Capacity Determination Model with Time Constraints and Batch Processing in Semiconductor Wafer Fabrication

晶圓的製造技術是一直不斷的演進，在此精密且複雜的製造過程中，為了避免在製品於生產線上等待過久而造成晶圓表面的製程缺陷，所以工程師會根據製程與產品特性制定一段時間來做為等候時間(Queue Time)的限制，而此一等候時間就稱之為時間限制(Time Constraints)。時間限制問題的嚴重性，尤其發生在時間限制較短、同一產品重複經過次數較多，以及批量加工生產之工作站。一般而言，批量加工生產之工作站同時具備了上述之特點。此外，到達批量工作站之產品除了需要等候批量工作站加工完畢外，還必須為了集批而增加額外的等候時間。因此，若發生等候時間大於時間限制時，其報廢晶片所造成的損失將特別嚴重。有鑑於此，本研究提出一套有效的批量生產機台之產能決策模式，以幫助管理者在面對時間限制與批量生產之產能決策問題時，能夠藉由此模式快速的作出最佳決策。而本研究的方法主要是以等候理論之GI/G/m模式為基礎，考量集批的特性並修正於等候模式之到達率與到達率變異係數平方。此外，因為集批所增加之額外等候時間也加以修正於期望等候時間計算模式中。最後，即是以等候線上產品之期望等候時間大於時間限制的機率方程式作為求解方程式，藉此制定所需之機台數。再者，本文利用eM-Plant物件導向模擬軟體及MiniTab實驗分析軟體進行研究，並藉由範例來說明與驗證本論文所提出產能決策模式之可行性與準確性，結果證實本文所提出之產能決策模式能有效的估算批量生產機台之機台數。

關鍵字

等候時間限制；等候理論；批量加工；產能規劃

並列摘要

Recently, wafer fabrication has become more complicated and lengthened the product queue time. To ensure final product yield, engineers need to set up queue time limits for particular machines during wafer processing; we name it as ”time constraints”. Time constraint problems are more serious when the time constraint is short, process is reentrant and batching. Generally, batch processing in wafer fabrication is matching these characteristics. To eradicate difficulties with time constraints and batching process, capacity planning must be addressed. This paper applied GI/G/m queuing theory to develop a capacity determination model for batch processing machines. The batching behavior is considered and taken as a factor to modify the mean and squared coefficient of variation of arrive rate in this model. By this queuing network model, the expected waiting time between machines in production systems can be estimated. Managers can also determine the capacity through the setting of expected rate of over time constraints. Furthermore, a checking table is derived for different utilizations, time constraints, and the probability of expected waiting time over time constraints. The approximate performance measures are compared with discrete-event simulation. The result shows the effectiveness of the proposed model and demonstrates that it is superior to the current planning method.

並列關鍵字

Time Constraints ； Queuing Theory ； Batch Processing ； Capacity Planning

參考文獻

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