Feedback Control of Cluster Tools: Stability Against Random Time Disruptions

In this research, we examine feedback control-based cluster tool scheduling methods to maintain consistent wafer sojourn times when a tool is subject to random disruptive events. In our previous work, we proposed a feedback control design that regulates wafer sojourn times not to exceed the upper limits on wafer delays in a deterministic processing environment. Although such a feedback controller may ensure that wafer delay upper limits are always satisfied, it does not necessarily guarantee that the tool always restores its initial tool state after the occurrence of time disruptive events. This article thus further examines under which conditions a feedback controller enforces the wafer sojourn times to be stabilized in a stochastic processing environment with unexpected random time disruptions. Note to Practitioners - In semiconductor manufacturing, excessive wafer sojourn times at wafer fabrication tools increase the risk of wafer quality failures. In particular, the wafer quality fluctuates when the sojourn times are inconsistent over different wafers. Therefore, in cluster tools, wafer sojourn times are often strictly regulated to be minimized or to remain constant with an objective of reducing the risk of wafer quality degradation. In this research, we examine a cluster tool scheduling framework that enables to maintain stable tool operations even when a tool is randomly disrupted by unexpected exceptional events.