在半導體產業中，其製造過程是非常繁瑣的，一片晶圓需經過數百道製程並耗時數個月才能完成生產，如何提升機台使用率已達到客戶交期是一個重要的議題。負荷平衡為黃光區存在的問題，若所需專用機台的第一層關鍵層沒有安排恰當，其可能會影響到後續層別的製程。故在本研究中，將提出一個整數規劃模型與啟發式演算法解決此負荷平衡的問題，將專用機台及拆批限制納入考量，本研究目標為最小化機台間負荷差異。專用機台限制是當產品在回流至製程中，其關鍵層加工的機台須與第一層關鍵層所使用的機器相同。拆批限制表示一張訂單可拆成數張子訂單，並允許其在不同機台上生產。在混合基因演算法中，第一步驟進行拆批決策，第二步驟將拆批後的訂單依序指派至機台；此外，本研究於演算法中加入區域搜尋及模糊邏輯控制，模糊邏輯控制打破以往傳統基因演算法參數皆固定，其是以連續兩世代平均適應值得差異來自行調整交換率及突變率。經由實驗數據證明，混合基因演算法能有效地解決拆批及專用機台限制下的負荷平衡問題。

In the semiconductor industry, the manufacturing processes are very complicated. One wafer lot passes through hundreds of operations and the processing procedure takes a few months to complete. In order to meet the customer deadline, how to utilize the machine capacity efficiency is an essential issue. Loading balance in photolithography area is a crucial problem. If the first layer did not appropriately assign due to the dedication scenarios, it would affect the following layer process. Therefore, in this study, the mathematical model is proposed to solve the loading balance problem for photolithography area. Taking machine dedication, and lot splitting restriction into account, we aim to minimize the loading difference between each machine. The machine dedication constraint is set for the layer-by-layer process on wafers so that the circuit patterns in critical layers can be correctly connected to provide particular functions. Lot splitting means that an order can be split into sub-orders and these sub-orders can be processed independently on machines. This research further proposed a hybrid genetic algorithm (HGA) to solve the lot splitting and capacity allocation problem to minimize the sum of loading level among machines. First, the algorithm focuses on the search of the best number of lot splitting, and then gradually transfers towards finding the optimal capacity allocation for each machine. Moreover, in this research, the local search mechanism is used to improve solution search to be more flexible and an auto-tuning approach is proposed to adopted the fuzzy logic controller to adjust the probability of crossover rate and mutation rate, by considering the change of the average fitness value of parents and offspring in two continuous generations. The experiment results demonstrate that the HGA can efficiently solve the loading balance problem under lot splitting and dedicated machine constraints.

摘要 I
ABSTRACT II
致謝 III
Contents IV
List of Tables V
List of Figures VI
Chapter 1: Introduction 1
1.1 Background and Motivation 1
1.2 Research Objective 3
1.3 Research Method 3
1.4 Organization of Thesis 4
Chapter 2: Literature Review 6
2.1 Capacity Planning and Scheduling Problem in Photolithography Area 6
2.1.1 Machine dedication 10
2.1.2 Machine capability 11
2.1.3 Reticle limitation 12
2.2 Lot Splitting 17
2.3 Genetic Algorithm 19
2.4 Fuzzy Logic Controller (FLC) 21
Chapter 3: Problem Definition 24
3.1 Problem Statement 24
3.2 Notations and Assumptions 27
3.3 Problem Formulation 29
Chapter 4: Methodology 35
4.1 Algorithm Framework 35
4.2 Steps of Hybrid Genetic Algorithm 37
4.2.1 Set parameters 37
4.2.2 Chromosome representation 37
4.2.3 Initial population generation 39
4.2.4 Unfeasible chromosomes repairing mechanism 39
4.2.5 Fitness evaluation 42
4.2.6 Selection operator 42
4.2.7 Generation replacement 42
4.2.8 Crossover operator 43
4.2.9 Mutation operator 44
4.2.10 Local search 45
4.2.11 Fuzzy logic controller 46
4.2.12 Termination 50
Chapter 5: Computational Study 51
5.1 Scenario Illustration 51
5.2 Comparison Results of LINGO and HGA 53
5.3 Comparison Results of Different Types GA 56
5.3.1 Objective value comparison 59
5.3.2 Runtime comparison 64
5.3.3 Convergence condition comparison 65
5.3.4 Relative improvement among GA and other algorithms 67
5.4 Without Lot Splitting and Variable Lot Splitting Analysis 68
Chapter 6: Conclusion 72
Reference 74
Appendix 81

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