Control Relevant Issues in Semiconductor Manufacturing: Stability and Disturbance Rejection

半導體製程持續研發使用大尺寸的晶圓，而元件則是愈做愈小，進而使得單一晶圓的成本降低而利潤提高，因此，品質控制顯得特別重要。一片晶圓的製程需要超過連續三百道以上的程序，而且重要的品質電性參數由於元件尺寸之故，量測非常耗時或困難，進而使得量測機台亦為一重大投資成本，此一特別的量測特性，使得半導體製程中的程序控制將有別於一般的化工程序。本文例舉出半導體製程中，常見的量測類型，及擾動型態。擾動型態一般可以分為三種：程序擾動、進料擾動、產品別擾動，而針對這三種型態，在論文中各提出如何消除各種甘擾的影響，進一步的使控制品質改善。 批次控制器是針對程序擾動最常使用的有效方法，文中研究了如何對於不同程序、擾動行為來設計有效、穩定的批次控制器。由於半導體製程的量測特性，量測每片晶圓不是常態，文中針對取樣間隔、量測延遲來討論控制器效能與穩定性，進而輔助設計所需要的量測機台數目。 通常在進行某一機台程序之前，會對晶圓進行前測，因此，對於部分程序，此進料型態之擾動以可以提前知道。於是本研究探討是否有可能透過重新安排進料的順序，使晶圓的控制品質更進一步得到改善。從一般的回饋控制器之頻率分析的角度來看，回饋控制器能夠有效地消除低頻訊號所造成的影響，因此我們的出發點則為：如何將晶圓重新安排進料順序使得進料擾動為一個低頻訊號。文中使用了化學機械研磨製程為例，並提出了單變數與多變數系統皆可使用之設計，以利於安排進料順序。 除了前述的兩項擾動外，一個工廠常常必須生產許多種產品別，因子化的狀態(State)估測，除了包含不同產品別的影響外，其他如量測機台別、生產機台別的影響亦能夠包含在內。然而，一個包含各種因子的系統的秩(Rank)是不足的，也就是說，這些狀態是無所得知的。透過選擇一個參考路徑，再經過變數轉換，相對狀態則變為可以估測了。除了各狀態的估測外，系統的輸出亦能夠做估測，本研究進而討論是否能夠設計生產路線使得系統輸出有較佳之表現。The quality control of integrated circuit (IC) processing is becoming more and more important as the wafer becomes larger and the feature size shrinks. However, an advanced IC fabrication process consists of 300+ steps with scarce and usually difficult quality measurements. Thus product yield may not be realized until months into production while in-line measurements are available on the order of a millisecond. The series production nature and measurement setup lead to a unique process control problem. In this work, typical disturbances are explained and the possibility for disturbance rejection to each type is explored. The disturbance types can be categorized into three types: tool-induced, feed-induced, and context-induced disturbance. For the tool-induced disturbance, feedback run-to-run controllers are usually used to deal with. To ensure stable process operation and ultimately meet the exacting requirements on final product quality, the typical advanced IC fabrication process requires many on-line sensors and off-line metrology tools for acquiring process and product information necessary for effective monitoring and control. However, the high cost associated with these measurement devices has made the economics of metrology a major factor. Various run-to-run controllers, carry out stability analyses, and analyze control system performance are derived. These results are then applied to the problem of rational metrology strategy selection where the effects of various metrology strategies on control system performance are systematically analyzed. In particular, if control performance takes priority over economics, results for determining maximum tolerable sampling intervals, maximum tolerable delay, and measurement priority are also presented. Usually, pre-measurement is available before wafers are processing in an equipment tool. Thus, capability of the run-to-run control by sequencing the incomings (feed-induced disturbance) such that improved control performance can be achieved. The frequency domain explanation is: a negative feedback system is effective to reject low frequency type of disturbance. From the feedback property, then the answer to the feed sequencing problem becomes clear: rearrange the feed in such a way that it gives a low frequency characteristic. The issues of controller tuning, model mismatches, and time-varying (slow drifting) parameters are also explored and the analyses reveal the robust performance of the proposed feeding policies. The feed sequencing problems are tested for systems with different dimensions, e.g., SISO, SIMO, and MIMO systems which include the model of an experimental CMP process. Besides tool-induce and feed-induced disturbance, there are possible other factors such as metrology tool bias, product type, or chamber that may induce disturbance. To involve all other types, the context-based state estimation method is usually used. The most important feature of a context-based system is rank deficiency, and the proposed method unbiasedly estimates relative status of each context and process output by state transformation. The transformed states are straightforward and physically meaningful. Furthermore, a solution of planning paths with guarantee of output performance is also investigated.誌謝 I Abstract II 摘要 IV Contents VI List of Figures IX List of Tables XII 1. Introduction 1 1.1 Overview 1 1.2 Process Characteristics 3 1.2.1 Disturbances 3 1.2.2 Measurement. 4 1.2.3 Control Architecture 5 1.3 Dissertation Organization 7 2. Sampling Effects to Run-to-Run Control 9 2.1 Introduction 9 2.1.1 Measurements Classification 9 2.1.2 Control 13 2.1.3 Measurement Strategies and Controller Performance 14 2.2 Effective Time Delay in R2R Control 15 2.2.1 Definition 15 2.2.2 Determination of Effective Time Delay 16 2.2.3 Controller Derivation and Stability 20 2.3 Control Performance 24 2.3.1 Disturbance 24 2.3.2 Effect of Sampling Intervals on Disturbance Model 25 2.3.3 Achievable Performance 26 2.4 Measurement Strategy 29 2.4.1 Effect of Sampling Intervals and Metrology Delay 30 2.4.2 Maximum Tolerable Effective Delay and Sampling Intervals 33 2.4.3 Measurement Priority in Queue for a Metrology Tool 35 2.5 Summary 36 3. Sequencing of Feed-induced Disturbance 38 3.1 Introduction 38 3.2 Feeding Sequence and R2R Control 40 3.2.1. Concept 40 3.2.1.1 Feedback and its limitation 40 3.2.1.2 Problem formulation. 43 3.2.1.3 A Heuristic approach 45 3.2.2. SISO System 48 3.2.2.1 Nominal performance 50 3.2.2.2 Effect of tuning constant 51 3.2.2.3 Effects of model mismatches 52 3.2.2.4 Effects of time-varying parameters 53 3.2.3. Non-square System 53 3.2.3.1 SIMO system 57 3.2.3.2 MIMO system 61 3.3 A Non-Square CMP Example 62 3.3.1. Multi-Zone CMP 62 3.3.2. Control 67 3.4. Summary 69 4. Context-based State Estimation 71 4.1 Introduction 71 4.2 Problem Definition and Formulation 74 4.2.1 System Definition 74 4.2.2 System Matrix and Characteristics 75 4.2.3 Reference Path Based State Transformation 76 4.3 Implementation of State Estimation 80 4.3.1 State Space Model 80 4.3.2 Reference Path Selection 86 4.3.2.1 Switching the reference path 89 4.4 Applications 90 4.4.1 Path Planning 90 4.4.2 Particle Count Estimation 95 4.4.2.1 Process and data description 96 4.4.2.2 Estimation results 97 4.5 Summary 100 5. Conclusions 101 Appendix 103 A. Load Strength Indicator 103 B. Covariance for Different Reference Paths 104 References 10