具備製程規格能力與垂直鎖定機台特性之微影作業區產能分配問題之研究

Abstract

晶圓製造為現今最複雜與高度競爭製造環境之一，因此，充分利用其現有產能來滿足顧客需求，為一相當重要的課題。隨著晶圓製造技術逐漸由微米層次邁向奈米層次，為提高產品良率而設定之製程規格能力與垂直鎖定機台限制，因而造成晶圓批在選取加工機台時，產生一更嚴格的挑選門檻。製程規格能力係指晶圓批必須要在能夠滿足其製程能力(製程規格)要求之機台上加工；垂直鎖定機台係指一晶圓批的第一關鍵層作業若於某一特定機台上加工，則其後續所有關鍵層作業必須回到同一機台上進行加工。本文即是針對在先進製造技術環境下具備製程規格能力與垂直鎖定機台特性之微影作業區產能分配問題(capacity allocation problem in photolithography area；CAPPA)，進行求解。文中，吾人藉由小型範例來說明CAPPA問題之解題模式，須以求取機台間之負荷平衡為目標。之後，本文分別提出不同之解題模式，分別為混合整數規劃模式、限制滿足問題方法、以線性規劃為基礎之演算法。在混合整數規劃模式中，為提高求解實務問題之解題效率，吾人採用深度優先搜尋策略與強分枝法則；在限制滿足問題方法中，吾人提出一估計機台間負荷不平衡上限值之估算模式，以減少在運用限制滿足問題方法求解最佳解或近似最佳解時，所需要的目標式上限值設定次數；在以線性規劃為基礎之演算法中，設計一能夠快速求解之混合整數線性規劃模式，以得出各製程規格能力在各機台於每一規劃週期之最佳負荷值，並以此作為後續工單分配之依據。之後，產生具備不同CAPPA問題特徵之題組，以進行演算法之穩健性測試。

Wafer fabrication is one of the most complex and high competence manufacturing. How to fully utilize the machine capacity to meet customer demand is a very important topic. As fabrication technology advances from micrometer level to nanometer level, more stringent machine selection restrictions, the so-called process window control and machine dedication control, are imposed on the production management of photolithography area. Process window means that a wafer needs to be processed on machines that can satisfy its process capability (process specification). Machine dedication means that after the first critical layer of a wafer lot is being processed on a certain machine, subsequent critical layers of this lot must be processed on the same machine to ensure good quality of final products. In this dissertation, we tackle the capacity allocation problem in the photolithography area, named CAPPA, arising from advanced wafer fabrication technology environment. We showed that a solution model for the CAPPA should be with an objective function of load balance. Firstly, we propose a mixed integer linear programming (MILP) model to balance the load of machines, and the depth-first search strategy incorporating strong branching rule are adopted to obtain an acceptable solution within a reasonable computational time for solving real CAPPA cases. Next, we model the CAPPA problem as a constraint satisfaction problem (CSP), which allows us to use the efficient search algorithm of constraint satisfaction approach in obtaining a good feasible solution. Finally, we propose a linear programming based heuristic (LPBH) algorithm to solve the CAPPA efficiently. The performance comparison is tested by real-world CAPPA cases taken from wafer fabrication photolithography area.