整合生產力與品質之短時段排程

Abstract

高額的設備資本投資和複雜的生產流程為半導體晶圓製造工廠的特性，因此提高工廠生產績效，例如:降低生產週期時間，提高生產率和良率，為近年來日益重要的指標，以縮短設備或研發投資的報酬率。為達到這些績效目標，大量過往研究主要處理端到端的製造問題，亦即使用單一層級直接求解，如機台的派工、整廠的生產規劃與排程。這些方式在實務上既難以管理，也可能產生不可執行的計畫。一個實務上常見的方式為將這些績效目標拆解成數個可執行的短時段決策層級，例如以天、以時、或是更小的時間窗格為單位的排程規劃。為使求解有效率，實務端在單一層及中簡化部分工廠複雜的特徵，例如以粗略的機台產能模型來求解中長期的產能規劃問題等。故各層級的決策既可以被獨立解決，不同層級之間也存在緊密連結。基於此多層次管理架構下做出決策的需要，本研究提出一個以目標與品質風險趨避為導向的短時段排程決策之設計，提供在日排程目標設定，機台產能配置，以及在機台健康狀況為導向之生產排程問題的階層式的決策。 由於半導體晶圓製造工廠具有迴流及共享設備群組產能的特性，面臨的挑戰為將工廠長期目標適當拆解至多個時間窗格和管理決策，以及它們之間的整合。其具體問題如下： 研究問題１：考量目標追蹤作業之日生產目標設定。 基於設備產能與生產線上可用晶圓在製品數量在每日早上設定每個主要站點該日生產目標數量為半導體工廠內常見且重要的生產管理方式。而後各個機台設備群組會根據各自的目標詳細地分配哪些設備須於哪些時段執行哪些製程的工序，並分派哪些晶圓批需被加工，以達成該生產目標。由於同一設備群組可加工多個站點，此機台分配與晶圓批分派會產生晶圓產流的變異。現行方法並未明確地解決這種目標引起的變異（TIV），也因此所得到的目標這定可能導致產出損失和過長的生產週期時間。 研究問題２：考量批量與停留時間限制之機台產能分配與排序於擴散區酸槽與爐管機台群組。 在給定目標下，擴散區酸槽與爐管機台群組的有效調度對於半導體製造的效率是一關鍵要素，其中爐管機台群組由於長加工時間，常成為生產的瓶頸。主要挑戰來自批量數量的要求、機台內部的排序和晶圓停留時間限制，構成了問題的複雜性。 研究問題３：整合機台健康的影響於生產排程。 監控關鍵設備的機台健康指標（EHI）有助於有效地維持製程品質並減少晶圓廢料，重工和無預警的設備故障。為了在生產力和品質風險之間取得平衡，需要模型能整合EHI於生產排程決策中。 研究問題４：以整體設備效率整合排程決策與製程控制 在未來的半導體廠和晶圓產品中，製程控制和生產排程決策的耦合將會越來越緊密。由於總體設備效率（OEE）由三個指標組成：機台可用性，機器性能和產品質量，故OEE提供了評估單一機台其生產排程與質量控制之協同效應的可能方式。現今大部分的OEE被視為延遲的指標，只收集歷史數據來分析機台效率。 在以上四個問題中，由研究問題１所決定的日生產目標為研究問題２與研究問題３欲達成的目標項目之一。而研究問題４所提供的度量方法可針對研究問題２與研究問題３所決定的作業決策，綜合評估其生產力與產品品質。 具體的挑戰如下： １）如何設定日生產目標以實現理想的半導體工廠績效，其中考量在追蹤日生產目標時產生晶圓產流的變異影響晶圓在製品的分布，及此變異又再影響設定日生產目標的雞生蛋、蛋生雞關係； ２）如何隨著時間的推移，有效的分配非等效的機台產能與選擇適當的晶圓，達成最大化實現日生產目標，同時考慮到停留時間限制和關鍵的機台內部排序的特性； ３）如何更進一步考量機台狀態耗損對生產計劃的影響，而分配非等效的機台產能與選擇適當的晶圓； ４）如何量化整合製程控制和生產計劃的協同效應，來評估工廠的績效。 為了克服這些挑戰，我們的方法有四個方面。 方法１：設計一個創新的日目標設定演算法(TaTIV)，其採用伯努利模型以估算因著追蹤日目標的機台分配在每個站點所造起的變異。而在給定該日初始晶圓在製品數量下，我們以一混和遞歸串聯等候線分析來近似晶圓流過各站點所需的時間。 方法２：開發一以瓶頸為中心推拉式集成分配機台產能和排序方法(P＆P BCIASM)，其首先將此問題已整數規劃模型建模，而後在求解時將此模型拆分為先解瓶頸站點、再解非瓶頸站點兩階段，如此可在短時間內找到可行的解決方案，而不會犧牲太多的最佳性。 方法３：提出一個混合整數線性規劃模型，將先進製程控制（APC）架構中的機台健康指數(EHI)及其對產品品質的影響納入考量，以權衡提高生產效率和降低品質風險之間的生產排程決策。 方法４：提出了一種新的廣義整體設備效能指標(GOEE)，其可利用來自工廠作業已可獲得的現成測量結果，例如晶圓產出的數量和不合格晶圓的數量。 本論文研究成果為論證了系統性的分解於複雜的洄流生產和作業管理以實現工廠績效目標之可行性。利用實際晶圓廠資料的分析和模擬解果顯示，關鍵的晶圓廠績效指標，如生產周期時間和產出量在不同層級的短時段決策中可以獲得有效提升以及在同時考慮機台健康狀況指標下，降低產生不良品風險，以利決策者考量多面向之評估。未來的研究可以擴展到更實際的應用於成本和效益分析。

Semiconductor wafer fabrication factories (fabs) are characterized as the high capital investment and complex operations. Improving fab production performance such as the cycle time, throughput rate, and yield, is critical to achieve a high return on investment. Given the fab performance target, bulk research has focused on solving the end-to-end manufacturing problem using a single level of methodology such as dispatching policies or fab-wide planning/scheduling, which is difficult to manage and/or produces infeasible plans. A practical and common method is to break the target down into several executable levels of short-interval decisions such as the schedule of daily, hourly, or even smaller time buckets. For example, Master Production Schedule (MPS), aiming to control the wafer-in-process (WIP) level and cycle time of the entire fab while satisfying delivery requirements of customer orders, considers fab in an aggregated and coarse granularity capacity model with simplified production flow dynamics. MPS schedules the quantities of wafer release and output for a fab using day or week as a time unit over a few months to one year. Then Daily Target Setting (DTS) determines the targeted number of wafers to be processed for each product type at each process step and the estimated machine capacity allocation to the step daily. The detailed Machine Allocation (MA) determines the allocation of available machine capacity in each machine group to various production steps that require the same machine group once every few hours and based on fab production states. Real-time Lot Dispatching (LD) executes priority rules and dispatches individual wafer lots to the appropriate and available machines. Each level takes the decisions from the upper level as its input information. For instance, the targets are critical linkages between MPS and MA. Improper targets misguide MA and make desirable fab performance unreachable. Additionally, the machine availability considered in MA is mostly in view of productivity, lacking of quality information from process control. Under such multiple-level managerial structure, the characteristics of reentrant process flow and shared machine group capacity lead to the problems of how to properly schedule the machine capacity in each level to reach the fab performance target, and how to further consider the quality information in the schedule. Motivated by the practical need, this dissertation presents the design of target-oriented and quality risk-averse short-interval scheduling, providing hierarchical decisions, i.e., daily target setting, machine allocation, and scheduling considering equipment information. Specific problems are as follows: P1) Setting daily production targets considering target tracking operations To fulfill MPS, Daily production target setting based on machine capacities and available WIP is an important practice in a semiconductor fab. Operations of individual machine groups will track their respective target guidance through detailed machine allocation and lot dispatching (MALD), inducing variations of wafer flows. Existing approaches do not explicitly address such target-induced variations (TIV), and the resultant target setting may incur throughput loss and prolonged cycle times. P2) Effective machine allocation and sequencing considering batching and waiting time limitations for wet-bench and furnace machine groups Under given targets, effective scheduling of furnace tools and its upstream tools, wet-bench, are important to operation efficiency of semiconductor fabrication, where furnace tool group may usually be a bottleneck, and are characterized by long processing times with batching requirements. The problem is further complicated by stringent limitations on waiting times between wet-bench and furnace, in addition to the heterogeneous tool configuration. P3) Integrating equipment health and quality risk in production scheduling Though productivity can be improved through proper scheduling decision, product quality is also critical to fab operation. Monitoring the Equipment Health Indicator (EHI) of critical machines helps effectively to maintain process quality and reduce wafer scrap, rework, and machine breakdowns. To balance between productivity and quality risk, there yet need models and illustrations of integration between EHI in scheduling decisions. P4) Evaluating scheduling decisions and quality risk from process control by Overall Equipment Effectiveness The coupling of process control and production scheduling will grow tight in future fab and products. Overall Equipment Effectiveness (OEE) serves as a possible way to evaluate the synergy effect for a single machine as OEE is composed by three indexes: machine availability, machine performance, and product quality. OEE nowadays is mostly viewed as a legacy index, which means only the historical data are collected to analyze the tool productivity. Among the problems, the daily targets decided from (P1) are the one of the objectives of (P2) and (P3), in which (P3) further considers the equipment health information. The metric of (P4) is provided to evaluate the overall effectiveness integrated productivity and product quality for (P2) and (P3). The challenges are as follows: C1) The investigation of how daily targets are set to achieve desirable fab performance by considering the chicken-and-egg relation that target induces variations through target-tracking MALD and affects wafer flows, WIP availability, and, in turn, the target setting; C2) The efficient allocation of heterogeneous tools and the selection of wafers over time so that fulfillments of production targets are maximized with the consideration of waiting time limitations and critical machine sequencing characteristics; C3) The further allocation of heterogeneous tools and the selection of wafers considering the impact of machine deterioration on production schedule; C4) The quantification of the synergy effect from integrating process control and production scheduling to evaluate the fab performance on different aspects. To overcome the challenges, our methodology is four folds. M1) A novel design of target-setting algorithm, TaTIV, is proposed and adopts a Bernoulli model for approximating the TIV of machine allocation at a process step under a given target. Under given initial WIPs of the day, the wafer flows of a step and wafer flow times are approximated through a hybrid and recursive tandem queue analysis. M2) A push-and-then-pull bottleneck centric integrated allocation and sequencing method, P&P BCIASM, is developed, in which an integer programming model is first formulated and then separated into two phases for finding a feasible solution in a short time without sacrificing much schedule optimality. M3) The notion of Equipment-Health-Index (EHI) in the Advanced Process Control (APC) framework is formulated in the novel mixed integer linear programming models and integrated in scheduling decisions to help evaluating the trade-offs between productivity improvement and quality risk reduction. M4) A novel index of generalized overall equipment effectiveness, GOEE, is proposed to exploit readily available measurements from fab operations such as the number of output wafers and the number of unqualified wafers from current measurements. The results and insights are described respectively. R1) TaTIV shows its superiority over the mean-value method. By improving wafer flow estimation, TaTIV reduces differences between targets and actual results. Such reduction indicates good execution to achieve MPS and results in appropriate allocations at the right time in reentrant line. The targets generated by TaTIV achieves less inter-step variations of machine allocation to steps, thereby improving the fab cycle time and throughput. R2) Test results over real fab data demonstrated the superiority of P&P BCIASM in furnace tool utilization and shorter average waiting time over heuristic rules. The deficiency of heuristic rule is due to the fixed pulling interval and batch strategy of maximal load. The consideration of taking different processing times of the upstream steps in heuristic rules to deal with waiting time limitation is suggested. The computation efficiency of the solution (30 seconds) with a stopping criterion of no more than 5% difference from optimality indicates a strong potential for both large size problems and applications. R3) The consideration of equipment health in scheduling helps to maintain productivity, i.e., large number of moves, with low risk of quality loss. The requirements on equipment health help to assign jobs to proper machines. Changing scheduling objectives from “quantity only” to “quantity with quality” by minimizing the total production cost is the focus of future research. R4) The proposed Generalized Overall Equipment Effectiveness (GOEE) attempts to enhance fab productivity by integrating process control and production scheduling. It thus helps to evaluate the forthcoming decisions in tool allocation optimization. The dissertation demonstrates the impacts of both productivity and product quality under the multiple-level managerial structure of complex re-entrant production lines. Future research can be extended to more practical applications to study the cost and benefits.