE...................................................87

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